Maths Grade 8 Term 3

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SENIOR PHASE

MATHEMATICS

LESSON PLANS

GRADE 8

7

8

9

Term 3

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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

- 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

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- A problem in context - Problem solving - Sharing - Whole numbers - Denominator - Multiples Assessment:

Add and subtract fractions

Informal

Resources: Board

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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:

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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. numerator

denominator

Grade 8: Term 3: Week 1: Day 1

2 4

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

2 6

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

5 2

What can you tell me about this number? 12₃

Revision: say if it is a proper or improper fraction, or a mixed number. 2 4 6 2 1 1 2 8 5 1 5 7 4 4 5 3 3 5 3 6 5 1 8 Concept development

Write the following on theboard.

Revise equivalent fractions with your learners. What fractions are equal to

• one half? • one quarter? • one third? • one fifth? • one sixth? Revise simplest form.

If 1₂ is 2₄; 3₆; 4₈; ₁₀5 and ₁₂6 in its simplest form, what will the following be in its simplest form? 4 6 ; 6 8 ; 3 9 ; 6 12 ; 10 15

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We can also do it as follows: 4 6 =4₆÷ 2 2 = 2₃

What number can be divided into 4 as well as into 6? 2

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

F4= {1, 2, 4} F₆= {1, 2, 3, 6} GCF = 2

So 2 is the biggest number that can divide into 4 and 6.

1 4

+

2 4

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 3x 4_{4 +} 1 4x 3₃ = _{12 +}4 ₁₂3 = 7 12

Add up the following: What do you

notice? Learners do the following in pairs: • Add up 1₃+ 1₄

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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. 2₄ b. 6₂ c. 11₂ d. 8 5 e. 1 5 f. 7 4 g. 4₅ h. 33₅ i. 3₆ j. 51₈

2. Write an equivalent fraction for

a. 11₂ b. 32₃ c. 41₂

d. 61₃ e. 23₄ f. 24₅

g. 31₄ h. 71₆ i. 51₆

j. 11₅

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

Example: + = = a. 2₅+4₅= b. 5₉+6₉= c. 3₄+2₄= d. 7 10+ 5 10= e. 5 6+ 3 6= f. 5 7+ 6 9 = g. 5₈+4₈= h. ₁₂9 +₁₂8 = i. 2₃+2₃= j. 10 15+ 9 15= 5 divided by 3 is 1 remainder

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4. Calculate and simplify it necessary. a. 1 4+ 1 2= b. 1 5+ 1 10= c. 1 3+ 1 6= d. 1 8+ 1 4= e. 1 5+ 1 4= f. 1 2+ 1 3= g. 1₇+1₂= h. 1₈+1₃= i. 2₄+2₃= j. 3₄+4₅=

5. Calculate and simplify.

a. 1 +1₂= b. 3 2+ 1 4= c. 2 1 4+ 8 = d. 41₂− 31₃= e. 21₆+ 11₅= f. 71₂− 13₄= g. 12₁₀−₁₅1 = h. ₁₅9 − 1₁₀3 = i. ₂₉1 + 12₇= j. 31 11+ 2 4 12=

Consolidation

We can only add fractions if they have the same denominators.

Learners who need support: Solve all addition sums by drawing number lines. Learners who are more than competent: Provide peer support.

Problem solving

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Multiply fractions - 50 Minutes Curriculum:

Multiply fractions

- Revise Finding fractions of whole numbers

- Revise Multiplication of common fractions, including mixed numbers

Teacher Note:

- Common fraction - Whole numbers - Mixed numbers - Multiplication

- A problem in context - Problem solving - Sharing

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Assessment: Multiply fractions Informal Resources: Board Writing book

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Introduction: Multiply fractions

Grade 8: Term 3: Week 1: Day 2 Let us multiply fractions: 1 2× 1 4

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

and then the denominators: 1 2× 1 4 We will first multiply the numerators and then the denominators. = 1₈

Concept development

Ask learners what they should remember when multiplying fractions. Do the following example on the board:

2 3 ×

1 4 = ₁₂2

If 4 = 4₁, how will we multiply the following fractions? 3 × 1₅ = 3₁ × 1₅ = 3₅ 1 2× 2 6 1 2× 2 6= 1 6 = ₁₂2 = ₁₂2 ÷ 2 2 = 1₆

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Ask learners to multiply the following fractions. Write it on the board: 2 4 × 6 2 = 12₈ = 3 2 = 11₂

The mixed number for this improper fraction is = 14₈

We can simplify this by determining the GCF, namely 4: = 11₂ Homework: Questions 3, 4, 5.

Do the following activities in your writing book: 1. Calculate. Example: × = a. 1 5× 2 3= b. 2 4× 1 3= c. 1 6× 3 7= d. 1₂×4₆= e. 7₈×2₄= f. 8₉×4₅= g. 1₅×2₃= h. 2₄×1₃= i. 1₆×3₇= j. 1₂×4₆= k. 7₈×2₄= l. 8₉×4₅= m. 6 7× 3 5= n. 2 3× 8 9= o. 2 8× 2 3= p. 3₄×6₉=

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2. Calculate the following. Example: ___ × ___ = × = a. ___ × ___ =4₉ b. ___ × ___ =₁₄8 c. ___ × ___ =6₈ d. ___ × ___ =12₁₆ e. ___ × ___ =18₆₃ f. ___ × ___ =₁₀6 g. ___ × ___ =22₃₆ h. ___ × ___ = 12₂₀ i. ___ × ___ =30₄₂ j. ___ × ___ =27₅₄

3. Calculate the following.

Example: × = × = = 2 a. 2 ×3₅= b. 4 ×5₆ = c. 11 ×₁₀3 = d. 9 ×1₂ = e. 2₃× 3 = f. 8 ×6₇= g. 6 ×2₃= h. 8₉× 5 = i. ₁₁6 × 7 = j. 10 ×4₈ =

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4. What whole number and fraction will give you the following answer? Example: ___ × ___ = × = × a. ___ × ___ =4₆ b. ___ × ___ =₁₈9 c. ___ × ___ =3₈ d. ___ × ___ =15₅₀ e. ___ × ___ =₂₁7 f. ___ × ___ =₂₄6 g. ___ × ___ =12₁₈ h. ___ × ___ = 18₂₄ i. ___ × ___ =2₉ j. ___ × ___ =₁₀8 5. Revision: simplify. F15 _{={1, 3, 5, 15}} F20_{= {1, 2, 4, 5, 10, 20}} GCF: 5 Example: = _÷ = a. ₁₂4 b. ₁₆8 c. ₂₀5 d.16 24 e. 7 21 f. 24 64 g. 50₈₀ h. 27₉₉ i. 48₇₂ j. ₁₀₀60

6. Multiply and simplify if possible. Example: × = = _÷ =

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a. 1₂×4₈= b. 7₇×3₆= c. ₁₀8 ×10₁₂= d. 1 3× 5 5= e. 1 2× 3 4= f. 1 2× 2 7= g. 4₅×3₄= h. 3₈×3₉= i. 2₃×5₆= j. 3 4× 1 2=

7. Revision: write the improper fractions as whole numbers and simplify if necessary. Example: = or = F2 = {1, 2} F4_{= {1, 2, 4} =} a. 19₃ b. 21₅ c. 20₆ d.32 7 e. 18 8 f. 21 9 g. 20 3 h. 64 10 i. 27 12 j. 70₁₁

8. Multiply and simplify. Example: × = = 3 = 3 a. 3₂×7₆= b. 6₃×6₅= c. 8₇×6₄= d. 5₄×9₈= e. 6₅×9₈= f. ₇9×6₃= GCF is 2

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g. 12₁₁×8₆= h. 4₂×10₉ = i. 11₉ ×14₁₂= j. 12₁₀×11₁₀ =

Consolidation

Learners who need support: Receive peer support.

Learners who are more than competent: Provide peer support.

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?

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Divide whole number by common fractions - 50 Minutes Curriculum:

Divide whole number by common fractions

- Divide whole numbers and common fractions by common fractions

- Use knowledge of reciprocal relationships to divide common fractions

Teacher Note:

- Common fraction - Division

- Mixed numbers

- A problem in context - Problem solving - Sharing

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Assessment:

Divide whole number by common fractions

Informal

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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÷ 4_{4 =} 1 2 15 9

= 1

6 9

= 1

6 9

÷ 3

_{3 = 1}

2 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.

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

4 ÷₁₀4 =

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 ÷3₄ = 3₁x 4₃ = 4 1 = 4 4 ÷8₅ 4 1= 5 8x 5 2= (simplify) 21₂= 1 2÷ 1 6 1 2x 6 1 = 6₂ = 3 2 3÷ 3 4 2 3x 4 3 = 8₉ 1 1₂÷ 21₄ =3₂÷9₄ = 3 2x 4 9 = 1 1÷ 2 3 = 2 3 Font groottes varieer –

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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 = = 4 a. 4 ÷ = b. 7 ÷ = c. 12 ÷ = d. 9 ÷ = e. 5 ÷ = f. 10 ÷ = g. 2 ÷ = h. 8 ÷ = i. 6 ÷ = j. 11 ÷ = 2. Calculate. Example: 4 ÷ = x = = 2 a. 3 ÷ = b. 6 ÷ = c. 8 ÷ = d. 2 ÷ = e. 4 ÷ = f. 7 ÷ = Whole number divided by a proper fraction. Whole number divided by a improper fraction.

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g. 9 ÷ = h. 10 ÷ = i. 5 ÷ = j. 12 ÷ = 3. Calculate. Example: ÷ = x = a. ÷ = b. ÷ = c. ÷ = d. ÷ = e. ÷ = f. ÷ = g. ÷ = h. ÷ = i. ÷ = j. ÷ = Common fraction divided by a common fraction. 4. Calculate. Example: 2 ÷ = x = x = a. 1 ÷ 2 = b. 1 ÷ 2 = c. 3 ÷ 4 = d. 3 ÷ 7 = e. 5 ÷ 2 = f. 5 ÷ 3 = g. 6 ÷ 4 = h. 2 ÷ 2 = i. 4 ÷ 5 = j. ÷ 9 =

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Consolidation

Emphasise that to divide by any number means to multiply by its reciprocal. Complete assessment and check answers.

Learners who need support: Give learners more problems with whole numbers multiplied by fractions. Peer support. Do corrections for homework.

Learners who are more than competent: Give learners five sums with fractions divided by fractions. Provide peer support.

Problem solving

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

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Concept Development - 50 Minutes Curriculum:

Concept Development

- Calculate the squares, cubes, square roots and cube roots of common fractions

Teacher Note:

- Common fraction - Cube number - Cube roots - Square number - Square roots - Mixed numbers

- A problem in context - Problem solving

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

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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 ² = 32 42 = ₁₆9 16 25= 16 25= 4 5 3 4 ³ = 33 43 = 27₆₄ 8 27 3 = 33₂₇8 = 2₃ 1. Calculate. Example: ² = = a. 1 4 ² b. 2 7 ² c. 5 6 ² d. 5₈ ² e. 3₄ ² f. 2₅ ² g. ² h. ² i. ² j. ² 2. Revision: calculate. Example: = = a. b. c. Homework: Complete this activity.

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d. e. = f. g. h. i. 3. Calculate. Example: ³ = = a. 1₄ ³ b. 1₃ ³ c. 6₆ ³ d. 4 8 ³ e. 2 3 ³ f. 2 7 ³ g. ³ h. ³ i. ³ j. 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

Problem solving

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Fractions, decimals and percentages - 50 Minutes Curriculum:

Fractions, decimals and percentages

- 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:

- A problem in context - Common fraction - Mixed numbers - Problem solving - Sharing - Whole numbers - Percent

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- Decrease - Increase

- Common fractions - Decimal fraction

- Equivalence between common fraction, decimal fraction and percentage Assessment:

Fractions, decimals and percentages

Informal

Resources: Writing books

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Introduction: Fractions, decimals and percentages

Introduce this lesson by revising the following.

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× 105 1 = 3₅× 105₁ = 315 5 = R63 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: ₁₀₀25 Simplify: 1 4 Decimal: 0,25 I can write 60% as ₁₀₀60 60 100 simplified is 6 10 = 3 5

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What percentage is 40c of R3,20? Do this step by step with your learners.

40 320× 100 1 = 4 000₃₂₀ = 100 8 = 12,5% 400 320 simplified is 100 8

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 = 240₆₀ = 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 20× 100 1 = 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. 37% b. 25% c. 83% d. 9% e. 56% f. 3% g. 8% h. 75% i. 92% j. 69% 18 100simplified is 9 50

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Simplest form Fraction 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% Percentage 10 100 1 10 3. Calculate. 40% of R20 = ₁₀₀40 × 20₁ = 800 100 = R8 a. 20% of R24 b. 70% of R15 c. 60% of R95 d. 80% of R74 e. 30% of R90 f. 50% of R65 4. Calculate the percentage.

Example: see example under concept development. 2. Write the following as a fraction in its simplest form.

a. 30c of R1,80 b. 80c of R1,60 c. 40c of R8,40 d. 70c of R2,10 e. 50c of R7,00 f. 30c of R3,60 5. Calculate the percentage increase.

Example: see example under concept development.

a. R50 of R70 b. R80 of R120 c. R15 of R18 d. R25 of R30 e. R100 of R120 f. R36 of R54 g. R120 of R150 h. R24 of R32 i. R90 of R120 j. R75 of R100

6. Calculate the percentage decrease.

Example: see example under concept development.

a. R20 of R15 b. R50 of R45 c. R18 of R15 d. R24 of R18 e. R90 of R80 f. R28 of R21 g. R45 of R36 h. R48 of R40 i. R99 of R90 j. R72 of R66

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Consolidation

We need to know that 100% is the same as 100

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 support: Let learners make drawings with the calculations. Make use of peer support.

Learners who are more than competent: What is 120% of R85? Provide peer support.

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.

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Place value, ordering and comparing decimals - 50 Minutes Curriculum:

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, accounts, loans, simple interest, hire purchase, exchange rates);

Place value, ordering and comparing decimals

- Solve problems in contexts involving percentages.

Teacher Note:

Assessment:

Informal

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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. Solve the following.

a. Find 80,6% of the number 110. b. What is 5,2% of 29?

c. What percentage is 36 of 82? d. What percentage is 13 of 121? e. What percentage is 55 of 149? f. What is 86,6% of 44?

g. What percentage is 61 of 116? h. 22,3% of a number is 123. What is the number? i. 57,1% of a certain number is 115. What is the number?

j. What percentage is 143 of 146? k. 81,8% of what number is 84? l. 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

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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 support: Make a drawing/diagram of your problem. Learners who are more than competent: Provide peer support.

Problem solving

See this lesson.

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

60× 100

1 = 40%

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

20× 100

1 = 10%

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

100×

150 000

1 = R22 500

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Place value, ordering and comparing decimals - 50 Minutes Curriculum:

- Revise: Ordering, comparing and place value of decimal fractions to at least 3 decimal places

- Solve problems in context involving decimal fractions

Teacher Note:

- Compare decimal fractions - Decimal fraction

- A problem in context - Problem solving Assessment:

Informal

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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

decimal comma. (LB to change)

Concept development

Revise place value of decimal fractions with your learners. Use your example on theboardand 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

Note that we can also say decimal

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2. Write the following in words. Example: 5,872

= 5 units + 8 tenths + 7 hundredths + 2 thousandths a. 3,378 b. 6,2914 c. 2,588

d. 2,037 e. 2,003 f. 14,030

g. 23,004 h. 400,404 i. 2,998

j. 45,026 k. Use a calculator to check your answers. 3. Write the following in the correct column.

thousands hundreds tens units tenths hundredths Thousandths

a. 2,869 2 , 8 6 9 b. 24,328 , c. 18,003 , d. 376,02 , e. 8674,5 , f. 2874,345 , g. 987,001 , h. 400,08 , i. 2000,203 ,

4. Write down the value of the underlined digit. Example: 3,476 = 0,07 or 7 hundredths a. 6,857 b. 4,37 c. 3,809 d. 8,949 e. 85,080 f. 34,004 g. 765,323 h. 7,660 i. 568,999 j. 87,608

5. Write the following in ascending order.

a. 0,04; 0,4; 0,004 b. 0,1; 0,11; 0,011 c. 0,99; 0,9; 0,999 d. 0,753; 0,8; 0,82 e. 0,67; 0,007; 0,06 f. 0,899; 0,98; 0,99 g. 0,202; 0,2; 0,22 h. 0,345; 0,45; 0,5 i. 0,003; 0,033; 0,030 j. 0,702; 0,72; 0,072

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6. Fill in <, >, = . a. 0,4 ___ 0,04 b. 0,05 ___ 0,005 c. 0,1 ___ 0,10 d. 0,62 ___ 0,26 e. 0,58 ___ 0,85 f. 0,37 ___ 0,73 g. 0,123 ___ 0,321 h. 0,2 ___ 0,20 i. 0,4 ___ 0,40 j. 0,05 ___ 0,050

Consolidation

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

Learners who need support: 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, 6}th_{, 7}th_{, 8}th_, 9th _{and 10}th _{place after the decimal comma?}

Problem solving

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Round off rational numbers - 50 Minutes Curriculum:

8.1.6.a rounding off;

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:

- 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

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1

₁

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.

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2

₂

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. 9,2 b. 4,5 c. 4,8 d. 6,4 e. 5,68 f. 5,999 g. 3,34 h. 7,82 i. 9,321 j. 100,383

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

If you struggle to round off, circle the number that is before the number

you need to round off to.

Example: 7,38 ≈ 7

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3

a. 1,181 b. 2,345 c. 8,655

d. 7,942 e. 5,229 f. 3,494

g. 4,715 h. 8,537 i. 5,9676

j. 8,6972

6. Round off to the nearest thousandth. Example: 18,2576 ≈ 18,258 a. 5,1272 b. 2,7864 c. 6,6628 d. 5,2336 e. 1,9813 f. 3,3336 g. 9,4581 h. 7,7857 i. 7,8176 j. 8,6491

Consolidation

Learners who need support: 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

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Equivalence between common and decimal fractions - 50 Minutes Curriculum:

Equivalence between common and decimal fractions

- Revise equivalent forms between: common fraction and decimal fraction forms of the same number

Teacher Note:

- Decimal fraction

- Equivalence between common fraction and decimal fraction Assessment:

Equivalence between common and decimal fractions

Informal

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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 remember how to write this as a common fraction?” Do the following on the board.

• 0,5 = 5 10 • 0,08 = 8 100 • 0,007 = 7 1 000 We say five-tenths • 0,287 = 2 10 + 8 100+ 7 1 000 We say eight-hundredths We say seven-thousandths

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

Example: = 0,06 a. b. c. d. e. f. g. h. i. j.

k. Learners use their calculators to convert between common and decimal fractions.

2. Write as a decimal fraction. Example: = 0,73 a. b. c. d. e. f. g. h. i. j.

3. Write as a decimal fraction. Example:

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a. b. c. d. e. f. g. h. i. j.

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. b. c. d. e. f. g. h. i. j.

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Consolidation

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

Learners who need support: Give learners more examples similar to those in Questions 1-4.

Learners who are more than competent: Write the following as decimal fractions 4 1000000, 789 100000, 1 365 100000, 389499 1000000, 237654

1000000 using scientific notation.

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? • ₁₀4 = 0,4 • 4 100= 0,04 • 4 1 000 = 0,004 • 1₅= 0,02 • ₂₅1 = 0,04

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Addition, subtraction and multiplication of decimal fractions - 50 Minutes Curriculum:

Addition, subtraction and multiplication of decimal fractions

- 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:

- 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

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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 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. 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 = a. 0,3 x 0,4 = b. 0,5 x 0,1 = c. 0,7 x 0,8 = d. 0,6 x 0,7 = e. 0,04 x 0,02 =

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3. Calculate. Example: 0,2 x 10 = 2 a. 0,7 x 8 = b. 0,4 x 9 = c. 0,7 x 8 = d. 0,03 x 8 = e. 0,06 x 5 = 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 = c. 0,3 x 0,4 x 100 = d. 0,8 x 0,04 x 100 = e. 0,3 x 0,2 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 = c. 2,578 x 40 = d. 17,654 x 60 = e. 28,342 x 20 =

Consolidation

When we multiply decimals we should look at the places (place value) after the decimal comma.

Problem solving

Multiply three-hundredths by nine-thousandths by 1 000.

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Divide decimal fractions by decimal fractions - 50 Minutes Curriculum:

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:

- Decimal fraction - Multiplication - Division - Estimate

- Estimate the possible answer before doing a calculation on a calculator Assessment:

Divide decimal fractions by decimal fractions

Informal

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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 = b. 0,6 ÷ 3 = c. 0,6 ÷ 2 =

d. 0,8 ÷ 2 = e. 1,8 ÷ 3 =

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 = b. 0,35 ÷ 7 = c. 0,63 ÷ 7 = d. 0,54 ÷ 6 = e. 0,12 ÷ 4 =

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?

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2,4 m

Round off to the nearest m Divide by 8

5,4 kg

Round off to the nearest kg Divide by 9

R3,75

Round off to the nearest rand

Divide by 25

2,5 ℓ

Round off to the nearest litre Divide by 5

1,44 kg

Round off to the nearest kilogram Divide by 12 R0,50

Round off to the nearest rand

Divide by 2

a. b. c.

d. e. f.

6. Complete the flow diagram.

Consolidation

When dividing decimals by whole numbers, you place the decimal comma in the same place as in the dividend.

Learners who need support: Give learners more examples like in this lesson. Learners who are more than competent: Peer support.

Problem solving

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Calculate the squares of rational numbers. - 50 Minutes Curriculum:

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:

- 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.

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1

Introduction: Calculate the squares of rational numbers

Introduce the topic by revising square numbers.

Concept development

Write the following on the board.

Do each calculation step by step with the learners using both methods. 72_{= 49 and square roots = 7²}