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
Topic: Whole Numbers
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
Topic: Whole Numbers
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]
GRADE 8 TERM 1 WEEK 1: Baseline Assessment Total [40]
MEMORANDUM
Test 1: Day 1
Content Area: Numbers, Operations and Relationships
QUESTION 1
Topic: Whole Numbers
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:
b) Fill in >, <, or to make the following TRUE.
<
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
Topic: Whole Numbers
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
Topic: Whole Numbers
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]
GRADE 8 TERM 1 WEEK 1: Baseline Assessment Total [92]
Test 2: Day 2
QUESTION 1
Topic: Whole Numbers
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
Topic: Whole Numbers
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
Topic: Whole Numbers
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
b) Fill in >, <, or to make the following TRUE.
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
Topic: Whole Numbers
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
Topic: Whole Numbers
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)
SUBJECT: MATHEMATICS GRADE 8
WEEK 2, LESSON 2
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)
Page 75 - 77
REVIEW AND CORRECTION OF HOMEWORK
5min
1.
a)
b)
c)
d)
e)
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. 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
CONSOLIDATION/CONCLUSION
AND OR HOMEWORK
4min
1. Write the following percentages as fractions in their simplest form:
a)
b)
c)
d)
e)
REFLECTION
ANSWERS: TERM 1 GRADE 8 WEEK 2 LESSON 2
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
SUBJECT: MATHEMATICS GRADE 8
WEEK 2, LESSON 3
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. Calculate:
a)
b)
c)
d)
e)
Page 75-77
REVIEW AND CORRECTION OF HOMEWORK
5min
2.
a)
b)
c)
d)
e)
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. 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
CONSOLIDATION/CONCLUSION
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
ANSWERS: TERM 1 GRADE 8 WEEK 2 LESSON 3
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
SUBJECT: MATHEMATICS GRADE 8
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
· 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. Calculate:
a)
b)
c)
d)
REVIEW AND CORRECTION OF HOMEWORK
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
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. Simplify:
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
m)
n)
CONSOLIDATION/CONCLUSION
AND OR HOMEWORK
4min
1.
Simplify:a)
b)
c)
d) (+4) – (-5)
e)
f)
g)
REFLECTION
ANSWERS: TERM 1 GRADE 8 WEEK 2 LESSON 4
MENTAL
CLASSWORK
1.
a)
b)
c)
d)
1. Simplify:
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
m)
n)
SUBJECT: MATHEMATICS GRADE 8
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
· Integers, natural numbers and Whole numbers.
· 4 operations
· Number Sentences
· Exponents
· Decimal, Fractions and Percentages
· Multiples and factors
COMPONENTS
TIME
TASKS/ACTIVITIES
CAPS
INTRODUCTION
(MENTAL MATHS)
3min
1. Simplify:
a)
b)
c)
REVIEW AND CORRECTION OF HOMEWORK
5min
1. Calculate the following:
a)
b)
c)
d)
= 74
e)
f)
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.
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
CONSOLIDATION/CONCLUSION
AND OR HOMEWORK
4min
1. Write the following percentages as fractions in their simplest form:
a)
b)
c)
d)
e)
REFLECTION
ANSWERS: TERM 1 GRADE 8 WEEK 2 LESSON 5
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
SUBJECT: MATHEMATICS GRADE 8
WEEK 2, LESSON 6
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
COMPONENTS
TIME
TASKS/ACTIVITIES
CAPS
INTRODUCTION
(MENTAL MATHS)
3min
1. Calculate
a)
b)
c)
d)
Page 75-77
REVIEW AND CORRECTION OF HOMEWORK
5min
1. Write the following percentages as fractions in their simplest form:
a)
b)
c)
d)
e)
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. 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
CONSOLIDATION/CONCLUSION
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
ANSWERS: TERM 1 GRADE 8 WEEK 2 LESSON 6
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
SUBJECT: MATHEMATICS GRADE 8
WEEK 2, LESSON 7
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. Calculate:
a)
b)
c)
d)
Page 75-77
REVIEW AND CORRECTION OF HOMEWORK
5min
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) 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%.
CONSOLIDATION/CONCLUSION
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
ANSWERS: TERM 1 GRADE 8 WEEK 2 LESSON 7
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
SUBJECT: MATHEMATICS GRADE 8
WEEK 2, LESSON 8&9
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
Calculate
1. 10% of 10
2. 20% of 20
3. 30% of 30
4. 40% of 40
5. 50% of 50
Page 75-77
REVIEW AND CORRECTION OF HOMEWORK
5min
1. a) Interest
LESSON
PRESENTATION AND CLASSWORK
20min
· 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. 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.
CONSOLIDATION/CONCLUSION
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 =
SUBJECT: MATHEMATICS GRADE 8
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
REVIEW AND CORRECTION OF HOMEWORK
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
CONSOLIDATION/CONCLUSION
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
ANSWERS: TERM 1 GRADE 8 WEEK 3 LESSON 1
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
SUBJECT: MATHEMATICS GRADE 8
WEEK 3, LESSON 2
TOPIC: WHOLE NUMBERS
CONCEPTS AND SKILLS TO BE ACHIEVED
By the end of the lesson, learners should know and be able to:
· 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
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
(MENTAL MATHS)
3min
1. List the factors of 12.
2. List the first 3 multiples of 5
Page 75-77
REVIEW AND CORRECTION OF HOMEWORK
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
PRESENTATION/DEVELOPMENT
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
CONSOLIDATION/CONCLUSION
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
ANSWERS: TERM 1 GRADE 8 WEEK 3 LESSON 2
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)
SUBJECT: MATHEMATICS GRADE 8
WEEK 3, LESSON 3
TOPIC: WHOLE NUMBERS
CONCEPTS AND SKILLS TO BE ACHIEVED
By the end of the lesson, learners should know and be able to:
· Determine the LCM of numbers to at least 3-digit whole numbers, by inspection or factorization
· Determine HCF of numbers
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
(MENTAL MATHS)
3min
1. List the factors of:
a. 100
b. 75
Page 75-77
REVIEW AND CORRECTION OF HOMEWORK
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
PRESENTATION/DEVELOPMENT
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
CONSOLIDATION/CONCLUSION
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
ANSWERS: TERM 1 GRADE 8 WEEK 3 LESSON 3
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
SUBJECT: MATHEMATICS GRADE 8
WEEK 3, LESSON 4
TOPIC: WHOLE NUMBERS
CONCEPTS AND SKILLS TO BE ACHIEVED
By the end of the lesson, learners should know and be able to:
· Determine the HCF of numbers to at least 3-digit whole numbers, by inspection or factorization.
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)
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
REVIEW AND CORRECTION OF HOMEWORK
1.
a. 100 and 75
b. 125 and 500
c. 50 and 75
d. 35 and 80
e. 12 and 48
LESSON
PRESENTATION/DEVELOPMENT
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
CONSOLIDATION/CONCLUSION
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
ANSWERS: TERM 1 GRADE 8 WEEK 3 LESSON 4
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
SUBJECT: MATHEMATICS GRADE 8
WEEK 3, LESSON 5
TOPIC: WHOLE NUMBERS
CONCEPTS AND SKILLS TO BE ACHIEVED
By the end of the lesson, learners should know and be able to:
· Solve problems involving whole numbers, including:
· comparing two or more quantities of the same kind (ratio)
· comparing two quantities of different kinds (rate)
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
· Fractions
· Ratio
COMPONENTS
TIME
TASKS/ACTIVITIES
CAPS
INTRODUCTION
(MENTALMATHS)
3min
1. Simplify
a. of 40
b. Simplify to lowest terms
REVIEW AND CORRECTION OF HOMEWORK
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
PRESENTATION/DEVELOPMENT
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?
CONSOLIDATION/CONCLUSION
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
ANSWERS: TERM 1 GRADE 8 WEEK 3 LESSON 5
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
SUBJECT: MATHEMATICS GRADE 8
WEEK 3, LESSON 6
TOPIC: WHOLE NUMBERS
CONCEPTS AND SKILLS TO BE ACHIEVED
By the end of the lesson, learners should know and be able to:
· 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
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
· Decimals
· Fractions
COMPONENTS
TIME
TASKS/ACTIVITIES
CAPS
INTRODUCTION
(MENTALMATHS)
3min
1.
2. as a percentage
3. write as simple ratio
Page 75-77
REVIEW AND CORRECTION OF HOMEWORK
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
PRESENTATION/DEVELOPMENT
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?
CONSOLIDATION/CONCLUSION
AND OR HOMEWORK
4min
1. What percentage is:
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
ANSWERS: TERM 1 GRADE 8 WEEK 3 LESSON 6
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
SUBJECT: MATHEMATICS GRADE 8
WEEK 3, LESSON 7
TOPIC: WHOLE NUMBERS
CONCEPTS AND SKILLS TO BE ACHIEVED
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
REVIEW AND CORRECTION OF HOMEWORK
5min
1. 8:12 2:3
2. Increase 40 in the ratio 2 : 3
4. = 60
LESSON
PRESENTATION/DEVELOPMENT
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
CONSOLIDATION/CONCLUSION
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
ANSWERS: TERM 1 GRADE 8 WEEK 3 LESSON 7
MENTAL
CLASSWORK
1.
2. Reduce
3. 20c as a percentage of R2
4. 10400 12
5. Calculate 8% of 10 400
1.
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. 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
SUBJECT: MATHEMATICS GRADE 8
WEEK 3, LESSON 8
TOPIC: WHOLE NUMBERS
CONCEPTS AND SKILLS TO BE ACHIEVED
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
REVIEW AND CORRECTION OF HOMEWORK
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
PRESENTATION/DEVELOPMENT
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)
CONSOLIDATION/CONCLUSION
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
ANSWERS: TERM 1 GRADE 8 WEEK 3 LESSON 8
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:
· Multiples and factors
· 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)
2. List the first 4 multiples of the following set of numbers.
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.
a) Did Sam make a profit or a loss?
b) Calculate the profit or loss for yesterday
c) What was % profit or loss?
(1)
(2)
(2)
Total
(25)
MEMORANDUM Total [25]
WEEKLY TEST Time 30minutes
Content Area:
· Multiples and factors
· 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)
2. List the first 4 multiples of the following set of numbers.
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
CONCEPTS AND SKILLS TO BE ACHIEVED
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
b) Final amount to be paid.
Amount P+SI 12500+3000 = R15500.00
SUBJECT: MATHEMATICS GRADE 8 - Term 1
WEEK 4 LESSON 2
TOPIC: Number operations and relationships - Whole numbers
CONCEPTS AND SKILLS TO BE ACHIEVED
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?
2. How much is 2 pula in rands?
3. How much is 10 pula in rands?
4. How much is 100 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
b) Final amount to be paid.
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
ANSWERS: TERM1 GRADE 8 WEEK 4 LESSON 2
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
SUBJECT: MATHEMATICS GRADE 8 - Term 1
WEEK 4 LESSON 3
TOPIC: Number operations and relationships – Exponents
CONCEPTS AND SKILLS TO BE ACHIEVED
· 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
ANSWERS: TERM1 GRADE 8 WEEK 4 LESSON 3
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 =
SUBJECT: MATHEMATICS GRADE 8 - Term 1
WEEK 4 LESSON 4
TOPIC: Number operations and relationships – Exponents
CONCEPTS AND SKILLS TO BE ACHIEVED
· 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
ANSWERS: TERM1 GRADE 8 WEEK 4 LESSON 4
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 =
SUBJECT: MATHEMATICS GRADE 8 - Term 1
WEEK 4 LESSON 5
TOPIC: Number operations and relationships – Exponents
CONCEPTS AND SKILLS TO BE ACHIEVED
Laws of the exponents
Establish general laws of exponents, limited to:
natural number exponents
· n
· (a n 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, 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
Simplify the following:
1. 3
2. (6 2
4.
Recap
2 min
Laws of exponents
HOMEWORK ACTIVITIES
Simplify the following:
1. 3
2. (a 4
LESSON REFLECTION
ANSWERS: TERM1 GRADE 8 WEEK 4 LESSON 5
Mental Maths
Topic
Homework
1.
2. n
3.
1. 3
2. (6 2 or or 576
4. 1
1. 3
2. (a 4
1
SUBJECT: MATHEMATICS GRADE 8 - Term 1
WEEK 4 LESSON 6
TOPIC: Number operations and relationships – Exponents
CONCEPTS AND SKILLS TO BE ACHIEVED
Laws of the exponents
Establish general laws of exponents, limited to:
natural number exponents
· n
· (a n 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, firs and the second law of the exponents.
COMPONENTS
TIME
TASKS/ACTIVITIES
CAPS
MENTAL MATHS
3 min
Simplify the following:
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
ANSWERS: TERM1 GRADE 8 WEEK 4 LESSON 6
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
SUBJECT: MATHEMATICS GRADE 8 - Term 1
WEEK 4 LESSON 7
TOPIC: Number operations and relationships – Exponents
CONCEPTS AND SKILLS TO BE ACHIEVED
· 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
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, firs and the second law of the exponents.
COMPONENTS
TIME
TASKS/ACTIVITIES
CAPS
MENTAL MATHS
3 min
Simplify the following:
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
ANSWERS: TERM1 GRADE 8 WEEK 4 LESSON 7
MENTAL MATHS
CLASSWORK
HOMEWORK
1. 4
2. 3
3.
1. 6
2.
3. 12
4. 0.3
1. 10
3. 7
4. 0.02
SUBJECT: MATHEMATICS GRADE 9
WEEK 4 LESSON 8
TOPIC: EXPONENTS
CONCEPTS AND SKILLS TO BE ACHIEVED
By the end of the lesson, learners should know and be able to:
· Calculate the squares, cubes , square roots and cube roots of rational numbers
· Solve problems in context involving numbers in exponential form
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
· Natural numbers
· Four Operations
· Squares
· Cubes
COMPONENTS
TIME
TASKS/ACTIVITIES
CAPS
INTRODUCTION
3min
1. Calculate
a.
b.
c.
d.
e.
Page 81-83
REVIEW AND CORRECTION OF HOMEWORK
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.
CONSOLIDATION/CONCLUSION
AND OR HOMEWORK
4min
1.Calculate:
a.
b.
c.
d.
e.
REFLECTION
ANSWERS: TERM 1 GRADE 8 WEEK 4 LESSON 8
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
SUBJECT: MATHEMATICS GRADE 8
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
By the end of the lesson, learners should know and be able to:
· 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
PRESENTATION/DEVELOPMENT
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
1. Find the missing denominator or numerator:
2. Express the following as decimals and as percentages
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) ;
1. Find the missing denominator or numerator:
2. Express the following as decimals and as percentages
0,025= 2,5%
3.a)
=
= =
=
=
b) 5
=
= =
=
=
1.a)
b) ,
c)
d)
2.
3.
4.
=
=
=
=
= 1
SUBJECT: MATHEMATICS GRADE 8
WEEK 5, LESSON 3 and 4
1. TOPIC: Common Fractions (Calculations using fractions: percentages, square, cubes and roots)
CONCEPTS AND SKILLS TO BE ACHIEVED
By the end of the lesson, learners should know and be able to:
· 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
PRESENTATION/DEVELOPMENT
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%
SUBJECT: MATHEMATICS GRADE 8
WEEK 5, LESSON 5&6
1. TOPIC: Decimal Fractions (ordering and rounding off)
2. CONCEPTS AND SKILLS TO BE ACHIEVED
By the end of the lesson, learners should know and be able to:
· 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