Maths Grade 8 Term 3 4b1o3s

MATHEMATICS

78 9

LESSON PLANS GRADE 8

Term 3

SENIOR PHASE

MATHEMATICS Grade 8: Term 3 Week 1 Day 1 Mental Maths - 10 Minutes Add and subtract fractions - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.b decimals, fractions and percentages; 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.2.f multiples and factors; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Add and subtract fractions - Revise Addition and subtraction of common fractions, including mixed numbers - Convert mixed numbers to common fractions in order to perform calculations with them - Use knowledge of multiples and factors to write fractions in the simplest form before or after calculations - Use knowledge of equivalent fractions to add and subtract common fractions. - Solve problems in contexts involving common fractions and mixed numbers, including grouping, sharing and finding fractions of whole numbers - Recognize equivalent forms between: common fractions (fractions where one denominator is a multiple of the other) Teacher Note: Keywords (See attached dictionary for definitions.) - Addition - Common fraction - Mixed numbers - Subtraction - Fraction in its simplest form - Multiples and factors - Equivalent fractions

- A problem in context - Problem solving - Sharing - Whole numbers - Denominator - Multiples Assessment: Add and subtract fractions Informal Resources: Board

MATHEMATICS Grade 8: Term 3 Week 1 Day 1 Mental Mathematics - 10 Minutes Times Tables: 7 x 9 = (63) 9 x 11 = (99) 8 x 3 = (24) 8 x 4 = (32) 4 x 7 = (28) 12 x 8 = (96) 7 x 12 = (84) 8 x 8 = (64) 6 x 7 = (42) Square Root: Square root of 144 = (12) Cube Root: Cube root of 125 = (5) Decimal Multiplication: 0,39 x 0,02 = (0,0078) Fraction Addition:

Fraction Subtraction:

Fraction Multiplication:

Grade 8: Term 3: Week 1: Day 1

Introduction: Add and subtract fractions

Revise proper fractions, improper fractions and mixed numbers with learners. Draw the following on the board. Ask learners which number is the numerator and which one is the denominator. 2 4

2 6 5 2

2

13

numerator denominator What can you tell me about this fraction using the words numerator and denominator? What can you tell me about this fraction using the words numerator and denominator? What can you tell me about this number?

Concept development Write the following on the board. Revision: say if it is a proper or improper fraction, or a mixed number. 2 4

6 2

7 4

1

12

4 5

3

35

8 5 3 6

Revise equivalent fractions with your learners.

1 5

1

58

What fractions are equal to • one half? • one quarter? • one third? • one fifth? • one sixth? Revise simplest form. 1

2

3

4

5

If is ; ; ; and 2 4 6 8 10 form? 4 6 3 6 10 ; ; ; ; 6 8 9 12 15

6 12

in its simplest form, what will the following be in its simplest

We can also do it as follows: 4 What number can 6 be divided into 4 4 2 as well as into 6? =6÷ 2 2

=3

Add up the following: 1 4

+

2 4

Also revise the highest common factor (HCF) with learners: 2

F4 = {1, 2, 4} F6 = {1, 2, 3, 6} GCF = 2 So 2 is the biggest number that can divide into 4 and 6.

What do you notice?

Learners do the following in pairs: 1 1 • Add up 3 + 4 3

4

• Add up 15 + 26

Revise: If we add up common fractions with different denominators we need to find the LCM. 3 : {3, 6, 9 ,12, 15, …}

4 : {4, 8, 12 , 16, 20, …} 1 3

x

=

4 + 4

1 4

x

3 3

3 4 + 12 12

7

= 12

Homework: Question 3, 4, 5 Do the following activities in your writing book. 1. Revision: say if it is a proper or improper fraction, or a mixed number. a.

2 4

6

8

c. 12

1

d. 5

e. 5

4

g. 5

1

b. 2

f. 3

h. 3 5

1

j. 5 8

i.

7 4

3 6

2. Write an equivalent fraction for 1

2

a. 1 2 1

c. 4 2

3

d. 6 3 g. 3

1

b. 3 3

4

e. 2 4

1 4

h. 7

1

j. 1 5

f. 2 5

1 6

i. 5

1 6

3. Add up the following, write it as a mixed number and simplify if necessary. Example: + 5 divided by 3 is 1 remainder = 2

4

a. 5 + 5 = 7

= 5

d. 10 + 10 = 5

4

10

9

g. 8 + 8 =

j. 15 + 15 =

5

6

5

3

b. 9 + 9 = e. 6 + 6 = 9

8

h. 12 + 12 =

3

2

c. 4 + 4 = 5

6

2

2

f. 7 + 9 =

i. 3 + 3 =

4. Calculate and simplify it necessary. 1 4

1 2

b. +

1 5

1

1

h. 8 + 3 =

a. + = 1

1

d. 8 + 4 =

1

1

1

1

3

1

=

e. 5 + 4 =

g. 7 + 2 = 3

1 10

4

j. 4 + 5 =

1 3

1 6

c. + = 1

1

2

2

f. 2 + 3 = i. 4 + 3 =

5. Calculate and simplify. 1

a. 1 + = 2 1

1

d. 42 − 3 3 = 12

1

g. 10 − 15 = 1

4

j. 311 + 2 12 =

b. 2 + 4 = 1

1

e. 26 + 1 5 = 9

3

h. 15 − 1 10 =

1

c. 24 + 8 = 1

3

f. 72 − 1 4 = i.

1 29

2

+ 17 =

Consolidation

We can only add fractions if they have the same denominators. Learners who need : Solve all addition sums by drawing number lines. Learners who are more than competent: Provide peer .

Problem solving

Add up any proper, improper and mixed numbers with different denominators.

MATHEMATICS Grade 8: Term 3 Week 1 Day 2 Mental Maths - 10 Minutes Multiply fractions - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.b decimals, fractions and percentages; 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.2.f multiples and factors; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Multiply fractions - Revise Finding fractions of whole numbers - Revise Multiplication of common fractions, including mixed numbers - Convert mixed numbers to common fractions in order to perform calculations with them - Use knowledge of multiples and factors to write fractions in the simplest form before or after calculations - Solve problems in contexts involving common fractions and mixed numbers, including grouping, sharing and finding fractions of whole numbers Teacher Note: Keywords (See attached dictionary for definitions.) - Common fraction - Whole numbers - Mixed numbers - Multiplication - Fraction in its simplest form - Multiples and factors - A problem in context - Problem solving - Sharing

Assessment: Multiply fractions Informal Resources: Board Writing book





Introduction: Multiply fractions Let us multiply fractions: 1 1 ×4 2

Ask the learners to identify the numerators: 1 1 × 2 4

and then the denominators: 1 2

1

×4

Concept development

We will first multiply the numerators and then the denominators. 1 =8

Ask learners what they should when multiplying fractions. Do the following example on the board: 2 1 × 3 4 2

= 12

4

If 4 = 1, how will we multiply the following fractions? 3 × 3

1 5

=1 × =

1 2

3 5

2

× 6 2

= 12 =

1 5

2 12 1

=6

÷

2 2

1 2

2

1

×6=6

Ask learners to multiply the following fractions. Write it on the board: 2 6 × 4 2 =

12 8

3

=2

1

= 12

4

The mixed number for this improper fraction is = 18

1

We can simplify this by determining the GCF, namely 4: = 12

Homework: Questions 3, 4, 5.

Do the following activities in your writing book: 1. Calculate.

Example: ×

a.

g. j.

×3 =

b.

4

e.

1 5

×3 =

2

h.

1 2

m. p.

1 5

1 2

d.

2

=

×6= 4

×6=

6 7

3 4

3

×5= 6

×9=

k. n.

2 4

1

×3=

7 2 ×4 8

=

f.

2 1 ×3 4

=

i.

×4=

l.

2 8 ×9 3

=

7 8

2

1 3 × 6 7

c.

o.

8 9

4

×5=

1 3 ×7 6

8 9

=

=

4

×5=

2 2 ×3 8

=

2. Calculate the following.

Example: ___ × ___ =

× = 4

a. ___ × ___ = 9 d. ___ × ___ =

12 16

22

g. ___ × ___ = 36 27

j. ___ × ___ = 54

8

6

b. ___ × ___ = 14

c. ___ × ___ = 8

12

i. ___ × ___ = 42

e. ___ × ___ =

18 63

h. ___ × ___ = 20

f. ___ × ___ =

3. Calculate the following.

Example: ×

= ×

=

=2 3

a. 2 × = 5 1

d. 9 × 2 = 2

g. 6 × 3 =

j. 10 ×

4 8

=

5

b. 4 × 6 = e. h.

2 3

×3=

8 × 9

5=

3

c. 11 × 10 = 6

f. 8 × 7 = i.

6 11

×7=

6 10

30

4. What whole number and fraction will give you the following answer?

Example: ___ × ___ =

×

= × 4

9

a. ___ × ___ = 6

15

c. ___ × ___ = 8

18

i. ___ × ___ = 9

7

d. ___ × ___ = 50

e. ___ × ___ = 21

12

g. ___ × ___ = 18

h. ___ × ___ = 24

8

j. ___ × ___ = 10

3

b. ___ × ___ = 18

6

f. ___ × ___ = 24 2

5. Revision: simplify. F15 ={1, 3, 5, 15} F20 = {1, 2, 4, 5, 10, 20} GCF: 5 Example:

= ÷

a.

4 12

=

b.

16

d. 24 g. j.

e.

50 80

h.

60 100

8 16

c.

27 99

i.

7 21

6. Multiply and simplify if possible. Example: ×

= = ÷

=

f.

5 20

24 64

48 72

a. d. g. j.

1 2

×8 =

4

b.

5

e.

4 5

×4 =

3

h.

1 3

3 4

×5= 1

×2 =

7 7

3

×6=

1 3 ×4 2

3 3 × 8 9

c.

=

f.

=

i.

8 10

1 2

10

× 12 = 2

×7=

2 5 × 3 6

=

7. Revision: write the improper fractions as whole numbers and simplify if necessary. Example:

= or =

F2 = {1, 2} F4 = {1, 2, 4} = a.

d. g. j.

19 3

b.

20 3

h.

32 7

e.

70 11

21 5

c.

64 10

i.

18 8

f.

20 6

21 9

27 12

8. Multiply and simplify. Example: × =

GCF is 2

= 3 a. d.

3 2

5 4

7

×6 = 9

= 3

×8=

b. e.

6 3

6

×5=

6 9 ×8 5

=

c. f.

8 6 ×4 7

9 7

6

=

×3=

g. j.

12 11

12 10

8

×6 = 11

× 10 =

h.

4 10 × 9 2

=

i.

11 9

14

× 12 =

Consolidation

Learners who need : Receive peer .

Learners who are more than competent: Provide peer .

Problem solving

a. What fraction is 5 days of seven weeks? b. What fraction is four months of 10 years? c. What fraction is 12 minutes of an hour?

MATHEMATICS Grade 8: Term 3 Week 1 Day 3 Mental Maths - 10 Minutes Divide whole number by common fractions - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.b decimals, fractions and percentages; 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.2.f multiples and factors; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Divide whole number by common fractions - Divide whole numbers and common fractions by common fractions - Convert mixed numbers to common fractions in order to perform calculations with them - Use knowledge of multiples and factors to write fractions in the simplest form before or after calculations - Use knowledge of reciprocal relationships to divide common fractions - Solve problems in contexts involving common fractions and mixed numbers, including grouping, sharing and finding fractions of whole numbers Teacher Note: Keywords (See attached dictionary for definitions.) - Common fraction - Division - Mixed numbers - Fraction in its simplest form - Multiples and factors - A problem in context - Problem solving - Sharing - Whole numbers

Assessment: Divide whole number by common fractions Informal Resources: Board Writing book





Introduction: Divide whole number by common fractions Introduce the topic by asking learners what a rational number is. Write the following examples on the board. Revise simplification of fractions. 4 8

4

=8÷

15 9

4 = 4

6

1 2

6

=1 =1 ÷ 9

9

2 3 =1 3 3

Revise multiplication of fractions. 1 4

3

×6

3 = 24 3

24

÷ 33 = (simplify)

1 = 8

Introduce the topic by revising dividing whole numbers by common fractions. 4÷

4 10

=

Tell learners that they are going to apply the last two days’ knowledge by completing this assessment.

Concept development

Write the following on the board. Introduce the division of fractions by going through the examples step by step with your learners. 3÷ 3

3 4

8

4

=1x3 4

=1

=4

4÷5 4 1

5 2

5

=8x

= (simplify)

1

22 =

1 2

1 2

1

÷6 6

x1 6

=2

=3

2 3

2 3

3

1

1

÷4

1 2 ÷ 24

8

=2x9

4

x3

=9

3

9

3

4

1

2

=2÷4

=1÷3 2

=3

Complete the assessment. Carefully go through each question. Calculate each sum.

Check your calculations. After the assessment, another classmate will mark your work. Homework: Complete this activity. Do the following activities in your writing book. 1. Calculate. Example: 3 ÷

= x

=

Whole number divided by a proper fraction.

= 4

a. 4 ÷ =

b. 7 ÷ =

d. 9 ÷ =

e. 5 ÷ =

g. 2 ÷ =

h. 8 ÷ =

j. 11 ÷ =

c. 12 ÷ =

f. 10 ÷ =

i. 6 ÷ =

2. Calculate.

Example: 4 ÷

= x

Whole number divided by a improper fraction.

=

a. 3 ÷ =

= 2

d. 2 ÷ =

b. 6 ÷ =

e. 4 ÷ =

c. 8 ÷ =

f. 7 ÷ =

g. 9 ÷ =

h. 10 ÷ =

i. 5 ÷ =

j. 12 ÷ =

3. Calculate.

Common fraction divided by a common fraction.

Example: ÷

= x

=

÷ =

a. ÷ =

d. ÷ =

e. ÷ =

g. ÷ = j.

b. ÷ = h. ÷ =

c. ÷ = f. i.

÷

=

÷ =

4. Calculate.

Example: 2 ÷

= x

= x

=

a. 1 ÷ 2 = d. 3 ÷ 7 = g. 6 ÷ 4 =

j. ÷ 9 =

b. 1 ÷ 2 =

e. 5 ÷ 2 =

h. 2 ÷ 2 =

c. 3 ÷ 4 = f. 5 ÷ 3 = i. 4 ÷ 5 =

Consolidation

Emphasise that to divide by any number means to multiply by its reciprocal. Complete assessment and check answers. Learners who need : Give learners more problems with whole numbers multiplied by fractions. Peer . Do corrections for homework. Learners who are more than competent: Give learners five sums with fractions divided by fractions. Provide peer .

Problem solving

Write a word sum for twelve divided by hundred and eight-tenths. Divide eight-ninths by eighteen halves.

MATHEMATICS Grade 8: Term 3 Week 1 Day 4 Mental Maths - 10 Minutes Concept Development - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.b decimals, fractions and percentages; 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.2.f multiples and factors; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Concept Development - Calculate the squares, cubes, square roots and cube roots of common fractions - Convert mixed numbers to common fractions in order to perform calculations with them - Use knowledge of multiples and factors to write fractions in the simplest form before or after calculations - Solve problems in contexts involving common fractions and mixed numbers, including grouping, sharing and finding fractions of whole numbers Teacher Note: Keywords (See attached dictionary for definitions.) - Common fraction - Cube number - Cube roots - Square number - Square roots - Mixed numbers - Fraction in its simplest form - Multiples and factors - A problem in context - Problem solving

- Sharing - Whole numbers Assessment: Concept Development Informal Resources: Board Writing book





Introduction: Fractions of squares, cubes, square and cube roots Revise: • Square and cube numbers

• Square roots and cube roots

Concept development Do the following with your learners on the board. 3 4

32

² = 42 =

16 25 3 4 3

16 25

=

33

=

3

3

4

=5

³ = 43 =

8 27

9 16

8

27

27 64 2

=3

Homework: Complete this activity. Do the following activities in your writing book: 1. Calculate. Example: a.

d. g. j.

² = =

1 4

²

²

e.

²

h.

b.

5 8

b.

²

2 7

3 4

5 6

²

c.

²

f.

²

i.

c.

2 5

²

² ²

2. Revision: calculate. Example: a.

=

=

d.

e.

f.

g.

h.

i.

b.

1 3

³

c.

³

f.

6 6

³

i.

=

3. Calculate.

Example: a. d. g. j.

³ = =

1 4

³ ³

e.

³

h.

4 8

³

2 3

³

2 7

³ ³

4. Revision: calculate. Example: a.

=

= b.

c.

d.

e.

f.

g.

h.

i.

Consolidation

It is important to understand the following: • Square numbers and square roots • Cube numbers and cube roots • Fractions Learners who need : Receive peer . Learners who are more than competent: Provide peer .

Problem solving

What is squared sixteen divided by twenty-five?

MATHEMATICS Grade 8: Term 3 Week 1 Day 5 Mental Maths - 10 Minutes Fractions, decimals and percentages - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.b decimals, fractions and percentages; 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Fractions, decimals and percentages - Solve problems in contexts involving common fractions and mixed numbers, including grouping, sharing and finding fractions of whole numbers - Revise: Find percentages of whole numbers. - Revise: Calculate the percentage of part of a whole - Revise: Calculate percentage increase of decrease of whole numbers - Recognize equivalence: common fraction, decimal fraction and percentage forms of the same number - Revise equivalent forms between: common fraction, decimal fraction and percentage forms of the same number. Teacher Note: Keywords (See attached dictionary for definitions.) - A problem in context - Common fraction - Mixed numbers - Problem solving - Sharing - Whole numbers - Percent

- Decrease - Increase - Common fractions - Decimal fraction - Equivalence between common fraction, decimal fraction and percentage Assessment: Fractions, decimals and percentages Informal Resources: Writing books





Introduction: Fractions, decimals and percentages Introduce this lesson by revising the following. 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

Fraction: 25% or (25 out of 100) Common fraction: Simplify:

1 4

Decimal: 0,25

Increase and decrease percentages Introduce this lesson by asking learners what a percentage is. Ask them what increase and decrease mean.

Concept development Write the following on the board. Do it step by step with your learners. What is 60% of R105? 60 100

3

×

=5× =

105 1

105 1

315 5

= R63

I can write 60 60% as 100 60 100

6

3

simplified is 10 = 5

Learners may use a calculator.

25 100

What percentage is 40c of R3,20? Do this step by step with your learners. 40 100 × 1 320 = =

4 000 320

400 320

100 8

simplified is

100 8

= 12,5% Calculate the percentage increase if the price of a bus ticket of R60 is increased to R84. Amount increased is R24. 24 60

=

×

100 1

240 60

= 40% Calculate the percentage decrease if the price of petrol goes down from 20 cents a litre to 18 cents. Amount decreased is 2 cents. 2 100 × 1 20 =

200 20

= 10% Homework: Question 5g-j and 6g-j Ask the learners to solve the following problems in their writing books. 1. Write the following as a fraction and decimal fraction.

Example: 18% or or 0,18 a. d. g. j.

37% 9% 8% 69%

=

b. 25% e. 56% h. 75%

18 100

simplified is

9 50

c. 83% f. 3% i. 92%

2. Write the following as a fraction in its simplest form. Percentage

10%

Fraction

10 100 1 10

Simplest form 3. Calculate.

20%

30%

40%

50%

60%

70%

80%

40% of R20 = =

40 100

×

800 100

20 1

= R8

a. 20% of R24 d. 80% of R74

b. 70% of R15 e. 30% of R90

c. 60% of R95 f. 50% of R65

4. Calculate the percentage. Example: see example under concept development.

a. 30c of R1,80 d. 70c of R2,10

b. 80c of R1,60 e. 50c of R7,00

c. 40c of R8,40 f. 30c of R3,60

5. Calculate the percentage increase. Example: see example under concept development. a. d. g. j.

R50 of R70 R25 of R30 R120 of R150 R75 of R100

b. R80 of R120 e. R100 of R120 h. R24 of R32

c. R15 of R18 f. R36 of R54 i. R90 of R120

6. Calculate the percentage decrease. Example: see example under concept development. a. d. g. j.

R20 of R15 R24 of R18 R45 of R36 R72 of R66

b. R50 of R45 e. R90 of R80 h. R48 of R40

c. R18 of R15 f. R28 of R21 i. R99 of R90

90%

100%

Consolidation

100

We need to know that 100% is the same as 100 is the same as 1. We need to know the equivalent of fractions, percentage and decimals in order to do calculations.

Learners who need : Let learners make drawings with the calculations. Make use of peer . Learners who are more than competent: What is 120% of R85? Provide peer .

Problem solving

I bought a top for R175. I got 25% discount. How much did I pay for it? Calculate the percentage decrease if the price of petrol goes down from 35c to 28c.

MATHEMATICS Grade 8: Term 3 Week 2 Day 1 Mental Maths - 10 Minutes Place value, ordering and comparing decimals - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.b decimals, fractions and percentages; 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.4 Solves problems in context including contexts that may be used to build awareness of other Learning Areas, as well as human rights, social, economic and environmental issues such as: 8.1.4.a financial (including profit and loss, budgets, s, loans, simple interest, hire purchase, exchange rates); 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Place value, ordering and comparing decimals - Solve problems in contexts involving percentages.

Teacher Note: Keywords (See attached dictionary for definitions.) Assessment: Place value, ordering and comparing decimals Informal Resources: Writing books





Introduction: Place value, ordering and comparing decimals Revise increasing and decreasing of percentages with your learners.

Concept development

In pairs, learners come up with a list of how they will solve a percentage problem. Make notes of the learners’ answers. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ Homework: Complete this activity

Learners do the following in their writing books: 1. a. c. e. g. i. j. l.

Solve the following. Find 80,6% of the number 110. b. What is 5,2% of 29? What percentage is 36 of 82? d. What percentage is 13 of 121? What percentage is 55 of 149? f. What is 86,6% of 44? What percentage is 61 of 116? h. 22,3% of a number is 123. What is the number? 57,1% of a certain number is 115. What is the number? What percentage is 143 of 146? k. 81,8% of what number is 84? What percentage is 22 of 26?

2. Solve the following. a. The original price of a shirt was R200. It was decreased by R150. What is the percentage decrease of the price of this shirt? b. Mary earns a monthly salary of R12 000. She spends R2 800 per month on food. What percentage of her monthly salary does she spend on food? 3. Mixed problems. Solve the following. a. Calculate 60% of R105 60 Amount = × 105 = 63 100

b. What percentage is 40c of R3,20? 40 100 100 Percentage = 320 × 1 = 8 = 12,5%

c. Calculate the percentage increase if the price of a bus ticket is increased from R60 to R84. Amount increased = R24. Therefore percentage increase is 24 100 × 1 = 40% 60

d. Calculate the percentage decrease if the price of petrol goes down from 20 cents a litre to 18 cents a litre. Amount decreased = 2 cents. Therefore percentage decrease is 2 100 × = 10% 20 1

e. Calculate how much a car will cost if its original price of R150 000 is reduced by 15%. Calculation involves finding 15% of R150 000 and then subtracting that amount from the original price. i.e. 15 150 000 × 1 = R22 500 100 Hence new price of car = R150 000 – R22 500 = R127 500

Consolidation

Sometimes problem solving is very complicated. Don’t be afraid to use visual aids such as graphs, diagrams and tables in solving maths problems. Learners who need : Make a drawing/diagram of your problem. Learners who are more than competent: Provide peer .

Problem solving See this lesson.

MATHEMATICS Grade 8: Term 3 Week 2 Day 2 Mental Maths - 10 Minutes Place value, ordering and comparing decimals - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.b decimals, fractions and percentages; 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Place value, ordering and comparing decimals - Revise: Ordering, comparing and place value of decimal fractions to at least 3 decimal places - Solve problems in context involving decimal fractions Teacher Note: Keywords (See attached dictionary for definitions.) - Compare decimal fractions - Decimal fraction - A problem in context - Problem solving Assessment: Place value, ordering and comparing decimals Informal Resources: Board Writing books





Introduction: Place value, ordering and comparing decimals Introduce the lesson by asking what a decimal fraction is. Write 4,236 on the board. Tell learners that in South Africa we make use of a Note that we can also say decimal number

decimal comma. (LB to change)

Concept development Revise place value of decimal fractions with your learners. Use your example on the board and label the decimal fraction. units

tenths

hundredths

thousandths

8, 924 Ask learners to write the decimal fraction in expanded notation: 8, 924 = 8 + 0,9 + 0,02 + 0,004 Homework: Questions 1g-j, 2g-j and 3g-j.

Learners do the following in their writing books: 1. Write the following in expanded notation: Example: 5,763 = 5 + 0,7 + 0,06 + 0,003 a. 9,371

b. 6,215

c. 34,672

d. 8,076

e. 9,304

f. 8,004

g. 16,003

h. 19,020

i. 56,003

j. 900,009 k. Show this using your calculator, e.g. 9 + 0,6 + 0,08 + 0,002

2. Write the following in words. Example: 5,872 = 5 units + 8 tenths + 7 hundredths + 2 thousandths a. d. g. j.

3,378 2,037 23,004 45,026

b. e. h. k.

6,2914 c. 2,588 2,003 f. 14,030 400,404 i. 2,998 Use a calculator to check your answers.

3. Write the following in the correct column. thousands

hundreds

tens

units

a.

2,869

2

,

b.

24,328

,

c.

18,003

,

d.

376,02

,

e.

8674,5

,

f.

2874,345

,

g.

987,001

,

h.

400,08

,

i.

2000,203

,

tenths

hundredths

Thousandths

8

6

9

4. Write down the value of the underlined digit. Example: 3,476 = 0,07 or 7 hundredths a. d. g. j.

6,857 8,949 765,323 87,608

b. 4,37 e. 85,080 h. 7,660

5. a. d. g. j.

Write the following in ascending order. 0,04; 0,4; 0,004 b. 0,1; 0,11; 0,011 0,753; 0,8; 0,82 e. 0,67; 0,007; 0,06 0,202; 0,2; 0,22 h. 0,345; 0,45; 0,5 0,702; 0,72; 0,072

c. 3,809 f. 34,004 i. 568,999

c. 0,99; 0,9; 0,999 f. 0,899; 0,98; 0,99 i. 0,003; 0,033; 0,030

6. a. d. g. j.

Fill in <, >, = . 0,4 ___ 0,04 0,62 ___ 0,26 0,123 ___ 0,321 0,05 ___ 0,050

b. 0,05 ___ 0,005 e. 0,58 ___ 0,85 h. 0,2 ___ 0,20

c. 0,1 ___ 0,10 f. 0,37 ___ 0,73 i. 0,4 ___ 0,40

Consolidation

The place value of decimal fractions after the decimal comma is tenths, hundredths and thousandths.

Learners who need : Let learners write a decimal number in expanded notation and then identify the value of each digit. Learners who are more than competent: What do we call the 4th, 5th, 6th, 7th, 8th, 9th and 10th place after the decimal comma?

Problem solving

What would you do to change this decimal fraction 9,768 to 9,008?

MATHEMATICS Grade 8: Term 3 Week 2 Day 3 Mental Maths - 10 Minutes Round off rational numbers - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.b decimals, fractions and percentages; 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.a rounding off; 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Round off rational numbers - Recognize equivalent forms: common fraction and decimal fraction forms of the same number - Revise: Rounding of decimal fractions to at least 2 decimal places - Use rounding off and a calculator to check results where appropriate Teacher Note: Keywords (See attached dictionary for definitions.) - Common fraction - Decimal fraction - Equivalence between common fraction and decimal fraction - Equivalent fractions - Rounding (decimals) - Calculator - Rounding - Use of a calculator Assessment: Round off rational numbers Informal

Resources: Board





Introduction: Round off rational numbers Introduce the topic by revising rational numbers.

Concept development Write the following on the board. Do the following with your learners: Round off to the nearest unit. 3,7 ≈ 4

5,62 ≈ 6

7,321 ≈ 7

3,2 ≈ 3

5,68 ≈ 5

7,329 ≈ 7

Round off to the nearest tenth. 8,26 ≈ 8,3

3,765 ≈ 3,8

5,293 ≈ 5,3

8,21 ≈ 8,2

3,768 ≈ 3,8

5,224 ≈ 5,2

Round off to the nearest hundredth. 3,472 ≈ 3,47

8,925 ≈ 8,93

3,478 ≈ 3,48

7,342 ≈ 7,34

Homework: Questions 3g-j, 4g-j, 5g-j, 6g-j.

1

1

1. What is a ___? a. Whole number b. Tenth c. Hundredth d. Thousandth

2. What is the symbol for rounding off?

3. Round off to the nearest whole number. Example: 6,7 ≈7 a. d. g. j.

9,2 6,4 3,34 100,383

b. 4,5 e. 5,68 h. 7,82

c. 4,8 f. 5,999 i. 9,321

If you struggle to round off, circle the number that is before the number you need to round off to. Example: 7,38 ≈ 7

4. Round off to the nearest tenth. Example:

5,84 ≈ 5,8

a. 5,24

b. 3,53

c. 5,55

d. 9,39

e. 7,513

f. 2,329

g. 8,632

h. 1,189

i. 6,7631

j. 8,9789 5. Round off to the nearest hundredth. Example: 8,957 ≈ 8,96 2

2

a. d. g. j.

1,181 7,942 4,715 8,6972

b. 2,345 e. 5,229 h. 8,537

c. 8,655 f. 3,494 i. 5,9676

6. Round off to the nearest thousandth. Example: 18,2576 ≈ 18,258 a. d. g. j.

5,1272 5,2336 9,4581 8,6491

b. 2,7864 e. 1,9813 h. 7,7857

c. 6,6628 f. 3,3336 i. 7,8176

Consolidation Learners who need : Learners circle the digit that will help them to round off. Learners who are more than competent: Write down the steps on how to use a scientific calculator to round off decimal numbers.

Problem solving

In real life, why do we round off decimal numbers? Give five examples.

3

MATHEMATICS Grade 8: Term 3 Week 2 Day 4 Mental Maths - 10 Minutes Equivalence between common and decimal fractions - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.b decimals, fractions and percentages; 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Equivalence between common and decimal fractions - Revise equivalent forms between: common fraction and decimal fraction forms of the same number Teacher Note: Keywords (See attached dictionary for definitions.) - Decimal fraction - Equivalence between common fraction and decimal fraction Assessment: Equivalence between common and decimal fractions Informal Resources: Board Writing books




Grade 8: Term 3 - Week 2: Day 4

Introduction: Equivalence between common and decimal fractions Introduce the lesson by asking learners to give you an example of • a common fraction • a decimal fraction Write it on the board (LB to change)

Concept development Write 0,5 on the board. Ask the learners: “Can you how to write this as a common fraction?” Do the following on the board. 5

We say five-tenths

• 0,5 = 10 8

We say eight-hundredths

• 0,08 = 100 7

We say seven-thousandths

• 0,007 = 1 000 2

8

7

• 0,287 = 10 + 100 + 1 000

Homework: Questions 1g-j, 2g-j, 3g-j, 4g-j and 5g-j.

Learners do the following in their writing books. 1. Write as a decimal fraction. Example:

= 0,06 a.

b.

d.

e.

g. j.

h.

c. f. i.

k. Learners use their calculators to convert between common and decimal fractions. 2. Write as a decimal fraction. Example: = 0,73

a.

b.

h.

d.

e.

g. j.

c. f. i.

k. Learners use their calculators to convert between common and decimal fractions. 3. Write as a decimal fraction. Example: = 5,1

b.

e.

a. d. g. j.

c.

i.

h.

f.

k. Learners use their calculators to convert between common and decimal fractions. 4. Write as a common fraction. Example: 8,4

a. 8,2

=

b. 18,19

c. 7,654

d. 4,73

e. 48,003

f. 8,2

g. 3,4

h. 62,38

i. 376,5

j. 8,476 5. Write the following as a decimal fraction.

Example: = = ,

a.

d.

g. j.

= = ,

b.

e.

h.

c.

f.

i.

Consolidation

The place (place value) after the comma determines the denominator of the comma fraction, e.g. •

4 10

•

4 100

•

4 1 000

• •

1 5

= 0,4 = 0,04 = 0,004

= 0,02

1 25

= 0,04

Learners who need : Give learners more examples similar to those in Questions 1-4. Learners who are more than competent: Write the following as decimal fractions 4 789 1 365 389499 237654 , , , , using scientific notation. 1000000 100000 100000 1000000 1000000

Problem solving

If the tenths digit is six and the units digit is three, what should I do to get an answer of 7,644?

MATHEMATICS Grade 8: Term 3 Week 2 Day 5 Mental Maths - 10 Minutes Addition, subtraction and multiplication of decimal fractions - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.b decimals, fractions and percentages; 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Addition, subtraction and multiplication of decimal fractions - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places - Revise: division of decimal fractions by whole numbers - Use knowledge of place value to estimate the number of decimal places in the result before performing calculations Teacher Note: Keywords (See attached dictionary for definitions.) - Addition - Decimal fraction - Multiplication - Subtraction - Division - Whole numbers - Estimate - Estimate the possible answer before doing a calculation on a calculator Assessment: Addition, subtraction and multiplication of decimal fractions Informal

Resources: Writing books





Introduction: Addition, subtraction and multiplication of decimal fractions Introduce this activity by telling learners that this is going to be an assessment activity. In pairs, they will solve the sums using the examples to guide them.

Concept development In pairs you are going to discover addition, subtraction and multiplication of decimal numbers. Homework: Complete the assessment.

Learners complete the following in their writing books. 1. Calculate. Example: 2,37 + 4,53 – 3,88 = (2 + 5 – 3) + (0,3 + 0,5 – 0,8) + (0,07 + 0,03 – 0,08) = 4 + 0 + 0,02 = 4,02 a. 2,15 + 8,21 – 7,21 =

b. 5,34 + 7,42 – 6,38 =

c. 4,29 + 8,34 – 3,38 =

d. 9,77 + 5,14 – 9,53 =

e. 6,36 + 8,42 – 4,47 = 2. Calculate. Example: 0,2 x 0,3

0,02 x 0,3

0,02 x 0,03

= 0,06

= 0,006

= 0,0006

a. 0,3 x 0,4 = d. 0,6 x 0,7 =

b. 0,5 x 0,1 = e. 0,04 x 0,02 =

c. 0,7 x 0,8 =

3. Calculate. Example: 0,2 x 10 =2 a. 0,7 x 8 =

b. 0,4 x 9 =

d. 0,03 x 8 =

e. 0,06 x 5 =

c. 0,7 x 8 =

4. Calculate. Example: 0,3 x 0,2 x 100 = 0,06 x 100 =6 a. 0,3 x 0,5 x 10 =

b. 0,9 x 0,02 x 10 =

d. 0,8 x 0,04 x 100 =

e. 0,3 x 0,2 x 100 =

c. 0,3 x 0,4 x 100 =

5. Calculate. Example: 5,276 x 30 = (5 x 30) + (0,2 x 30) + (0,07 x 30) + (0,006 x 30) = 150 + 6 + 2,1 + 0,18 = 150 + 6 + 2 + 0,1 + 0,1 + 0,08 = 1 562 + 0,2 + 0,08 = 1 562,28 a. 1,365 x 10 =

b. 4,932 x 30 =

d. 17,654 x 60 =

e. 28,342 x 20 =

c. 2,578 x 40 =

Consolidation

When we multiply decimals we should look at the places (place value) after the decimal comma. Learners who need : Receive peer . Learners who are more than competent: Provide peer .

Problem solving

Multiply three-hundredths by nine-thousandths by 1 000. Divide a decimal with two places after the decimal by a whole number.

MATHEMATICS Grade 8: Term 3 Week 3 Day 1 Mental Maths - 10 Minutes Divide decimal fractions by decimal fractions - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.b decimals, fractions and percentages; 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Divide decimal fractions by decimal fractions - Extend multiplication to multiplication by decimal fractions not limited to one decimal place - Extend division to division of decimal fractions by decimal fractions - Use knowledge of place value to estimate the number of decimal places in the result before performing calculations Teacher Note: Keywords (See attached dictionary for definitions.) - Decimal fraction - Multiplication - Division - Estimate - Estimate the possible answer before doing a calculation on a calculator Assessment: Divide decimal fractions by decimal fractions Informal Resources:

Board





Introduction: Division Introduce this lesson by giving learners some quick recall activities. a. 8 ÷ 4 =

b. 35 ÷ 7 =

c. 42 ÷ 7 =

d. 55 ÷ 5 =

e. 63 ÷ 9 =

f. 12 ÷ 2 =

g. 30 ÷ 5 =

h. 16 ÷ 4 =

i. 81 ÷ 9 =

j. 121 ÷ 11 =

k. 54 ÷ 6 =

l. 42 ÷ 6 =

m. 35 ÷ 5 =

n. 125 ÷ 25 =

o. 144 ÷ 12 =

Concept development Look at the examples in this lesson and do them with your learners on the board. Homework: Questions 1 g-j. Learners do the following in their writing books. 1. Calculate the following. Example: 0,4 ÷ 2 = 0,2 a. 0,8 ÷ 4 = d. 0,8 ÷ 2 =

b. 0,6 ÷ 3 = e. 1,8 ÷ 3 =

c. 0,6 ÷ 2 =

2. Revision: round off your answers in 1 to the nearest whole number. 3. Revision: calculate the following. Example: 0,25 ÷ 5 = 0,05

a. 0,81 ÷ 9 = d. 0,54 ÷ 6 =

b. 0,35 ÷ 7 = e. 0,12 ÷ 4 =

c. 0,63 ÷ 7 =

4. Round off your answers in 3 to the nearest tenth. 5. Solve the following problems. a. I have R45,75. I have to divide it by five. What will my answer be? b. My mother bought 12,8 m of rope. She has to divide it into four pieces. How long will each piece be? c. You need seven equal pieces from 28,7 m of rope. How long will each piece be?

6. Complete the flow diagram. a.

d.

R0,50

b.

2,4 m

c.

5,4 kg

Divide by 2

Divide by 8

Divide by 9

Round off to the nearest rand

Round off to the nearest m

Round off to the nearest kg

R3,75

e.

2,5 ℓ

f.

1,44 kg

Divide by 25

Divide by 5

Divide by 12

Round off to the nearest rand

Round off to the nearest litre

Round off to the nearest kilogram

Consolidation

When dividing decimals by whole numbers, you place the decimal comma in the same place as in the dividend. Learners who need : Give learners more examples like in this lesson. Learners who are more than competent: Peer .

Problem solving

Divide a decimal with two places after the decimal by a whole number.

MATHEMATICS Grade 8: Term 3 Week 3 Day 2 Mental Maths - 10 Minutes Calculate the squares of rational numbers. - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.b decimals, fractions and percentages; 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Calculate the squares of rational numbers. - Calculate the squares, cube, square roots and cube roots of decimal fractions. - Solve problems in context involving decimal fractions - Revise equivalent forms between: common fraction and decimal fraction forms of the same number Teacher Note: Keywords (See attached dictionary for definitions.) - Cube number - Cube roots - Decimal fraction - Square number - Square roots - A problem in context - Problem solving - Equivalence between common fraction and decimal fraction Assessment: Calculate the squares of rational numbers. Informal

Resources: Board Writing books




Grade 8: Term 3: Week 3: Day 2: Part 1

Introduction: Calculate the squares of rational numbers Introduce the topic by revising square numbers. 72 = 49 and square roots

49 = 7²

Concept development Write the following on the board. Do each calculation step by step with the learners using both methods.

= 0,7 x 0,7 = 0,49

=

or

4 100

0,04 0,2 × 0,2

= 0,2

7 2 ) 10 7 7 = x 10 10 49 = 100 = 0,49

(

(0,7)2

or

2 2 = x 10 10 2 = 10 = 0,2

4 2 ) 100 4 4 = x 100 100 16 = 10000 = 0,0016

(

(0,04)2 = 0,04 x 0,04

or

= 0,0016

4 1000

0 ,004 =

0 , 02 × 0 , 02

= 0,02

or

2 2 x 100 100 2 = 100 = 0,02 =

Homework: Questions 1g-j; 2g-j; 3g-j; 4g-j; 5g-j; 6g-j. Choose any two sums and say where you will use it in real life.

1

1. Calculate. Example 1: (0,7)2

Example 2: (1,5)²

= 0,7 x 0,7

1,5 x 1,5

= 0,49

= 2,25

a. (0,6)2 d. (0,1)2 g. (1,2)2 j. Add up a, b, c and d.

b. (0,2)2 e. (0,5)2 h. (1,4)2 k. Subtract d from e.

c. (0,3)2 f. (0,4)2 i. (1,6)2

2. Calculate.

You may use a calculator.

Example 2: (0,13)²

Example 1: (0,04)2 = 0,04 x 0,04

0,0169

= 0,0016 a. (0,03)2

b. (0,05)2

c. (0,01)2

d. (0,04)2

e. (0,12)2

f. (0,16)2

g. (0,11)2

h. (0,08)2

i. (0,09)2

j. (0,14)2

k. Add up a and b and then subtract e from it.

3. Calculate. Example: 0 ,04 =

0,2 × 0,2

= 0,2 a.

0,9

b.

0,1

c. 0,25

d.

0,36

e.

0,49

f.

0,81

g.

0,64

h.

0 ,121

i.

0 ,144

j.

0, 4

2

4. Calculate. Example: =

0 , 004 0 , 02 × 0 , 02

= 0,02 a. 0,0009 d. g. j.

c. 0,0001

0,0049

b. 0,0016 e. 0,0004

0 , 0064

0 , 0081

0 , 0144

h.

f. 0,0121 i.

0 , 0036

Consolidation

It is important to look at the place value when we multiply by decimal numbers.

Use both methods (see concept development) to calculate square roots. It is important to understand place value of decimals numbers. Learners who need : Do the sums first in common fraction form, e.g. (0,6)2 = 6/10 x 6/10 = 36/100 = 0,36 Solve square roots using both methods. Learners who are more than competent: What is 0,00012 squared? Explain by means of common and decimal fractions how you solved it. What is the square root of 0,000000016? Write your answer in scientific notation.

Problem solving

If the side of a square tile is 0,6 m, what is the area of the tile? Problem: why did we not use

0,4 and

0,004 in this activity?

3

Grade 8: Term 3: Week 3: Day 2: Part 2

Introduction: Calculate the cube number of rational numbers Introduce the topic by revising cube numbers and cube roots. 23 =8

3

27

=3

Concept development Write the following on the board. Do each calculation step by step with the learners using both methods.

(0,1)3 = 0,1 x 0,1 x 0,1 = 0,001

(0,01)3 = 0,01 x 0,01 x 0,01 = 0,000001

Where in real life will you use this? (e.g. calculating volume)

1 3 ) 10 1 1 1 = x x 10 10 10 1 = 1000 = 0,001

( or

1 3 ) 100 1 1 1 = x x 100 100 100 1 = 1000000 = 0,000001

( or

4

0,027

3

=

3

− 0 ,027

3

=

0 ,3 × 0 ,3 × 0 ,3

3

Where in real life will you use this? (e.g. the volume of a cube is given to you and you need to work out the height)

− 0 ,3 × − 0 ,3 × − 0 ,3

= -0,3

= 0,3

Homework: Questions 2d and 3d. Learners do the following in their writing books. 1. Calculate. Example: (0,1)3 = 0,1 x 0,1 x 0,1 = 0,001 a. (0,3)3

b. (0,2)3

c. (0,4)3

d. (0,5)3

e. (1,2)³

f. (0,6)³

2. Calculate. Example: (0,01)3 = 0,01 x 0,01 x 0 x 01 = 0,000001 a. (0,03)3

b. (0,02)3

c. (0,04)3

d. (0,05)3

e. (0,08)³

f. (0,08)³

b.

c.

3. Calculate. Example:

3

0,027

= 3 0 ,3 × 0 ,3 × 0 ,3 = 0,3 a.

3

0,008

d.

3

0 ,125

3

0,081

3

0,001 5

4. Calculate. Example:

3

− 0 ,027

= − 0 ,3 × − 0 ,3 × − 0 ,3 = -0,3 3

a.

3

− 0,008

d.

3

− 0 ,125

b.

3

− 0,081

c. 3 − 0,001

Consolidation

It is important to look at the place value of decimal numbers when we multiply with decimal numbers. Use both methods to calculate cube roots. Place value of decimal numbers are important. Learners who need : Solve all the sums using both methods. Solve all calculations using both methods. Learners who are more than competent: What is 0,00009 cubed? What is the cube root of 0,00004?

Problem solving

If the height of a cube is 0,35 m, what is the volume of the cube? Problem: we can say

3

− 0,064 . Can we say

− 0,9 ? Why or why not?

6

MATHEMATICS Grade 8: Term 3 Week 3 Day 3 Mental Maths - 10 Minutes Assessment 1.1 - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.b decimals, fractions and percentages; 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.2.f multiples and factors; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.a rounding off; 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Assessment 1.1 - Revise Addition and subtraction of common fractions, including mixed numbers - Revise Finding fractions of whole numbers - Revise Multiplication of common fractions, including mixed numbers - Divide whole numbers and common fractions by common fractions - Calculate the squares, cubes, square roots and cube roots of common fractions - Convert mixed numbers to common fractions in order to perform calculations with them - Use knowledge of multiples and factors to write fractions in the simplest form before or after calculations - Use knowledge of equivalent fractions to add and subtract common fractions. - Use knowledge of reciprocal relationships to divide common fractions - Solve problems in contexts involving common fractions and mixed numbers, including grouping, sharing and finding fractions of whole numbers - Revise: Find percentages of whole numbers. - Revise: Calculate the percentage of part of a whole - Revise: Calculate percentage increase of decrease of whole numbers - Calculate amounts if given percentage increase or decrease - Recognize equivalent forms between: common fractions (fractions where one denominator is a multiple of the other) - Recognize equivalent forms: common fraction and decimal fraction forms of the same

number - Recognize equivalence: common fraction, decimal fraction and percentage forms of the same number - Revise: Ordering, comparing and place value of decimal fractions to at least 3 decimal places - Revise: Rounding of decimal fractions to at least 2 decimal places - Use rounding off and a calculator to check results where appropriate - Solve problems in context involving decimal fractions - Revise equivalent forms between: common fraction and decimal fraction forms of the same number - Revise equivalent forms between: common fraction, decimal fraction and percentage forms of the same number. Teacher Note: Keywords (See attached dictionary for definitions.) - Addition - Common fraction - Mixed numbers - Subtraction - Whole numbers - Multiplication - Division - Cube number - Cube roots - Square number - Square roots - Fraction in its simplest form - Multiples and factors - Equivalent fractions - A problem in context - Problem solving - Sharing - Percent - Decrease - Increase - Denominator - Multiples - Decimal fraction - Equivalence between common fraction and decimal fraction - Common fractions - Equivalence between common fraction, decimal fraction and percentage - Compare decimal fractions - Rounding (decimals) - Calculator - Rounding - Use of a calculator Assessment: Assessment 1.1

Formal Assessment task 1.1 All 60 Marks

Resources: Sample assessment





Introduction: Assessment 1.1

Tell learners that they are going to write an assessment to assess what they have learnt this term. They can use their previous work to help them.

Concept development Week 1 Day 1 – Week 3 Day 2 • Add and subtract fractions • Multiply fractions • Divide whole number by common fractions • Fractions of squares, cubes, square and cube roots • Fractions, decimals and percentages • Place value, ordering and comparing decimals • Round off rational numbers • Equivalence between common and decimal fractions • Addition, subtraction and multiplication of decimal fractions • Division • Calculate the squares of rational numbers Homework: No homework.

1. Revision: say if it is a proper or improper fraction, or a mixed number. 4

3

a. 5

b. 3 5

c.

2. Write an equivalent fraction for 1

3

a. 6 3

3 6

(3)

4

b. 2 4

c. 2 5

(3)

3. Add up the following, write it as a mixed number and simplify if necessary 2

4

5

a. + = 5 5

6

b. 9 + 9 =

4. Calculate and simplify it necessary. 1

1

1

a. + = 4 2 2

4

e.

5. Calculate. a.

1 5

1

b. 5 + 10 =

d. 8 3 ÷ 95 = 2

×3 =

b.

5 8

2 4

3

2

1

1

c. 4 + 4 =

(3)

c. 3 + 6 = f.

²

1

×3=

c.

1 3 ×7 6

(6)

=

(3)

6. What whole number and fraction will give you the following answer? 4

9

3

b. ___ × ___ = 18

a. ___ × ___ = 6

c. ___ × ___ = 8

(3)

7. Write the following as a fraction and decimal fraction. a. 56%

(1)

8. Write the following as a fraction in its simplest form.

(2)

Percentage

10%

Fraction

10 100 1 10

Simplest form

20%

30%

40%

50%

60%

70%

80%

90%

100%

9. Calculate the percentage. 50c of R7,00

10. Calculate the percentage increase. R36 of R54

(2) (2)

11. Calculate the percentage decrease.

(2)

R28 of R21

12. Solve the following. a. What is 86,6% of 44? b. Mary earns a monthly salary of R12 000. She spends R2 800 per month on food. What percentage of her monthly salary does she spend on food? (4) 13. Write the following in expanded notation: (1)

900,009 14. Write the following in words. 23,004

(1)

15. Write the following in the correct column.

(4)

thousands

hundreds

tens

units

tenths

a.

24,328

,

b.

376,02

,

c.

8674,5

,

d.

987,001

,

hundredths

Thousandths

16. Write down the value of the underlined digit. 568,999 17. Write the following in ascending order. 0,67; 0,007; 0,06 18. Fill in <, >, = . 0,123 ___ 0,321 19. Round off to the nearest whole number. 5,68 20. Round off to the nearest tenth. 7,513

(5)

21. Round off to the nearest hundredth. (1)

7,942 22. Round off to the nearest thousandth.

(1)

5,1272 23. Write as a decimal fraction.

(1)

24. Write as a common fraction. 48,003

(1)

25. Calculate. a. 4,29 + 8,34 – 3,38 =

b. 0,7 x 0,8 =

d. 0,8 x 0,04 x 100 =

e. 28,342 x 20 =

c. 0,6 x 8 = f. (0,16)2

26. Solve the following problems. I have R45,75. I have to divide it by five. What will my answer be?

(6)

(3)

27. Complete the flow diagram. 2,5 ℓ

Divide by 5

Round off to the nearest litre

(2) Total: 60

Consolidation

In this lesson we revised the following: Week 1 Day 1 – Week 3 Day 2 • Add and subtract fractions • Multiply fractions • Divide whole number by common fractions • Fractions of squares, cubes, square and cube roots • Fractions, decimals and percentages • Place value, ordering and comparing decimals • Round off rational numbers • Equivalence between common and decimal fractions • Addition, subtraction and multiplication of decimal fractions • Division • Calculate the squares of rational numbers Tell learners to identify the concepts that they are not clear about, write it on a piece of paper and put it on the teacher’s desk. Start the next lesson with those concepts. Learners who need : Receive peer, group or teacher . Learners who are more than competent: Provide peer or group .

Problem solving

Do all the problems you did in Week 1 Day 1 – Week 3 Day 2.

MATHEMATICS Grade 8: Term 3 Week 3 Day 4 Mental Maths - 10 Minutes Pythagoras - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 4:MEASUREMENT 8.4.1 Solves problems involving: 8.4.1.a length; 8.4.1.b perimeter and area of polygons and circles; Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Pythagoras - Investigate the relationship between the lengths of the sides of a right-angled triangle to develop the Theorem of Pythagoras. - Determine whether a triangle is a right-angled triangle or not, if the length of the three sides of the triangle a re known. - Use the Theorem of Pythagoras a missing length in a right-angled triangle, leaving irrational answers in surd form. Teacher Note: Keywords (See attached dictionary for definitions.) - Theorem of Pythagoras - Right-angle triangle Assessment: Pythagoras Informal






Introduction:Pythagoras Introduce the lesson by telling learners that you are going to learn about Pythagoras theorem. Years ago, a man named Pythagoras discovered an amazing fact about triangles. Draw the following on the board. What is the size of c? (42) A

What is the size of a? (32) What is the size of b? (52) What do you notice?

32 + 42 = 52 B

C

9 + 16 = 25 25 = 25

Concept development We can say that a2 + b2 = c2 What do we call the largest side of the triangle? (hypotenuse) The theorem only applies to right-angled triangles. Homework: Complete drawings. Do the following in your writing books. 1. Write an equation for the following and solve it.

2. Make drawings to show the following. What do you notice? Side A

Side B

Side C

a.

6

8

10

b.

15

25

20

c.

45

36

27

d.

20

12

16

e.

9

15

12

3. What is the hypothesis? Highlight it in all your drawings.

Consolidation Learners who need : Receive peer . Learners who are more than competent: Provide peer .

Problem solving

Give two examples of where we can use Pythagoras in real life.

MATHEMATICS Grade 8: Term 3 Week 3 Day 5 Mental Maths - 10 Minutes Theorem of Pythagoras - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 4:MEASUREMENT 8.4.1 Solves problems involving: 8.4.1.a length; 8.4.1.b perimeter and area of polygons and circles; Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Theorem of Pythagoras - Investigate the relationship between the lengths of the sides of a right-angled triangle to develop the Theorem of Pythagoras. - Determine whether a triangle is a right-angled triangle or not, if the length of the three sides of the triangle a re known. - Use the Theorem of Pythagoras a missing length in a right-angled triangle, leaving irrational answers in surd form. Teacher Note: Keywords (See attached dictionary for definitions.) - Theorem of Pythagoras - Right-angle triangle Assessment: Theorem of Pythagoras Informal






Introduction: Theorem of Pythagoras Introduce the lesson by revising the theorem of Pythagoras.

Concept development Do the following on the board. Ask the learners to give you an equation for the following.

4

5

a

c

3

b

42 + 32 = 52

a2 + b2 = c2

Left-hand side (LHS) = right-hand side (RHS)

16 + 9 = 25 25 = 25 Homework: Questions 1d and 2d.

Do the following in your writing books. 1. Write an equation for the following and use the given sides to prove the theorem of Phytagorus. Example: see concept development. a.

104

b. 5

4

78

130

3 c.

d.

33 55 44

51

68

85

2. Write an equation for the following: Example: see concept development.

a

a.

b.

c

c.

b

m

n o

d.

g h i

s r t


Problem solving

If you have the hypothesis and one side of a right-angled triangle, how will you calculate the other side?







Introduction: Theorem of Pythagoras Introduce the topic by asking learners why we need to know the theorem of Pythagoras.

Concept development Do the following on the board.

3 cm

2 = 3 2 + 4 2 = 9 2 + 16 ² 2 = 25 2

x

2

= 25 ² = 5

4 cm

Homework: Questions 1e-f. Do the following in your writing books. 1. Find the lengths of the unknown sides in the following right-angled triangles. You may use a calculator. Example: see concept development.

a.

b.

4 cm

a

a

3,5 cm

5 cm

6,4 cm

c.

d. a

10 cm

15 cm 7 cm

a

12 cm

e.

f. a 7 cm

2,2 cm

75 cm

a

0,5 cm

Consolidation Learners who need : learners in writing an equation for the lengths of the sides of the right-angled triangle. Learners who are more than competent: Learners draw two of their own rightangled triangles and give them to a friend to solve the third side.

Problem solving

Create your own problem using the Theorem of Pythagoras.






Grade 8: Term3: Week 4: Day 2

Introduction: Theorem of Pythagoras Introduce the topic by asking learners what a diagonal is.

Concept development

Let the diagonal be .

Do the following on the board. Find the length of the diagonal of the rectangle.

8 cm

4 cm

5 cm

3 cm

2 = 3 2 + 4 2 = 9 2 + 16 ² 2 = 25 2

2

2 = 5 2 + 8 2 2 = 25 2 + 64 ² 2 = 89 2 = 89 2

= 25 ² = 5

Homework: Questions 1d and 2d. Do the following in your writing books.

1. Find the lengths of the of the diagonal of the rectangle. Example: see concept development. a.

21 mm

b.

28 mm

30 mm

50 mm

c.

d.

2. Find the length of the diagonal of the rectangle. Example: see concept development. a.

2 cm

b.

1,2 cm

c.

9,2 cm

12,2 cm

d.

Consolidation Learners who need : Learners highlight the triangle before doing the calculation. Learners who are more than competent: Provide peer .

Problem solving

Create your own theorem of Pythagoras problem.






Grade 8: Term 3 - Week 4: Day 3:

Introduction: Theorem of Pythagoras

Introduce the lesson by asking learners what they know about the theorem of Pythagoras. Write the keywords on the board.

Concept development Find the unknown sides.

16 cm

16 2 = 2 + 5 2 256 2 = 2 + 25 ² 2 = 231 ²

2 = 231 2 = 15,2 cm

10 cm Homework: Question 1d. Learners do the following in their writing books. 1. Find the unknown side. a.

75 mm 6 cm

10,8 cm

b.

c.

d.


Problem solving

If you have an equilateral triangle, you are given two sides, namely the length and the height of the triangle. How will you calculate the third side?

MATHEMATICS Grade 8: Term 3 Week 4 Day 4 Mental Maths - 10 Minutes Area and perimeter of a square - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.b decimals, fractions and percentages; 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 4:MEASUREMENT 8.4.1 Solves problems involving: 8.4.1.a length; 8.4.1.b perimeter and area of polygons and circles; Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Area and perimeter of a square - Extend multiplication to multiplication by decimal fractions not limited to one decimal place - Extend division to division of decimal fractions by decimal fractions - Calculate the squares, cube, square roots and cube roots of decimal fractions. - Use knowledge of place value to estimate the number of decimal places in the result before performing calculations - Solve problems in context involving decimal fractions - Revise equivalent forms between: common fraction and decimal fraction forms of the same number - Investigate the relationship between the lengths of the sides of a right-angled triangle to develop the Theorem of Pythagoras. - Determine whether a triangle is a right-angled triangle or not, if the length of the three sides of the triangle a re known. - Use the Theorem of Pythagoras a missing length in a right-angled triangle, leaving irrational answers in surd form. Teacher Note:

Keywords (See attached dictionary for definitions.) - Decimal fraction - Multiplication - Division - Cube number - Cube roots - Square number - Square roots - Estimate - Estimate the possible answer before doing a calculation on a calculator - A problem in context - Problem solving - Equivalence between common fraction and decimal fraction - Theorem of Pythagoras - Right-angle triangle Assessment: Area and perimeter of a square Informal Resources: Board Writing books





Introduction: Area and perimeter of a square Revise the perimeter and the area of a square. Perimeter of a square = 4

Area of a square = 2

Also revise:

If 1 = 10 , then 1 2 = 100 2 If 1 = 100 , then 1 2 = 10 000 2

Concept development

Where in real life will we use the perimeter and area of a square?

Draw the following on the board. Do it step by step with your learners. 4,5

4,5

• Calculate the perimeter. • Calculate the area.

Perimeter = 4

= 4 (4,5 ) = 18

Area = 2

= 4,5 x 4,5 = 20,25 ²

Write your answer in . = 20,25 ² 100 = 10 cm x 10 = 180 = 2 025 ²

If the area is 2 025 ² what will the answer be in ²? 1 = 10 1 ² = 1 x 1 1 ² = 10 x 10 1 ² = 100 ²

∴

2 025 ² 100

= 20,25 ²

Homework: Complete the activities. Learners do the following in their writing books. 1. Calculate the a. Area b. Perimeter Give your answers in , and .

Length of the square is: Example: 2,5 Perimeter

= 4

Area

= ×

= 4 (4,5 ) = 10

= 2,5 x 2,5 = 6,25 ²

= 4 (25 ) = 100 Metre

= 25 x 25 = 625 ²

= 4 ( 0,025) = 0,1

= 0,025 x 0,025 = 0,000625 ²

Millimetre

a. 4,1 b. 0,4

c. 3,2

d. 45

2. If this is the area of a square, what is the length of one side? Calculate the perimeter. a. 6,76 ² Example: 1, ²

1,2 because Area: 1,2 x 1,2 = 1,44 ² Perimeter: 4 (1,2 ) = 4,8

3. Construct each of these squares. 4. Write the following in ².

Example: 1, ² 1,2 x 1,2 12 x 12 144 ²

1,44 = 1,2

b. 102,01 ² c. 29,16 ² d. 51,84 ²

a. 3,24 ² b. 5,29 ²

c. 57,76 ²

5. Write the following in ².

Example: 256 ² ²

= , ²

a. 576 ²

b. 3 769 ² c. 1 681 ²


Example: 21 × 21 = 441 ² ² 1 = 100 1 ² = 1 x 1 1 ² = 100 x 100 = 0,0441 ² 1 ² = 10 000 ²

a. 15 15 b. 24 24 c. 31 31

Consolidation Learners who need : Receive peer Learners who are more than competent: Provide peer .

Problem solving

I have 32 tiles of 30 x 30 . Will I be able to cover 3 m²?

MATHEMATICS Grade 8: Term 3 Week 4 Day 5 Mental Maths - 10 Minutes Area and perimeter of a square - Assessment 1.2 - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 4:MEASUREMENT 8.4.1 Solves problems involving: 8.4.1.b perimeter and area of polygons and circles; 8.4.5 Calculates, by selecting and using appropriate formulae 8.4.5.a perimeter of polygons and circles; 8.4.5.b area of triangles, rectangles, circles and polygons by decomposition into triangles and rectangles; 8.4.6 Converts between: 8.4.6.a mm² « cm² « m² « km² Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Area and perimeter of a square - Assessment 1.2 - Use appropriate formulae to calculate perimeter and area of: Squares - Solve problems, with or without a calculator involving perimeter and area of polygons and circles - Use and convert between appropriate SI Units including mm²↔cm²↔m²↔km² Teacher Note: Keywords (See attached dictionary for definitions.) - Area - Area of a square - Formulae - Square - Area of a circle

- Area of a rectangle - Area of a triangle - Calculator - Circles - Polygon - Problem solving - Use of a calculator - Convert between SI units: cm²↔m² - Convert between SI units: m²↔km² - Convert between SI units: mm²↔cm² - Convert between SI units: mm²↔m² Assessment: Area and perimeter of a square - Assessment 1.2 Formal Assessment task 1.2 All 40 Marks








Concept development Week 3 Day 4 – Week 4 Day 3 • Pythagoras • Theorem of Pythagoras Homework: No homework.

1. Write an equation for the following and solve it. a.

b.

g h

i (8) 2. Make drawings of the following triangles. Side A

Side B

Side C

a.

6

8

10

b.

15

25

20

3. What is the hypothesis? Highlight it in all your drawings.

(10)

(2)

4. Write an equation for the following and calculate each side 33 55 44

(5)

5. Find the lengths of the unknown sides in the following right-angled triangles. You may use a calculator. 15 cm a (5) 12 cm

6. Find the lengths of the of the diagonal of the rectangle. 30 mm

50 mm (5) 7. Find the unknown side. 10,8 cm

(5) Total: 40

Consolidation

In this lesson we revised the following: Week 3 Day 4 – Week 4 Day 3 • Pythagoras • Theorem of Pythagoras Tell learners to identify the concepts that they are not clear about, write it on a piece of paper and put it on the teacher’s desk. Start the next lesson with those concepts. Learners who need : Receive peer, group or teacher . Learners who are more than competent: Provide peer or group .

Problem solving


MATHEMATICS Grade 8: Term 3 Week 5 Day 1 Mental Maths - 10 Minutes Area + perimeter of a rectangle - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 4:MEASUREMENT 8.4.1 Solves problems involving: 8.4.1.b perimeter and area of polygons and circles; 8.4.5 Calculates, by selecting and using appropriate formulae 8.4.5.a perimeter of polygons and circles; 8.4.5.b area of triangles, rectangles, circles and polygons by decomposition into triangles and rectangles; 8.4.6 Converts between: 8.4.6.a mm² « cm² « m² « km² Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Area + perimeter of a rectangle - Use appropriate formulae to calculate perimeter and area of: Rectangles - Solve problems, with or without a calculator involving perimeter and area of polygons and circles - Use and convert between appropriate SI Units including mm²↔cm²↔m²↔km² Teacher Note: Keywords (See attached dictionary for definitions.) - Area of a rectangle - Rectangle - Area of a circle - Area of a square - Area of a triangle

- Calculator - Circles - Polygon - Problem solving - Use of a calculator - Convert between SI units: cm²↔m² - Convert between SI units: m²↔km² - Convert between SI units: mm²↔cm² - Convert between SI units: mm²↔m² Assessment: Area + perimeter of a rectangle Informal Resources: Board Writing books





Introduction: Area and perimeter of a rectangle


Revise the following with your learners: Perimeter of a rectangle Area of a square 2( + ) or 2 +2 = x Also revise:

If 1 = 10 , then 1 2 = 100 2 If 1 = 100 , then 1 2 = 10 000 2

Concept development

Draw the following on the board. 3,8 2,1

• Calculate the perimeter • Calculate the area

Perimeter

Area

= 2 ( + ) = 2 ( 3,8 + 2,1 ) = 2 5,9 = 11,8

= x = 3,8 x 2,1 = 14,44 ²

Write the area answer in ² and ². ² 1 = 10 = 14,44 ² 1 ² = 1 x 1 = 14,44 ² x 100 1 ² = 10 x 10 = 1 444 ² 1 ² = 100 ²

² =

14,44 ² 10 000

1 = 100 1 ² = 100 x 100 1 ² = 10 000 ²

= 0,001444 ²

Homework: Complete this activity. Learners do the following in their writing books.

1. Calculate the a. Area b. Perimeter Give your answers in , and .

The dimensions of the rectangle are: Perimeter 2 ( + ) = 2 ( 2,1 + 1,8 ) = 7,8 Millimetres

= 78

Metres = 0,078 a. 0,9 x 1,5 c. 2,1 x 1,9

Area x = 2,1 x 1,8 = 3,78 ² = 3,78 ² x 100 = 378 ²

3,78 ² 10 000

= 0,000378 ²

b. Length = 1,3 ; breadth = 1,1 d. Length = 2,8 ; breadth = 1,7

2. If this is the area of a rectangle, what is the possible length and breadth?

Example: 4,14 ² Area: 2,3 x 1,8 Perimeter: 2(2,3 + 1,8 ) = 8,2 a. 2,7 ² d. 46,92 ²

Consolidation

b. 24,7 ²

c. 17,94 ²

Learners who need : Receive peer . Learners who are more than competent: Provide peer .

Problem solving

You need to tile a room of 4,2 × 3,5 . The tiles you want to buy are 45 × 45 . How many tiles do you need?

MATHEMATICS Grade 8: Term 3 Week 5 Day 2 Mental Maths - 10 Minutes Area and perimeter of a triangle - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 4:MEASUREMENT 8.4.1 Solves problems involving: 8.4.1.b perimeter and area of polygons and circles; 8.4.5 Calculates, by selecting and using appropriate formulae 8.4.5.a perimeter of polygons and circles; 8.4.5.b area of triangles, rectangles, circles and polygons by decomposition into triangles and rectangles; 8.4.6 Converts between: 8.4.6.a mm² « cm² « m² « km² Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Area and perimeter of a triangle - Use appropriate formulae to calculate perimeter and area of: Triangles - Calculate the areas of polygons, to at least 2 decimal places, by decomposing them into rectangle and/or triangles - Solve problems, with or without a calculator involving perimeter and area of polygons and circles - Use and convert between appropriate SI Units including mm²↔cm²↔m²↔km² Teacher Note: Keywords (See attached dictionary for definitions.) - Area of a triangle - Triangle - Area

- Polygon - Area of a circle - Area of a rectangle - Area of a square - Calculator - Circles - Problem solving - Use of a calculator - Convert between SI units: cm²↔m² - Convert between SI units: m²↔km² - Convert between SI units: mm²↔cm² - Convert between SI units: mm²↔m² Assessment: Area and perimeter of a triangle Informal Resources: Board Writing books





Introduction: Area and perimeter of a triangle Revise the following with your learners: Perimeter of a triangle 1 =2 x h Also revise:

If 1 = 10 , then 1 2 = 100 2 If 1 = 100 , then 1 2 = 10 000 2

Concept development

Draw the following on the board. Area 1

1 2

2,3 5

Write your answer in ². 5,75 ² x 100 = 575 ²

=2 x h

5 x 2,3 = 2,5 x 2,3 = 5,75 ²

Write your answer in ². 5,75 ² 10 000 = 0,000575 ²

Homework: Complete this activity.

Learners do the following in their writing books. 1. Calculate the a. Area b. Perimeter Give your answers in , and . The dimensions of the triangle are:

Example: Base = 6

Height = 2,6


Area: 1 + ℎ 2 1

= (6 ) × 2,6 ) 2

Millimetres:

Metres:

7,8 ² × 100 = 780 ²

7,8 ² 10 000

= 0,00078 ²

= 3 x 2,6 = 7,8 ²

a. Base: 8 Height: 1,5

d. Base: 9,4 Height: 2,25

c. Base: 10 Height: 7,3

b. Base: 4,6 Height: 2,9

2. If this is the area of a triangle what is the possible height and base? Example: 7,35 ²

Area: (7 ) × ,

Base =

Height = ,

a. 16,2 ² d. 51,84 ²

b. 5,52 ²

c. 33,12 ²

3. Draw the height of each triangle and calculate the area. You will need a ruler. Note: the height of a triangle is the line segment drawn from any vertex perpendicular to the opposite side. Example:

B

A

D

A

C

D

B

C

a.

b.

A

A

B B

C

C

c. A

C

b. A

C

B B


Problem solving

The triangular area is 10,5 ². You have 2 025 ² tiles. How many do you need to tile the area?

MATHEMATICS Grade 8: Term 3 Week 5 Day 3 Mental Maths - 10 Minutes Area and perimeter of a circle - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 4:MEASUREMENT 8.4.1 Solves problems involving: 8.4.1.b perimeter and area of polygons and circles; 8.4.5 Calculates, by selecting and using appropriate formulae 8.4.5.a perimeter of polygons and circles; 8.4.5.b area of triangles, rectangles, circles and polygons by decomposition into triangles and rectangles; 8.4.6 Converts between: 8.4.6.a mm² « cm² « m² « km² Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Area and perimeter of a circle - Use and describe the relationship between the radius, diameter and circumference of a circle in calculations - Use and describe the relationship between the radius, and area of a circle in calculations - Solve problems, with or without a calculator involving perimeter and area of polygons and circles - Use and describe the meaning of the irrational number Pi (π) in calculations involving circles. - Use and convert between appropriate SI Units including mm²↔cm²↔m²↔km² Teacher Note: Keywords (See attached dictionary for definitions.) - Circle

- Diameter - Radius - Circumference - Area - Circles - Area of a circle - Area of a rectangle - Area of a square - Area of a triangle - Calculator - Polygon - Problem solving - Use of a calculator - Irrational numbers - Convert between SI units: cm²↔m² - Convert between SI units: m²↔km² - Convert between SI units: mm²↔cm² - Convert between SI units: mm²↔m² Assessment: Area and perimeter of a circle Informal Resources: Board Writing books





Introduction: Area and perimeter of a circle Revise the following with your learners: Circumference of a circle = π d or 2 π r

Area of a circle = π 2

Also revise:

Where in real life will we use the perimeter and area of a circle?

If 1 = 10 , then 1 2 = 100 2 If 1 = 100 , then 1 2 = 10 000 2

Concept development

π is an irrational number and is given as 3,141592654 to the 9th decimal place.

Draw the following on the board. circumference

circumference diameter

= π = 3,14159 π represents the value of the circumference divided by the diameter.

22 7

or 3,14 are approximate rational values.

Tell the learners that • the radius is the distance from the centre to the edge. • the diameter starts at the side of the circle, goes through the centre and ends on the other side. What can you tell me about the diameter? (diameter = 2x radius) = 2

What is the circumference? (The circumference is the distance around the edge of the circle.) = π

or

2 π

The area of a circle is = π x ²

Homework: Complete this activity. Learners do the following in their writing books.

1. Calculate the area of the circles. The radius of the circle is 3 : Example: = π ² = (3,14159) (3²) = 28,27 ² a. 4 d. 4,3

b. 2,8 e. 5,9

c. 3,7 f. 10,1

b. 78,54 ²

c. 113,098 ²

2. If the area of the circle is ___ , what is the radius?

Example: 50,265 ² = 3,14159 (4²) a. 12,566 ² d. 314,159 ²

Consolidation Learners who need : Receive peer

Learners who are more than competent: Provide peer .

Problem solving

The triangular area is 10,5 ². You have 2 025 ² tiles. How many do you need to tile the area?

MATHEMATICS Grade 8: Term 3 Week 5 Day 4 Mental Maths - 10 Minutes Area and perimeter problem solving - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 4:MEASUREMENT 8.4.1 Solves problems involving: 8.4.1.b perimeter and area of polygons and circles; Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Area and perimeter problem solving - Solve problems, with or without a calculator involving perimeter and area of polygons and circles Teacher Note: Keywords (See attached dictionary for definitions.) - Area of a circle - Area of a rectangle - Area of a square - Area of a triangle - Calculator - Circles - Polygon - Problem solving - Use of a calculator Assessment: Area and perimeter problem solving Informal






Introduction: Area and perimeter problem solving

Introduce this lesson by asking learners to share everything they have done on area and perimeter so far. Perimeter of a square = 4

Perimeter of a rectangle 2( + ) or 2 +2 Area of a triangle 1 = 2 x h

Circumference of a circle = d or 2 r

Area of a square = 2 Area of a square = x

Area of a circle = π 2

If 1 = 10 , then 1 2 = 100 2 If 1 = 100 , then 1 2 = 10 000 2

Concept development

In this lesson learners will solve problems. Give learners the formula and ask them for what it is. • Perimeter of a square = 4 • Perimeter of a rectangle = 2 ( × ) or 2 + • Area of a square = ² • Area of a rectangle = × • Area of a triangle = ( × ) • Diameter of a circle: d = 2r • Circumference of a circle: C = Pi d or 2 Pi r • Area of a circle: A = PI r²

Ask learners how they will solve the problems. Make notes on the board. Write a summary below. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

Homework: Complete the word problems. Learners do the following in their writing books. 1. Solve the following. a. If the perimeter of a square is 52 , what is the length of each side? If the area of a rectangle is 200 ², and its length is 50 , what is its breadth?

b. You live in a rectangular-shaped home that is 150 long and 902 m wide. You want to plant shrubs around the home. You are to plant the shrubs 70 apart. Approximately how many shrubs will you need to surround the house? c. A room of which the area is 14,82 ² has a length of 100 longer than the width. What are the dimensions of the room? d. Find the area of a circular sector of which the cord is the side of the square inscribed in a circle with a 3 -radius.



MATHEMATICS Grade 8: Term 3 Week 5 Day 5 Mental Maths - 10 Minutes Surface area, volume and capacity of a cube. - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 4:MEASUREMENT 8.4.1 Solves problems involving: 8.4.1.c volume and surface area of rectangular prisms and cylinders. 8.4.5 Calculates, by selecting and using appropriate formulae 8.4.5.c volume of triangular and rectangular-based prisms and cylinders. 8.4.6 Converts between: 8.4.6.b mm³ « cm³ « m³ 8.4.6.c ml (cm³) « l « kl Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Surface area, volume and capacity of a cube. - Use appropriate formulae to calculate the surface area, volume and capacity of Cubes - Describe the interrelationship between surface area and volume of the objects mentioned above - Use and convert between appropriate SI Units including mm³↔cm³↔m³ - Use and convert between appropriate SI Units including ml(cm)³↔l↔kl Teacher Note: Keywords (See attached dictionary for definitions.) - Area - Capacity - Cube - Surface area of a prism - Volume of a cube

- Volume - Surface area - Convert between SI units: mm³↔m³ - S.I. Unit - Convert between SI units Assessment: Surface area, volume and capacity of a cube. Informal Resources: Board Writing books





Introduction: Surface area, volume and capacity of a cube Revise: Volume of a cube = ³

Surface area of a cube A = the sum of the areas of all the faces.

Concept development

Write the following on the board. Volume

Capacity

Volume of a solid is the amount of space it occupies.

Capacity of a cube • An object with a volume of 1 3 will displace exactly 1 ml of water. • An object with a volume of 1 3 will displace exactly 1 of water. Surface area

Capacity is the amount of liquid a container holds when it is full.

The total area of the surface of a geometric solid.

Ask learners if they can still what each one means. Draw the following on the board and revise it with your learners. Volume

4

Capacity

Surface area

Note: an object with a volume of 1 3 will displace 1 ml of water.

Net of the cube. How many faces (surfaces) are there? Shape?

∴ An object that is 64 3 will displace 64 ml water or 0,064

= 3 = (4 )3 = 64 3 Cubic

1 000 000

Cubic

Litre

1 000 000 000

Cubic

1

1 000

1 000 000

1 000

0, 001

1

1 000

1

0,000001

0,001

4

Surface area = sum of the area of al the faces. = 6 (area of a face) = 6a² = 6 (4 )² = 6 x 16 ² = 96 ²

Homework: Questions 1e and f. Learners do the following in their writing books. 1. Label and complete calculate the volume, capacity and surface area of the following. Example: see concept development. a.

2

d. Area of base: 25 ² Height: _____

Consolidation

b.

3,2

e. Length: _____ Breadth: _____ Height: 1,2

c. Length: 4,6 Breadth: _____ Height: _____

f. Area of base: 81 ² Height: _____

Learners who need : Receive peer Learners who are more than competent: Provide peer .

Problem solving

How much water can a container of 32 by 32 by 32 contain?

MATHEMATICS Grade 8: Term 3 Week 6 Day 1 Mental Maths - 10 Minutes Surface area, volume and capacity of a prism. - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 4:MEASUREMENT 8.4.1 Solves problems involving: 8.4.1.c volume and surface area of rectangular prisms and cylinders. 8.4.5 Calculates, by selecting and using appropriate formulae 8.4.5.c volume of triangular and rectangular-based prisms and cylinders. 8.4.6 Converts between: 8.4.6.b mm³ « cm³ « m³ 8.4.6.c ml (cm³) « l « kl Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Surface area, volume and capacity of a prism. - Use appropriate formulae to calculate the surface area, volume and capacity of Rectangular prisms - Describe the interrelationship between surface area and volume of the objects mentioned above - Use and convert between appropriate SI Units including mm³↔cm³↔m³ - Use and convert between appropriate SI Units including ml(cm)³↔l↔kl Teacher Note: Keywords (See attached dictionary for definitions.) - Capacity - Rectangular prism - Surface area of a prism - Volume of a prism

- Volume of a rectangular prism - Surface area - Volume - Convert between SI units: mm³↔m³ - S.I. Unit - Convert between SI units Assessment: Surface area, volume and capacity of a prism. Informal Resources: Board Writing books





Introduction: Surface area, volume and capacity of a prism Volume of a prism = × × ℎ • • • •

Surface area of a prism SA = the sum of the areas of all its faces.

Capacity of a prism • An object with a volume of 1 3 will displace exactly 1 ml of water. • An object with a volume of 1 3 will displace exactly 1 of water.

If 1 = 10 , then 1 3 = 1 000 3 If 1 = 100 , then 1 3 = 1000 000 3 106 ³ An object with a volume of 1 3 will displace exactly 1 of water. An object with a volume of 1 3 will displace exactly 1 of water.

Concept development

Write the following on the board. Volume

Capacity

Volume of a solid is the amount of space it occupies.

Surface area

Capacity is the amount of liquid a container holds when it is full.

The total area of a surface of a geometric solid.

In groups, ask learners to complete this. Draw the following on the board and revise it with your learners. Volume 4

2 1,5

= x x ℎ = 4 x 1,5 x 2 ) = 12 3

Capacity

Surface area

Note: an object with a volume of 1 3 will displace 1 ml of water.

Describe the face (surface)? 4

∴ An object that is 12 3 will displace 12 ml.

Cubic

1 000 000 000

Cubic 1 000 000

Cubic

Litre

1

1 000

1 000 000

1 000

0, 001

1

1 000

1

0,000001

0,001

2

1,5

Surface area: = 2 + 2 ℎ + 2ℎb = 2 (1,5 x 4 ) + 2(4 x 2 ) = 12 ² + 16 ² +6 ² = 34 ²

Homework: Complete this activity. Learners do the following in their writing books. 1. Calculate the volume, capacity and surface area. Example: see concept development. a.

b.

5 3,2

2,1

d. Area of base: 24 ² Height: 2,5

8,5

c. Length: 7,3 Breadth: 5,5 Height: 3,8 2,9

3,2

Consolidation

Learners who need : Receive peer . Learners who are more than competent: Provide peer .

Problem solving

A container has a square base of 8 . What is the height of the box if its volume is 384 ³?

MATHEMATICS Grade 8: Term 3 Week 6 Day 2 Mental Maths - 10 Minutes Surface area, volume and capacity of a triangular prism. - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 4:MEASUREMENT 8.4.1 Solves problems involving: 8.4.1.c volume and surface area of rectangular prisms and cylinders. 8.4.5 Calculates, by selecting and using appropriate formulae 8.4.5.c volume of triangular and rectangular-based prisms and cylinders. 8.4.6 Converts between: 8.4.6.b mm³ « cm³ « m³ 8.4.6.c ml (cm³) « l « kl Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Surface area, volume and capacity of a triangular prism. - Use appropriate formulae to calculate the surface area, volume and capacity of Triangular prisms - Describe the interrelationship between surface area and volume of the objects mentioned above - Use and convert between appropriate SI Units including mm³↔cm³↔m³ - Use and convert between appropriate SI Units including ml(cm)³↔l↔kl Teacher Note: Keywords (See attached dictionary for definitions.) - Capacity - Surface area of a prism - Volume of a prism - Volume of a rectangular prism

- Surface area - Volume - Convert between SI units: mm³↔m³ - S.I. Unit - Convert between SI units Assessment: Surface area, volume and capacity of a triangular prism. Informal Resources: Writing books





Introduction: Surface area, volume and capacity of a triangular prism Revise the following: Volume of a triangular prism 1 = × ℎ × ℎ

Surface area of a rectangular prism. A = the sum of the area of all its faces.

2

• • • •

Capacity • An object with a volume of 1 3 will displace exactly 1 ml of water. • An object with a volume of 1 3 will displace exactly 1 of water.


Concept development

Tell the learners that you are going to introduce the following to them. Write the concept on the board. • x-intercept and y-intercept • gradient

Volume

Capacity

Surface area

Area of triangle

Revise the concepts with the learners. Draw the following on the board and revise it with your learners. Volume

3

1

5

2

Capacity

Surface area

Note: an object with a volume of 1 3 will displace 1 ml of water. ∴ An object that is 15 3 will displace 64 ml of water.

Describe the face (surface)

3 1,5

= 2 x ℎ x ℎ =

1 (5 ) x 3 x 2 ) 2

= 2,5 x 3 x 2 = 15 ³

= 2 (area of triangle) + 3 (area of rectangles) 1 = 2 (2(5 ) x 3 ) + 3(3 x 2 ) = 15 ² + 18 ² = 33 ²

Cubic

1 000 000

Cubic

Litre

1 000 000 000

Cubic

1

1 000

1 000 000

1 000

0, 001

1

1 000

1

0,000001

0,001

Homework: Complete this activity. Learners do the following in their writing books. 1. Calculate the volume, capacity and surface area. Example: see concept development. a.

9

18

12

b. Length: 4,5 Height of triangle: 2,9 Height of solid: 3,4

Consolidation

b.

9

4,8

5,1

c. Area of triangle: 19 ² Height: 2,5 ²


Problem solving

What is the volume, capacity and surface area of a triangular prism with a base of 25 ² which is 12 long? (Answer: 25 ² x 12 = 300 ³)

MATHEMATICS Grade 8: Term 3 Week 6 Day 3 Mental Maths - 10 Minutes Surface area, volume and capacity of cubes and prisms problems - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 4:MEASUREMENT 8.4.1 Solves problems involving: 8.4.1.c volume and surface area of rectangular prisms and cylinders. Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Surface area, volume and capacity of cubes and prisms problems - Solve problems, with of without a calculator, involving surface area, volume and capacity Teacher Note: Keywords (See attached dictionary for definitions.) - Calculator - Capacity - Use of a calculator - Surface area - Volume Assessment: Surface area, volume and capacity of cubes and prisms problems Informal Resources: Writing books





Introduction: Surface area, volume and capacity of cubes and prisms problems Revise the following: The volume of a prism = × × ℎ The volume of a cube = ³

The volume of a triangular prism 1 = 2 × ℎ × ℎ

Surface are of a prism A = the sum of the area of all its faces.

Capacity • An object with a volume of 1 3 will displace exactly 1 ml of water. • An object with a volume of 1 3 will displace exactly 1 of water

Revise the following: • If 1 = 10 , then 1 3 = 1 000 3 • If 1 = 100 , then 1 3 = 1000 000 3 106 ³ • An object with a volume of 1 3 will displace exactly 1 of water. • An object with a volume of 1 3 will displace exactly 1 of water.

Concept development

Revise the following with your learners. Give them the formula and ask them what it is for. • • • • •

The volume of a prism = the area of the base x height The surface area of a prism = the sum of the area of all its faces. The volume of a cube = The volume of a rectangular prism = × × The volume of a rectangular prism = ( × ) x height of the prism.

Homework: Complete the activities. Learners do the following in their writing books.

1. Calculate the volume, capacity and surface area of ___. Give your answers in , and . a. The length of one edge of a cube is 2,75 .

b. The length, breadth and height of a rectangular prism is 4,25 , 3,75 and 2,95 . c. The height of the triangular prism is 3,65 , the triangles’ height is 4,65 and the base is 5,58 .

Consolidation


Problem solving

Create your own word problems to solve the volume, capacity and surface area of a • cube • rectangular prism • triangular prism

MATHEMATICS Grade 8: Term 3 Week 6 Day 4 Mental Maths - 10 Minutes Surface area, volume: problems - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 4:MEASUREMENT 8.4.1 Solves problems involving: 8.4.1.c volume and surface area of rectangular prisms and cylinders. Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Surface area, volume: problems - Solve problems, with of without a calculator, involving surface area, volume and capacity Teacher Note: Keywords (See attached dictionary for definitions.) - Calculator - Capacity - Use of a calculator - Surface area - Volume Assessment: Surface area, volume: problems Informal Resources: Writing books





Introduction: Surface area, volume: problems Revise the following: Volume of a prism = × × ℎ

Volume of a triangular prism 1 = 2 × ℎ × ℎ • • • •

Volume of a triangular prism 1 = 2 × ℎ × ℎ

Volume of a prism = × × ℎ

Surface area of a prism A = the sum of the area of all its faces.

Volume of a cube = ³

Capacity • An object with a volume of 1 3 will displace exactly 1 ml of water. • An object with a volume of 1 3 will displace exactly 1 of water.


Concept development

Revise all the definitions above.

Learners do the following in their writing books. 1. Calculate the volume and surface area of a prism if AB = 8 cm, BC = 6 cm and CF = 16 cm. A C

B D

F

E 2. What is the volume, capacity and surface area of this cubic water container? The length of one side is1,2 m.

Consolidation



MATHEMATICS Grade 8: Term 3 Week 6 Day 5 Mental Maths - 10 Minutes Assessment 2.1 - 0 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 4:MEASUREMENT 8.4.1 Solves problems involving: 8.4.1.b perimeter and area of polygons and circles; 8.4.5 Calculates, by selecting and using appropriate formulae 8.4.5.a perimeter of polygons and circles; 8.4.5.b area of triangles, rectangles, circles and polygons by decomposition into triangles and rectangles; Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Assessment 2.1 - Use appropriate formulae to calculate perimeter and area of: Squares - Use appropriate formulae to calculate perimeter and area of: Rectangles - Use appropriate formulae to calculate perimeter and area of: Triangles - Calculate the areas of polygons, to at least 2 decimal places, by decomposing them into rectangle and/or triangles - Use and describe the relationship between the radius, diameter and circumference of a circle in calculations - Use and describe the relationship between the radius, and area of a circle in calculations - Solve problems, with or without a calculator involving perimeter and area of polygons and circles Teacher Note: Keywords (See attached dictionary for definitions.) - Area

- Area of a square - Formulae - Square - Area of a rectangle - Rectangle - Area of a triangle - Triangle - Polygon - Circle - Diameter - Radius - Circumference - Circles - Area of a circle - Calculator - Problem solving - Use of a calculator Assessment: Assessment 2.1 Formal Assessment task 2.1 All 60 Marks








Concept development Week 4 Day 5 – Week 6 Day 4 • Area and perimeter of a square • Area and perimeter of a rectangle • Area and perimeter of a triangle • Area and perimeter of a circle • Area and perimeter problem solving • Surface area, volume and capacity of a cube • Surface area, volume and capacity of a prism • Surface area, volume and capacity of a triangular prism • Surface area, volume and capacity of cubes and prisms problems • Surface area, volume: problems Homework: No homework.

1. Calculate the area and perimeter if all the sides are equal: 3,2cm. Give your answer in , and . (6) 2. If this is the area of a square, what is the length of one side? Calculate the perimeter.

29,16 ²

(3)


57,76 ²

(1)


3 769 ²

(1)

31 31

(1)

17,94 ²

(3)

33,12 ²

(3)

9. If the area of the circle is , ² , what is the radius?

(3)


6. If this is the area of a rectangle, what is the possible length and breadth?

7. If this is the area of a triangle what is the possible height and base?

8. Calculate the area of the circle. The radius of the circle is 5,9 :

(3)

10. Solve the following. a. You live in a rectangular-shaped home that is 150 long and 902 m wide. You want to plant shrubs around the home. You are to plant the shrubs 70 apart. Approximately how many shrubs will you need to surround the house? (3) b. Find the area of a circular sector of which the cord is the side of the square inscribed in a circle with a 3 -radius. (3)

11. Label and complete calculate the volume, capacity and surface area of the following. a.

b.

3,2

8,5

2,9

3,2

c.

9

4,8

5,1 (18)

12. Calculate the volume, capacity and surface area of ___. Give your answers in , and .

The height of the triangular prism is 3,65 , the triangles’ height is 4,65 and the base is 5,58 . (6) 13. Calculate the volume and surface area of a prism if AB = 8 cm, BC = 6 cm and CF = 16 cm. A

C

B D

F

E

(6)

14. What is the volume, capacity and surface area of this cubic water container? The length of one side is1,2 m. (3) Total: 60

Consolidation

In this lesson we revised the following: Week 4 Day 5 – Week 6 Day 4 • Area and perimeter of a square • Area and perimeter of a rectangle • Area and perimeter of a triangle • Area and perimeter of a circle • Area and perimeter problem solving • Surface area, volume and capacity of a cube • Surface area, volume and capacity of a prism • Surface area, volume and capacity of a triangular prism • Surface area, volume and capacity of cubes and prisms problems • Surface area, volume: problems

Tell learners to identify the concepts that they are not clear about, write it on a piece of paper and put it on the teacher’s desk. Start the next lesson with those concepts. Learners who need : Receive peer, group or teacher . Learners who are more than competent: Provide peer or group .

Problem solving


MATHEMATICS Grade 8: Term 3 Week 7 Day 1 Mental Maths - 10 Minutes Data collection - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 5:DATA HANDLING 8.5.1 Poses questions relating to human rights, social, economic, environmental and political issues in own environment. 8.5.2 Selects appropriate sources for the collection of data (including peers, family, newspapers, books, magazines, the Internet). 8.5.4 Performs simple experiments using random number generators, coins, spinners, dice and cards in order to collect data. Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Data collection - Pose questions relating to social, economic, and environmental issues - Select appropriate sources for the collection of data (including peers, family, newspapers, books, magazines), including distinguishing between samples and populations. Teacher Note: Keywords (See attached dictionary for definitions.) - Population - Samples Assessment: Data collection Informal






Introduction: Data collection In Grade 7 we learnt that if we want to solve a problem, the first step is to collect data about the problem. We can use data collected by other people for different purposes (called secondary data) or we can collect new data directly from the source (called primary data). The population refers to the entire group of individuals or objects in which we are interested, in generalising the conclusions of our research. If we are able to ask everybody (the population) then it is called a census. If the group (population) is very large, we can ask some of the people – this is called a sample of the population. The best way to prevent bias in a survey is to select the sample using a random method. Surveys can help you decide what needs changing, where money should be spent, what products to purchase, what problems there might be, or may answer many other questions you might have. A common method of collecting primary data for a survey is to use a questionnaire. So if we want to know something, we need to start with posing questions or data (information) collection. In this lesson we are going to look at discrete and continuous data and how to collect it from the most appropriate source by asking questions.

Concept development 1. Ask students to define "continuous data" and "discrete data". Once students have had some time to reflect on these and develop a definition in their own words, provide them with the following: • Discrete data is data that can only take certain values • Continuous data is data that can take any value (within a range) 2. Ask learners to classify the following examples as "continuous data" or “discrete data". • The amount of rainfall recorded each day for seven days (discrete) • The amount of money earned during an eight-hour workday (continuous) • The weight of newspapers collected at each house on a route (discrete) • The length of hair-growth over a one-month period (continuous)

3. You think most people in your school get to school by bus. You want to investigate this by means of a survey. A tally chart can be used to record your data. Write a hypothesis for your survey. : (Hypothesis: most learners from our A hypothesis is an school use the bus to get to school.) idea that you want to investigate to see if it 4. Who will you use for your survey? is true or false. (Answer: population – all learners of the school, or a sample – only a portion of them, randomly selected, say 20% per grade) 5. If the population is too big and you need to select a sample, how will you go about selecting a sample to eliminate bias? (Answer: to eliminate bias the sample must be randomly selected across the grades and across the possible transport methods. If we decided to only survey 20% of the population, it will be biased to stand at the bus stop and ask every fifth learner. It will also be biased if we only ask learners in the higher or lower grades. Instead, it will be less biased if we take an alphabetical list of all learners and select every fifth name to participate in the survey.) 6. Design a simple questionnaire for your survey, using multiple choice questions. Your data must also include: a. Grade of learner b. Gender c. Transport method Answer: Transport survey for Rhodes High We want to determine the most popular method of transport to school. Please assist us by answering a few questions. Which grade are you? (tick the correct box) Grade 8

Grade 9

Grade 10

Grade 11

Grade 12

Gender? (tick the correct box) Boy

Girl

Which transport method do you use MOST to get to school? (only tick one box) Walk

Bicycle

If other, please specify:

Bus

Motorcar

Other

Homework: See problem solving. Learners do the following in their writing books. 1. Classify the following data as either discrete data or continuous data. a. The number of times that a movement authority is sent to a train from a relay station is recorded for several trains over a two-week period. The movement authority, which is an electronic transmission, is sent repeatedly until a return signal is received from the train. b. A quality technician records the length of material in a roll product for several products selected from a production line. c. The number of aces in five-card poker hands is noted by a gambler over several weeks of gambling at a casino. 2. Survey people in your school to find out what their favourite movie is. a. Write a hypothesis for your survey project. b. Who will you ask? Define your population. c. How will you select a sample from your population? d. How will you ensure that your survey eliminates bias? e. Design a simple questionnaire for your survey, using multiple-choice questions to establish grade, gender, favourite movie type and favourite movie.

Consolidation Data can be classified as discrete or continuous data. Discrete data contains distinct values, whereas continuous data can assume any value within a range. For example, the number of phone calls a company receives would be discrete data. You can only have distinct, whole number values. You can't have, for example, 4,375 calls. There is either a phone call or there isn't; there aren't fractions of calls. Continuous data would be like temperatures, lengths, and so on. Usually, anything you have to use a measuring device for is continuous data. Temperatures, lengths, etc can all be anywhere on a range; they don't have to have distinct values. Learners who need : Pair learners with competent peers and work through the concept development examples again, but change the numbers before doing the problem solving activities. Learners who are more than competent: Provide peer .

Problem solving Design the survey In making a survey, it is very important that you first decide what questions you want answered. Make sure that you are asking all the questions that interest you. There won't be time to go back to those surveyed to get more information. Write a hypothesis for your survey. Create a survey that lists all of the popular sodas. Be sure to create an "other" option. Ask how much soda each student drinks per day. You can define soda consumption around a common quantity such as millilitres. Will the choice of soda be discreet or continuous data? What type of data will the consumption of soda be?

MATHEMATICS Grade 8: Term 3 Week 7 Day 2 Mental Maths - 10 Minutes Organise data - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 5:DATA HANDLING 8.5.5 Organises (including grouping where appropriate) and records data using tallies, tables and stem-and-leaf displays. Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Organise data - Organize (including grouping where appropriate) and record data using Tallies - Organize (including grouping where appropriate) and record data using Tables - Organize (including grouping where appropriate) and record data using Stem-and-leaf displays - Group data into intervals Teacher Note: Keywords (See attached dictionary for definitions.) - Tally - Table - Stem-and-leaf plot Assessment: Organise data Informal Resources:

Board Writing books





Introduction: Organise data After we have collected data, we need to organise it to be able to make some conclusions. We can organise the data using tallies, tables and stem-and-leaf tables. Tally is a way of counting data to make it easy to display in a table. A tally mark is used to keep track of counting. Vertical bars are made for each number, and a diagonal bar is made for every five numbers, forming bundles of 5’s. When the set of data values are spread out, it is difficult to set up a frequency table for every data value as there will be too many rows in the table. So we group the data into class intervals (or groups) to help us organise, interpret and analyse the data. Ideally, we should have between five and ten rows in a frequency table. Bear this in mind when deciding on the size of the class interval (or group). Stem-and-leaf tables (plots) are special tables where each data value is split into a “leaf” (usually the last digit) and a “stem” (the other digits). The "stem" values are listed down, and the "leaf" values go right (or left) from the stem values. The "stem" is used to group the scores and each "leaf" indicates the individual scores within each group. In this lesson we are going to look at how to determine the group intervals, also called class intervals, when we group the data.

Concept development Write the following table on the board. The number of calls from motorists per day for roadside service was recorded for a month. The results were as follows: 28

122 217 130 120

86

80

90

70

40

145 187 113

90

68

174 194 170

100

75

104

123 100

97

75

82

81

120 140 109 120

How will we group these numbers into class intervals? Ask learners to make suggestions. After discussing their suggestions, show them the following method. Smallest value = 28 Highest value = 217 Difference = highest value – smallest value = 217 – 28 = 189

Now we decide that we want five class intervals. Therefore:

189 5

= 37,8 = 40 (round off to the next 10)

Now we can construct a table with three columns, and then write the data groups or class intervals in the first column. The size of each group is 40. So the groups will start at 0, 40, 80, 120, 160 and 200 to include all of the data. Class interval

Tally

Frequency

Note: we need six groups (one more than we thought at first).

0 - 39 40 - 79 80 - 119 120 - 159 160 - 199 200 - 239

Next we can go through the list of data values. For the first data value in the list, 28, place a tally mark against the group 0-39 in the second column. For the second data value in the list, 122, place a tally mark against the group 120-159 in the second column. For the third data value in the list, 217, place a tally mark against the group 200-239 in the second column. Continue this process until all of the data values in the set are tallied. Class interval

Tally

Frequency

0 - 39

1

40 - 79

5

80 - 119

12

120 - 159

8

160 - 199

4

200 - 239

1

Homework: See problem solving. Learners do the following in their writing books. 1. The data shows the mass of 40 students in a class to the nearest kg. Construct a frequency table for the data using an appropriate scale. 55 60 75 49 52

70 48 64 66 76

57 58 65 62 71

73 54 57 76 61

55 69 71 61 53

59 51 78 63 56

64 63 76 63 67

72 78 62 76 71

2. The following table represents the time taken by a group of learners to answer mental maths questions (in seconds). Construct a frequency table for the data using an appropriate scale. 20 26 16 14

25 8 21 15

24 19 17 21

33 31 11 18

13 11 34 17

3. A researcher is interested in knowing how many calls teenagers make in a month. He monitored the calls of 18 learners randomly selected from your school. The following data was recorded during the month: 53, 35, 67, 48, 63, 42, 48, 55, 33, 50, 46, 45, 59, 40, 47, 51, 66, 53 Construct a frequency table for the data using an appropriate scale.

Consolidation When the set of data values is spread out, it is difficult to set up a frequency table for every data value as there will be too many rows in the table. So we group the data into class intervals (or groups) to help us organise, interpret and analyse the data. To group the data into class intervals: Step 1: Find the range. The range of a set of numbers is the difference between the smallest and the biggest numbers in the set. Step2: Find the intervals. The intervals separate the scale into equal parts. Divide the range by the interval or the number of groups you want to create. Step 3: Draw the frequency table using the selected scale and intervals. Learners who need : Pair learners with competent peers and work through the concept development examples again, but change the numbers before doing the problem solving activities. Learners who are more than competent: Provide peer .

Problem solving

The following table represents the test scores of your class in mathematics. Construct a frequency table for the data, using an appropriate scale. 58 63 78 52 55

68 46 62 64 74

60 61 68 65 74

71 52 55 74 59

53 67 69 59 51

62 54 81 66 59

MATHEMATICS Grade 8: Term 3 Week 7 Day 3 Mental Maths - 10 Minutes Summarise data - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 5:DATA HANDLING 8.5.6 Summarises grouped and ungrouped numerical data by determining mean, median and mode as measures of central tendency, and distinguishes between them. Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Summarise data - Summarize data using measures of dispersion, including Mean - Summarize data using measures of dispersion, including Median - Summarize data using measures of dispersion, including Mode - Summarize data using measures of dispersion, including Range - Summarize data using measures of dispersion, including Extremes Teacher Note: Keywords (See attached dictionary for definitions.) - Mean (or Average) - Median - Mode - Extreme Assessment: Summarise data Informal






Introduction: Summarise data We use the following as measures of central tendency:

The range is the difference between the biggest and the smallest number. The mode is the value that appears the most. The median is the middle value. The mean is the total of the numbers divided by how many numbers there are. In this lesson we are going to revise these measures of central tendency and we are going to look at summarising data using measures of dispersion, like range and extremes.

Concept development Revise with the learners the following concepts: mean, median, mode and range. Measure

Mean

Definition

How to calculate

To find the mean, you The mean is the total of need to add up all the the numbers divided by data, and then divide how many numbers this total by the number there are. of values in the data

To find the median, you need to put the values in order, then find the The median is the middle value. If there are Median middle value. two values in the middle, then you find the mean of these two values. The mode is the value which appears most The mode is the value often in the data. It is Mode that appears the most. possible to have more than one mode if there is more than one value which appears the most. To find the range, you first need to find the The range is the lowest and highest values difference between the in the data. The range is Range biggest and the smallest found by subtracting the number. lowest value from the highest value

Example Data set: 2, 2, 3, 5, 5, 7, 8 Adding up the numbers gives: 2 + 2 + 3 + 5 + 5 + 7 + 8 = 32 There are seven values, so you divide the total by 7: 32 ÷ 7 = 4.57... So the mean is 4.57 The numbers in order: 2 , 2 , 3 , (5) , 5 , 7 , 8 The middle value is marked in brackets, and it is 5. So the median is 5. The data values: 2,2,3,5,5,7,8 The values that appear most often are 2 and 5. They both appear more times than any of the other data values. So the modes are 2 and 5 The data values: 2,2,3,5,5,7,8 The lowest value is 2 and the highest value is 8. Subtracting the lowest from the highest gives: 8 - 2 = 6 So the range is 6.

We use a measure of central tendency to describe where the peak on a graph is located.

1. Ask learners to calculate the mean, mode, median and range for the following: a. (2,23,3,3,4) Answer: Range = 21 Mean = 7 Median = 3 Mode(s) = 3 b. (1,22,20,29,29,29,24) Answer: Range = 28 Mean = 22 Median = 24 Mode(s) = 29 c. (29,9,1,26,25) Answers: Range = 28 Mean = 18 Median = 25 Mode(s) = none

The mean average is not always a whole number. to start by arranging the data from small to big. Note: if there is an even amount of numbers, the median will be the value that is halfway between the middle pair of numbers.

Ask learners what they understand under the term ‘measure of dispersion’. Once the learners have had some time to reflect on this term and develop a definition in their own words, provide them with the following: • A measure of dispersion measures how spread out a set of data is. We use a measure of dispersion to describe how much spread there is in the distribution of data. When we look at a graph of a frequency table, we will notice a peak and a spread on either side of the peak. We use different measures of dispersion like: range, minimum values and maximum values, together with measures of central location to interpret the data series. 2. Ask learners to find the minimum value, maximum value and range of the following data: 29, 31, 24, 29, 30, 25 Answer: Start by arranging the 24, 25, 29, 29, 30, 31 data in sequence small large from small to large Identify the minimum and maximum values: Minimum = 24, maximum = 31 The range: Range = maximum – minimum = 31–24 = 7. Thus the range is 7.

Homework: See problem solving.

Learners do the following in their writing books. 1. Use the data series below and calculate: a. The mean b. The mode c. The median d. Minimum value e. Maximum value

f. The range 8

14

15

50

-6

19

3

37

12

10

2. David made a frequency table to show the numbers of pets owned by 10 people. The range is 6. What might the total number of pets be? Explain. 3. The frequency table of your survey shows a minimum value of 43 and a maximum value of 336. What is the range?

4. Ethan's scores in six subjects are 72, 48, 72, 72, 72, and 84. What is his average score? 5. The following table represents the car ownership rates by the age of the home owners in South Africa in the year 2011. Find the range of the given data. Age in years 15-24 15-34 35-44 45-54

Percentage of home owners 17.9 45.6 66.2 74.9

6. The table shows the number of fruits sold by a street vendor on seven consecutive days. Using the table, calculate the mean number of fruit sold per day. What is the minimum value, maximum value and range?

Fruits sold

Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

6

8

10

12

16

4

14

Consolidation We use a measure of central tendency to describe where the peak on a graph is located. The range is the difference between the biggest and the smallest number. The mode is the value that appears the most. The median is the middle value. The mean is the total of the numbers divided by how many numbers there are. The measure of dispersion describes how much spread there is in the distribution of data. We use different measures of dispersion like range, minimum values and maximum values. Learners who need : Pair learners with competent peers and work through the concept development examples again, but change the numbers before doing the class work activities. Make sure that they first arrange the data from small to big in their writing books. Learners who are more than competent: Provide peer .

Problem solving The scores of learners of four teams A, B, C, and D in their math tests were recorded. Each team reported an average of 90%. Which of the following measures of central tendency was used by the teams? Team A: Team B: Team C: Team D:

85, 81, 91, 96, 97 93, 92, 90, 90, 91 85, 81, 94, 93, 90 85, 89, 90, 90, 90

: We use the following as measures of central tendency:

• range • mode • median • mean

MATHEMATICS Grade 8: Term 3 Week 7 Day 4 Mental Maths - 10 Minutes Bar graphs - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 5:DATA HANDLING 8.5.7 Draws a variety of graphs by hand/technology to display and interpret data including: 8.5.7.a bar graphs and double bar graphs; 8.5.8 Critically reads and interprets data presented in a variety of ways in order to draw conclusions and make predictions sensitive to the role of: Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Bar graphs - Draw a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including" Bar graphs and double bar graphs - Critically read and interpret data represented in: Words - Critically read and interpret data represented in: Bar graphs Teacher Note: Keywords (See attached dictionary for definitions.) - Bar graph - Double bar graph - Word problems Assessment: Bar graphs Informal






Introduction: Bar graphs In Grade 7 we learnt that a bar graph is a visual display used to compare the amounts or frequency of occurrence of different characteristics of data. This type of display allows us to • compare groups of data • make generalisations about the data quickly. When reading a bar graph there are several things we must pay attention to: the graph title, two axes, including axes labels and scale, and the bars. Since bar graphs are used to graph frequencies or amounts of data in discrete groups, we will need to determine which axis is the grouped data axis, as well as what the specific groups are, and which is the frequency axis. The height of the bars are particularly important since they give us information about specific data. To draw a bar graph you have to start with your frequency table. From the frequency table, decide on the range and scale of the frequency data axis (vertical axis) and the grouped data axis (horizontal axis). Draw the vertical and horizontal axes and label them. Write the graph title at the top. Mark the data on the graph for each data group and draw the bar. Add the colour or shading of the bar to the legend (key). In this lesson we are going to draw bar graphs from raw data, then we are going to interpret the information and answer questions related to the bar graphs.

Concept development Start by revising bar graphs. Refer to Grade 7 Term 4 Week 6 Day 3 for revision. Bar graphs are used to show data that is discrete. A bar graph allows us to compare data like amounts or frequency or categories.

: Discrete data is data that can only take certain values.

A bar graph also allows us to make generalisations about the data and to see differences in the data. In a bar graph we place the independent variable on the x-axis and the dependent variable on the y-axis. The independent variable is the category or subject we are collecting the data from r about. The dependent variable is the data we are collecting or what we are measuring.

Ask learners to make a quality bar graph of the following data. A quality bar graph consists out of: T – Title A – Axis I – Interval L – Labels S – Scale

Number of games played as Springbok captain 29 1 1 36 18 1 10 16 12 73 3 1

Player JF Pienaar Strauss AJ Richter GH Teichmann J Krige J Erasmus JH van der Westhuizen AN Vos RB Skinstad JW Smit V Matfield Johan Muller

Analyse your data and answer the following questions. a. What is the independent variable? (names of players) b. The dependent variable? (number of games captained) c. What are we comparing with this graph? (number of games captained) d. In general, what can we say about the number of games played by each Springbok captain? (JW Smit captained the most games and GH Teichman second most, four players only captained one game) the Answers: answers are in Games captained brackets. 80 70 60 50 40 30 20 10 0

73

36

29

18 10 1

1

1

Games captained

16

12 3

1

Homework: See problem solving. Learners do the following in their writing books. 1. The following table shows the sales of cars per month. Create a bar graph for the data. Month January February March April May June July August September October November December

Sales in R’00 000 15 14 13 11 9 7 2 7 8 11 12 14

Analyse and interpret your graph and answer the following questions. a. Where do you think this data came from? b. How can this data and graph be useful for the car dealer? c. What scale did you used for your graph? Explain why. d. Calculate the mean, mode and median. e. What can these answers tell you? f. What is the data range? g. What does the range tell you about the data? h. Is there any extreme data (very small or large data)? Why do you think this data varies so much from the mean? i. If you want to determine the sales for all car dealers, how will you go about that? j. How can you provide for any bias in your data?

Consolidation

Bar graphs are used to compare categorical data using bars. For example amount of rainfall on different days in a week, the favourite colours of Grade 8 learners, the number of students enrolled in different grades in a school in a particular academic year, etc. A bar graph is a visual display used to compare the amounts or frequency of occurrence of different characteristics of data. Learners who need : Pair learners with competent peers and work through the concept development examples again, but change the numbers before doing the problem solving activities. Learners who are more than competent: Provide peer .

Problem solving Use the data collected form your class regarding their favourite movie star. 1.Compile a frequency table using tallies. 2.Draw a bar graph using your frequency table. 3.Analyse and interpret your graph and answer the following questions. a. What is the independent variable? b. The dependent variable? c. What are we comparing with this graph? d. Who is the most favourite movie star? e. Who is the least favourite movie star? f. What scale did you used for your graph? Explain why. g. Calculate the mean, mode and median. h. What can these answers tell you? i. What is the data range? j. What does the range tell you about the data? k. If you want to determine the most popular movie star in your school, how will you go about that? l. How can you provide for any bias in your data?

Name Denise John Jason Matapelo Beatrix Opelo Lisa Gugu Sipho Lorato

Movie star Johnny Depp Julia Roberts Julia Roberts Nicolas Cage Brad Pitt Jennifer Aniston Jennifer Aniston Brad Pitt Julia Roberts Johnny Depp

Name Elias Simon Edward Susan Philip Ben Lauren Tefo Alicia Masa

Movie star Julia Roberts Nicolas Cage Johnny Depp Julia Roberts Johnny Depp Brad Pitt Julia Roberts Jennifer Aniston Johnny Depp Julia Roberts

MATHEMATICS Grade 8: Term 3 Week 7 Day 5 Mental Maths - 10 Minutes Bar graphs - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 5:DATA HANDLING 8.5.7 Draws a variety of graphs by hand/technology to display and interpret data including: 8.5.7.a bar graphs and double bar graphs; 8.5.8 Critically reads and interprets data presented in a variety of ways in order to draw conclusions and make predictions sensitive to the role of: Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Bar graphs - Critically read and interpret data represented in: Words - Critically read and interpret data represented in: Double bar graphs Teacher Note: Keywords (See attached dictionary for definitions.) - Word problems - Bar graph - Double bar graph Assessment: Bar graphs Informal Resources:

Writing books





Introduction: Bar graphs A bar graph is a visual display used to compare the amounts or frequency of occurrence of different characteristics of data. A double bar graph is similar to a regular bar graph, but gives two pieces of related information for each item on the vertical axis, rather than just one. This type of display allows us to compare two related groups of data, and to make generalisations about the data quickly.

Concept development Revise the construction of a double bar graph – refer to lesson Grade 7 Term 4 Week 6 Day 4. Exam results that the 80 two sets of data on a double bar graph 60 must be related. 40 20 0

Term 1

Term 2 Literacy %

Term 3

Term 4

Numeracy %

Homework: See problem solving. Learners do the following in their writing books. The table below represents the expenditure per learner for primary and high schools. Draw a bar graph. Year 1985 1990 1995 2000

Expenditure per learner Primary schools High schools 325 225 361 240 418 274 425 277

Analyse your data and answer the following questions. a. b. c. d.

What is the independent variable? The dependent variable? What are we comparing with this graph? In general, what can we say about the expenditure per learner?

2. From 1994 to 2006, the percentage of households in your town that recycled increased. Examine the table to see how many households are helping our environment: Households that recycle

1994 2006

Metal cans

Plastics

Paper

56% 81%

52% 84%

58% 83%

Draw a bar graph to illustrate the increase. Analyse your graph and answer the following questions. a. Where do you think this data came from? b. How can this data and graph be useful for recycle companies? c. What scale did you used for your graph? Explain why. d. Calculate the mean, mode and median. e. Compare the mean, mode and median for 1994 to 2006. f. What can these answers tell you? g. What is the data range? h. What does the range tell you about the data? i. How can you provide for any bias in your data? 3. The table shows the median age of men and women at the time of their first marriage. Create a double bar graph to represent this data. What conclusions can you draw? Year 1940 1950 1960 1970 1980 1990 Men 24,3 22,8 22,8 23,2 24,7 26,1 Women 21,5 20,3 20,3 20,8 22 23,9

Consolidation

A bar graph is a visual display used to compare the amounts or frequency of occurrence of different characteristics of data. A double bar graph is similar to a regular bar graph, but gives two pieces of related information for each item on the vertical axis, rather than just one. This type of display allows us to compare two related groups of data, and to make generalisations about the data quickly. Learners who need : Pair learners with competent peers and work through the concept development examples again, but change the numbers before doing the problem solving activities. Learners who are more than competent: Provide peer .

Problem solving Terry asked the children in her class how many hours per day they watch TV and how much time they spend doing homework. TV Study TV Study

0 1 2 3

0 0,5 2 0,5

1 1,5 2 2,5

1 2 3 4

1 1,5 3 1,5

1 1,5 3 3,5

1 2 3 3

1 2,5 4 2,5

1 1 1 1 2 0,5 0,25 0,25 0,25 1,5 4 4 5 5 6 1,5 2 1,5 2 3

Make a frequency table. Make a bar graph. Compare the mean, mode and median between watching TV and doing homework. What does this information tell us? Explain.

MATHEMATICS Grade 8: Term 3 Week 8 Day 1 Mental Maths - 10 Minutes Histograms - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 5:DATA HANDLING 8.5.7 Draws a variety of graphs by hand/technology to display and interpret data including: 8.5.7.c pie charts; 8.5.8 Critically reads and interprets data presented in a variety of ways in order to draw conclusions and make predictions sensitive to the role of: Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Histograms - Draw a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including" Pie charts - Critically read and interpret data represented in: Words - Critically read and interpret data represented in: Pie charts Teacher Note: Keywords (See attached dictionary for definitions.) - Pie chart - Word problems Assessment: Histograms Informal






Introduction: Histograms A histogram is a particular kind of bar graph that summarises data points falling in various ranges. The main difference between a normal bar graph and a histogram is that a bar graph shows you the frequency of each element in a set of data, while a histogram shows you the frequency of a range of data. In a histogram the bars must touch, because the data elements we are recording are numbers that are grouped, and form a continuous range from left to right.

Concept development Revise the steps in the construction of a histogram.

Revise how to compute the interval width.

Example of a histogram

161-165

156-160

151-155

146-150

8 6 4 2 0

141-145

Height of learners

135-140

Constructing a histogram: Step 1 - Count the number of data points Step 2 - Summarise on a tally sheet Step 3 - Compute the range Step 4 - Determine the number of intervals Step 5 – Compute the interval width Step 6 – Determine the interval starting points Step 7 - Count the number of points in each interval Step 8 - Plot the data Step 9 - Add a title and legend

Height of learners

Let us use the following example: 28

122 217 130 120

86

80

90

70

40

145 187 113

90

68

174 194 170

100

75

104

123 100

97

75

82

120 140 109 120

81

Arranged from small to large, it will be as follows: 28 40 68 70 75 75 80 81 82 86 90 90 97 100 100 104 109 113 120 120 120 122 123 130 140 145 170 174 187 194 217

Smallest value = 28 Highest value = 217 Difference = highest value – smallest value = 217 – 28 = 189

Ideally we do not want more than 10 class intervals

Now we decide that we want five class intervals. 189 Therefore: 5 =37,8 = 40 (round to the next 10)

Once we have determined the range and the class intervals, we must organise the data into a frequency table. Class interval

Tally

Frequency

0 - 39

1

40 - 79

5

80 - 119

12

120 - 159

8

160 - 199

4

200 - 239

1

With the data in a frequency table it is easy to construct a histogram.

200-239

160-199

120-159

80-119

40-79

14 12 10 8 6 4 2 0

0-39

Histogram example

Frequency

Homework: See problem solving. Learners do the following in their writing books. 1. Let us consider the following set of numbers. 43 55 83 85 90 90 95 96 97 101 105 105 112 115 115 119 124 128 135 135 135 137 138 145 155 160 185 189 202 209 232 15 56 a. b. c. d. e. f. g.

70

98 100 105 105 110 111 112 116 120 120 127 130 130 134

Compute the range Determine the number of intervals Compute the interval width – show your calculations. Determine the interval starting points Count the number of points in each interval (frequency table) Plot the data Add a title and legend

2. Use the following data to draw a histogram. 33 35 73 65 80 70 85 76 87 81 95 85 102 95 105 114 108 125 115 125 117 128 125 145 140 175 169 192 189 222 16 28 56 58 63 63 68 69 70 74 78 78 85 88 88

92

97 101 108 108 108 110 111 118 128 133 158 162 175 182

What is the mean, mode and median?

to complete a frequency table first.

Consolidation

The main difference between a normal bar graph and a histogram is that a bar graph shows you the frequency of each element in a set of data, while a histogram shows you the frequency of a range of data. In a histogram the bars must touch, because the data elements we are recording are numbers that are grouped, and form a continuous range from left to right. Constructing a histogram: Step 1 - Count the number of data points Step 2 - Summarise on a tally sheet Step 3 - Compute the range Step 4 - Determine the number of intervals Step 5 - Compute the interval width Step 6 - Determine the interval starting points Step 7 - Count the number of points in each interval Step 8 - Plot the data Step 9 - Add a title and legend

we use histograms to summarise large data sets graphically

Learners who need : Pair learners with competent peers and work through the concept development examples again, but change the numbers before doing the problem solving activities. Learners who are more than competent: Provide peer .

Problem solving

A bank wants to improve its customer service. Before deciding to hire more workers, the manager decides to get some information on the waiting times customers currently experience. During a week, 50 customers were randomly selected, and their waiting times recorded. The data is as follows: a. Construct a frequency table of the data. b. Create a histogram. c. Must he hire more people? Motivate your answer.

18,5 5,8 4,4 0,8 10,9

9,1 1,8 3,8 0,1 0,1

3,1 1,5 5,8 9,7 5,9

6,2 1,9 1,9 2,6 1,4

1,3 0,4 3,6 0,8 0,3

0,5 3,5 2,5 1,2 5,5

4,2 5,2 0,0 10,8 8,5 11,1 0,3 1,2 4,5 5,8 1,5 0,7 2,9 3,0 3,2 2,8 4,8 0,9 1,6 2,2

MATHEMATICS Grade 8: Term 3 Week 8 Day 2 Mental Maths - 10 Minutes Histograms - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 5:DATA HANDLING 8.5.7 Draws a variety of graphs by hand/technology to display and interpret data including: 8.5.7.b histograms with given and own intervals; 8.5.8 Critically reads and interprets data presented in a variety of ways in order to draw conclusions and make predictions sensitive to the role of: Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Histograms - Draw a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including" Histograms with given intervals - Critically read and interpret data represented in: Words - Critically read and interpret data represented in: Histograms Teacher Note: Keywords (See attached dictionary for definitions.) - Word problems Assessment: Histograms Informal Resources:

Newspaper Board Writing books





Introduction: Histograms Part of the power of histograms is that they allow us to analyse extremely large data sets by reducing them to a single graph that can show primary, secondary and tertiary peaks in data as well as give a visual representation of the statistical significance of those peaks. Frequency 8 6 4 2 0

0-10

11-20 21-30 31-40 41-50 Frequency

This plot represents data with a well-defined peak that is close to the median and the mean. While there are "outliers," they are of relatively low frequency. Thus it can be said that deviations in this data group from the mean are of low frequency.

Concept development Ask learners to find histograms with different shapes in a newspaper. Histograms can come in different shapes. The two most common shapes are the bell-shaped curve also known as the “normal” distribution and the skewed distribution. Asked learners if they can draw these two shapes and explain in words what they mean.

After giving them some time to make drawings and to explain, draw the following histograms on the board.

Height of learners

Histogram C

Height of learners

161-165

156-160

151-155

146-150

141-145

8 6 4 2 0

136-140

Skewed distribution (skewed to the right)

131-135

161-165

156-160

151-155

146-150

141-145

136-140

8 6 4 2 0

131-135

161-165

156-160

151-155

146-150

Skewed distribution (skewed to the left)

141-145

Normal distribution (bell-shaped)

136-140

Histogram B

131-135

6 4 2 0

Histogram A

Height of learners

Looking at these three histograms, what can you tell us regarding the height of the learners in the class? Answer: In histogram A, most learners are close to the average height, with a few learners taller and a few shorter. In histogram B, most learners are short with a few learners that are very tall. In histogram C, most learners are tall with a few learners that are very short. Homework: See problem solving. Learners do the following in their writing books.

1. Look at the following histogram and answer the questions. Jazz music lovers 80

72

60

63

40

24

20 0

9

1990-1995

1996-2000

2001-2005

2006-2010

Jazz lovers

a. What shape is this histogram? b. Which year has the maximum number of jazz music lovers? c. Which year has the minimum number of jazz music lovers? d. What is the total number of jazz music lovers from 2001to 2005? e. What is the total number of jazz music lovers from 2000 to 2010? f. Which decade had more jazz music lovers? g. What can you conclude about jazz music lovers if you look at this graph? 2. Answer the following questions about this histogram. a. What is the shape of the graph? Project data b. For how many hours do less than 10 people work on the project? 30 c. For how many hours do 20 people work 25 20 on the project? 20 15 d. What is the total number of people 15 working for at least 20 hours? 10 5 e. What is the total number of people 5 working for at least between 0 1-10 11-20 21-30 31and 40 hours? Hours Hours Hours f. How many people Number of people work for between 11and 30 hours?

25

31-40 Hours

Consolidation

Histograms can come in different shapes. The two most common shapes are the bell-shaped curve also known as the “normal” distribution and the skewed distribution. Learners who need : Pair learners with competent peers and work through the concept development examples again, but change the numbers before doing the problem solving activities. Learners who are more than competent: Provide peer .

Problem solving Consider the following data set. 57 31 45 37 57 3 78

66 60 36 88 63 32 18

73 32 49 41 59 82 39

92 22 42 54 15 48 77

77 25 56 42 62 37 97

a. Sort the data in increasing order. b. Make a histogram for this data with classes 0–19, 20–39, 40–59, 60–79 and 80–99. c. Make a histogram for this data with classes 0–50 and 51–99. d. Make a histogram for this data with classes 0–4, 5–9, 10–14, 15–19, . . . , 85–89, 90–94 and 94–99. e. Discuss the advantages and disadvantages of each of the histograms. f. What do you learn from each? g. Overall, which one is the most informative? Why?

MATHEMATICS Grade 8: Term 3 Week 8 Day 3 Mental Maths - 10 Minutes Pie charts - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 5:DATA HANDLING 8.5.7 Draws a variety of graphs by hand/technology to display and interpret data including: 8.5.7.d line and broken-line graphs; 8.5.8 Critically reads and interprets data presented in a variety of ways in order to draw conclusions and make predictions sensitive to the role of: Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Pie charts - Draw a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including" Broken-line graphs - Critically read and interpret data represented in: Words - Critically read and interpret data represented in: Broken-line graphs Teacher Note: Keywords (See attached dictionary for definitions.) - Broken line graph - Word problems Assessment: Pie charts Informal






Introduction: Pie charts A pie chart is a circular chart in which the circle is divided into sectors. Each sector visually represents an item in a data set to match the amount of the item as a percentage or fraction of the total data set. Pie charts are useful to compare different parts of a whole amount. They are often used to present financial information, e.g. a company's expenditure can be shown to be the sum of its parts, including different expense categories such as salaries, borrowing interest, taxation and general running costs (i.e. rent, electricity, heating etc). It is simple to read a pie chart. Just look at the required sector representing an item (or category) and read off the value. A pie chart is used to compare the different parts that make up a whole amount.

Concept development Revise the pie chart and how to draw a pie chart with the learners. Make sure it adds up to 100%

Steps: 1. Convert all of your data points to percentages of the whole data set. 2. Convert the percentages into angles. Since a full circle is 360 degrees, multiply this by the percentages to get the angle for each section of the pie. 3. Draw a circle on a blank sheet of paper, using the com. While a com is not necessary, using one will make the chart much neater and clearer by ensuring the circle is even. 4. Draw a horizontal line, or radius, from the centre to the right edge of the circle, using the ruler or straight edge. This will be the first baseline. 5. Measure the largest angle in the data with the protractor, starting at the baseline, and mark it on the edge of the circle. Use the ruler to draw another radius to that point. 6. Use this new radius as a baseline for your next largest angle and continue this process until you get to the last data point. You will only need to measure the last angle to its value since both lines will already be drawn. 7. Label and shade the sections of the pie chart to highlight whatever data is important for your use.

180 º 90 º

90 º


Learners do the following in their writing books. 1. Ahmed is the treasurer of the Grade 8 class at The Sunshine High School. His class raised money for activities through various events. The total raised was R2440. Ahmed used a pie graph to show the amount of money each event raised. Study the graph and answer the following questions. Fund-raising events

9% 11%

25%

Flea market Dance Bake sale

15%

Flower sale 17%

24%

Dinner Car wash

a. What percentage of the total money was raised at the flea market? b. How much money was raised at the flea market? c. What percentage of the total money was raised at the car wash? d. How much money was raised at the car wash? e. How much more money was raised at the flea market than at the car wash? f. How much money was raised at the bake sale? g. How much more money was raised at the dance than at the bake sale? h. Find the difference between the money raised at the flower sale and at the dinner. i. Ahmed offered a suggestion for next year. Since the flea market and dance raised about half of the total amount of money, he feels that the class should have two dances and two flea markets instead of the car wash and spaghetti dinner. Do you agree? Explain. 2. More Grade 9 learners travel to school by car in school A than in school B. Look at the two pie charts below and say if you agree with this statement. Give reasons for your answer. Car Bus Walk Bike

School A

Other

School B

3. Your expenditure for the week is: Expense

Value

Rent

450,75

Food

220,50

Transport

77,88

Draw a pie chart to display this information.

Consolidation A pie chart is a circular chart in which the circle is divided into sectors. Each sector visually represents an item in a data set to match the amount of the item as a percentage or fraction of the total data set. A pie chart is actually a very clever visual design that conveys one fact above all others with a minimum of visual cues. The circle (the "pie") represents some kind of whole, which is made up of the slices. Add up all the slices and you get the complete pie. Enlarge one part, and other parts will need to shrink. What this means is that the pie chart first and foremost represents the size relationship between the parts and the entire thing. If a company has five divisions, and the pie chart shows profits per division, the sum of all the slices/divisions is the total profit of the company.

If the parts do not sum up to a meaningful whole, they cannot be represented in a pie chart. It makes no sense to show five different occupations in a pie chart, because there are obviously many missing. The total of such a subsample is not meaningful, and neither is the comparison of each individual value to the artificial whole. Learners who need : Pair learners with competent peers and work through the concept development examples again, but change the numbers before doing the problem solving activities. Learners who are more than competent: Provide peer .

Problem solving

A sample shows that on average every person in South Africa generates about 240g of plastic waste per day. This table shows the different categories of plastic waste and the amount in grams generated per day. Draw a pie chart to display this information.

Plastic category

PET PVC PS HDPE LDPE PP

Plastic waste generated per person per day. (in grams) 120 48 24 12 31,2 4,8

MATHEMATICS Grade 8: Term 3 Week 8 Day 4 Mental Maths - 10 Minutes Broken-line graph - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 5:DATA HANDLING 8.5.8 Critically reads and interprets data presented in a variety of ways in order to draw conclusions and make predictions sensitive to the role of: 8.5.8.a context (e.g. rural or urban, national or provincial); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Broken-line graph - Critically analyze data by answering questions related to: Data categories, including data intervals - Critically analyze data by answering questions related to: Data sources and contexts - Critically analyze data by answering questions related to: Central tendencies - (mean, mode, median - Critically analyze data by answering questions related to: Scales used on graphs Teacher Note: Keywords (See attached dictionary for definitions.) - Data categories - Data collection - Mean (or Average) - Median - Mode - Central tendencies - Scale

Assessment: Broken-line graph Informal Resources: Writing books





Introduction: Broken-line graph Introduce this lesson by telling learners that you can replace a bar graph by a line graph if the data on the horizontal axis is continuous such as time, temperature or age.

Concept development Tell learners in the case of a this case the data is plotted as a series of points that are ed by straight lines Meteorologists use line graphs to show monthly rainfall.

Businesses often use line graphs to show information about profits.

This means that with some line graphs it might be possible to continue the line to show what might happen in the future.

Line graphs are useful as they show trends and can easily be extended.

The line graph below shows rainfall measured over a period of six months for Town A. Town A

A line graph basically shows it going straight up. What happens to this graph?

120

80 60

Maximum

40

A broken-line graph will have numbers “all over the place.”

June

May

April

March

0

Febuary

20

January

Rainfall in mm

100

It simply means it can go up and down, like this example.

Drawing a broken line. We will use an example of the profit you made selling sweets over ten months. We will also describe each step

Profit on sweets sold 160 140 120

Rand

100 80 60 40

October

September

August

July

June

May

April

March

Febuary

0

January

20

In January a profit of R50 was made. In February a profit of R120 was made. The points are connected with a straight line that shows that profit increased. In March a profit of R70 was made. The points, February and March, are connected with a straight line that shows that profit decreased.

The profit in April was R90, in May R100 and in June R150. The points, March, April, May and June, are connected with a straight line that shows that profit increased over these months. The profit in July was R90, in August R80, in September R60 and in October R50. The points, March, April, May and June, are connected with a straight line that shows that profit decreased over these months. The graph goes up and down showing profit increase and decrease. Homework: Complete this activity. Learners do the following in their writing books.

1. Draw a broken-line graph of the heart rate of a Grade 8 learner. Describe the graph. Time of the day

Beats per minutes

9:00

68

9:30

73

10:00

88

10:30

120

11:00

77

11:30

75

12:00

72

12:30

72

13:00

100

a. Use the words increase and decrease. b. Explain why you think the heart rate increases at a certain time of the day.

2. Measure your heart rate. Draw a graph. Compare it with the graph drawing in Question 1.

Consolidation A broken-line graph shows information by plotting points of information on the graph with dots and connecting them with a line that is not straight. Learners who need : Receive peer . Learners who are more than competent: Provide peer .

Problem solving

Find a broken-line graph in a newspaper or the internet. Redraw it and then describe it.

MATHEMATICS Grade 8: Term 3 Week 8 Day 5 Mental Maths - 10 Minutes Select the right graph - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Select the right graph - Critically analyze data by answering questions related to: Samples and populations - Critically analyze data by answering questions related to: Dispersion of data - Critically analyze data by answering questions related to: Error and bias in the data Teacher Note: Keywords (See attached dictionary for definitions.) - Population - Samples - Dispersion of data Assessment: Select the right graph Informal Resources: Writing books





Introduction: Select the right graph Using graphs to represent data makes it easier for the researcher to interpret and understand the data. There are many different types of graphs, each with its own unique advantages. It is important to select the most appropriate graph for your data set.

Concept development Ask learners to make a list of all the types of graphs they know. Now ask them to list all the advantages and disadvantages that they can associate with the different types of graphs. Once students have had some time to reflect on the different types of graphs and developed a list of advantages and disadvantages, provide them with the following: Type of Graph Bar graph and double bar graph

Histogram

Line graph

Pie chart

Description A bar graph displays discrete data in separate columns. A double bar graph can be used to compare two data sets. Shows discrete or continuous variable data in a similar way to column graphs, but without the gap between the columns.

A line graph plots continuous data as points and then s them with a line. Multiple data sets can be graphed together, but a key must be used A pie chart displays data as a percentage of the whole. Each pie section should have a label and percentage. A total data number should be included

• •

• • •

•

• • •

Advantages Visually strong Can easily compare two or three data sets Visually strong Can compare to normal curve Usually vertical axis is a frequency count of items falling into each category Can compare multiple continuous data sets easily Interim data can be inferred from graph line Visually appealing Shows percentage of total for each category

Disadvantages Graph categories can be reordered to emphasise certain effects • Use only with discrete data • Cannot read exact values because data is grouped into categories • More difficult to compare two data sets • Use only with continuous data Use only with continuous data

•

• • • • • •

No exact numerical data Hard to compare two data sets "Other" category can be a problem Total unknown unless specified Best for three to seven categories Use only with discrete data


Learners do the following in their writing books. Choose which of the following graphs will you use to best represent your data in the following research projects. A. Bar graph B. Histogram

the answer is in brackets.

C. Pie chart a. The body masses of 500 male learners. (Histogram) b. The number of Biology undergraduates belonging to the different University Colleges. (Pie chart) c. The proportion of seedlings in a forest destroyed by fungus, herbivores, pathogens, trampling or wilting. (Pie chart) d. The number of first class degrees in biology for each year between 1980 and 1990. (Bar graph) e. The average number of eggs laid by five varieties of chickens. (Pie chart) f. The number of learners who ed matric with and without mathematics and science. (Pie chart)

g. The size of farms found in the Karoo. (Histogram) h. The frequency of students belonging to Anglican, Catholic, Jewish, Islamic, Hindi and Buddhist faiths. (Bar graph)

Consolidation A graph can be a useful tool in the evaluation of data. The most commonly used graphs are pie charts, line graphs, histograms and bar graphs. The questions you have about a set of data determine which type of graph to use. Generally, the advantages of each type of graph are as follows: Line graphs are useful for understanding general trends in data and for estimating data between or outside the data points given. Bar graphs work well with data in categories. They are also helpful in understanding trends in data. Pie charts are useful for data that represents parts of a total or whole. A histogram is useful to understand the spread of data.

Problem solving The following table shows the number of glasses of water you drink during the week. Day Glasses of water Monday 6 Tuesday 7 Wednesday 9 Thursday 8 Friday 10 Saturday 12 Sunday 5

a. What kind of graph would not be helpful in spotting general trends? b. If you had forgotten to write down how many glasses of water you drank on Thursday, what kind of graph would best help you guess? c. What kind of graph would be most helpful for quickly determining whether your water intake was the same for two or more days?

MATHEMATICS Grade 8: Term 3 Week 9 Day 1 Mental Maths - 10 Minutes Report data - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Report data - Summarize data in short paragraphs that includes: Drawing conclusions about the data - Summarize data in short paragraphs that includes: Making predictions based on the data - Summarize data in short paragraphs that includes: Identifying sources of error and bias in the data - Summarize data in short paragraphs that includes: Choosing appropriate summary statistics for the data(mean, median, mode and range) - Summarize data in short paragraphs that includes: The role of extremes in the data Teacher Note: Keywords (See attached dictionary for definitions.) Assessment: Report data Informal Resources: Writing books





Introduction: Report data we started to collect data to solve a specific problem. We compiled a questionnaire to collect the data, then we organised and summarised the data using tallies and tables. With the tables we could calculate the mean and median, and establish the mode. We could also determine the range of the data. In this format it was still difficult for us to understand the data. We then used different types of graphs to represent our data. This helped us to interpret and analyse our data. The final and most important step in this process is to write a report on our research. During this step we can change our data into information. We can draw conclusions and make predictions. In this lesson we are going to look at: • The basic outline of a report • Drawing conclusions about the data • Making predictions based on the data

• Identifying sources of error and bias in the data • Choosing appropriate summary statistics for the data (mean, median, mode, range)

Concept development Ask learners what they think should be included in the report. Make a list of their suggestions on the board and arrange it to form a content page. Here is a suggested outline: 1. Aim This is the general aim of the project.

: for the conclusions to make sense to the reader, he/she must understand the aim of the research. Therefore always start the report with the aim of the research.

2. Hypothesis A specific statement or prediction that you can show to be true or false. 3. Plan What data do you need? Who will you get it from? How will you collect it? How will you record it? How will you make sure the data is reliable? Why? Give reasons for the choices you made.

4. Analysis This is where you do the calculations and draw charts. Compare groups with the mean and median. The range is a measure of how spread out the group is. Graphs are good for representing data visually.

Do you still the different and how to calculate them?

5. Conclusions Do your results agree with the hypothesis? How confident are you? What went wrong? How did you deal with it? What would you do differently if you did the research again?

6. Appendices It is good practice to include a copy of the questionnaire. The appendices may also include tables related to sample selection, instructions to interviewers, and so on. 7. References If you used any secondary data or research you must acknowledge your sources here. I love sport Homework: See problem solving.

Learners do the following in their writing books. Use the information from this favourite sport survey and write a report summarising the data and draw conclusions. Name

Favourite sport

Name

Favourite sport

Denise

Tennis

Elias

Squash

John

Rugby

Simon

Soccer

Jason

Soccer

Edward

Rugby

Matapelo

Soccer

Susan

Rugby

Beatrix

Rugby

Philip

Tennis

Opelo

Tennis

Ben

Squash

Lisa

Soccer

Lauren

Soccer

Gugu

Tennis

Tefo

Rugby

Sipho

Soccer

Alicia

Soccer

Lorato

Squash

Masa

Soccer

Possible solution:

Sport

Tally

Frequency

Tennis

4

Rugby

5

Soccer

8

Squash

3

Students' favourite sport 9 8 7 6 5 4 3 2

Tennis Tennis

Rugby Rugby

Soccer Soccer

Squash Squash

Students' favourite sport

Squash 15%

Soccer 40%

Tennis 20%

Rugby 25%

Conclusion: In this survey 40% of the learners prefer soccer. The second most popular sport is rugby with 25% of the learners selecting rugby as their favourite sport. Only three learners (15%) preferred squash as their favourite sport. Most learners (65%) like playing an invasion sport (soccer 40% + rugby 25%), opposed to ball and racket sports, only 35% (tennis 20% + squash 15%).

Consolidation Reporting on your data is the most important step of your research.

Suggested outline: 1. Aim 2. Hypothesis 3. Plan 4. Analysis 5. Conclusions 6. Appendices 7. References Learners who need : Pair learners with competent peers and work together on their reports. Learners who are more than competent: Provide peer .

Problem solving Hypothesis:

Boys prefer science and maths above social sciences. Use the following data set and write a report on your findings. Include your frequency table, graphs and conclusions. Also compare the favourite subjects of boys to those of girls. Name

Favourite subject

Name

Favourite subject

Denise

Maths

Elias

History

John

Arts

Simon

Maths

Jason

History

Edward

Sciences

Matapelo

Sciences

Susan

History

Beatrix

Sciences

Philip

Arts

Opelo

Maths

Ben

Maths

Lisa

History

Lauren

Language

Gugu

Arts

Tefo

Maths

Sipho

Maths

Alicia

History

Lorato

Maths

Masa

Language

MATHEMATICS Grade 8: Term 3 Week 9 Day 2 Mental Maths - 10 Minutes Data handling cycle - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 5:DATA HANDLING 8.5.1 Poses questions relating to human rights, social, economic, environmental and political issues in own environment. 8.5.2 Selects appropriate sources for the collection of data (including peers, family, newspapers, books, magazines, the Internet). 8.5.3 Designs and uses questionnaires with a variety of possible responses in order to collect data (alone and/or as a member of a group or team) to answer questions. 8.5.4 Performs simple experiments using random number generators, coins, spinners, dice and cards in order to collect data. 8.5.5 Organises (including grouping where appropriate) and records data using tallies, tables and stem-and-leaf displays. 8.5.6 Summarises grouped and ungrouped numerical data by determining mean, median and mode as measures of central tendency, and distinguishes between them. Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Data handling cycle - Pose questions relating to social, economic, and environmental issues - Select appropriate sources for the collection of data (including peers, family, newspapers, books, magazines), including distinguishing between samples and populations. - Design and use simple questionnaires to answer questions: - Organize (including grouping where appropriate) and record data using Tallies - Organize (including grouping where appropriate) and record data using Tables - Organize (including grouping where appropriate) and record data using Stem-and-leaf displays - Group data into intervals - Summarize data using measures of dispersion, including Mean

- Summarize data using measures of dispersion, including - Summarize data using measures of dispersion, including - Summarize data using measures of dispersion, including - Summarize data using measures of dispersion, including Teacher Note: Keywords (See attached dictionary for definitions.) - Population - Samples - Tally - Table - Mean (or Average) - Median - Mode - Extreme Assessment: Data handling cycle Informal Resources: Board

Median Mode Range Extremes





Introduction: Data handling cycle: Assessment 4.4: Part 1 Data handling is a process of collecting, organising, representing, analysing and interpreting data. The visual representation of data is of major importance.

In the next two lessons we are going to revise the process by doing a practical research project.

Concept development Write the following questions on the board. Boys in grade 8 are taller than girls in the same grade? Is there any link between a person’s height and their hand span? Divide the class in groups (research teams). Each team must prepare a plan on how they will go about answering the above question. They must start with the aim of their research and hypothesis. Questions that might help them to plan: What data do you need? Who will you get it from? How will you collect it? How will you record it? How will you make sure the data is reliable? Why? Give reasons for the choices you made.

Each group gets an opportunity to present their aim, hypothesis and plan to the rest of the class. Once all the research teams have presented their plans, they get the opportunity to change their plans based on what they heard from the other teams. Their plans are submitted and then they can start collecting and recording their data. Learners who need : Make sure the groups are mixed. Learners who are more than competent: Peer .

MATHEMATICS Grade 8: Term 3 Week 9 Day 3 Mental Maths - 10 Minutes Data handling cycle - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 5:DATA HANDLING 8.5.1 Poses questions relating to human rights, social, economic, environmental and political issues in own environment. 8.5.2 Selects appropriate sources for the collection of data (including peers, family, newspapers, books, magazines, the Internet). 8.5.3 Designs and uses questionnaires with a variety of possible responses in order to collect data (alone and/or as a member of a group or team) to answer questions. 8.5.4 Performs simple experiments using random number generators, coins, spinners, dice and cards in order to collect data. 8.5.5 Organises (including grouping where appropriate) and records data using tallies, tables and stem-and-leaf displays. 8.5.6 Summarises grouped and ungrouped numerical data by determining mean, median and mode as measures of central tendency, and distinguishes between them. 8.5.7 Draws a variety of graphs by hand/technology to display and interpret data including: 8.5.7.a bar graphs and double bar graphs; 8.5.7.b histograms with given and own intervals; 8.5.7.c pie charts; 8.5.7.d line and broken-line graphs; 8.5.8 Critically reads and interprets data presented in a variety of ways in order to draw conclusions and make predictions sensitive to the role of: 8.5.8.a context (e.g. rural or urban, national or provincial); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Data handling cycle - Pose questions relating to social, economic, and environmental issues

- Select appropriate sources for the collection of data (including peers, family, newspapers, books, magazines), including distinguishing between samples and populations. - Design and use simple questionnaires to answer questions: - Organize (including grouping where appropriate) and record data using Tallies - Organize (including grouping where appropriate) and record data using Tables - Organize (including grouping where appropriate) and record data using Stem-and-leaf displays - Group data into intervals - Summarize data using measures of dispersion, including Mean - Summarize data using measures of dispersion, including Median - Summarize data using measures of dispersion, including Mode - Summarize data using measures of dispersion, including Range - Summarize data using measures of dispersion, including Extremes - Draw a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including" Bar graphs and double bar graphs - Draw a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including" Histograms with given intervals - Draw a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including" Pie charts - Draw a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including" Broken-line graphs - Critically read and interpret data represented in: Words - Critically read and interpret data represented in: Bar graphs - Critically read and interpret data represented in: Double bar graphs - Critically read and interpret data represented in: Pie charts - Critically read and interpret data represented in: Histograms - Critically read and interpret data represented in: Broken-line graphs - Critically analyze data by answering questions related to: Data categories, including data intervals - Critically analyze data by answering questions related to: Data sources and contexts - Critically analyze data by answering questions related to: Central tendencies - (mean, mode, median - Critically analyze data by answering questions related to: Scales used on graphs - Critically analyze data by answering questions related to: Samples and populations - Critically analyze data by answering questions related to: Dispersion of data - Critically analyze data by answering questions related to: Error and bias in the data - Summarize data in short paragraphs that includes: Drawing conclusions about the data - Summarize data in short paragraphs that includes: Making predictions based on the data - Summarize data in short paragraphs that includes: Identifying sources of error and bias in the data - Summarize data in short paragraphs that includes: Choosing appropriate summary statistics for the data(mean, median, mode and range) - Summarize data in short paragraphs that includes: The role of extremes in the data Teacher Note: Keywords (See attached dictionary for definitions.) Assessment: Data handling cycle Informal

Resources:





Introduction: Data handling cycle: In the previous lesson learners prepared a research project based on the following questions: Boys in grade 8 are taller than girls in the same grade? Is there any link between a person’s height and their hand span? They presented their plan to the rest of the class and had the opportunity to refine their plan before starting with collecting and recording of data. In this lesson they will continue with the data handling cycle. Use the data collected in the previous lesson.

Concept development Write the following questions on the board. Is the hand span of Grade 7 girls smaller than that of boys in the same grade? Is there any link between a person’s height and their hand span? In your group/research teams, use the data you collected and recorded to: • Organise your data in a frequency table.

• Calculate the mode, mean and median. • Calculate the data range. • Draw a stem-and-leaf display • Represent your data in a graph. You may use more than one type of graph. • Interpret you graphs and tables and write a report under the following headings: 1. Aim 2. Hypothesis 3. Plan 4. Analysis 5. Conclusions 6. Appendices 7. References Learners who need : Make sure the groups are mixed. Learners who are more than competent: Peer .

MATHEMATICS Grade 8: Term 3 Week 9 Day 4 Mental Maths - 10 Minutes Data handling cycle - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 5:DATA HANDLING 8.5.1 Poses questions relating to human rights, social, economic, environmental and political issues in own environment. 8.5.2 Selects appropriate sources for the collection of data (including peers, family, newspapers, books, magazines, the Internet). 8.5.3 Designs and uses questionnaires with a variety of possible responses in order to collect data (alone and/or as a member of a group or team) to answer questions. 8.5.4 Performs simple experiments using random number generators, coins, spinners, dice and cards in order to collect data. 8.5.5 Organises (including grouping where appropriate) and records data using tallies, tables and stem-and-leaf displays. 8.5.6 Summarises grouped and ungrouped numerical data by determining mean, median and mode as measures of central tendency, and distinguishes between them. 8.5.7 Draws a variety of graphs by hand/technology to display and interpret data including: 8.5.7.a bar graphs and double bar graphs; 8.5.7.b histograms with given and own intervals; 8.5.7.c pie charts; 8.5.7.d line and broken-line graphs; 8.5.8 Critically reads and interprets data presented in a variety of ways in order to draw conclusions and make predictions sensitive to the role of: 8.5.8.a context (e.g. rural or urban, national or provincial); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Data handling cycle - Pose questions relating to social, economic, and environmental issues

- Select appropriate sources for the collection of data (including peers, family, newspapers, books, magazines), including distinguishing between samples and populations. - Design and use simple questionnaires to answer questions: - Organize (including grouping where appropriate) and record data using Tallies - Organize (including grouping where appropriate) and record data using Tables - Organize (including grouping where appropriate) and record data using Stem-and-leaf displays - Group data into intervals - Summarize data using measures of dispersion, including Mean - Summarize data using measures of dispersion, including Median - Summarize data using measures of dispersion, including Mode - Summarize data using measures of dispersion, including Range - Summarize data using measures of dispersion, including Extremes - Draw a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including" Bar graphs and double bar graphs - Draw a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including" Histograms with given intervals - Draw a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including" Pie charts - Draw a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including" Broken-line graphs - Critically read and interpret data represented in: Words - Critically read and interpret data represented in: Bar graphs - Critically read and interpret data represented in: Double bar graphs - Critically read and interpret data represented in: Pie charts - Critically read and interpret data represented in: Histograms - Critically read and interpret data represented in: Broken-line graphs - Critically analyze data by answering questions related to: Data categories, including data intervals - Critically analyze data by answering questions related to: Data sources and contexts - Critically analyze data by answering questions related to: Central tendencies - (mean, mode, median - Critically analyze data by answering questions related to: Samples and populations - Critically analyze data by answering questions related to: Dispersion of data - Critically analyze data by answering questions related to: Error and bias in the data - Summarize data in short paragraphs that includes: Drawing conclusions about the data - Summarize data in short paragraphs that includes: Making predictions based on the data - Summarize data in short paragraphs that includes: Identifying sources of error and bias in the data - Summarize data in short paragraphs that includes: Choosing appropriate summary statistics for the data(mean, median, mode and range) - Summarize data in short paragraphs that includes: The role of extremes in the data Teacher Note: Keywords (See attached dictionary for definitions.) Assessment: Data handling cycle Informal

Resources: Board





Introduction: Data handling cycle: Assessment 2.2 : Part 1 Data handling is a process of collecting, organising, representing, analysing and interpreting data. The visual representation of data is of major importance.

In the next two lessons we are going to do a mini research project for assessment.

Concept development Write the following questions on the board. The more time you spend doing homework, the better your school marks will be. Divide the class in groups (research teams). Each team must prepare a plan on how they will go about answering the above question. They must start with the aim of their research and hypothesis. Questions that might help them to plan: What data do you need? Who will you get it from? How will you collect it? How will you record it? How will you make sure the data is reliable? Why? Give reasons for the choices you made. Each group gets an opportunity to present their aim, hypothesis and plan to the rest of the class. Once all the research teams have presented their plans, they get the opportunity to change their plans based on what they heard from the other teams. Their plans are submitted and then they can start collecting and recording their data. Learners who need : Make sure the groups are mixed. Learners who are more than competent: Peer .

MATHEMATICS Grade 8: Term 3 Week 9 Day 5 Mental Maths - 10 Minutes Data handling cycle - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); 5:DATA HANDLING 8.5.7 Draws a variety of graphs by hand/technology to display and interpret data including: 8.5.7.a bar graphs and double bar graphs; 8.5.7.b histograms with given and own intervals; 8.5.7.c pie charts; 8.5.7.d line and broken-line graphs; 8.5.8 Critically reads and interprets data presented in a variety of ways in order to draw conclusions and make predictions sensitive to the role of: 8.5.8.a context (e.g. rural or urban, national or provincial); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Data handling cycle - Critically read and interpret data represented in: Words - Critically read and interpret data represented in: Bar graphs - Critically read and interpret data represented in: Double bar graphs - Critically read and interpret data represented in: Pie charts - Critically read and interpret data represented in: Histograms - Critically read and interpret data represented in: Broken-line graphs - Critically analyze data by answering questions related to: Data categories, including data intervals - Critically analyze data by answering questions related to: Data sources and contexts - Critically analyze data by answering questions related to: Central tendencies - (mean, mode, median - Critically analyze data by answering questions related to: Scales used on graphs - Critically analyze data by answering questions related to: Samples and populations

- Critically analyze data by answering questions related to: Dispersion of data - Critically analyze data by answering questions related to: Error and bias in the data - Summarize data in short paragraphs that includes: Drawing conclusions about the data - Summarize data in short paragraphs that includes: Making predictions based on the data - Summarize data in short paragraphs that includes: Identifying sources of error and bias in the data - Summarize data in short paragraphs that includes: Choosing appropriate summary statistics for the data(mean, median, mode and range) - Summarize data in short paragraphs that includes: The role of extremes in the data Teacher Note: Keywords (See attached dictionary for definitions.) Assessment: Data handling cycle Formal Assessment task 2.2 All 100 Marks






Introduction: Data handling cycle: Assessment 2.2 : Part 2 In the previous lesson learners prepared a research project based on the following questions: The more time you spend doing homework, the better your school marks will be. They presented their plan to the rest of the class and had the opportunity to refine their plan before starting with collecting and recording of data. In this lesson they will continue with the data handling cycle. Use the data collected in the previous lesson.

Concept development Write the following questions on the board. Is the hand span of Grade 7 girls smaller than that of boys in the same grade? Is there any link between a person’s height and their hand span? In your group/research teams, use the data you collected and recorded to: • Organise your data in a frequency table.

• Calculate the mode, mean and median. • Calculate the data range. • Draw a stem-and-leaf display • Represent your data in a graph. You may use more than one type of graph. • Interpret you graphs and tables and write a report under the following headings: 1. Aim 2. Hypothesis 3. Plan 4. Analysis 5. Conclusions 6. Appendices 7. References Learners who need : Make sure the groups are mixed. Learners who are more than competent: Peer .

MATHEMATICS Grade 8: Term 3 Week 10 Day 1 Mental Maths - 10 Minutes Revision - 50 Minutes Curriculum: 1:NUMBERS, OPERATIONS AND RELATIONSHIPS 8.1.2 Recognises, classifies and represents the following numbers in order to describe and compare them: 8.1.2.c numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots; 8.1.6 Estimates and calculates by selecting and using operations appropriate to solving problems that involve: 8.1.6.b multiple operations with rational numbers (including division with fractions and decimals); Milestone / Lesson Objective: Mental Maths - Use a rage of strategies to perform and check written and mental calculations with whole numbers including Adding, subtracting and multiplying in columns - Revise: Squares to at least 12 ² and their square roots. - Revise: Cubes to at least 6³ and their cube roots - Multiply and divide with integers - Perform calculations involving all four operations with integers. - Revise Addition and subtraction of common fractions, including mixed numbers - Revise: Addition, subtraction, multiplication and of decimal fractions to at least 3 decimal places Revision Teacher Note: Keywords (See attached dictionary for definitions.) Assessment: Revision

Resources:





Introduction: Revision Tell learners that they are going to revise what they have learnt this term. They can use their previous work to help them.

Concept development Week 1 Day 1 – Week 1 Day 5

• Add and subtract fractions • Multiply fractions • Divide whole number by common fractions • Fractions of squares, cubes, square and cube roots • Fractions, decimals and percentages Homework: Week 2 Day 1 – Week 3 Day 2.

Consolidation

In this lesson we revised the following: Week 1 Day 1 – Week 1 Day 5 See bullet points above. Tell learners to identify the concepts that they are not clear about, write it on a piece of paper and put it on the teacher’s desk. Start the next lesson with those concepts. Learners who need : Receive peer, group or teacher . Learners who are more than competent: Provide peer or group .

Problem solving



Resources:







• Place value, ordering and comparing decimals • Round off rational numbers • Equivalence between common and decimal fractions • Addition, subtraction and multiplication of decimal fractions • Division • Calculate the squares of rational numbers Homework: Week 3 Day 4 – Week 4 Day 3.

Consolidation


Problem solving



Resources:







• Pythagoras • Theorem of Pythagoras Homework: Week 4 Day 5 – Week 6 Day 4.

Consolidation

In this lesson we revised the following: Week 3 Day 4 – Week 4 Day 3 See bullet points above.

Tell learners to identify the concepts that they are not clear about, write it on a piece of paper and put it on the teacher’s desk. Start the next lesson with those concepts. Learners who need : Receive peer, group or teacher . Learners who are more than competent: Provide peer or group .

Problem solving



Resources:







• Area and perimeter of a square • Area and perimeter of a rectangle • Area and perimeter of a triangle • Area and perimeter of a circle • Area and perimeter problem solving • Surface area, volume and capacity of a cube • Surface area, volume and capacity of a prism • Surface area, volume and capacity of a triangular prism • Surface area, volume and capacity of cubes and prisms problems • Surface area, volume: problems Homework: Week 7 Day 1 – Week 9 Day 4.

Consolidation


Problem solving



Resources:







• Collect data • Organise data • Summarise data • Bar graphs • Pie charts • Histograms • Represent data • Analyse data • Report data Homework: No homework.

Consolidation


Problem solving


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