Mathematics Senior Phase JC D14-Homemathsjcd14.co.za/doc/Grade_8_Term_1_Lesson_Plans_Final.docx · Web viewWhole Numbers Concepts: Marks Doubling and halving Use doubling and halving

Grade 8

Term 1

Mathematics

Lesson Plan

GRADE 8 TERM 1 WEEK 1: Baseline Assessment Total [40]

Test 1: Day 1

Content Area: Numbers, Operations and Relationships

QUESTION 1

Topic: Whole Numbers

Concepts:

Marks

1.1 Doubling and halving

Use doubling and halving to work out

a)

b)

(3)

(3)

1.2 Multiplying and dividing by 10, 100, 1 000

a) Multiply without using a calculator

i)

ii)

iii)

b) Divide without using a calculator

i)

ii)

iii)

(1)

(1)

(1)

(1)

(1)

(1)

1.3 Rounding off numbers to the nearest 5 , 10 , 100 and 1000

Round of 2 672, 567:

a) to the nearest thousand

b) to the nearest hundred

c) to the nearest ten

d) to the nearest unit

(1)

(1)

(1)

(1)

1.4 Ordering and comparing whole numbers

a) Arrange the following in ascending order:

b) Fill in >, <, or to make the following TRUE.

i) 697 059 697 095

ii) 75001 + 9 75 100

iii) 18,005 18,040

(1)

(1)

(1)

(1)

1.5 Place value

What is the place value of 7 in the number 2807550

(1)

1.6 Sequence numbers on number grid and on number line

Which numbers are represented by letters A , B and C

0

10

20

40

C

A

B

(3)

Total

[18]

QUESTION 2


Concepts:

Marks

2.1 Commutative law

If , then

(1)

2.2 Associative law

If , then

(1)

2.3 Distributive law

Complete:

(3)

2.4 Adding and subtracting 0

Complete

a)

(1)

2.5 Multiplying and dividing by 1

Complete

___

(1)

2.6 Inverse operation for addition and subtraction

Complete

(1)

2.7 Inverse operation for multiplication and division

Complete

(1)

Total

[ 9 ]

QUESTION 3


Concepts:

Marks

3.1 Add in columns

Add without using a calculator

765 462

+ 325 968

(1)

3.2 Subtract in columns

Subtract without using a calculator

832 764

298 998

(1)

3.3 Multiply in columns

Multiply without using a calculator

345

13

(2)

3.4 Long division

Divide without using a calculator

24 259 560

(3)

3.5 Estimating

Work out the following:

Operation

Estimate Solution

Check solution on your calculator (round off your answer to 2 decimal places)

(6)

Total

[13]


MEMORANDUM

Test 1: Day 1

Content Area: Numbers, Operations and Relationships

QUESTION 1


Concepts:

Marks

1.1 Doubling and halving

a)

b)

(2)

(2)

1.2 Multiplying and dividing by 10, 100, 1 000

a)Multiply without using a calculator

b) Divide without using a calculator

(6)

1.3 Rounding off numbers to the nearest 5 , 10 , 100 and 1000

a) 2 673 000

b) 2 672 600

c) 2 672 570

d) 2 672 563

(4)

1.4 Ordering and comparing whole numbers

a) Arrange the following in ascending order:


<

iv) 697 059 697 095

<

v) 75001 + 9 75 100

<

vi) 18,005 18,040

(1)

(3)

1.5 Place value

What is the place value of 7 in the number 2807550

Thousand

(1)

1.6 Sequence numbers on number grid and on number line

Which numbers are represented by letters A , B and C

0

10

20

40

C

A

B

(3)

Total

[21]

QUESTION 2


Concepts:

Marks

2.1 Commutative law

If , then

(1)

2.2 Associative law

If , then

(1)

2.3 Distributive law

Complete:

(3)

2.4 Adding and subtracting 0

Complete

(1)

2.5 Multiplying and dividing by 1

Complete

2342

(1)

2.6 Inverse operation for addition and subtraction

Complete

(1)

Total

[8]

QUESTION 3


Concepts:

Marks

3.1 Add in columns

Add without using a calculator

765 462

+ 325 968

1091430

(1)

3.2 Subtract in columns

Subtract without using a calculator

832 764

298 998

533766

(1)

3.3 Multiply in columns

Multiply

345

13

1035

+ 3450

4485

(2)

3.4 Long division

Divide

10815

24 259 560

- 24

19

- 0

195

-192 (method)

36

- 24

120

-120

0

(3)

3.5 Estimating

Work out the following:

Operation

Estimate Solution

Check solution on your calculator (round off your answer to 2 decimal places)

Between 76 and 80

79

65,36

2337

(6)

Total

[13]


Test 2: Day 2

QUESTION 1


Concepts:

Marks

1.1 HCF

Determine the HCF of 27 and 45

(3)

1.2 LCM

Determine the LCM of 6, 8 and 12

(4)

1.3 Ratio

a) Write the following ratios in simplest form 14 : 21 : 56

b) b) The ratio of boys to girls in a class is 3:4. How many girls are there in the class if there are 12 boys?

(7)

1.4 Rate

Khanya builders are paid R480 for 8 hours of work, while Rex builders are paid R660 for 12 hours of work. Which company is paid the higher rate?

(5)

1.5 Speed, distance & time

A taxi travels 2 hours to make a 220 km trip. How fast does it travel?

(3)

Total

[22]

QUESTION 2


Concepts:

Marks

2.1 Profit and loss

A bookshop sells a book marked R 149, 50. The cost of the book to the shop is R 75, 50.

a) Calculate the profit made on each book sold

b) Find the percentage profit (correct to 1 decimal places) made by the shop on each book sold.

(2)

(2)

2.2 Discount

A shop owner gives 30% discount on CD’s. After a discount you have to pay R 150. 00. What is the price for a CD without the discount?

(4)

2.3 Budgets

Copy and complete the table.

Item

Expenses

Percentage

Total Monthly Income

R25000

Mortgage Bond

R7000

a)

Transport

b)

8%

Groceries

R3000

c)

School Fees

R4000

d)

Savings

e)

10%

Surplus

f)

g)

Total

(7)

2.4 Accounts and Simple Interest

Cyril opens a savings account at the bank. He deposits R3000. Each year he gets simple interest of R360.

a) How much money will Cyril have after five years?

b) How many years will it take his money to double?

(2)

(6)

2.5 Loans and Simple Interest

Jessica borrows R5 000 from her parents to pay for a sector. They say she can pay them back in five years’ time when she is working and they agree that the interest rate will be 3% per year for the period of the loan.

2.5.1. How much interest will Jessica owe her parents in 5 years’ time?

2.5.3. How much will she have to repay altogether then?

(3)

(2)

Total

[28]

QUESTION 3


Concepts:

Marks

3.1 Comparing and representing numbers in exponential form

a) Write the following in exponential form.

i) 8 =

ii) 81=

b) Complete the following statements by using

i)

ii)

iii) ____

(1)

(1)

(1)

(1)

(1)

3.2 Finding squares up to and cubes up to

Calculate

a)

b)

(2)

(2)

3.3 Square and cube roots

Calculate

a)

b)

(1)

(1)

3.4 Differentiate between and

Is ? Show by calculation.

(3)

3.5 Multiple operations

Calculate

(3)

Total

[ 17]

QUESTION 4

Topic: Integers

Concepts:

Marks

4.1 Counting, ordering and comparing integers

a) Find the numbers represented by A, B, C and D.

-30

-20

B

C

D

A

0

-10

b) Use


vii) –

viii) 1 – 2 + 3 11 – 22 + 13

iii)

(4)

(1)

(1)

(1)

4.2 Count forwards and backwards in integers for any interval

On a particular day the temperature in Johannesburg reads at 5am. At 12 mid-day the temperature reads. At 7pm it reads

a) By how many did the temperature increase from 5am to 12 noon?

b) By how many decrease did the temperature decrease from 12 noon to 7pm?

(1)

(1)

4.3 Add and subtract with integers

Simplify

a)

+

(1)

(3)

4.4 Recognize and use associative property of addition and multiplication for integers

Show by calculation whether each of the following is true or false.

a)

b)

(2)

(2)

4.5 Recognize and use commutative property of addition and multiplication for Integers

Show by calculation whether each of the following is true or false.

a)

b)

(2)

(2)

4.6 Solve problems in contexts involving addition and subtraction of integers

What was the maximum temperature at 4am if it increased by

by 12 mid-day and start decreases by to by 21h00?

(4)

Total

[25]

GRADE 8 TERM 1 WEEK 1: Baseline Assessment

MEMORANDUM

Test 2: Day 2

QUESTION 1

1.1 HCF

F27 = {3 ; 9 ; 27}

F45 = {3 ; 5 ; 9 ; 15 ; 45}

HCF = 9

(3)

1.2 LCM

Determine the LCM of 6, 8 and 12

(4)

1.3 Ratio

a)

Number of girls

(7)

1.4 Rate

10 rolls = 5 ÷ 2 = 2,5

20x = 30 × 5 OR 10 + 10 + 10

20x = 150 = 2,5 + 2,5 + 2,5

x = 7,5 = 7,5 tablespoons

(5)

1.5 Speed, distance & time

(3)

Total

[22]

QUESTION 2


Concepts:

Marks

2.1 Profit and loss

a) Profit

b) Percentage profit

(2)

(2)

2.2 Discount

(4)

2.3 Budgets

Item

Expenses

Percentage

Total Monthly Income

R25000

Mortgage Bond

R7000

a) 28%

Transport

b) R2000

8%

Groceries

R3000

c) 12%

School Fees

R4000

d) 16%

Savings

e) R2500

10%

Surplus

f) R6500

g) 26%

Total

(7)

2.4 Accounts and Simple Interest

a) He will have

b)

(2)

(6)

2.5 Loans and Simple Interest

2.5.1.

2.5.2.

(3)

(2)

Total

[28]

QUESTION 3


Concepts:

Marks

3.1 Comparing and representing numbers in exponential form

a) Write the following in exponential form.

iii)

iv)

c) Complete the following statements by using

iv)

v)

vi)

(1)

(1)

(1)

(1)

(1)

3.2 Finding squares up to and cubes up to

Calculate

(2)

(2)

3.3 Square and cube roots

Calculate

(1)

(1)

3.4 Differentiate between and

No.

(3)

3.5 Multiple operations

Calculate

(3)

Total

[17 ]

QUESTION 4

Topic: Integers

Concepts:

Marks

4.1 Counting, ordering and comparing integers

a)

b)

<

ix) –

x) 1 – 2 + 3 11 – 22 + 13

>

iii)

(4)

(3)

4.2 Count forwards and backwards in integers for any interval

a) Temperature increase

b)Temperature decrease

(1)

(1)

4.3 Add and subtract with integers

+=

(1)

(3)

4.4 Recognize and use associative property of addition and multiplication for integers

a) False

and

b) True

and

(2)

(2)

4.5 Recognize and use commutative property of addition and multiplication for Integers

a) True

5 and

b) True

and

(2)

(2)

4.6 Solve problems in contexts involving addition and subtraction of integers

The maximum temperature was

(4)

Total

[25]

GRADE 8 REVISION EXERCISES Day 3

REMEDIAL WORKSHEET

PATTERNS

Write down the next five terms in each of the sequences below. In easch case, describe the relationship between consecutive terms.

a) 100; 95; 90; 85; __________________________________________________________________________________________________________________________________

b) 0,3; 0,5; 0,7; 0,9; _________________________________________________________________________________________________________

c) 6; 18; 54; 162; __________________________________________________________________________________________________________________________________

d) 1; 3; 6; 10; 15; __________________________________________________________________________________________________________________________________________________________________________________________________________________

e) 20; 31; 42; 53; _________________________________________________________________________________________________________

f) 10; 9,7; 9,4; 9,1; _________________________________________________________________________________________________________

g) 18 000; 1 800; 180; 18; _________________________________________________________________________________________________________

SUBJECT: MATHEMATICS GRADE 8

WEEK 2, LESSON 1

REVISION

RESOURCES

Sasol-Inzalo workbook1(3-10), ruler, pencil, eraser, calculators, notebook. Tablets and DVD(GDE 03 02 2014; GDE 15 01 2014)

PRIOR KNOWLEDGE

· Integers, natural numbers and Whole numbers.

· 4 operations

· Number Sentences

· Exponents

· Decimal, Fractions and Percentages

· Multiples and factors

· Equations

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTAL MATHS)

3min

1. Simplify :

a)

b)

c)

d)

e)

REVIEW AND CORRECTION OF HOMEWORK

0min

No homework

LESSON

PRESENTATION AND CLASSWORK

18min

· The teacher gives the learners activity, and makes learners answers the activity individual .The teacher will move around marking the work done by the learners.

· The teacher addresses the common mistake made by learners on the smart board, white board or Chalkboard.

1. Calculate:

a)

b)

c)

d)

e)

f)

g)

h)

i)

CONSOLIDATION/CONCLUSION

AND OR HOMEWORK

6min

1. Simplify :

a)

b)

c)

d)

e)

REFLECTION

ANSWERS: TERM 1 GRADE 8 WEEK 2 LESSON 1

MENTAL

CLASSWORK

1.

a)

b)

c)

d)

1.

a)

b)

c)

d)

e)

f)

g)

h)

i)


WEEK 2, LESSON 2

REVISION

RESOURCES


PRIOR KNOWLEDGE


· 4 operations

· Number Sentences

· Exponents



· Equations

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTAL MATHS)

3min

1. Simplify:

a)

b)

c)

d)

Page 75 - 77


5min

1.

a)

b)

c)

d)

e)

LESSON


18min



1. Write the following as a percentages:

a)

e)

b)

f )

c)

h)

d)

i)

2. Write the following percentages as a common fractions:

a)

b)

c)

d)

e)

f)

3. How much is sold if 100% is sold


AND OR HOMEWORK

4min

1. Write the following percentages as fractions in their simplest form:

a)

b)

c)

d)

e)

REFLECTION


MENTAL

CLASSWORK

1.

a)

b)

c)

d)

1.

a)

e)

b)

f )

c)

h)

d)

i)

2.

a)

b)

c)

d)

e)

f)

3. How much is sold if 100% is sold = all is sold


WEEK 2, LESSON 3

REVISION

RESOURCES


PRIOR KNOWLEDGE


· 4 operations

· Number Sentences

· Exponents



· Equations

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTAL MATHS)

3min

1. Calculate:

a)

b)

c)

d)

e)

Page 75-77


5min

2.

a)

b)

c)

d)

e)

LESSON


18min



1. Convert the following to decimal fractions:

a)

b)

c)

d)

e)

f)

g)

2. What percentage is:

a)

of 100

b) 5 of 60

c) 8 of 40

d) 15 of 15

e) 90 0f 150

3. Calculate:

a) 25% of 60

b) 80% of 70

c) 20% of 200

d) 10% of 230


AND OR HOMEWORK

4min

1. Calculate :

a) 6% of 1200cars

b) 100% of 560 men

c) 10% of R1,00

d) 12% of 820kg

e) 65% of 2000 jobs

f) 34,5% of R200

g) 19% of R2000

REFLECTION


MENTAL

CLASSWORK

1. Calculate:

a)

b)

c)

d)

e)

1.

a)

b)

c)

d)

e)

f)

g)

2.

a)

of 100 = 20%

b) 5 of 60 = 8,33%

c) 8 of 40 = 20%

d) 15 of 15 = 100%

e) 90 0f 150 = 60%

3. Calculate:

a) 25% of 60 = 15

b) 80% of 70 = 56

c) 20% of 200 = 40

d) 10% of 230 = 23


WEEK 2, LESSON 4

REVISION

RESOURCES

Sasol-Inzalo workbook1 (3-10), ruler, pencil, eraser, calculators, notebook. Tablets and DVD(GDE 03 02 2014; GDE 15 01 2014)

PRIOR KNOWLEDGE


· 4 operations

· Number Sentences

· Exponents



· Equations

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTAL MATHS)

3min

1. Calculate:

a)

b)

c)

d)


5min

1.

a) 6% of 1200cars = 72 cars

b) 100% of 560 men = 560 men

c) 10% of R1,00 = R0,10

d) 12% of 820kg = 98,4 kg

e) 65% of 2000 jobs = 1300jobs

f) 34,5% of R200 = R69

g) 19% of R2000 = R380

LESSON


18min



·

1. Simplify:

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

m)

n)


AND OR HOMEWORK

4min

1.

Simplify:a)

b)

c)

d) (+4) – (-5)

e)

f)

g)

REFLECTION


MENTAL

CLASSWORK

1.

a)

b)

c)

d)

1. Simplify:

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

m)

n)


WEEK 2, LESSON 5

REVISION

RESOURCES

Sasol-Inzalo workbook1 (3-10), ruler, pencil, eraser, calculators, notebook. Tablets and DVD(GDE 03 02 2014; GDE 15 01 2014)

PRIOR KNOWLEDGE


· 4 operations

· Number Sentences

· Exponents



COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTAL MATHS)

3min

1. Simplify:

a)

b)

c)


5min

1. Calculate the following:

a)

b)

c)

d)

= 74

e)

f)

LESSON


18min



2. Write the following as a percentages:

e)

e)

f)

f )

g)

h)

h)

i)

3. Write the following percentages as a common fractions:

g)

h)

i)

j)

k)

l)

4. How much is sold if 100% is sold


AND OR HOMEWORK

4min


a)

b)

c)

d)

e)

REFLECTION


MENTAL

CLASSWORK

1.

a)

b)

c)

1.

a)

e)

b)

f )

c)

h)

d)

i)

2.

a)

b)

c)

d)

e)

f)

How much is sold if 100% is sold = all is sold


WEEK 2, LESSON 6

REVISION

RESOURCES


PRIOR KNOWLEDGE


· 4 operations

· Number Sentences

· Exponents



COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTAL MATHS)

3min

1. Calculate

a)

b)

c)

d)

Page 75-77


5min


a)

b)

c)

d)

e)

LESSON


18min



1. Convert the following to decimal fractions:

a)

b)

c)

d)

e)

f)

g)


a)

of 100

b) 5 of 60

c) 8 of 40

d) 15 of 15

e) 90 0f 150

3. Calculate:

a) 25% of 60

b) 80% of 70

c) 20% of 200

d) 10% of 230


AND OR HOMEWORK

4min

2. Calculate :

a) 6% of 1200cars

b) 100% of 560 men

c) 10% of R1,00

d) 12% of 820kg

e) 65% of 2000 jobs

f) 34,5% of R200

g) 19% of R2000

REFLECTION


MENTAL

CLASSWORK

1. Calculate:

a)

b)

c)

d)

e)

1.

a)

b)

c)

d)

e)

f)

g)

2.

a)

of 100 = 20%

b) 5 of 60 = 8,33%

c) 8 of 40 = 20%

d) 15 of 15 = 100%

e) 90 0f 150 = 60%

3. Calculate:

a) 25% of 60 = 15

b) 80% of 70 = 56

c) 20% of 200 = 40

d) 10% of 230 = 23


WEEK 2, LESSON 7

REVISION

RESOURCES


PRIOR KNOWLEDGE


· 4 operations

· Number Sentences

· Exponents



· Equations

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTAL MATHS)

3min

1. Calculate:

a)

b)

c)

d)

Page 75-77


5min

LESSON


18min

The teacher gives the learners activity, and makes learners answers the activity individual .The teacher will move around marking the work done by the learners.

The teacher addresses the common mistake made by learners on the smart board, white board or Chalkboard.

1. Calculate:

a) 12% of R8 000

b) 18% of R24 000

2. Calculate the amount of profit in each of the following cases. The information is about a car dealer who buys and sells used vehicles.

a) A car is bought for R40 000 and sold it at a profit R52 000.

b) A small truck is bought for R100 000 and sold at a profit of 28%.

c) A bakkie is bought for R120 000 and sold at a profit of 30%.


AND OR HOMEWORK

4min

1. In each case below, calculate how much interest must be paid.

(a) An amount of R6 000 is borrowed for 1 year at 9% interest.

(b) An amount of R21 000 is borrowed for 3 years at 11% interest per year.

(c) An amount of R45 000 is borrowed for 10 years at 12% interest per year.

REFLECTION


MENTAL

CLASSWORK

1. Calculate:

is

is

1. Calculate:

a) 12% of R8 000 = R960

b) 18% of R24 000 = R4 320

2. a) Profit = R52 000 – R40 000

= R12 000

b) Profit =

= R28 000

c) Profit =

= R36 000


WEEK 2, LESSON 8&9

REVISION

RESOURCES


PRIOR KNOWLEDGE


· 4 operations

· Number Sentences

· Exponents



· Equations

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTAL MATHS)

3min

Calculate

1. 10% of 10

2. 20% of 20

3. 30% of 30

4. 40% of 40

5. 50% of 50

Page 75-77


5min

1. a) Interest

LESSON


20min



1. Smart Outfitters is offering a 50% discount on a pair of jeans that was selling at R150. How much will a customer have to pay for the jeans?

2. Kenny buys earphones for R30 each and sells them for R55 each. Calculate his profit percentage. Round off your answer to one decimal place.

3. Mr. Molepo bought a house for R250000 and sold it at a loss of 10%. Calculate the selling price of the house.

4. Calculate the amount that will be in the bank after 4 years if R2 500 was invested at 9% p.a. simple interest.


AND OR HOMEWORK

2min

1. After using mrbartonmaths.com, your mark in your maths test went from 34 to 46. What percentage increase is this?

2.

One of the country’s Municipalities serves about million people. Of these people, 10% receives drinking water by tanker. How many people is this?

3. A pair of jeans marked at R250-00 is sold at a discount of 13%. Determine the selling price.

REFLECTION

ANSWERS: TERM 1 GRADE 8 WEEK 2 LESSON 8&9

MENTAL

CLASSWORK

HOMEWORK

Calculate

1. 10% of 10 = 1

2. 20% of 20 = 4

3. 30% of 30 = 9

4. 40% of 40 = 16

5. 50% of 50 = 25

1.

=

= R75

2. Profit % =

=

= 45,5%

3.

4.

1. Percentage change

2. million

million

people

3. Selling Price =


WEEK 3, LESSON 1

TOPIC: WHOLE NUMBERS

CONCEPTS AND SKILLS TO BE ACHIEVED

By the end of the lesson, learners should know and be able to:

· Determine Multiples,

· Factors and

· prime factors

RESOURCES

Sasol-Inzalo workbook 1(18-24), ruler, pencil, eraser, calculators, notebook. Tablets and DVDs(GDE 15 01 2014; GDE 20 01 2014)

PRIOR KNOWLEDGE

· Numbers

· Factors

· Prime numbers

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTALMATHS)

3min

1. Define the following termsa. Multiple?

b. Factors

c. Prime numbers

Page 75-77


NO HOMEWORK FIRST LESSON

LESSON

PRESENTATION/DEVELOPMENT

10min

The teacher explains the multiples and factors and prime factors.

A multiple is the product of two natural numbers e.g. 8 × 1

Multiples of 8 = {8; 16; 24; … }

A factor is a number that divides exactly into a whole number with no remainder e.g. 8 ÷ 2

Factors of 12 = { 1; 2; 3; 4; 6; 12}

When 12 is divided by any one of its factors there is no remainder

Prime Factors are factors that are prime .Example (2,3 ,5 ………..)

CLASSWORK

12min

1. List factors of the following sets of numbers.

a. 36

b. 18

c. 50

d. 49

e. 100

2. List the prime factors of the following set of numbers.

a. 20

b. 18

c. 50

d. 100

3. List the multiples of the following set of numbers.

a. 20

b. 18

c. 50

d. 100


AND OR HOMEWORK

5min

1. Write the first 10 Multiples of :

a) 2

b) 3

c) 4

d) 5

e) 6

f) 7

g) 8

h) 9

REFLECTION


MENTAL

CLASSWORK

1. Define the following terms

a) Multiple?

b) Factors

c) Prime numbers

1.

a. 36 = ( 1;2;3;4;6;9;12;18;36)

b. 18 = (1;2;3;6;9;18)

c. 50 = (1;2;5;10;25;50)

d. 49 = (1;7;49)

e. 100=1;2;4;5;10;20;25;50;10)

2.

a. 20 = (2)

b. 18 = (2;3)

c. 50 = (2;5)

d. 100 = (2;5)

3. List the first 4 multiples of the following set of numbers.

a. 20 = (20;40;60 and 80)

b. 18 = (18:36;54 and 72)

c. 50 = (50;100;150 and 200)

d. 100 = (100;200;300 and 400


WEEK 3, LESSON 2




· Determine prime factors of numbers to at least 3-digit whole numbers.

· Determine the LCM of numbers to at least 3-digit whole numbers,

by inspection or factorization.

RESOURCES


PRIOR KNOWLEDGE

· Numbers

· Factors

· Prime numbers

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTAL MATHS)

3min

1. List the factors of 12.

2. List the first 3 multiples of 5

Page 75-77


5min

2. Write the first 6 Multiples of :

a) 2 = (2;4;6;8;10;12)

b) 3 = (3;6;9;12;15;18;21)

c) 4 = (4;8;12;16;20;24)

d) 5 = (5;10;15;20;25;30)

e) 6 = (6;12;18;24;30;36)

f) 7 = (7;14;21;28;35;42)

g) 8 = (8;16;24;32;48;48)

h) 9 = (9;18;27;36;45;54)

LESSON


8min

The teacher asks learners to write down the factors of the following numbers: 2; 5; 7; 11

What do you notice?

Prime numbers are those numbers that have two different factors: 1 and itself

i.e. 2 =1 and 2; 5 =1 and 5 etc.

Numbers that have more than two factors are called the composite numbers: i.e. 6 =1;2;3;6

The prime factors of a number are factors that are prime numbers i.e. the prime factors of 60

2 ×2 ×3 ×5

Discussion question: If I ask you to list factors of 12 and prime factors of 12 would you give the same answers. Explain your answer. Expected answers prime factors are prime numbers and factors may include prime factors and composite numbers.

i) Factors of 12 = 1; 2; 3; 4; 6 and 12

ii) Prime factors of 12 = 2; 3

CLASSWORK

10min

1. List the prime factors of the following set of numbers:

a. 2

b. 4

c. 6

d. 11

e. 19

f. 26

g. 51

h. 60

i. 75

j. 100

k. 121

l. 150

m. 1000


AND OR HOMEWORK

4min

1. Determine the LCM of the following numbers:

a. 5 and 7

b. 6 and 4

c. 10 and 25

d. 3 and 4

e. 15 and 10

REFLECTION


MENTAL

CLASSWORK

1. 12 = (1;2;3;4;6;12)

2. 5 = (5;10 and 15)

1. List the prime factors of the following set of numbers:

a. 2 = (2)

b. 4 = (2)

c. 6 = (2,3)

d. 11 =(11)

e. 19 = (19)

f. 26 = (2, 13 )

g. 51 = (3, 17,51)

h. 60 = (2, 3 )

i. 75 = (3,5)

j. 100 = (2,5)

k. 121 = (11)

l. 150 = (3,5)

m. 1000 = (2,5)


WEEK 3, LESSON 3




· Determine the LCM of numbers to at least 3-digit whole numbers, by inspection or factorization

· Determine HCF of numbers

RESOURCES


PRIOR KNOWLEDGE

· Numbers

· Factors

· Prime numbers

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTAL MATHS)

3min

1. List the factors of:

a. 100

b. 75

Page 75-77


5min

1.

a. 5 and 7 = 35

b. 6 and 4 = 24

c. 10 and 25 = 50

d. 3 and 4 = 12

e. 15 and 10 = 30

LESSON


8min

The teachers remind learners on Highest Common Factors (HCF) and Lowest Common Multiple (LCM).

Example 1:

Highest common factor( HCF): The biggest number that will divide exactly (remainder is zero) into all the numbers in question e.g.

factors of 12: 1, 2, 3, 4, 6, 12

12 = 2 ×2 ×3

factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 OR

30 = 2 × 3 ×5

Common factors are 1, 2 ,3 and 6

HCF = 2 ×3

HCF is 6.

= 6

Example 2:

Lowest common multiple (LCM): The smallest number that can be divided by all the numbers in question with remainder equal to zero

e.g.

multiples of 6: 6; 12; 18 ;24 ... 6 = 2 × 3

multiples of 8; 8; 16; 24; 32; … 8 = 2 ×2 ×2

common multiplies of 6&8: 24; 48; OR

= 2 ×2 ×2×3

=24

The LCM is 24.

CLASSWORK

10min

Find the HCF and LCM of the given numbers

1. 36 and 48

2. 16 and 18

3. 24 and 50


AND OR HOMEWORK

4min

Find the HCF of the given numbers

a. 100 and 75

b. 125 and 500

c. 50 and 75

d. 35 and 80

e. 12 and 48

REFLECTION


MENTAL

CLASSWORK

1.

a. 100 = (1;2;4;5;10;25;50;100)

b. 75 = (1;3;5;15;25)

Find the HCF and LCM of the given numbers

HCF

LCM

36 and 48

12

144

16 and 18

2

288

24 and 50

2

600


WEEK 3, LESSON 4




· Determine the HCF of numbers to at least 3-digit whole numbers, by inspection or factorization.

RESOURCES


PRIOR KNOWLEDGE

· Numbers

· Factors

· Prime numbers

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTALMATHS)

1. List the HCF of the given numbers

a. 2 and 3

b. 4 and 5

c. 7 and 10

d. 14 and 19

e. 51 and 21

Page 75-77


1.

a. 100 and 75

b. 125 and 500

c. 50 and 75

d. 35 and 80

e. 12 and 48

LESSON


AND CLASSWORK

The teacher allows learners to pair themselves and the following activity is given to them.

1. Find the HCF of the given set:

a. 1 and 2

b. 3 and 7

c. 5 and 20

d. 14 and 21

e. 28 and 42

f. 27 and 63

g. 39 and 78

h. 28 and 126

i. 34 and 85

j. 20 and 40

k. 10 and 70


AND OR HOMEWORK

1. Find the LCM of the given set:

a. 1 and 3

b. 2 and 7

c. 10 and 12

d. 11 and 5

e. 7 and 5

f. 6 and 7

REFLECTION


MENTAL

CLASSWORK

a. 2 and 3 = 1

b. 4 and 5 = 1

c. 7 and 10 = 1

d. 14 and 19 = 1

e. 51 and 21 = 1

1. Find the HCF of the given set:

a. 1 and 2 = 1

b. 3 and 7 = 1

c. 5 and 20 = 5

d. 14 and 21 = 7

e. 28 and 42 = 7

f. 27 and 63 = 9

g. 39 and 78 = 13

h. 28 and 126 = 14

i. 34 and 85 = 17

j. 20 and 40 = 5

k. 10 and 70 = 5


WEEK 3, LESSON 5




· Solve problems involving whole numbers, including:

· comparing two or more quantities of the same kind (ratio)

· comparing two quantities of different kinds (rate)

RESOURCES


PRIOR KNOWLEDGE

· Numbers

· Fractions

· Ratio

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTALMATHS)

3min

1. Simplify

a. of 40

b. Simplify to lowest terms


5min

a. 1 and 3 = 3

b. 2 and 7 = 14

c. 10 and 12 = 60

d. 11 and 5 = 55

e. 7 and 5 = 35

f. 6 and 7 = 42

LESSON


8min

Teacher begins by creating a scenario: how many boys do we have in this class?

How many girls?

How can we write the number of girls to number of boys as a ratio?

Example 1: Ratio

Find simplest form of ratio 27 min to 1 hours convert to same unit 27:90 then divide by a common factor 9

3:10

Example 2

Share 60 apples among three people in the ratio 1:2:3

How many apples did each one get?

Find the total ratio=6

Express each share as a fraction of total ratio:

First shareX =10

Second share X =20

Third share =30

Example 2 Rate

You are travelling at 60 km/hr. How much distance will you cover 3 hours if you travel at that rate?

Distance = time x speed therefore to calculate any of the values you make any of the values the subject of the formula. Example here is

Distance =time x speed =60 x 3 = 180km

If you cover a distance of 450km at a speed of 90 km/hr. how much time would you take?

CLASSWORK

8min

1. Calculate distance travelled at a speed of 80km/hr in 5hrs

2. Share R80 in the ratio 3:5

3. 5 oranges cost R60 what the amount needed to buy 21 oranges?


AND OR HOMEWORK

6min

1. Find the simplest form of each of these ratios 8:12

2. Increase 40 in the ratio 2 : 3

REFLECTION


MENTAL

CLASSWORK

1. 0f 40

20

2. Simplify to its simplest form

1. Calculate distance travelled at a speed of 80km/hr.in 5 hrs.

Speed 80km/hr., time 5 hrs. Distance ?

D 16km

2. Share R80 in the ratio 3:5 3 5 8

80: 80

30: 50

3. 5 oranges cost R60 what the amount needed to buy 21 oranges?

oranges R60

R12 each

R12 21


WEEK 3, LESSON 6




· Solve problems involving whole numbers, including:

· sharing in a given ratio where the whole is given

· increasing or decreasing of a number in a given ratio

RESOURCES


PRIOR KNOWLEDGE

· Numbers

· Decimals

· Fractions

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTALMATHS)

3min

1.

2. as a percentage

3. write as simple ratio

Page 75-77


4min

1.

a) 6% of 1200cars = 72 cars

b) 100% of 560 men = 560 men

c) 10% of R1,00 = R0,10

d) 12% of 820kg = 98,4 kg

e) 65% of 2000 jobs = 1300jobs

f) 34,5% of R200 = R69

g) 19% of R2000 = R380

LESSON


10min

The teacher illustrate more on ratio giving the following example

To increase 40 in the ratio means that the 40 represents two parts and must be increased so that the new number represents 3 parts.

If 40 represent two parts, 20 represents 1 part.

The increased number will therefore be 20 3 = 60.

(a) Increase 56 in the ratio 2: 3 28 84

(b) Decrease 72 in the ratio 4: 3 18 3 54

CLASSWORK

9min

Calculate the following questions

1. Which ratio is the smallest: 1: 5 or 1: 6?

2. Increase a mark of 28% in the ratio 3: 4.

3.

4. Determine the value of :

5. Burger meals are available in 3 sizes: regular, large and extra-large. They are ordered in the ratio 2: 3: 5. Out of 36 ordered how many are extra-large?


AND OR HOMEWORK

4min


a) 20 of 100

b) 5 of 60

c) 8 of 40

d) 15 of 15

e) 90 0f 150

2. Calculate:

a) 25% of 60

b) 80% of 70

c) 20% of 200

d) 10% of 230

REFLECTION


MENTAL

CLASSWORK

1. 5% of 45

2.25

2.40/60 as a percentage 100

66.7%

3. 30:40 write as simple ratio

1. Which ratio is the smallest: 1: 5 or 1: 6?

0.2

0.16

is the smallest

2. Increase a mark of 28% in the ratio

3 : 4 9.3 4

37.3%

3. Share 90 fruits in the ratio 2:3 90: 90

36:54


WEEK 3, LESSON 7



By the end of the lesson, learners should know and be able to: : Percentages and decimal fractions in financial contexts such as:

· profit

· loss

· discount

· VAT

RESOURCES

Sasol-Inzalo workbook 1(26 - 28), ruler, pencil, eraser, calculators, notebook. Tablets and DVD(GDE 22 01 2014)

PRIOR KNOWLEDGE

· Numbers

· Fractions

· Percentages

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTALMATHS)

3min

1.

2. Reduce

3. 20c as a percentage of R2

4. 10400 12

5. Calculate 8% of 10 400

Page 75-77


5min

1. 8:12 2:3

2. Increase 40 in the ratio 2 : 3

4. = 60

LESSON


8min

My friend ordered 100 bananas at R1 each. He sold them at school during break at R3 a banana.

1. How much did he pay to order the 100 bananas?

2. How much did he get after selling the hundred bananas?

3. How much money did he gain? What word do we use for the amount he gained?

4. How do we calculate the gain /profit?

5. Calculate the % profit?

6. Calculate the VAT he has to pay?

7. If he buys 200 bananas he will get a discount of 15%, how much is the discount?

Profit / loss = selling price – cost price

Or

Profit / loss = Income - all expenses

If the answers are positive you have made a profit

If the answers are negative you have made a loss

CLASSWORK

10min

1. Sam’s Cafe received R600 yesterday, but expenses such as wages, food and electricity came to R450.

a) Did Sam make a profit or a loss?

b) Calculate the profit or loss for yesterday

c) What was % profit or loss?

2. A worker earns R21000.00 per month, 25% goes to the deductions, 51% goes to the expenses, 5% goes to the savings, 10% goes to his church

Calculate:

1. His salary after deductions

2. How much money goes to his expenses

3. How much goes to his church

4. How much is his salary per year


AND OR HOMEWORK

4min

1. Calculate :

a) 6% of 1200cars

b) 100% of 560 men

c) 10% of R1,00

d) 12% of 820kg

e) 65% of 2000 jobs

f) 34,5% of R200

g) 19% of R2000

REFLECTION


MENTAL

CLASSWORK

1.

2. Reduce

3. 20c as a percentage of R2

4. 10400 12

5. Calculate 8% of 10 400

1.


Profit


Profit SP-BP

R600 R450

R150

c) What was % profit or loss

100

= 33.3%

1. His salary after deductions

R21000 R5 250

2. How much money goes to his

expenses

R21000 R10 710

3. How much goes to his church

R21000 R2 100

4. How much is his salary per year


WEEK 3, LESSON 8



By the end of the lesson, learners should know and be able to: Use percentages and decimal fractions in financial contexts such as:

· budgets,

· accounts,

· loans,

RESOURCES

Sasol-Inzalo workbook 1(26 - 28), ruler, pencil, eraser, calculators, notebook. Tablets and DVD(GDE 22 01 2014)

PRIOR KNOWLEDGE

· Numbers

· Percentages

· Decimals

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTALMATHS)

3min

Calculate

1. 20% of R4000.00

2. 15% of R2500.00

3. 18% of R3000.00

Page 75-77


4min

1.

a)

of 100 = 20%

b) 5 of 60 = 8,33%

c) 8 of 40 = 20%

d) 15 of 15 = 100%

e) 90 0f 150 = 60%

2.

a) 25% of 60 = 15

b) 80% of 70 = 56

c) 20% of 200 = 40

d) 10% of 230 = 23

LESSON


9min

What happens when you borrow money: You pay back with interest.

Why do we take loans? To buy houses ,cars and so on

We are going to discuss how simple interest is calculated

Example: I applied for a loan of R8000 to buy a television set, the simple interest was 10 % per annum for two years.

QUESTION1

(i) What is the rate?

(ii) What is the time I should spend paying the loan?

(iii) How is simple interest calculated?

A formula is used simple interest (SI) = tell me what these words stand for

P=amount borrowed t= time r = rate

CLASSWORK

10min

1. Musa buys a new radio for R125 excluding VAT. He pays cash and gets a 5% cash discount. How much will he pay in total including VAT?

2. Peter buys 10 apples at R2.50 each. He sells each apple for R4.00. How much profit does he make if he sells 50% of his apples at full price and the rest at a 25% discount?

3. You receive R300 pocket money every month. You want to go to a movie once a week. The entrance fee is R30 and a cold drink is R8. The taxi fare is R10. Will you be to go every week? Compile a budget for the month(4weeks)


AND OR HOMEWORK

4min

1. 1. Ann buys a phone for R350 excluding VAT. How much VAT will she pay .How much will she pay in total.

2. Suzy borrowed R4000 from a bank for a period of two years and six months at simple annual interest rate of 4, 7%. How much must she repay at the end of the time period.

REFLECTION


MENTAL

CLASSWORK

1. R800

2. R375

3. R540

1. Discount

Amount paid including VAT =

= R135, 375

2. Cost price = R2,50 10apples

= R25

Selling price of 5 apple (54) =R20

Selling price of Discounted one (5 = R15

Total selling amount = R35

Hence the Profit =R35 – R25 = R10

3.

fee

R30

Drink

R8

Tax fee

R10

Total

R48

Total for the month = = R192

Yes I will make it.

Page 177 of 344

GRADE 8 MATHEMATICS – TERM 1 LESSON PLANS

GRADE 8 TERM 1 WEEK3 LESSON 9: Total [25]

WEEKLY TEST Time 30minutes

Content Area:


· LCM and HCF

· Ratio and Rate

· Maths of Finance

Concepts:

Marks

1. List factors of the following sets of numbers.

a. 36

b. 18

c. 50

d. 49

e. 100

(1)

(1)

(1)

(1)

(1)


a. 20

b. 18

c. 50

d. 100

(2)

(2)

(2)

(2)

3. What is the HCF for:

a. 15 and 45

b. 10n and 20

c. 2 and 6

d. 16 and 64

e. 21 and 63

f. 24 and 36

g. 18 and 21

(1)

(1)

(1)

(1)

(1)

(1)

(1)

4. Sam’s Cafe received R600 yesterday, but expenses such as wages, food and electricity came to R450.



c) What was % profit or loss?

(1)

(2)

(2)

Total

(25)

MEMORANDUM Total [25]

WEEKLY TEST Time 30minutes

Content Area:


· LCM and HCF

· Ratio and Rate

· Maths of Finance

Concepts:

Marks

1.

a. 36 = (1;2;3;4;6;9;12;18;36)

b. 18 = (1; 2;3;6;9;18)

c. 50 = (1;2;4;10;25;50)

d. 49 = (1;7;49)

e. 100 = (1;2;4;5;10;25;50;100)

(1)

(1)

(1)

(1)

(1)


a. 20 = (20;40;60;80)

b. 18 = (18:36;54;72)

c. 50 = (50;100;150)

d. 100 = (100;200;300 ;400)

(2)

(2)

(2)

(2)

3. What is the HCF for:

a. 15 and 45 = 15

b. 10 and 20 = 10

c. 2 and 6 = 2

d. 16 and 64 = 16

e. 21 and 63 = 21

f. 24 and 36 = 12

g. 18 and 21 = 3

(1)

(1)

(1)

(1)

(1)

(1)

(1)

4.

a. Did Sam make a profit or a loss?

Profit

b. Calculate the profit or loss for yesterday

Profit SP-BP

R600 R450

R150

c. What was % profit or loss

100

= 33.3%

(1)

(2)

(2)

Total

(25)

SUBJECT: MATHEMATICS GRADE 8 - Term 1

WEEK 4 LESSON 1

TOPIC: Number operations and relationships - Whole numbers


Simple interest

Solve problems that involve whole numbers, percentages and decimal fractions in financial contexts such as:

· Simple interest

· Hire Purchase

· Exchange rates

RESOURCES

Sasol-Inzalo workbook 1(26 - 28), ruler, pencil, eraser, calculators, notebook. Tablets and

DVD(GDE 22 01 2014)

PRIOR KNOWLEDGE

Percentages, fractions, budget

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

MENTAL MATHS

3 min

Calculate

1. 20% of R4000.00

2. 15% of R2500.00

3. 18% of R3000.00

Page 75-77

HOMEWORK

5 min

Calculation of budget

KEYWORDS:

Budget, accounts, loans, Exchange rates, rand, currency and dollar

LESSON DEVELOPMENT

20 min

What happens when you borrow money: You pay back with interest.

Why do we take loans? To buy houses ,cars and so on

We are going to discuss how simple interest is calculated

Example: I applied for a loan of R8000 to buy a television set, the simple interest was 10 % per annum for two years.

QUESTION1

(i) What is the rate?

(ii) What is the time I should spend paying the loan?

(iii) How is simple interest calculated?

A formula is used simple interest (SI) = tell me what these words stand for

P=amount borrowed/invested or initial amount

t= time in years, r = rate

QUESTION 2

From the above example

(i) What is the simple interest charged

(ii) What is the final amount to be paid

SI = = = 80 10 2=R1600

Amount to be paid its P+SI= amount =8000+1600= R9600

CLASSWORK

My friend took a loan to buy a car for R 6 500 and has to pay back a loan in 2 years at 12% interest.

Calculate

1. Simple interest

2. Final amount to be paid.

Recap

2 min

Explain the formula for calculating Si and how to get final amount

HOMEWORK ACTIVITIES

Andile wants to buy a flat screen. He takes a loan of R12500 at 12% interest per annum for 2 years.

a) Calculate Si

b) Final amount to be paid.

LESSON REFLECTION

ANSWERS: TERM1 GRADE 8 WEEK 4 LESSON 1

Mental Maths

Classwork

Homework

1. 20% of R4000.00 R4000

R800.00

2. 15% of R2500.00 R2500

R375.00

3. 18% of R3000.00 R3000

R540.00

My friend took a loan to buy a car for

R 6 500 and has to pay back a loan in 2 years at 12% interest.

Calculate

1. Simple interest

SI = = = R1560

2. Final amount to be paid.

Amount P+SI 6500+1560 = R8060

Andile wants to buy a flat screen. He takes a loan of R12500 @ 12% per annum for 2 years.

a)Calculate Si

SI = = = R3000


Amount P+SI 12500+3000 = R15500.00


WEEK 4 LESSON 2

TOPIC: Number operations and relationships - Whole numbers


Exchange rate

Solve problems that involve whole numbers, percentages and decimal fractions in financial contexts such as:

· Exchange rates

RESOURCES

Sasol-Inzalo workbook 1(26 - 28), ruler, pencil, eraser, calculators, notebook. Tablets and

DVD(GDE 22 01 2014)

PRIOR KNOWLEDGE

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

MENTAL MATHS

3 min

Calculate

If I have a R100 pocket money to use in Botswana and the exchange rate is:

1 pula R1,35

1. How much is 1 pula in rands?




5. How much money do I have in pula?

Page 75-77

HOMEWORK

5 min

Andile wants to buy a flat screen. He takes a loan of R12500 at 12% interest per annum for 2 years.

a)Calculate Si

SI = = = R3000


Amount P+SI 12500+3000 = R15500.00

KEYWORDS:

Budget, accounts, loans Exchange rates, rand, currency and dollar

LESSON DEVELOPMENT

20 min

Exchange rate

Read the extract of exchange rates below

When we visit another country we have to exchange our rands for the currency that is used in that country, for example:

· If we go to Britain, we must get British pounds (£)

· If we go to America, we must get US dollars ($)

· If we go to most countries in Europe, we must get Euros (€)

· I we go to Japan, we must get Japanese Yen (¥) and so on

The currencies of the different countries are not worth the same amount. That means a $1 is not the same as R1. That is why we need exchange rates. Exchange rates changes every day.

On 8 June 2012 some of the exchange rates were:

US$1=R8,4661

£1=R 12,9772

€1=R 10,5563

Aus$1= R 8,33502

¥1= R 0,106737

1 Botswana Pula=R 1,0812

1 Malawi Kwacha= R 0,03111

1 Zambian Kwacha= R 0,001592

1 Swiss franc=R 8,78813

That means if we wanted to buy US$1,we would have paid R 8,47.we can also say that it costR8,47 per dollar ( R 8,47/dollar)

The American dollar is stronger than the rand. We pay several rands for $1.

The Japanese is weaker than the rand. This means that we have to pay less than R1 for Japanese yen

Converting Currencies

If the exchange rate is given as 1 unit = R…, then we can:

· Convert from rand to any other currency by dividing

· Convert from any other currency to rand by multiplying

Example 1

To Convert $1000 to a South African Rand. We multiply by the rate.

R8,4661X $1000 = R8466,10

To convert from R 2500 to British Pound Steeling. We divide.= £236.83

The teacher must read and discuss the extract about the exchange rates through asking learners probing questions.

CLASSWORK

Use the previous exchange rates to do the following calculations:

1.Convert R12000 Australian $

2. Convert 200 000 $ to rands

Recap

2 min

Explain the formula for calculating Si and how to get final amount

HOMEWORK ACTIVITIES

1) Convert R10 000 Zambian Kwacha to Rands

2) Convert R25400 to Swiss franc

LESSON REFLECTION


Mental Maths

Classwork

Homework

1) 1 pula R1.35

2) 2 pula R2.70

3) 10 pula R13.50

4) 100 pula R135

5)

1. Convert R12 000 Australian $

1 Australian $ R8.33502

R12 000

1440.22 Australian $ R12 000

2. Convert 200 000 US $ to rands

1$ R8.4661

200 000$

R8.4661 200 000US$

/ 200 000 US $ R1 693 22

1. Convert R10 000 Zambian

Kwacha to rands

1 Zambian kwacha R0.001592

R10 000

6 281 407 ZK

2. Convert R25 400 to Swiss franc

1SK R8.78813

R25 400

2845 SK


WEEK 4 LESSON 3

TOPIC: Number operations and relationships – Exponents


· Laws of the exponents

· Establish general laws of exponents, limited to: natural number exponents

·

RESOURCES

Sasol-Inzalo workbook 1(53-73), ruler, pencil, eraser, calculators, notebook. Tablets and DVDs

(GDE 12 02 2014; GDE 17 02 2014; GDE 19 02 2014)

PRIOR KNOWLEDGE

Squares, cubes, representing the numbers in an exponential form, expanding the exponents.

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

MENTAL MATHS

3 min

Simplify:

1)

2)

3)

Page 81-83

HOMEWORK

5 min

Revise previous questions

1. Convert R10 000 Zambian

Kwacha to rands

1 Zambian kwacha R0.001592

R10 000

6 281 407 ZK

2. Convert R25 400 to Swiss franc

1SK R8.78813

R25 400

2845 SK

KEYWORDS:

Base, exponent, square root and power

LESSON DEVELOPMENT

20 min

The teacher demonstrate how to multiply as shown below

LAW 1: MULTIPLICATION

When you multiply the powers of the same base, you add the exponents:

m × n = m + n

CLASSWORK

Simplify:

1. a8 a =

2. 53 52 =

3. 42 40 =

4. a² a²=

Recap

2 min

When you multiply the powers of the same base, you add the exponents:

HOMEWORK ACTIVITIES

1. 42 41=

2. p p=

3. w³ w² =

LESSON REFLECTION


Mental Maths

Topic

Homework

1.

2.

3.

1. a8 × a

2. 53 × 52

3. 42 40

4. a² a²

1. 42 41

2.

3. w³ w² =


WEEK 4 LESSON 4



· Laws of the exponents

· Establish general laws of exponents, limited to: natural number exponents

· , if m > n

RESOURCES

Sasol-Inzalo workbook 1(53-73), ruler, pencil, eraser, calculators, notebook. Tablets and DVDs(GDE 12 02 2014; GDE 17 02 2014; GDE 19 02 2014)

PRIOR KNOWLEDGE

Squares, cubes, representing the numbers in an exponential form, expanding the exponents, first law of the exponents.

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

MENTAL MATHS

3 min

Simplify:

1.

2.

3.

Page 81-83

HOMEWORK

5 min

Revise previous questions

1. 42 41

2.

3. w³ w² =

KEYWORDS:

Base, exponent, square root and power

LESSON DEVELOPMENT

20 min

The teacher demonstrate how to multiply as shown below

LAW 2: DIVISION

When you divide the powers of the same base, you subtract the exponents:

m n = m - n

Classwork

Simplify:

1. a8 a3

2. 23 22

3. 32 32

4. a² a

Recap

2 min

When you divide the powers of the same base, you subtract the exponents:

HOMEWORK ACTIVITIES

1. 65 62=

2. =

3. 3³ 3² =

LESSON REFLECTION


Mental Maths

Classwork

Homework

1.

2.

3.

1. a8 a3

2. 23 22

3. 32 32 = 1

4. a² a

1. 65 62=

2.

3. 3³ 3² =


WEEK 4 LESSON 5



Laws of the exponents

Establish general laws of exponents, limited to:

natural number exponents

· n

· (a n n

·

RESOURCES


PRIOR KNOWLEDGE

Squares, cubes, representing the numbers in an exponential form, expanding the exponents, firs and the second law of the exponents.

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

MENTAL MATHS

3 min

Simplify the following:

1.

2. n

3.

Page 81-83

HOMEWORK

5 min

1. 65 62

2.

3. 3³ 3² =

KEYWORDS:

Base, exponent and power

LESSON DEVELOPMENT

AND

CLASSWORK

20 min

The teacher will do the calculations on the board, by asking learners probing questions:

Law 3: n

2

Law 4: (a n n

(2 3)4

Definition:

or 1

CLASSWORK


1. 3

2. (6 2

4.

Recap

2 min

Laws of exponents

HOMEWORK ACTIVITIES


1. 3

2. (a 4

LESSON REFLECTION


Mental Maths

Topic

Homework

1.

2. n

3.

1. 3

2. (6 2 or or 576

4. 1

1. 3

2. (a 4

1


WEEK 4 LESSON 6



Laws of the exponents

Establish general laws of exponents, limited to:

natural number exponents

· n

· (a n n

·

RESOURCES


PRIOR KNOWLEDGE


COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

MENTAL MATHS

3 min


1.

2. 5

3.

Page 81-83

HOMEWORK

5 min

1. 3

2. (a 4

1

KEYWORDS:

Base, exponent and power

LESSON DEVELOPMENT

AND

CLASSWORK

20 min

Sometimes people had to deal with very big/very small numbers e.g. light travels at 299800 km/s.

It is more convenient to write such numbers in a short way, scientific notation provides just that.

· Place a decimal comma after the first non-zero digits

· Count how many places the decimal comma was moved to get there

· If the decimal comma was moved to the left times then you take the number from step 1 and multiply it by

Example 1: 420000

4,2

CLASSWORK

A. Simplify the following:

1. 3

2. (5 4

4.

5. 2

6. 2

7. ( 4

B. Write the squares and the cubes of the following: a) 1 b) 4 c) 6

C. Write the following in scientific notation:

1) 630000000

Recap

2 min

Laws of exponents

HOMEWORK ACTIVITIES

A. Simplify the following:

1. 4

2. (5 4

3. 3

B. Write in scientific notation:

1) 2100000000

LESSON REFLECTION


Mental Maths

Topic

Homework

1.

2. 5

3.

1. 3

2. (5 4

4.

5. 2

6. 2

7. ( 4

4

2. (5 4

3. 3


WEEK 4 LESSON 7



· squares and square roots

· Recognize and use the appropriate laws of operations using numbers involving exponents and square and cube roots

· Perform calculations involving all four operations with numbers that involve squares, cubes, square roots and cube roots of integers

RESOURCES


PRIOR KNOWLEDGE


COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

MENTAL MATHS

3 min


1.

2.

3.

Page 81-83

HOMEWORK

5 min

4

2. (5 4

3. 3

KEYWORDS:

base, exponent, square root, square, perfect squares and cubes

LESSON DEVELOPMENT

CLASSWORK

20 min

The formula for the area of a square is area (side)2

1. What is the area of a square with side 4 units? 16 square units

2. What is the length of the side of a square if its area is 25 square units? 5 units

3. How did you get the answer to question 2? 5

4. How does the operation you did in question1 compare to what you did in 2? Reverse operation

The name of the operation that is the inverse (opposite) of squaring is taking the square root

It has a symbol : 5

Notice that 2 4, since and squaring are inverses.

Numbers that gives a rational roots are known as perfect squares:

Example:

2

3

4

5

CLASSWORK

Find without the use of a calculator:

1.

2.

3.

4.

Recap

2 min

Numbers that gives a rational roots are known as perfect squares

HOMEWORK ACTIVITIES

Find without the use of a calculator:

1.

3.

4.

LESSON REFLECTION


MENTAL MATHS

CLASSWORK

HOMEWORK

1. 4

2. 3

3.

1. 6

2.

3. 12

4. 0.3

1. 10

3. 7

4. 0.02


WEEK 4 LESSON 8

TOPIC: EXPONENTS



· Calculate the squares, cubes , square roots and cube roots of rational numbers

· Solve problems in context involving numbers in exponential form

RESOURCES


PRIOR KNOWLEDGE

· Natural numbers

· Four Operations

· Squares

· Cubes

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

3min

1. Calculate

a.

b.

c.

d.

e.

Page 81-83


5min

1. 10

2. 7

3. 0.02

LESSON

PRESENTATION/DEVELOPMENT AND CLASSWORK

18min

The teacher puts the learners in pairs and allows them to work on the following activity.

1. Write these expanded forms as powers:

a.

b.

c.

2. Write these powers in expanded form:

a.

b.

c.

3. Determine the values:

a.

b.

c.

d.

e.


AND OR HOMEWORK

4min

1.Calculate:

a.

b.

c.

d.

e.

REFLECTION


MENTAL MATHS

CLASSWORK

1. Calculate

a.

b.

c.

d.

e.

1.

a.

b.

.

c.

2.

a.

b.

c.

3.

a.

b.

c.

d.

e.

WEEK 4 REVISION MULTIPLE CHOICE

1.

A. 2

B. 2

C.

D. All are correct

2.

A.

B.

C.

D. 2

3. What is the base of the following power ² =

A. 2

B. 3

C. 4

D

=

A. 4

B. 5

C. 3

D. 9

5. 64 expressed in exponential form is…

A. 88

B .444

C

D. 5

6. Fill in the correct sign = ;< or >4 * 3

A. <

B. >

C. =

D. None

7. Which numbers are arranged in ascending order?

A. 10; 16; 305; 22

B. 305; 22; 10; 16

C. 305; 10; 16 22

D. 22; 16; 305; 10

8. (a²) (a4) =

A.

B.

C.

D.

9. 2 2 =

A. 4

B. 2

C. 4

D. 2

10. =

A.

B.

C

D.

MEMO

1. A

2. D

3. D

4. C

5. C

6. B

7. B

8. A

9. B

10. A


WEEK 5, LESSON 1 and 2

1. TOPIC: Common Fractions (Equivalent forms and calculations using fractions and calculation techniques)

2. CONCEPTS AND SKILLS TO BE ACHIEVED


· Recognise equivalent forms between:

· Common fractions (fractions where one denominator is a multiple of the other).

· Common fractions and decimal fraction in the forms of the same number.

· Common fraction, decimal fraction and percentage forms of the same number.

3. RESOURCES

DBE workbook(2-12), Sasol-Inzalo workbook2(1-29), textbook, calculators, DVDs(GDE 04 08 2014; GDE 21 07 2014; GDE 23 07 2014; GDE 28 07 2014; GDE 30 07 2014)

4. PRIOR KNOWLEDGE

· Multiplication, multiples, percentages, equivalence

· Converting mixed numbers to common fractions

· Factors, equivalent fractions, place value

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

5. INTRODUCTION

(Mental maths)

4 Mins

Ask the learners to:

(a) List the multiples of 3 and 6 less than 40, and then identify the common multiples and LCM.

(b) Write down any five different fractions that are equivalent to.

(c) Arrange the following fractions in ascending order (from smallest to biggest).

Page 100-106

6. REVIEW AND

CORRECTION OF HOMEWORK

0 Mins

7. LESSON


25 Mins

1. Consider the following figures. What fraction is the shaded part? Give answers in simplest form.

2. Complete the table

Common Fraction

Percentage

Decimal Fraction

0,25

0,5

0,75

0,3

3. Rewrite each of the following as an equivalent fraction, with the denominator 24.

a)

b)

4. Rewrite the following fractions with a common denominator and then arrange the original fractions in ascending order (smallest to biggest):

5. Use the following examples to demonstrate how the denominators can be made the same using appropriate calculation techniques.

Engage the learners while doing these examples on the board

a) (same denominators)

1

b) (different denominators)

a) multiples of 8

multiples of 4

LCM = 8

6. When adding and subtraction fractions follow the following steps

1. Convert mixed numbers to improper fractions

2. Make the denominators the same by using the HCF of the denominators

3. Remember to multiply the numerations with the same numbers as what was used to change the denominator to the HCF.

( what you do at the bottom do it also on the top)

4. Now keep the numerator the same as the HCF and either add or subtract only the numerator.

5. Simplify the answer.

e.g:2

= ……………1

= …………..2 and 3

= ………….4

8. CLASSWORK

25 Mins

Classwork:

1. Find the missing denominator or numerator:

a)

b)

c)

2. Express the following as decimals and as percentages

a) ________= __________%

b) ________= __________%

c) ________= __________%

3. Calculate

b) 5

ANSWERS



0,025= 2,5%

3.a)

=

=

=

=

=

b) 5

=

=

=

=

=

9. CONSOLIDA-TION/CONCLU-SION AND HOMEWORK.

6 Mins

Homework:

1. Compare the following and use the signs to indicate their relationships.

a)

b)

c)

d)

2. Continue for a further three equivalent fractions:

3. Arrange in descending order:

4. Calculate:

10. REFLECTION

Answers Week 5 Lesson 1 & 2

Mental Maths

Classwork

Homework

a) M3=

M6

Common M

LCM

b) = = = = =

c) ;



0,025= 2,5%

3.a)

=

= =

=

=

b) 5

=

= =

=

=

1.a)

b) ,

c)

d)

2.

3.

4.

=

=

=

=

= 1


WEEK 5, LESSON 3 and 4

1. TOPIC: Common Fractions (Calculations using fractions: percentages, square, cubes and roots)



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

· Calculate the percentage of part of a whole

· Calculate percentage increase or decrease

· Solve problems in contexts involving percentages

2. RESOURCES

DBE workbook(2-12), Sasol-Inzalo workbook2(1-29), textbook, calculators, DVDs( GDE 04 08 2014; GDE 21 07 2014; GDE 23 07 2014; GDE 28 07 2014; GDE 30 07 2014)

3. PRIOR KNOWLEDGE

· Number knowledge and calculation techniques for common fractions, developed in Grade 7.

· Squares ; cubes; square roots; and cube roots of whole numbers

· Area, surds, exponents

· Addition, subtraction, multiplication and division of fractions

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

4. INTRODUCTION

(Mental maths)

5 Mins

Ask learners to

Calculate:

=

=

=

=

=

=

=

=

=

Page 100-106

5. REVIEW AND

CORRECTION OF HOMEWORK

5 Mins

1.a)

b) ,

c)

d)

2.

3.

4.

=

=

=

=

= 1

6. LESSON


20 Mins

Work with learners to do the following calculations:

1. When one works with squares and cubes, remember the power indicate how many times the base number must be multiplied by itself

means 2 x 2

And means 2 x 2 x 2 ( 2; 3 times)

Also if you get a fraction in brackets with a power the power belongs to both the numerator and the denominator.

=

e.g.

= =

2. When a fraction is inside a root the root belongs to both the numerator and the denominator

e.g.

=

Or

But

When then root is only around the numerator or the denominator you can’t use it for both.

Or

Or

Or

3. A novel was marked at R 120, but the store manager offered Lesedi a discount of 25 percent. Calculate the discount in rands.

25 percent of R 120 translates into: R 30

the discount is R 30

4. A box of chocolate was marked at R 180, but the store manager offered Mark a discount of 20 percent. Calculate the discounted price in rands.

1st approach:

20 percent of R 180 translates into: × R 36

Discounted price: R 180 R 36 R 144

2nd approach:

The store manager is subtracting 20% from the price.

20 % translates into (or 20 of every hundred)

100 20 80

The discount price will be 80% of R 180.

the discounted price : R 144

7. CLASSWORK

25 Mins

Classwork

Calculate:

1.

1. 11

1. 4

1.

1.

1.

1.

1. Calculate 60% of R105

1. Calculate the percentage increase if the price of a bus ticket of R60 is increased to R85

1. Calculate how much a car will cost if its original price of R150 000 is reduced by 15%

ANSWERS

a)

b) 11

1

c) 4

d)

e)

1

f)

g)

h) Calculate 60% of R105

i) Calculate the percentage increase if the price of a bus ticket of R60 is increased to R85

R85-R60

R41.67

j) Calculate how much a car will cost if its original price of

R150 000 is reduced by 15%.

R22 500

R150 000-R22 500=R127 500

8. CONSOLIDA-TION/CONCLU-SION AND HOMEWORK.

5 Mins

1. Simplify each of the following expressions without using a

calculator:

1.

1.

2. What percentage is 40c of R3.20?

9. REFLECTION

Answers Week 5 Lesson 3 & 4

Mental Maths

Classwork

Homework

Ask learners to

Calculate:

= 1

= 2

= 3

= 4

= 5

= 1

= 2

= 3

= 4

ANSWERS

a)

b) 11

1

c) 4

d)

e)

1

f)

h) Calculate 60% of R105

i) Calculate the percentage increase if the price of a bus ticket of R60 is increased to R85

R85-R60

R41.67

j) Calculate how much a car will cost if its original

price of R150 000 is reduced by 15%.

R22 500

R150 000-R22 500=R127 500

a)

b)

0

2. Percentage

12,5%


WEEK 5, LESSON 5&6

1. TOPIC: Decimal Fractions (ordering and rounding off)

2. CONCEPTS AND SKILLS TO BE ACHIEVED


· Ordering, comparing and place value of decimal fractions to at least 3 decimal places

· Rounding off decimal fractions to at least 2 decimal places.

· Add, subtract and multiply decimal fraction to at least 3 decimal places.

3. RESOURCES

DBE workbook(2-12), Sasol-Inzalo workbook2(1-29), textbook, calculators,DVDs( GDE 04 08 2014; GDE 21 07 2014; GDE 23 07 2014; GDE 28 07 2014; GDE 30 07 2014)

4. PRIOR KNOWLEDGE

· Ordering, counting and comparing decimal fractions done in Grade 7

· Calculations with decimal fractions done in grade 7

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

5. INTRODUCTION

(Mental maths)

2 Mins

1) Ask the learners which one of the following is bigger, the first or the

second number?

4, 3 or 4, 33?

7, 34 or 7, 35?

2) Ask the learners if they can think

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