maths grade 8 term 3

7/30/2019 Maths Grade 8 Term 3

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LESSON PLANS

GRADE 8

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 and their square roots.

- Revise: Cubes to at least 6 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


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- A problem in context

- Problem solving

- Sharing

- Whole numbers

- Denominator

- Multiples

Assessment:


Informal

Resources:

Board


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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 fractionsRevise 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 anddenominator?

2

6

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

5

2

What can you tell me about this number?1

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

1

3

5

Concept developmentWrite the following on the board.

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

is

;

;

;

and

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

=

2

2

=

What number canbe divided into 4as 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 divideinto 4 and 6.

+

Revise: If we add up common fractions with different denominators we need tofind the LCM.

: {3, 6, 9 ,12, 15, }

: {4, 8, 12 , 16, 20, }

x

4

4+

x

3

3

= 412

+ 312

=

Add up the following: What do younotice?

Learners do the following inpairs:

Add up

+

Add up 1

+ 2


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Homework: Question 3, 4, 5

Do the following activities in yourwriting book.

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

a.

b.

c. 1

d.

e.

f.

g.

h. 3

i.

j. 5

2. Write an equivalent fraction for

a. 1

b. 3

c. 4

d. 6

e. 2

f. 2

g. 3

h. 7

i. 5

j. 1

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

Example:

+

=

=

a.

+

= b.

+

= c.

+

=

d.

+

= e.

+

= f.

+

=

g.

+

= h.

+

= i.

+

=

j.

+

=

5 divided by 3is 1 remainder


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4. Calculate and simplify it necessary.

a.

+

= b.

+

= c.

+

=

d.

+

= e.

+

= f.

+

=

g.

+

= h.

+

= i.

+

=

j.

+

=

5. Calculate and simplify.

a. 1 +

= b.

+

= c. 2

+ 8 =

d. 4

3

= e. 2

+ 1

= f. 7

1

=

g.

= h.

1

= i.

+ 1

=

j. 3

+ 2

=

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


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Multiply fractions - 50 Minutes



compare them:








decimals);


Mental Maths








places

Multiply fractions

- Revise Finding fractions of whole numbers

- Revise Multiplication of common fractions, including mixed numbers



after calculations


grouping, sharing and finding fractions of whole numbers

Teacher Note:


- Common fraction

- Whole numbers

- Mixed numbers

- Multiplication

- Fraction in its simplest form- Multiples and factors


- Problem solving

Sharing


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Assessment:

Multiply fractions

Informal

Resources:

Board

Writing book


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Times Tables:

4 x 12 = (48)

11 x 3 = (33)

7 x 4 = (28)

4 x 9 = (36)

7 x 11 = (77)

7 x 12 = (84)

6 x 12 = (72)

8 x 6 = (48)

6 x 8 = (48)

Square Root:


Cube Root:



0,61 x 0,13 = (0,0793)

Fraction Addition:




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Introduction: Multiply fractions


Let us multiplyfractions:

Ask the learnersto identify thenumerators:

and then thedenominators:

We will firstmultiply thenumerators andthen the

denominators.=

Concept developmentAsk learners what they should remember when multiplying fractions.

Do the following example on the board:2

31

4

=

If 4 =

, how will we multiply the following fractions?

3

=

=

=

=

=

22

=


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Ask learners to multiply the following fractions. Write it on the board:2

46

2

=

=

= 1

The mixed number for this improper fraction is = 1

We can simplify this by determining the GCF, namely 4: = 1

Homework: Questions 3, 4, 5.

Do the following activities in yourwriting book:

1. Calculate.

Example:

=

a.

= b.

= c.

=

d.

= e.

= f.

=

g.

= h.

= i.

=

j.

= k.

= l.

=

m. = n.

= o.

=

p.

=


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2. Calculate the following.

Example: ___ ___ =

=

a. ___ ___ =

b. ___ ___ =

c. ___ ___ =

d. ___ ___ =

e. ___ ___ =

f. ___ ___ =

g. ___ ___ =

h. ___ ___ =

i. ___ ___ =

j. ___ ___ =


Example:

=

=

= 2

a. 2

= b. 4

= c. 11

=

d. 9

= e.

3 = f. 8

=

g. 6

= h.

5 = i.

7 =

j. 10

=


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

Example: ___ ___ =

=

a. ___ ___ =

b. ___ ___ =

c. ___ ___ =

d. ___ ___ =

e. ___ ___ =

f. ___ ___ =

g. ___ ___ =

h. ___ ___ =

i. ___ ___ =

j. ___ ___ =

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

Example:

=

=

a.

b.

c.

d.

e.

f.

g.

h.

i.

j.

6. Multiply and simplify if possible.

Example:

=

=

=


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a.

= b.

= c.

=

d.

= e.

= f.

=

g.

= h.

= i.

=

j.

=

7. Revision: write the improper fractions as whole numbers and simplify ifnecessary.

Example:

=

or

=

F2 = {1, 2}

F4 = {1, 2, 4} =

a.

b.

c.

d.

e.

f.

g.

h.

i.

j.

8. Multiply and simplify.

Example:

=

= 3

= 3

a.

= b.

= c.

=

d.

= e.

= f.

=

GCF is 2


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g.

= h.

= i.

=

j.

=

ConsolidationLearners who need support: Receive peer support.


Problem solvinga. 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



compare them:








decimals);


Mental Maths








places

Divide whole number by common fractions

- Divide whole numbers and common fractions by common fractions



after calculations

- Use knowledge of reciprocal relationships to divide common fractions



Teacher Note:


- Common fraction

- Division

- Mixed numbers

- Fraction in its simplest form

- Multiples and factors- A problem in context

- Problem solving

- Sharing

Whole numbers


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Assessment:


Informal

Resources:

Board

Writing book


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Times Tables:

3 x 4 = (12)

6 x 9 = (54)

12 x 3 = (36)

8 x 9 = (72)

3 x 11 = (33)

8 x 12 = (96)

11 x 6 = (66)

8 x 6 = (48)

6 x 8 = (48)

Square Root:


Cube Root:



0,93 x 0,29 = (0,2697)

Fraction Addition:




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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

4=

9= 1

6

9= 1

6

93

3= 1

Revise multiplication of fractions.

6

3

24=

3

3= (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 bycompleting this assessment.

4

0=

Concept developmentWrite the following on the board.

Introduce the division of fractions by going through the examples step by step withyour learners.

3

=

x

=

= 4

4

=

x

= (simplify)

2

=

6

x

6

=6

= 3

x

=

9

1

2

=

9

=

x

9

=

=


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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 yourwriting 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 numberdivided by a

proper fraction.

Whole number

divided by aimproper 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 fractiondivided 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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ConsolidationEmphasise 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 fractionsdivided by fractions. Provide peer support.

Problem solvingWrite 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



compare them:








decimals);


Mental Maths








places

Concept Development

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



after calculations



Teacher Note:


- Common fraction

- Cube number

- Cube roots

- Square number

- Square roots

- Mixed numbers- Fraction in its simplest form



Problem solving


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- Sharing

- Whole numbers

Assessment:

Concept Development

Informal

Resources:

Board

Writing book


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Times Tables:

4 x 11 = (44)

3 x 4 = (12)

6 x 11 = (66)

3 x 3 = (9)

4 x 12 = (48)

6 x 8 = (48)

8 x 8 = (64)

7 x 8 = (56)

11 x 12 = (132)

Square Root:


Cube Root:



0,79 x 0,22 = (0,1738)

Fraction Addition:




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Introduction: Fractions of squares, cubes, square and cube rootsRevise: Square and cube numbers

Square roots and cube roots

Concept development

Do the following with your learners on the board.

3

4 =

3

4=

9

16

16

25=

16

25=

4

5

3

4 =

3

4=

27

64

8

27

=8

27 =

2

3

1. Calculate.

Example:

=

=

a.1

4 b.

2

7 c.

5

6

d.5

8 e.

3

4 f.

2

5

g.

h.

i.

j.

2. Revision: calculate.

Example:

=

=

a.

b.

c.

Homework: Complete this activity.

Do the following activities in yourwriting book:


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d.

e.

= f.

g.

h.

i.

3. Calculate.

Example:

=

=

a.1

4 b.

1

3 c.

6

6

d.4

8 e.

2

3 f.

2

7

g.

h.

i.

j.

4. Revision: calculate.

Example:

=

=

a.

b.

c.

d.

e.

f.

g.

h.

i.

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

Problem solvingWhat is squared sixteen divided by twenty-five?


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Fractions, decimals and percentages - 50 Minutes



compare them:







decimals);


Mental Maths






- 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



- 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 percentageforms of the same number.

Teacher Note:



- 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:


Informal

Resources:

Writing books


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Times Tables:

12 x 11 = (132)

4 x 8 = (32)

11 x 11 = (121)

6 x 4 = (24)

9 x 12 = (108)

12 x 12 = (144)

8 x 7 = (56)

8 x 6 = (48)

6 x 6 = (36)

Square Root:


Cube Root:



0,78 x 0,05 = (0,039)

Fraction Addition:




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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?

5

=

5

5

=5

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:5

Simplify:

Decimal: 0,25

I can write

60% as

simplified is

=

5

Learners may use a calculator.


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What percentage is 40c of R3,20?

Do this step by step with your learners.

=

4 000

320

=

8

= 12,5%

simplified is

8

Calculate the percentage increase if the price of a bus ticket of R60 is increasedto R84. Amount increased is R24.

=240

60

= 40%

Calculate the percentage decrease if the price of petrol goes down from 20cents a litre to 18 cents. Amount decreased is 2 cents.

=200

20

= 10%

Homework: Question 5g-j and 6g-j

Ask the learners to solve the following problems in theirwriting 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%

8

simplified is

9

5


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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

=

=8

= R8

a. 20% of R24 b. 70% of R15 c. 60% of R95d. 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 R8,40d. 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 R18d. R25 of R30 e. R100 of R120 f. R36 of R54g. 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 R15d. R24 of R18 e. R90 of R80 f. R28 of R21g. 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

is the same as 1.

We need to know the equivalent of fractions, percentage and decimals in order todo calculations.

Learners who need support: Let learners make drawings with the calculations. Makeuse of peer support.

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

Problem solvingI 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 to28c.


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Place value, ordering and comparing decimals - 50 Minutes



compare them:




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);8.1.6 Estimates and calculates by selecting and using operations appropriate to solving



decimals);


Mental Maths


numbers including Adding, subtracting and multiplying in columns- Revise: Squares to at least 12 and their square roots.






places

Place value, ordering and comparing decimals

- Solve problems in contexts involving percentages.

Teacher Note:


Assessment:


Informal

Resources:

Writing books


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Times Tables:

12 x 3 = (36)

11 x 11 = (121)

12 x 9 = (108)

9 x 11 = (99)

11 x 4 = (44)

12 x 6 = (72)

12 x 7 = (84)

8 x 6 = (48)

6 x 6 = (36)

Square Root:


Cube Root:



0,13 x 0,12 = (0,0156)

Fraction Addition:




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Introduction: Place value, ordering and comparing decimals

Revise increasing and decreasing of percentages with your learners.

Concept developmentIn 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 theirwriting 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 numbi. 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 thepercentage 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

Amount =

105 = 63


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ConsolidationSometimes problem solving is very complicated. Dont 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.


Problem solvingSee this lesson.

b. What percentage is 40c of R3,20?

Percentage =4

=

8= 12,5%

c. Calculate the percentage increase if the price of a bus ticket is increased fromR60 to R84.

Amount increased = R24. Therefore percentage increase is4

= 40%

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

= 10%

e. Calculate how much a car will cost if its original price of R150 000 is reduced by15%. Calculation involves finding 15% of R150 000 and then subtracting thatamount from the original price. i.e.

= R22 500

Hence new price of car = R150 000 R22 500 = R127 500


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Place value, ordering and comparing decimals - 50 Minutes



compare them:







decimals);


Mental Maths








places


- 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


- Problem solving

Assessment:


Informal

Resources:

Board

W iti b k


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Times Tables:

9 x 8 = (72)

12 x 4 = (48)

3 x 11 = (33)

9 x 4 = (36)

11 x 4 = (44)

6 x 8 = (48)

6 x 12 = (72)

6 x 6 = (36)

8 x 6 = (48)

Square Root:


Cube Root:



0,33 x 0,22 = (0,0726)

Fraction Addition:




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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 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 theirwriting 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 decimalnumber


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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. 2,588d. 2,037 e. 2,003 f. 14,030g. 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. 34,004g. 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; 0,999d. 0,753; 0,8; 0,82 e. 0,67; 0,007; 0,06 f. 0,899; 0,98; 0,99g. 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 ___ 0,10d. 0,62 ___ 0,26 e. 0,58 ___ 0,85 f. 0,37 ___ 0,73g. 0,123 ___ 0,321 h. 0,2 ___ 0,20 i. 0,4 ___ 0,40

j. 0,05 ___ 0,050

ConsolidationThe 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 expandednotation 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 solvingWhat would you do to change this decimal fraction 9,768 to 9,008?


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Round off rational numbers - 50 Minutes



compare them:






8.1.6.a rounding off;


decimals);


Mental Maths








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 calculatorAssessment:



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Resources:

Board


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Times Tables:

3 x 4 = (12)

12 x 9 = (108)

11 x 9 = (99)

8 x 11 = (88)

9 x 7 = (63)

12 x 12 = (144)

11 x 7 = (77)

11 x 12 = (132)

7 x 12 = (84)

Square Root:


Cube Root:



0,51 x 0,08 = (0,0408)

Fraction Addition:




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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. 4,8d. 6,4 e. 5,68 f. 5,999g. 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. 8,655d. 7,942 e. 5,229 f. 3,494g. 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. 6,6628d. 5,2336 e. 1,9813 f. 3,3336g. 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 roundoff.

Learners who are more than competent: Write down the steps on how to use ascientific calculator to round off decimal numbers.

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


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Equivalence between common and decimal fractions - 50 Minutes



compare them:







decimals);


Mental Maths








places

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:


Informal

Resources:

BoardWriting books


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Times Tables:

3 x 7 = (21)

9 x 8 = (72)

4 x 6 = (24)

3 x 3 = (9)

9 x 3 = (27)

8 x 12 = (96)

11 x 12 = (132)

11 x 8 = (88)

12 x 6 = (72)

Square Root:


Cube Root:



0,51 x 0,08 = (0,0408)

Fraction Addition:




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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 acommon fraction? Do the following on the board.

0,5 =5

10

0,08 = 8100

0,007 =7

1 000

We sayfive-tenths

0,287 =2

10+

8

100+

7

1 000

We sayeight-hundredths

We sayseven-thousandths

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


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Learners do the following in theirwriting 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 decimalfractions.


Example:

= 0,73

a.

b.

c.

d.

e.

f.

g.

h.

i.

j.



Example:

= 5,1


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

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

Learners who are more than competent: Write the following as decimal fractions4

1000000,

789

100000,

1 365

100000,389499

1000000,237654

1000000using scientific notation.

Problem solvingIf the tenths digit is six and the units digit is three, what should I do to get an answerof 7,644?

4

10= 0,4

4

100= 0,04

4

1 000= 0,004

1

5= 0,02

1

25= 0,04


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Addition, subtraction and multiplication of decimal fractions - 50 Minutes



compare them:







decimals);


Mental Maths








places

Addition, subtraction and multiplication of decimal fractions


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


- Addition

- Decimal fraction

- Multiplication

- Subtraction

- Division

- Whole numbers

- Estimate

- Estimate the possible answer before doing a calculation on a calculatorAssessment:



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Resources:

Writing books


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Times Tables:

9 x 3 = (27)

11 x 3 = (33)

12 x 9 = (108)

6 x 9 = (54)

4 x 12 = (48)

7 x 7 = (49)

12 x 8 = (96)

6 x 6 = (36)

6 x 7 = (42)

Square Root:


Cube Root:



0,57 x 0,11 = (0,0627)

Fraction Addition:




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Introduction: Addition, subtraction and multiplication of decimalfractions

Introduce this activity by telling learners that this is going to be an assessmentactivity. 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 ofdecimal numbers.

Homework: Complete the assessment.

Learners complete the following in theirwriting 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 =

ConsolidationWhen we multiply decimals we should look at the places (place value) after thedecimal comma.

Learners who need support: Receive peer support.


Problem solving

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


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Divide decimal fractions by decimal fractions - 50 Minutes



compare them:







decimals);


Mental Maths








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


- Decimal fraction

- Multiplication

- Division

- Estimate

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

Assessment:

Divide decimal fractions by decimal fractionsInformal

R


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Board


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Times Tables:

8 x 3 = (24)

3 x 9 = (27)

8 x 9 = (72)

12 x 9 = (108)

4 x 9 = (36)

8 x 7 = (56)

11 x 12 = (132)

11 x 6 = (66)

7 x 8 = (56)

Square Root:


Cube Root:



0,77 x 0,21 = (0,1617)

Fraction Addition:




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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.



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 piecebe?


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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

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 thesame 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 solvingDivide a decimal with two places after the decimal by a whole number.


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Calculate the squares of rational numbers. - 50 Minutes



compare them:







decimals);


Mental Maths








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


same number

Teacher Note:


- Cube number

- Cube roots

- Decimal fraction

- Square number

- Square roots


- Problem solving


Assessment:

Calculate the squares of rational numbers.

Informal


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Resources:

Board

Writing books


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Times Tables:

4 x 12 = (48)

9 x 12 = (108)

9 x 4 = (36)

7 x 11 = (77)

3 x 12 = (36)

7 x 7 = (49)

8 x 7 = (56)

11 x 12 = (132)

11 x 7 = (77)

Square Root:


Cube Root:



0,93 x 0,29 = (0,2697)

Fraction Addition:




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1

Introduction: Calculate the squares of rational numbers

Introduce the topic by revising square numbers.

Concept development


Do each calculation step by step with the learners using both methods.

72 = 49 and square roots = 7

(0,7)2

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

(0,04)2

= 0,04 x 0,04

= 0,0016

49,0

100

49

107

107

)10

7( 2

=

=

= x

oror

0016,0

10000

16

1004

1004

)100

4( 2

=

=

= x

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

49

04,0

2,02,0 =

= 0,2

004,0

02,002,0 =

= 0,02

2,0

10

2

10

2

10

2100

4

=

=

= x

or or

02,0

100

2

100

2

100

21000

4

=

=

= x

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.


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2

1. Calculate.

Example 1: (0,7)2 Example 2: (1,5)

= 0,7 x 0,7 1,5 x 1,5

= 0,49 = 2,25

a. (0,6)2 b. (0,2)2 c. (0,3)2

d. (0,1)2 e. (0,5)2 f. (0,4)2

g. (1,2)2 h. (1,4)2 i. (1,6)2

j. Add up a, b, c and d. k. Subtract d from e.

2. Calculate.

Example 1: (0,04)2 Example 2: (0,13)

= 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.

You may

use acalculator.

3. Calculate.

Example:

=

= 0,2

a. b. c.

d. e. f.

g. h. i.

j.

04,0

2,02,0

9,0 25,0

36,0 81,0

64,0

1,0

49,0

121,0 144,0

4,0


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3

004,0

02,002,0

0009,0 0016,0 0001,0

0049,0 0004,0 0121,0

0064,0 0081,0 0144,0

0036,0

4. Calculate.

Example:

=

= 0,02

a. b. c.

d. e. f.

g. h. i.

j.

ConsolidationIt 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 isimportant to understand place value of decimals numbers.

Learners who need support: 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 bymeans 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 and in this activity?4,0 004,0


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4

Introduction: Calculate the cube number of rational numbers

Introduce the topic by revising cube numbers and cube roots.

Concept development


Do each calculation step by step with the learners using both methods.

23

= 8

(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 reallife will you use

this? (e.g.calculating

volume)

001,0

1000

1

10

1

10

1

10

1

)

10

1( 3

=

=

= xx

or

or

000001,0

1000000

1

100

1

100

1

100

1

)100

1(

3

=

=

= xx

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

3 27

= 3


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5

3 027,0

3 3,03,03,0 =

= 0,3

3 027,0

3 3,03,03,0 =

= -0,3

Homework: Questions 2d and 3d.

Where in real lifewill you use this?(e.g. the volume

of a cube is givento you and you

need to work outthe height)


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) f. (0,6)

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) f. (0,08)

3. Calculate.

Example:

== 0,3

a. b. c.

d.

3 027,0

3 3,03,03,0

3 008,0 3 081,0 3 001,0

3 125,0


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6

4. Calculate.

Example:

== -0,3

a. b. c.

d.

3 027,0

3 3,03,03,0

3 008,0 3 081,0 3 001,0

3 125,0

Problem: we can say . Can we say ? Why or why not?3 064,0 9,0

ConsolidationIt 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 areimportant.

Learners who need support: 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 cuberoot of 0,00004?

Problem solvingIf the height of a cube is 0,35 m, what is the volume of the cube?


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Assessment 1.1 - 50 Minutes



compare them:







8.1.6.a rounding off;

8.1.6.b multiple operations with rational numbers (including division with fractions anddecimals);


Mental Maths





- Multiply and divide with integers- Perform calculations involving all four operations with integers.



places

Assessment 1.1


- 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



- 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)


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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


same number

- Revise equivalent forms between: common fraction, decimal fraction and percentage

forms of the same number.

Teacher Note:


- Addition- Common fraction

- Mixed numbers

- Subtraction

- Whole numbers

- Multiplication

- Division

- Cube number

- Cube roots

- Square number

- Square roots- Fraction in its simplest form


- Equivalent fractions


- Problem solving

- Sharing

- Percent

- Decrease

- Increase

- Denominator- Multiples

- 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


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Formal

Assessment task 1.1

All

60 Marks

Resources:

Sample assessment


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Times Tables:

3 x 12 = (36)

6 x 3 = (18)

6 x 11 = (66)

7 x 3 = (21)

3 x 9 = (27)

6 x 12 = (72)

8 x 6 = (48)

12 x 12 = (144)

6 x 8 = (48)

Square Root:


Cube Root:



0,39 x 0,02 = (0,0078)

Fraction Addition:




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Grade 8: Term 3 - Week 3: Day 3

Introduction: Assessment 1.1Tell learners that they are going to write an assessment to assess what they havelearnt this term. They can use their previous work to help them.

Concept developmentWeek 1 Day 1 Week 3 Day 2


Multiply fractions


Fractions of squares, cubes, square and cube roots






Division

Calculate the squares of rational numbers

Homework: No homework.


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

2. Write an equivalent fraction for

a.4

5b. 3

5c.

a. 6

b. 2

4 c. 24

5

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

a.

5+

4

5= b.

5

9+

9= c.

4+

4=

4. Calculate and simplify it necessary.

a.

4+

= b.

5+

= c.

+

=

5. Calculate.

a.

5

= b.

4

= c.

7=

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

a. ___ ___ =4

b. ___ ___ =9

c. ___ ___ =

d. 8

945

= e. 5

f.

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

a. 56%

Simplest form

Fraction

100%90%80%70%60%50%40%30%20%10%Percentage

10

100

1

10

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

9. Calculate the percentage.

50c of R7,00

10. Calculate the percentage increase.

R36 of R54

(3)

(3)

(3)

(6)

(3)

(3)

(1)

(2)

(2)

(2)


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21. Round off to the nearest hundredth.

7,942

22. Round off to the nearest thousandth.

5,1272


24. Write as a common fraction.

48,003

25. Calculate.

a. 4,29 + 8,34

3,38 = b. 0,7 x 0,8 = c. 0,6 x 8 =

d. 0,8 x 0,04 x 100 = e. 28,342 x 20 =

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

27. Complete the flow diagram.

2,5

Round off to the

nearest litre

Divide by 5

f. (0,16)2

(1)

(1)

(1)

(1)

(6)

(3)

(2)

Total: 60


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ConsolidationIn this lesson we revised the following:

Week 1 Day 1 Week 3 Day 2


Multiply fractions


Fractions of squares, cubes, square and cube roots






Division

Calculate the squares of rational numbers

Tell learners to identify the concepts that they are not clear about, write it on apiece of paper and put it on the teachers desk. Start the next lesson with thoseconcepts.

Learners who need support: Receive peer, group or teacher support.

Learners who are more than competent: Provide peer or group support.

Problem solvingDo all the problems you did in Week 1 Day 1 Week 3 Day 2.


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Pythagoras - 50 Minutes



compare them:






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;


Mental Maths




- Revise: Cubes to at least 6 and their cube roots- Multiply and divide with integers




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 irrationalanswers in surd form.

Teacher Note:


- Theorem of Pythagoras

- Right-angle triangle

Assessment:

Pythagoras

Informal


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Resources:

Board

Writing books


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Times Tables:

8 x 11 = (88)

6 x 9 = (54)

4 x 8 = (32)

12 x 11 = (132)

4 x 6 = (24)

8 x 7 = (56)

12 x 12 = (144)

7 x 8 = (56)

11 x 12 = (132)

Square Root:


Cube Root:



0,74 x 0,03 = (0,0222)

Fraction Addition:




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Introduction:Pythagoras

Introduce the lesson by telling learners that you are going to learn aboutPythagoras theorem.

Years ago, a man named Pythagoras discovered an amazing fact about triangles.

Draw the following on the board.

Concept development

We can say that a2 + b2 = c2

What do we call the largest side of the triangle? (hypotenuse) The theorem onlyapplies to right-angled triangles.

A

B C

What is the size of c? (42)

What is the size of a? (32)

What is the size of b? (52)

What do you notice?

32 + 42 = 52

9 + 16 = 25

25 = 25

Homework: Complete drawings.

Do the following in yourwriting books.

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


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Consolidation

Learners who need support: Receive peer support.


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

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

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

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


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Theorem of Pythagoras - 50 Minutes



compare them:






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;


Mental Maths




- Revise: Cubes to at least 6 and their cube roots- Multiply and divide with integers




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 irrationalanswers in surd form.

Teacher Note:


- Theorem of Pythagoras

- Right-angle triangle

Assessment:

Theorem of Pythagoras

Informal


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Resources:

Board

Writing books


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Times Tables:

4 x 3 = (12)

7 x 11 = (77)

4 x 12 = (48)

4 x 7 = (28)

12 x 3 = (36)

12 x 6 = (72)

6 x 12 = (72)

11 x 6 = (66)

11 x 7 = (77)

Square Root:


Cube Root:



0,57 x 0,11 = (0,0627)

Fraction Addition:




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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

3

42 + 32 = 52

16 + 9 = 25

25 = 25

a c

b

a2 + b2 = c2 Left-hand side (LHS) =right-hand side (RHS)

Homework: Questions 1d and 2d.

Do the following in yourwriting books.

1. Write an equation for the following and use the given sides to prove the theoremof Phytagorus.Example: see concept development.

a. b.

c. d.

4

3

5

130

104

78

44

33

55 51

68

85


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Theorem of Pythagoras - 50 Minutes



compare them:

8.1.2.c numbers written in exponential form including square

maths grade 8 term 3

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