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Grade 8

Term 3

Mathematics

Mathematics Teaching Plan: Term 3 Grade 8 (ATP)

Weeks

Topic

Concept & Skills

DATE COMPLETED

CURRICULUM COVERAGE PER TERM

PAGE NUMBERS

CAPS

DBE workbook

Sasol-Inzalo

DVD Resources

Textbook/Other Resources

Y/N

%

Week 1(17-20 July)

REMEDIAL AND REVISION LESSONS

REMEDIAL AND REVISION LESSON 1 & 2 GEOMETRY

REMEDIAL AND REVISION LESSON 3 & 4 EXPONENTS,PATTERNS AND FUNCTIONS

REMEDIAL AND REVISION LESSON 5 EXPRESSIONS (FACTORS)

REMEDIAL AND REVISION LESSON 6 EQUATIONS

REMEDIAL AND REVISION LESSON 7 & 8 GRAPHS

LESSON 9 – WEEKLY ASSESSMENT

Week 2 (23-27 July)

Algebraic Equations

Lesson 1: Extend solving equations to include:

2

using additive and multiplicative inverse

1

0.2

equations of the form: a product of factors = 0.

1

0.5

Lesson 2: Extend solving equations to include:

3

using additive and multiplicative inverse

1

0.7

equations of the form: a product of factors = 0.

1

0.9

Solve equations using laws of exponents

1

1.1

Lesson 3:

4

determine numerical value of an expression by substitution

1

1.4

identify variables and constants in given formulae or equations

1

1.6

Use substitution in equations to generate tables of ordered pairs.

1

1.8


1

2.1

Lesson 4:

4

determine numerical value of an expression by substitution

1

2.3

identify variables and constants in given formulae or equations

1

2.5

Use substitution in equations to generate tables of ordered pairs.

1

2.8


1

3.0

Lesson 5: Determine, interpret and justify equivalence of different descriptions of the same relationship or rule presented:

5

verbally

1

3.2

in flow diagrams

1

3.4

in tables

1

3.7

by formulae

1

3.9

by equations

1

4.1


5

verbally

1

4.4

in flow diagrams

1

4.6

in tables

1

4.8

by formulae

1

5.0

by equations

1

5.3


5

verbally

1

5.5

in flow diagrams

1

5.7

in tables

1

6.0

by formulae

1

6.2

by equations

1

6.4

Lesson 8:

3

Analyse and interpret global graphs of problem situations, with a special focus on constant, increase or decrease

1

6.7

Interpret graphs with special focus on the x-intercept an y-intercept of linear graphs

1

6.9

Interpret graphs with special focus on the gradient of linear graphs

1

7.1

Lesson 9: Assessment

Week 3 (30 July -03 Aug)

Graphs

Lesson 1:

1

Use tables of ordered pairs to plot points and draw graphs on the Cartesian plane

1

7.3

Lesson 2:

1


1

7.6

Lesson 3:

1


1

7.8

Lesson 4:

1


1

8.0

Lesson 5: Recognise, describe and perform transformations with points on a co-ordinate plane, focusing on:

2

Reflecting a point/triangle in the y-axis or x-axis

1

8.3

Translating a point/triangle t within and across quadrants

1

8.5

Lesson 6: Recognise, describe and perform transformations with points on a co-ordinate plane, focusing on:

2

Reflecting a point/triangle in the y-axis or x-axis

1

8.7

Translating a point/triangle t within and across quadrants

1

8.9

Transformation

Lesson 7: Recognise, describe and perform transformations with triangles on a co-ordinate plane, focusing on the co-ordinates of the vertices when:

1

Reflecting a triangle in the x-axis or y-axis

1

9.2

Lesson 8 :Recognise, describe and perform transformations with triangles on a co-ordinate plane, focusing on the co-ordinates of the vertices when:

1

Rotating a triangle around the origin

1

9.4


Week 4 (06 Aug - 17 Aug)

Transformation

Lesson 1 and 2: Enlargements and reductions

1

Use proportion to describe the effect of enlargement or reduction on area and perimeter of geometric figures.

1

9.6

Collect, organize and summarize data (Gr8 revision)

LESSON 3 and 4:

4

Pose questions relating to social, economic, and environmental issues.

1

9.9

Select and justify appropriate sources for the collection of data.

1

10.1

Distinguish between samples and populations, and suggest appropriate samples for investigation.

1

10.3

Select and justify appropriate methods for collecting data.

1

10.6

LESSON 5 and 6:Organize and record data using tally marks, tables, stem-and-leaf displays

3

tally marks

1

10.8

tables

1

11.0

stem-and-leaf display

1

11.2

LESSON 7 and 8: Group data into intervalsSummarize data using measures of central tendency, including:

4

mean

1

11.5

median

1

11.7

mode

1

11.9

range; extremes

1

12.2



Representing data

Lesson 1: Draw a variety of graphs by hand/ technology to display and interpret data including:

2

bar graphs and double graphs

1

12.4

histograms with given and own intervals

1

12.6


2

pie chart

1

12.8

broken line graphs

1

13.1


4

Interpret, analyse and report data

bar graphs and double bar graphs

1

13.3

histograms with given and own intervals

1

13.5

pie charts

1

13.8

broken-line graphs

1

14.0

LESSON 4&5:Critically read and interpret data represented in:

6

words

1

14.2

bar graphs

1

14.4

double bar graphs

1

14.7

pie charts

1

14.9

histograms

1

15.1

broken-line graphs

1

15.4

LESSON 6&7:Critically analyse data by answering questions related to :

7

data categories, including data intervals

1

15.6

data sources and contexts

1

15.8

central tendencies – (mean, mode, median)

1

16.1

scales used on graphs

1

16.3

samples and populations

1

16.5

dispersion of data

1

16.7

error and bias in the data

1

17.0

Interpret, analyse and report data

LESSON 8:Summarize data in short paragraphs that include

5

drawing conclusions about the data

1

17.2

making predictions based on the data

1

17.4

identifying sources of error and bias in the data

1

17.7

choosing appropriate summary statistics for the data(mean, median mode)

1

17.9

the role of extremes in the data

1

18.1

Lesson 9: Revision and/or assessment: PROJECT


Probability

Lesson 1 and 2: Consider a simple situation (with equally likely outcomes) that can be described using probability and:

2

list all the possible outcomes;

1

18.3

determine the probability of each possible outcome using the definition of probability

1

18.6

Lesson 3 and 4: Consider a simple situation (with equally likely outcomes) that can be described using probability and:

2

list all the possible outcomes;

1

18.8

determine the probability of each possible outcome using the definition of probability

1

19.0

Lesson 5 and 6 :

2

predict with reasons the relative frequency of the possible outcomes for a series of trials based on probability.

1

19.3

compare relative frequency with probability and explain possible differences;

1

19.5

Lesson 7 and 8 :

2

predict with reasons the relative frequency of the possible outcomes for a series of trials based on probability.

1

19.7

compare relative frequency with probability and explain possible differences;

1

20.0


Week 7 (03 Sep - 07 Sep)

Geometry of 3-D objects

Lesson 1: Classifying 3-D objects

1

Describe, name and compare the 5 Platonic solids in terms of the shape and number of faces, the number of vertices and the number of edges.

1

20.2


1


1

20.4


1


1

20.6


1


1

20.9

LESSON 5Building 3-D modelsUse nets to make models of geometric solids, including:

2

Cubes

1

21.1

Prisms

1

21.3


2

Cubes

1

21.6

Prisms

1

21.8


1

Pyramids

1

22.0


1

Pyramids

1

22.2


FORMAL ASSESSMENT: ASSIGNMENT

Week 8 (10 Sep - 14 Sep)

Surface area and volume of 3-D objects

Lesson 1:

1

Use appropriate formulae to calculate the surface area, volume and capacity of cubes rectangular prisms and triangular prisms

1

22.5

Lesson 2

1

Use appropriate formulae to calculate the surface area, volume and capacity of cubes rectangular prisms and triangular prisms

1

22.7

Lesson 3

1

Describe the interrelationship between surface area and volume of a cube, rectangular and triangular prisms.

1

22.9

Lesson 4

1

Describe the interrelationship between surface area and volume of a cube, rectangular and triangular prisms.

1

23.2

Lesson 5:

1

Solve problem, with or without a calculator, involving surface area.

1

23.4

Lesson 6:

1

Solve problem, with or without a calculator, involving volume and capacity.

1

23.6

Lesson 7: Use and convert between appropriate SI units, including:

3

1

23.9

1

24.1

1

24.3

Lesson 8: Use and convert between appropriate SI units, including:

3

1

24.5

1

24.8

1

25.0


TOTAL OF SUB-TOPICS

109

Type of Assessment

Concepts & Skills Assessed

Date to be completed

Test(26 March - 28 March)

FORMAL ASSESSMENT: TEST (END OF THE TERM)Important considerations: • Include Multiple Choice Questions.• Ensure coverage of Cognitive levels as prescribed in CAPS p157.• Ensure that the questions are grade-appropriate.• The test and the memo should be moderated.

Grade 8

Term 3

Mathematics Lesson Plan

0

165

SUBJECT: MATHEMATICS GRADE 8

TERM 3 WEEK 1 REVISION LESSON 1&2

TOPIC: GEOMETRY

TIME : 60 MINUTES

TOTAL : 49 MARKS

QUESTION 1

In the diagram below, and

Calculate the value of x and y

(4)

QUESTION 2

Q

T

R

S

P

Determine the value of and in the following diagram:

(6)

QUESTION 3 Calculate the value of the unknown “”.

(3)

QUESTION 4 In the diagram, OK = ON, KNLM, and =160°. Calculate the value of .Give reasons for your answers.

(5)

QUESTION 5

Determine the size of in each figure. Show all the necessary steps and give reasons for your answers.

B

A

5.1.1

C

D

Q

5.1.2

P

T

S

W

5.1.3

V

Y

(3)

(3)

(3)

QUESTION 6

Determine the size of , showing all necessary steps and give reasons for all statements that use geometrical theorems:

6.1.1

6.1.2

6.1.3

QUESTION 7

Consider the following diagram, in which it is given: , DE=EI, DF‖ IG, and GH=IH

7.1.1 Determine, with reasons, the size of .

7.1.2 State whether the following statements are correct or not ? Explain your answer.

a) is similar to

b) ) is congruent to

(4)

(4)

(5)

(5)

(2)

(2)

MEMORANDUM

TOTAL : 48 MARKS

QUESTION 1

[ Co-int ∠s ; AB‖ CD]

(vertically Opposite angles)

(4)

QUESTION 2

; PS‖ QT

Alternatively

(

OR

(6)

QUESTION 3

AB‖CD]

(3)

QUESTION 4

In the diagram, OK = ON, KN‖LM, and =160°. Calculate the value of . Give reasons for your answers.

(5)

QUESTION 5

5.1.1 The figure below is a parallelogram

5.1.2

2x - 20° + 75° + 80° + x = 360°

2x + x + 80° + 75° - 20° = 360°

3x + 135° = 360°

3x + 135° -135° = 360° - 135°

3x = 225°

=

= 75°

5.1.3

]

x + 38° + 38° = 180°

x + 76° = 180°

x + 76° - 76° = 180° -76°

x = 104°

(3)

(3)

(3)

QUESTION 6 - Calculate x

6.1.1

AB//CD ]

+ 115°= 180°

+ 115° -115° = 180° - 115°

= 65° Or any other method

6.1.2

2x + x + 20 = 125

3x + 20° = 125°

3x + 20° -20° = 125° - 20°

3x = 105°

=

= 35°

6.1.3 BD‖FG]

AB‖CE]

(5)

(4)

(4)

QUESTION 7

7.1.1 H

Since DE= EI, then = [Sides opp; equal ∠s]

Let = =

+ + 30° = 180

2 + 30° = 180°

2 + 30° - 30° = 180° - 30°

2 = 150°

=

= 75°

= 30° [Alt ∠s;DF‖IG]

= 75° (vertically opp to exterior angle adjacent to angle DIE)

IGH = 75° [ ∠s opp equal sides]

Let =

+ 75° + 75° = 180° (

+ 150° = 180°

+ 150° - 150° = 180° -150°

= 30°

= 30°

7.1.2a) True, same shape and corresponding angles

7.1.2b) NO, Same shape ,corresponding angles but not same size

(5)

(2)

(2)


TERM 3 WEEK 1 REVISION LESSON 3 &4

TOPIC: EXPONENTS , PATTERNS AND FUNCTIONS

TIME: 60 MINUTES

TOTAL: 47 MARKS

QUESTION 1 Simplify the following:

a)

b)

c)

d)

e)

f)

(2)

(2)

(2)

(2)

(2)

(2)

QUESTION 2

2. Study the pattern below and then answer the questions that follow.

2 ; 5 ; 8 ; x ; y ; z ; …

2.1Find the terms represented by x ; y and z

2.2Describe the pattern in 2.1 in your own words

2.3Write down the equation representing the general term of this pattern in the form Tn = …..

2.4Use your formula to find the 9th term in the sequence

(4)

(3)

(3)

(2)

QUESTION 3

Consider the table below

Position of the term

1

2

3

4

5

Term

1

4

9

3.1 Complete the table.

3.2 Write down the 5th term

3.3 Write down the general rule

(4)

(3)

(2)

QUESTION 4

4.1 In the flow diagram below the input and output values are given. Determine the rule to find the output values.

-3

-2

-1

0

7

5

3

1

4.2 Use the input and output values to determine the rule and use the rule to complete the table.

-4

-2

0

8

6

2

-2

-14

(4)

(4)

QUESTION 5 Given a function defined by , represent this relationship:

5.1 In a flow diagram

5.2 On a table

(3)

(3)


WEEK 1, REVISION LESSON 3 &4

MEMORANDUM

TIME : 60 MINUTES

TOTAL : 47 MARKS

QUESTION 1

a)

b)

c)

d)

e)

f)

(2)

(2)

(2)

(2)

(2)

(2)

QUESTION 2

2.12 ; 5 ; 8 ; x ; y ; z ; …

2.2The number is multiplied by three and one is subtracted to get the next term. OR add three to the previous term to get the next term.

2.3

2.4

(4)

(3)

(3)

(2)

QUESTION 3

3.1

Position of the term

1

2

3

4

5

Term

1

4

9

16

25

3.2

3.3

(4)

(3)

(2)

QUESTION 4

4.1In the flow diagram below the input and output values are given. Determine the rule to find the output values.

-3

-2

-1

0

7

5

3

1

4.2 Use the input and output values to determine the rule and use the rule to complete the table.

-4

-2

0

6

8

6

2

-2

-14

-18

The general rule

(4)

(4)

QUESTION 5

5.1

-2

-1

0

1

-4

-3,5

-3

-2,5

5.2 On a table

X

-2

-1

0

1

Y

-4

-3,5

-3

-2,5

(3)

(3)


TERM 3 WEEK 1 REVISION LESSON 5

TOPIC: EXPRESSIONS(FACTORS)

TIME: 30 MINUTES

TOTAL: 25 MARKS

QUESTION 1 List factors of the following sets of numbers.

(a) 36

(b) 18

(c) 50

(d) 49

(e) 100

(1)

(1)

(1)

(1)

(1)

QUESTION 2 State whether the following expression are like or unlike:

(a)

(b)

(c)

(d)

(e) 4y ; 2xy

(1)

(1)

(1)

(1)

(1)

QUESTION 3

Simplify:

(a) ( )

(b) ()

)

(d)

(2)

(2)

(2)

(2)

QUESTION 4

Factorize the following:

(a)

(b)

(c)

(2)

(2)

(3)

MEMORANDUM

QUESTION1

(a) 36 = (1;2;3;4;6;9;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;25;50;100)

(1)

(1)

(1)

(1)

(1)

QUESTION 2

(a) ( like)

(b) (unlike)

(c) (unlike)

(d) (like)

(e) (unlike)

(1)

(1)

(1)

(1)

(1)

QUESTION 3

(a) ( )

(b) ()

)

(d)

)

(2)

(2)

(2)

(2)

QUESTION 4

(a)

(b)

(c)

(2)

(2)

(3)



TOPIC: EQUATIONS

TIME: 30 MINUTES

TOTAL: 24 MARKS

QUESTION 1 Solve for :

a)

(2)

b)

(2)

c)

(2)

d)

(2)

e)

(2)

f)

(2)

g)

(2)

h)

(2)

i)

(2)

j)

(2)

k)

(2)

l)

(2)


WEEK 1, REVISION LESSON 6

MEMORANDUM

TIME: 30 MINUTES

TOTAL: 24 MARKS

QUESTION 1 Solve for :

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

(2)

(2)

(2)

(2)

(2)

(2)

(2)

(2)

(2)

(2)

(2)

(2)



TOPIC: GRAPHS

TIME: 60 MINUTES

TOTAL: 50 MARKS

QUESTION 1 Given :

1.1 Copy and complete the table using the equation given above;

-1

0

1

2

1.2 Use your table in 1.1 to draw a graph defining the equation :

1.3 Is the graph an increasing or decreasing function? Explain.

(6)

(6)

(2)

QUESTION 2 Study the straight line graphs below and complete the following statements:

2.1 The equation of the line CD is…

2.2 The equation of the line AB is…

2.3 If DE=2, the coordinates of E are……

(3)

(3)

(3)

QUESTION 3 State whether the following graphs are linear or non-linear:

(6)

QUESTION 4 The line graph shows the number of cars that a company sold between July and December of 2014.

(a) Is the data shown in the graph discrete or continuous? Explain your answer

(b) How many cars were sold in August?

(c) During which months were the maximum and minimum number of cars sold?

(d) How many more cars were sold in November than in July?

(e) Between which months did the car sales decrease?

(f) Would you say that the car sales generally improved over the 6 months? Explain your answer.

(2)

(2)

(2)

(2)

(2)

(3)

QUESTION 5 Study the graph below and answer the questions that follows:

5.1 Which day is the coldest day of the week?

5.2 What is the minimum temperature of the graph?

5.3 What is the maximum value of the graph?

5.4 On which day was the temperature recorded as being 30°C?

(2)

(2)

(2)

(2)



MEMORANDUM

TIME: 60 MINUTES

TOTAL: 50 MARKS

QUESTION 1 Given :

1.1

-1

0

1

2

-5

-3

-1

1

1.2

1.3 The graph is increasing because the gradient is positive.

(6)

(6)

(2)

QUESTION 2:

2.1

The equation of the line CD is a vertical and the gradient is undefined ()

2.2

The equation of the line AB is sloping line and the gradient is positive ()

2.3 If DE=2, the coordinates of E are (2;-2)

(3)

(3)

(3)

QUESTION 3

A) Linear

B) Non Linear

C) Non Linear

(6)

QUESTION 4

a) Discrete (cars and month are natural numbers)

b) 30 cars

c) maximum December and minimum September

d)

cars

e) Between August and September: Between October and November

f) There was a general improvement since there is more increase compared to the decrease

(2)

(2)

(2)

(2)

(2)

(3)

QUESTION 5

5.1 Day 6

5.2 17

5.3 33

5.4 Day 2

(2)

(2)

(2)

(2)



TOPIC: ASSESSMENT

TIME: 30 MINUTES

TOTAL: 20 MARKS

CHOOSE THE CORRECT ANSWER FOR EACH QUESTION

1. Calculate the size of x (2)

A. 50

B. 60

C. 120

D. 12

2. What is the value of b in the diagram below (2)

A. 30

B. 60

C. 50

D. 150

3. What is the value of angle Ĉ (2)

A. 35

B. 45

C. 25

D. 15

4. Calculate of the given diagram: (2)

A. 22

B. 32

C. 38

D.

5 .Determine the size of on the following diagram: (2)

A. 45

B. 65

C. 75

D. 35

6. Calculate the value of angle n in the diagram below. (2)

A. 60

B. 70

C. 100

D. 120

7. Calculate the value of x (2)

A. 50

B. 60

C. 80

D. 90

8. Calculate the size of angle N. (2)

A. 70

B. 80

C. 100

D. 30

9. What is the size of ? (2)

A. 18

B. 68

C. 59

D. 58

10. Calculate the value of y (2)

A. 34

B. 44

C. 54

D. 55

MEMORANDUM

1. A

2. C

3. A

4. D

5. C

6. D

7. A

8. A

9. D

10. A

[2x10]


WEEK 2: LESSON 1

TOPIC: ALGEBRAIC EQUATIONS

CONCEPTS AND SKILLS TO BE ACHIEVED

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

· Extend solving equations to include:

· Using additive and multiplicative inverses.

· Equations of the form: a product of factors.

RESOURCES

GDE ATP Term 3

DBE workbook 2(Page 128-132), Sasol-Inzalo workbook 2(page 149), ruler, pencil, eraser, calculators, notebook, DVDs

(GDE 17 03 2014).

PRIOR KNOWLEDGE

· Like and unlike terms

· Expressions

· Variables

· Exponents

· Equations

· Substitution

· Additive and multiplicative inverse

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

REVIEW AND CORRECTION OF HOMEWORK

No homework since it is the first lesson

Page 25

LESSON

PRESENTATION/ DEVELOPMENT

10 MIN

Create a situation

CLASS ACTIVITIES

15 MIN

The teacher put learners in groups of five and gives them an activity to work on. The teacher moves around the classroom, assisting the learners and checking for progress

1. Solve the following equations:

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

m)

CONSOLIDATION/ CONCLUSION

AND OR HOMEWORK

5 min

VERY IMPORTANTS POINTS TO ILLUSRATE ARE:

· An equation is a mathematical sentence that is true for some numbers, but false for other numbers.

· Two equations are called equivalent if they have the same solution.

HOMEWORK

1. Are the following statements True or False?

a)

b)

c)

d)

e)

REFLECTION

ANSWERS: TERM 3 GRADE 8 WEEK 2: LESSON 1

Mental Maths

Class work

Homework

No mental Maths

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

m)

a) False

b) False

c) False

d) False

e) True


WEEK2: LESSON 2



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

Extend solving equations to include:

· using additive and multiplicative inverse

· Equations of the form: a product of factors = 0.

· Solve equations using laws of exponents

RESOURCES

GDE ATP Term 3


(GDE 17 03 2014).

PRIOR KNOWLEDGE


· Expressions

· Variables

· Exponents

· Equations

· Substitution

· Additive and multiplicative inverse.

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS


6min

1

a) False

b) False

c) False

d) False

e) True

Page 25

LESSON

PRESENTATION/DEVELOPMENT AND CLASSWORK

20min

The teacher put learners in groups of five and gives them an activity to work on. The teacher moves around the classroom, assisting the learners and checking for progress

1. Solve the following equations:

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

m)

n)

CONSOLIDATION/CONCLUSION

AND OR HOMEWORK

4min


· An equation is a mathematical sentence that is true for some numbers but false for other numbers.


HOMEWORK

1. Find the original number. Justify.

a) A number multiplied by 10 is 80.

b) Add 83 to a number and the answer is 100.

c) Divide a number by 5 and the answer is 4.

d) Multiply a number by 4 and the answer is 20.

e) Twice a number is 100.

f) A number raised to the power 5 is 32.

g) A number raised to the power 4 is 81.

h) Fifteen times a number is 90.

i) 93 added to a number is −3.

j) Half a number is 15.

REFLECTION

ANSWERS: TERM 3 GRADE 8 WEEK 2: LESSON 2

Mental Maths

Classwork

Homework

Included in the lesson

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

m)

n)

a) 8

b) 17

c) 20

d) 5

e) 50

f) 2

g) 3

h) 6

i) -96

j) 30


WEEK 2: LESSON 3

TOPIC:ALGEBRAIC EQUATION


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

· determine numerical value of an expression by substitution

· identify variables and constants in given formulae or equations

· Use substitution in equations to generate tables of ordered pairs.


RESOURCES

GDE ATP Term 3


(GDE 17 03 2014).

PRIOR KNOWLEDGE


· Expressions

· Variables

· Exponents

· Equations

· Substitution

· Additive and multiplicative inverse.

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS


5min

a) 8

b) 17

c) 20

d) 5

e) 50

f) 2

g) 3

h) 6

i) -96

j) 30

Page 25

LESSON

PRESENTATION/

DEVELOPMENT

10min

The teacher discusses the additive and multiplication inverses.

Example: The additive inverse of −5 is 5, because −5 + 5 = 0.The additive inverse of +5 is −5 as well.

Example:

The multiplicative inverse of 2 is , because

N.B. the additive inverse of a number a is the number that, when added to a, yields zero

Multiplicative inverse of a number or reciprocal of a number.

CLASSWORK

10min

1. State the additive inverses of the following:

a) 5

b) -5

c) 17

d) 0,1

e)

2. State the multiplicative inverse of the following:

a) 3

b) -6

c)

3. Solve the following equations

a)

b)

c)

CONSOLIDATION/ CONCLUSION

AND OR HOMEWORK

5min


· An equation is a mathematical sentence that is true for some numbers but false for other numbers.


· The additive inverse of a number a is the number that, when added to a, yields zero.

HOMEWORK

Write the equations below in words using “a number” in place of the letter symbol.

Then write what you think “the number” is in each case.

Example: 4 + = 23. Four plus a number equals twenty-three. The number is 19.

a) 8 = 72

b) 2 + 5 = 21

c) 12 + 9 = 30

d) 30 + 2 = 40

e) (e) 5 + 4 = 3 + 10

REFLECTION

ANSWERS TERM 3: GRADE 8: WEEK 2: LESSON 3

Mental Maths

Class work

Homework

None

1.

a) -5

b) 5

c) -17

d) -0,1

e)

2.

a)

b)

c)

3.

a)

b)

c)

a) Eight multiplied by a number equals to seventy two. The number is 9

b) Two multiplied by a number plus five equals twenty one. The number is 8

c) Twelve plus a number multiplied by nine equals thirty. The number is 2

d) Thirty plus two times a number equals to forty. The number is5

e) Five multiplied by a number plus four equals three times a number plus ten. The number is 3


WEEK 2 LESSON 4

TOPIC: Algebraic equations



· determine numerical value of an expression by substitution

· identify variables and constants in given formulae or equations

· Use substitution in equations to generate tables of ordered pairs.


RESOURCES

GDE ATP Term 3


(GDE 17 03 2014).

PRIOR KNOWLEDGE

TermExpression

Variable Number sentences

Place holderProperties of numbers

Squares, cubes and exponentsSquare roots and cube roots

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

MENTAL MATHS

3 min

Study the equation:

1. How many letter symbols does the equation have? (List them.)

2. Is it possible to solve this “equation”?

3. Complete the table:

2

1

5

3

4

-5

-10

Page 25

HOMEWORK

5 min

a) Eight multiplied by a number equals to seventy two. The number is 9

b) Two multiplied by a number plus five equals twenty one. The number is 8

c) Twelve plus a number multiplied by nine equals thirty. The number is 2

d) Thirty plus two times a number equals to forty. The number is5

e) Five multiplied by a number plus four equals three times a number plus ten. The number is 3

KEYWORDS:

Equations, ordered pairs and tables

LESSON DEVELOPMENT

15 min

A specific input number, for example 10, and the output number associated with it (52 in the case of the function described by) is called an ordered pair.

Ordered pairs can be represented in a table.

-2

-1

0

1

2

3

4

0

1

2

3

4

5

6

(-2; 0)

Ordered pairs can also be written in brackets: (input number; output number).

For example the ordered pairs you entered into the table can be written as

(-2; 0), (-1; 1), (0; 2), (1; 3), (2; 4), (3; 5), (4; 6)

Complete the table by writing the ordered pairs in brackets below the table, as shown in table above.

Then choose two more input numbers and write down two additional ordered pairs that belong to each given function.

For the function with the rule and (10; 45) and (20; 85)

In the function indicated bythe letter symbol in the formula () represents the input or independent variable while the other letter symbol () represents the output or dependent variable.

(c) For the function with the rule

-5

-3

1

2

-17

Complete the table and then write the ordered pairs in brackets below the table

1.

1

2

3

4

-3

2.

-12

-7

-2

3

102

If there is precisely one value of for each value of , we say that is a function of

(a) For the function with the rule

5

0

-3

18

34

(b) For the function with the rule

5

1

0

-3

-17

Recap

2 min

The use of substitution in order to get the value of is important. Learners must substitute appropriately. Strategies of solving by inspection and elimination are also important. They should also differentiate between the dependent and the independent variables.

HOMEWORK ACTIVITIES

2 min


0

1

2

3

18

LESSON REFLECTION

ANSWERS: TERM3 GRADE 8 WEEK 2 LESSON 4

MENTAL MATHS

CLASSWORK

HOMEWORK

Study the equation:

1. (2.)

2. No, there are two unknowns

3.

2

1

5

3

4

-5

-10

12

7

27

17

22

-23

-48

1.

1

2

3

4

5

9

6

3

0

-3

(1;9), (2;6), (3;3), (4;0), (5;-3)

2.

-12

-7

-2

3

10

146

51

6

11

102

(-12;146), (-7;51), (-2;6), (3;11), (10;102)


0

1

2

3

4

2

3

6

11

18

(0;2), (1;3), (2;6), (3;11), (4;18)


WEEK 2, LESSON 5

TOPIC: Functions and Relationships


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

Determine, interpret and justify equivalence of different descriptions of the same relationship or rule presented:

· verbally

· in flow diagrams

· in tables

· by formulae

· by equations

RESOURCES

GDE ATP Term 3

DBE workbook 2 (Page 150-126), Sasol-Inzalo workbook 2(Page 137), textbook, pencil, eraser, calculator. DVDs( GDE 03 03 2014; GDE 05 03 2014)

PRIOR KNOWLEDGE

• Concepts and skills developed in Grade 7

• Calculation using integers

• Substituting into rules

• Functions and relationships with flow diagrams, tables, number sentences,

equations and formulae

COMPONENTS

TIME

TASKS/ACTIVITIES

COMMENT

INTRODUCTION

(Mental maths)

2 min

1.

2.

3.

4.

Solutions:

1.

2.

3.

4.

Page 22

REVIEW AND

CORRECTION OF HOMEWORK

0

1

2

3

4

2

3

6

11

18

(0;2), (1;3), (2;6), (3;11), (4;18)

LESSON PRESENTATION

DEVELOPMENT

15 min

Teacher Activity

1. Find the output values in each flow diagram and use a table to show the input/output values relationship.

a)

-2

-1

0

1

2

b)

-2

-1

0

1

2

Teacher Activity- Solutions

2.

a)

-2

-1

0

1

2

-8

-5

-2

1

4

Input Values

-2

-1

0

1

2

Output Values

-8

-5

-2

1

4

-2

-1

0

1

2

0

3

6

9

12

b)

Input Values

-2

-1

0

1

2

Output Values

0

3

6

9

12

CLASSWORK

10 min

Learner Activity

· Find the output values in each flow diagram and use a table to show the input/output values relationship.

a)

-3

-2

0

2

3

b)

-2

-1

0

1

2

HOMEWORK

3 min

Activity

1. Find the output values in each flow diagram and use a table to show the input/output values relationship.

a)

-2

-1

0

1

2

b)

-2

-1

0

1

2

ANSWERS: TERM 3 GRADE 8 WEEK 2 LESSON 5

Mental Maths

Classwork

Homework

1. -8

2. 0

3.

4.

Learner Activity - Solutions

Find the output values in each flow diagram and use a table to show the input/output values relationship.

a)

Input Values

-3

-2

0

2

3

Output Values

-4

0

8

16

20

b)

Input Values

-2

-1

0

1

2

Output Values

1

-1

-3

-5

-7

a)

Input Values

-2

-1

0

1

2

Output Values

-2

0

2

4

6

b)

Input Values

-2

-1

0

1

2

Output Values

-1

-2

-3

-4

-5


WEEK 2, LESSON 6



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


· verbally

· in flow diagrams

· in tables

· by formulae

· by equations

RESOURCES

GDE ATP Term 3

DBE workbook 2 (Page 150-126), Sasol-Inzalo workbook 2(Page 137), textbook, pencil, eraser, calculator. DVDs( GDE 03 03 2014; GDE 05 03 2014)

PRIOR KNOWLEDGE

• Concepts and skills developed in gr. 7





COMPONENTS

TIME

TASKS/ACTIVITIES

COMMENT

INTRODUCTION

(Mental maths)

2 min

1.

2.

3.

4.

Solutions:

Page 22

REVIEW AND


5 min

a)

Input Values

-2

-1

0

1

2

Output Values

-2

0

2

4

6

b)

Input Values

-2

-1

0

1

2

Output Values

-1

-2

-3

-4

-5

LESSON PRESENTATION

DEVELOPMENT

10 min

Teacher Activity:

1. Represent the following number relationships on a flow diagram.

a) 3 added to 4 gives a sum which results to a negative 14 when multiplied by a negative 2.

b) Negative 2 multiplied by 3 and subtract 1 gives a result of a negative 7.


a) When a number is multiplied by 4 and 2 subtracted from the product, the result is a negative 1.

b) When a number is multiplied by negative 3 and the product added to 4, the result is 2.

Teacher Activity - Solutions:

1.

a)

1

2

b)

2.

a)

b)

CLASSWORK

Learner Activity


a) 1 added to 3 gives a sum which results to a negative 8 when multiplied by a negative 2.

b) Negative 1 multiplied by 2 and subtract 3 gives a result of a negative 5.


c) When a number is multiplied by 3 and 1 subtracted from the product, the result is a negative 2.

d) When a number is multiplied by negative 1 and the product added to 3, the result is 2.

Learner Activity – Solutions

1.

-2

2

a)

b)

2.

a)

b)

HOMEWORK

Learner Activity


a) 3 added to negative 5 gives a sum which results to 8 when multiplied by a negative 4.

b) Negative 6 multiplied by 2 and add 3 gives a result of a negative 9.


a) When a number is multiplied by negative 3 and 3 subtracted from the product, the result is a negative 1.

b) When a number is multiplied by negative 4 and the product added to 1, the result is 3.

Homework – Solutions

1.

a)

1

3

b)

2.

a)

b)


Mental Maths

Classwork

Homework

1.

2.

3.

1.

-2

2

a)

b)

2.

a)

b)

1.

a)

1

3

b)

2.

a)


WEEK 2, LESSON 7


· CONCEPTS AND SKILLS TO BE ACHIEVED



· verbally

· in tables

· by formulae

· by equations

RESOURCES

GDE ATP Term 3

DBE workbook 2 (Page 150-126), Sasol-Inzalo workbook 2 (Page 137), textbook, pencil, eraser, calculator. DVDs( GDE 03 03 2014; GDE 05 03 2014)

PRIOR KNOWLEDGE

• Concepts and skills developed in gr 7





COMPONENTS

TIME

TASKS/ACTIVITIES

COMMENT

INTRODUCTION

(Mental maths)

2 min

1. 2+2+2+5=

2. 11 =

3. 12 12=

Page 22

REVIEW AND


1.

a)

1

3

b)

2.

a)

b)

LESSON PRESENTATION

DEVELOPMENT

10 min

Activity

1. Find the rule that describes the relationship between the input and the output values in this table.

Input Values ()

1

2

3

8

12

33

Output Values()

12

14

16

26

34

76

Answer:

Using equations to determine the rule:

First find the common difference between the output values. In this case it is equal to 2. Then construct equations making use of the term and the constant difference.

Output value 1 or

2. In the flow diagram below the input and output values are given. Determine the rule to find the output values.

2

3

4

-3

-5

-7

CLASSWORK

10 min

Learner Activity 1


-1

0

1

0

3

6

2. Use the input and output values to determine the rule and use the rule to complete the table.

-3

-2

-1

0

2

6

5

0

2

Learner Activity 1 - Solutions

2.

-3

-2

-1

0

1

2

6

5

4

3

2

1

CONSOLIDATION

CONCLUSION AND HOMEWORK.

3 min

Homework


-3

-2

-1

0

7

5

3

1

2. Use the input and output values to determine the rule and use the rule to complete the table.

-4

-2

0

8

6

2

-2

-14


Classwork

Homework

2.

-3

-2

-1

0

1

2

6

5

4

3

2

1

1.

2.

-4

-2

0

1

8

6

-2

-10

-14


WEEK 2 LESSON 8




· Analyse and interpret global graphs of problem situations, with a special focus on constant, increase or decrease

· Interpret graphs with special focus on the -intercept an -intercept of linear graphs

· Interpret graphs with special focus on the gradient of linear graphs

RESOURCES

GDE ATP Term 3


(GDE 17 03 2014).

PRIOR KNOWLEDGE

Revise the following done in Grade 8:

-- analyse and interpret global graphs of problem

situations, with a special focus on the following

trends and features:

♦♦ linear or non-linear

♦♦ constant, increasing or decreasing

♦♦ discrete or continuous

Extend the above with special focus on the

following features of linear graphs:

-- -intercept and y-intercept

-- gradient

COMPONENTS

TIME

TASKS/ACTIVITIES

COMMENTS

INTRODUCTION

(Mental maths)

Match column A with column B

2 Mins

Column A

Column B

1. Gradient undefined

a)

2. Gradient is 0

b)

3. Gradient is positive

c)

4. Gradient is negative

d)

Page 22

LESSON PRESENTATION

DEVELOPMENT

10 Mins

Straight line graphs: Gradient and intercepts

· The intercepts are the points where a graph cuts (intersects with) the -axis and the -axis.

· The slope of the graph is called the gradient.

· The gradient (m) measures the steepness of a line.

· The gradient tells us how much we go up or down

(the change in ) for each step we go along (the change in ).

Demonstration

Do the following demonstration and allow learners to observe and explain their observations:

· Use a ruler and a marble/ small ball.

· Place the ruler high against the wall and let the marble roll down the ruler.

· Place the ruler at a lower level then before and roll the marble down the ruler again.

· Repeat this until the ruler is flat on the table.

Ask learners the following questions:

a) What do you observe in the speed of the marble as it moves down the ruler at different heights?

b) Explain this occurrence.

Discussion:

· When the slope of the ruler is steep the marble roll faster down.

· As the height (slope) of the ruler becomes lower the marble moves slower down.

· When the ruler is flat the marble does not roll.

· The higher the ruler is the steeper it is and the lower it is the less steep it becomes.

· Slope in mathematics are referred to as gradient.

CLASSWORK

10 Mins

Activity 1:

Determine the gradient of the following lines and state whether the lines are increasing, decreasing or constant.

1) The line passing through the points (2;1) and (4;3)

2) The line passing through the points (-1;3) and (-3;3).

CONSOLIDATION

CONCLUSION AND HOMEWORK.

3 Mins

Activity 2

1) Calculate the intercepts

Draw the graph of on the set of axis below

· Find the y-intercept by making x = 0

· Find the x-intercept by making y = 0

· Join the two intercepts.

2) Use any two points:

Draw the graph for

· Use any two input or x-values

· It is easy to use values close to 0 e.g. –1 and 1

· Substitute them into the equation to find the output values.

· You can check your calculations by using a third x-value and y-value

· Plot the point

-1

0

1

-2

0

2

REFLECTION

You may have noticed that the equations of straight lines look similar.

The equation of a straight line is: y = mx + c. m tells us the gradient of the line.

c tells us where the line crosses the y-axis.

This is called the y-intercept and it has the coordinates (0; c).

GRADIENT

· Gradient means the steepness or slope of the line.

INTERCEPT

· The point where a line crosses one of the axes

ANSWERS: GRADE 8: TERM 3: WEEK 2: LESSON 8

Mental Maths

Classwork

Homework

a) Gradient is positive

b) Gradient is undefined

c) Gradient is negative

d) Gradient is 0

Activity 1

1)

The line is increasing because the gradient is positive.

2)

The line is constant because the gradient is 0.

Activity 2

1)

2)


WEEK 2, LESSON 9

1. TOPIC: Weekly Assessment

MULTIPLE CHOICE TEST

GRADE 8

TERM 3 WEEK 2

Circle the letter of the correct answer.

QUESTION 1

The correct equation for the flow diagram below is:

-2

3

5

-5

5

9

x

A.

B.

C.

D.

QUESTION 2

The correct set of output values is:

-2

-1

0

2

2

a

b

c

d

A: ; ; ;

B: ; ; ;

C: ; ; ;

D: ; ; ;

QUESTION 3

The equation represented by the graph below is:

A.

B.

C.

D.

QUESTION 4

Choose a table that best represent the description:

“A number is added to a negative two and their sum multiplied

by three”.

A:

B:

C:

D:

MULTIPLE CHOICE TEST MEMORANDUM

GRADE 8

TERM 3 WEEK 2

1. B

2. D

3. A

4. C


WEEK 3: LESSON 1

REVISION(GRAPHS AND EQUATIONS)



Use tables of ordered pairs to plot points and draw graphs on the Cartesian plane.

RESOURCES

GDE ATP Term 3

DBE workbook(60-90), Sasol-Inzalo workbook(47-74), ruler, pencil, eraser, calculators, notebook, grid paper; DVDs(GDE 03 11 2014; GDE 05 11 2014)

PRIOR KNOWLEDGE

· Plotting points to draw graphs

· Flow diagrams

· Tables

· Equations

COMPONENTS

TIME

TASKS/ACTIVITIES

Comments

INTRODUCTION/MENTAL MATHS

2 min

Complete the table for y values:

X

-4

-3

-2

-1

0

1

Y = x - 3

Page 145


No homework since it’s the first lesson.

LESSON

PRESENTATION/DEVELOPMENT

15min

The teacher discusses the characteristics of coordinate System and ordered pairs and give the learners the following notes.

A coordinate system is a two-dimensional number line, for example, two perpendicular number lines or axes.

The coordinate system/ Cartesian plane:

The horizontal axis is called the x-axis and the vertical axis is called the y-axis.

The center of the coordinate system (where the lines intersect) is called the origin. The axes intersect when both x and y are zero. The coordinates of the origin are (0, 0).

An ordered pair contains the coordinates of one point in the coordinate system. A point is named by its ordered pair of the form of (x, y). The first number corresponds to the x-coordinate and the second to the y-coordinate.

Educator does Examples of plotting points with learners.

CLASS WORK

10min

1. Copy and complete a table of values for:

-3

-2

-1

0

1

2

3

-2

Plot the above ordered pairs on the Cartesian plane provided below.

2. Calculate the output values of y, and write x and y in ordered pairs.

x y

y =2(x – 3)

y =

1

2

3


AND/OR HOMEWORK

3 min

VERY IMPORTANT POINTS TO ILLUSTRATE ARE:

· Input value – the number substituted for the variable in a formula or rule.

· Output – the answer for a particular value.

· The rule is a process that mixes the input values and output values.

· The other name for co-ordinate plane is Cartesian plane.

· The other name for an ordered pair is a point.

Plot the following ordered pair in a coordinate plane:

a) A (0; 0)

b) B(3;2)

c) C(-4;2)

d) D(-5;0)

e) E(-2;-2)

f) F(3;-1)

REFLECTION


MENTAL MATHS

CLASS WORK

X

-4

-3

-2

-1

0

1

Y = x - 3

-7

-6

-5

-4

-3

-2

1.

-3

-2

-1

0

1

2

3

-2

-1

0

1

2

3

4

2.

HOMEWORK


WEEK 3: LESSON 2




· Use tables of ordered pairs to plot points and draw graphs on the Cartesian plane.

RESOURCES

GDE ATP Term 3


PRIOR KNOWLEDGE


· Flow diagrams

· Tables

· Equations

· Formula

COMPONENTS

TIME

TASKS/ACTIVITIES

Comments

INTRODUCTION/ MENTAL MATHS

2 Min

Complete the table for y-values:

X

-4

-3

-2

-1

0

1

y = x + 6

Page 145

LESSON


5min

Do the following activities with learners.

Activity 1

Set up a table of ordered pairs (Table method).

Sketch the graph of a linear function given by the equation

by using the following steps:

Step 1 - the -value is the dependent variable so select a set of values to represent.

Step 2 - use the equation and substitute each -value to calculate the corresponding -value.

Step 3 – plot the ordered pairs on a Cartesian plane

Answer

-3

-2

-1

0

1

2

-3

-1

1

3

5

7

CLASS WORK

15min

1. Complete the following flow diagram:

2. Use the flow diagram below to complete the table.

a)

Input value

1

2

3

4

5

50

86

Output value

36

75

b) Describe by means of a formula how the input and output values are related. Use the letter for output values and letter for input values.


AND/OR HOMEWORK

5min







1.1 Complete the following flow diagrams below.

1.2

2. Sketch the following graphs using the table method

(NB: axis must start from -3 to 3):

2.1.

REFLECTION


MENTAL MATHS

CLASSWORK

Complete the table for y-values:

x

-4

-3

-2

-1

0

1

y = x + 6

2

3

4

5

6

7

1.

2.

a)

Input value

1

2

3

4

5

10

13

50

86

Output value

9

12

15

18

21

36

75

156

264

b)

HOMEWORK

Sketch the following graphs using the table method (NB: x must start from -3 to 3):

2.1 y = x – 3

2.2 y = x + 2


WEEK 3: LESSON 3




· Use tables of ordered pairs to plot points and draw graphs on the Cartesian plane

RESOURCES

GDE ATP Term 3


PRIOR KNOWLEDGE


· Flow diagrams

· Tables

· Equations

· Formula

· Substitutions

COMPONENTS

TIME

TASKS/ACTIVITIES

Comments

INTRODUCTION/MENTAL MATHS

2 min

Let , complete the table for the values of A:

B

12

4

8

16

20

H

8

6

4

10

12

A

Page 145


5 min

1. 2; 1; 0 ; -1 ; -2

2. Sketch the following graphs using the table method (NB: x must start from -3 to 3):

2.1

2.2

LESSON


8 min

The teacher discusses the use of the formulae in determining the out value.

A formula is a mathematical expression, comprised of numbers and symbols, each with a specific meaning. It defines the process of getting the output.

WORKED EXAMPLE

If the perimeter of a square is given by and a side is represented by s, Determine P if .

Solution

CLASS WORK

13 min

Learners individually must calculate the following:

1. If the distance covered (d) is represented by the formula where s represents speed and t represents time, determine the distance covered in 4, 7 hours at a constant speed of 100km/h.

2.

If the area of a triangle is given by, determine the area if b = 5cm and h =20cm.

3. Study the table below and answer the questions that follow:

x

1

2

3

6

9

y=x+1

(a) Complete the table

b) Which are the input values?

c) Which are the output values?

d) Which are the two variables in the table above?

e) Which one is the dependent variable? Explain why.

f) Which one is the independent variable? Explain why.

4. Write down the formula for the function illustrated in the table below.

x

1

2

3

4

5

6

y

15

10

5

0

-5

-10

CONSOLIDATION/ CONCLUSION AND/OR HOMEWORK

4 min







1. Here is an example of a relationship between two quantities:

In each arrangement there are some black dots and some white dots.

a) How many white dots are there if there is one black dot?

b) How many white dots are there if there are two black dots?

c) How many white dots are there if there are three black dots?

d) How many white dots are there if there are four black dots?

e) How many white dots are there if there are five black dots?

f) How many white dots are there if there are six black dots?

g) How many white dots are there if there are seven black dots?

h) How many white dots are there if there are ten black dots?

i) How many white dots are there if there are twenty black dots?

j) How many white dots are there if there are one hundred black dots?

REFLECTION

ANSWERS: GRADE 8 TERM 3 WEEK 3 LESSON 3

MENTAL MATHS

CLASS WORK

Let A = ½ B x H, complete the table for the values of A:

B

12

4

8

16

20

H

8

6

4

10

12

A

48

12

16

80

120

1.

2.

3.

x

1

2

3

6

9

2

3

4

7

10

a)

b)

c)

d)

e)

4.

HOMEWORK

BLACK DOTS

1

2

3

4

5

6

7

10

20

100

WHITE DOTS

6

10

14

18

22

26

30

42

82

402


WEEK 3: LESSON 4




· Use tables of ordered pairs to plot points and draw graphs on the Cartesian plane

RESOURCES

GDE ATP Term 3


PRIOR KNOWLEDGE

· Input and output values

· Flow diagrams

· Tables

· Equations

COMPONENTS

TIME

TASKS/ACTIVITIES

Comments

INTRODUCTION

2 min

1 chicken has 4 legs.

For 2 chickens, how many legs are there?



Let learners complete the table below:

Number of chickens ()

1

2

3

6

9

Number of legs ()

4

8

Page 145


5 min

BLACK DOTS

1

2

3

4

5

6

7

10

20

100

WHITE DOTS

6

10

14

18

22

26

30

42

82

402

LESSON


10 min

Ask learners to complete the table looking for the relationship between the input values and the output values.

Input value

1

2

3

4

5

6

Output value

4

14

19

Discuss how learners found their ANSWERS. Some learners may have resorted to looking for relationships between the output values. At this level they must be encouraged to look for the relationship between the input and output value

e.g.

=

From the pattern that emerges it becomes easy to find the formula

Ask learners to write formulae that provide the same information as the verbal representations below. Let them use for the input value and for the output value.

a) Multiply the input value by 11, then subtract 3 to get the output value.

Answer:

b) Multiply the square of the input value by 6, then add 4 times the input value to get the output value.

Answer:

c) Add 3 to the input value, then subtract the sum from 50 to get the output value.

Answer:

CLASS WORK

10 min


X

1

2

3

30

40

60

Y

7

12

17

152

202

302


x

1

6

9

12

18

20

y

1

36

81

144

324

400

CONSOLIDATION/CONCLUSION AND/OR HOMEWORK

3 min

VERY IMPORTANTS POINTS TO ILLUSTRATE ARE:







x

1

6

9

12

18

20

y

3

38

83

146

326

402

2. Use the instructions in the flow diagram to complete the table.

Input value

1

2

3

4

5

10

23

50

86

Output value

REFLECTION

ANSWERS: GRADE 8 TERM 3 WEEK 3 LESSON 4

MENTAL MATHS

CLASS WORK

1 chicken has 4 legs.




Let learners complete the table below:

Number of chickens ()

1

2

3

6

9

Number of legs ()

4

8

12

24

36

4x

1.

2.

HOMEWORK

1.

2.

Input value

1

2

3

4

5

10

23

50

86

Output value

5

8

11

14

17

32

71

152

260


WEEK 3: LESSON 5

TOPIC: TRANSFOMATION


By the end of the lesson, learners should know and be able to: recognise, describe and perform transformations with points on the co-ordinate plane, focusing on:

· Reflecting a point on the y-axis and x-axis

· Translating a point within and across quadrants

RESOURCES

ATP third term

Sasol–Inzalo workbook (47-74), DBE workbook (60-90), ruler, pencil, eraser, calculator, notebook, exercise books. DVDs(GDE 10 11 2014; GDE 12 11 2014)

PRIOR KNOWLEDGE

· The names of different 2D-shapes from grade 7.

· How to draw simple shapes using a pencil.

· Know the co-ordinate plane formed.

· Know the characteristics of co-ordinate plane.

· Quadrants.

· Know what a point is

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTAL MATHS)

3 min

Remind learners of the importance of transformation.

Group learners in different groups and give them the following activity:

Define the following terms:

1. Cartesian plane

2. Origin

3. Point

4. Transformation

5. Reflection

6. Translation

7. Quadrants

Page 145

Transformation

Recognize, describe and perform transformation.


5 min

It is important to give homework and do remediation:

Homework is very important communication between a teacher and the learners. It’s a diagnostic tool for teacher self-evaluation and for learner evaluation. As it is the first lesson, the teachers must emphasize the importance of homework.

LESSON

PRESENTATION /DEVELOPMENT

10min

· The teacher explains all the important terminology in transformation and give the learners notes, starting with the terms given in the introduction.

· The teacher writes the terms (from introduction) and explanation thereof, on the board

· The teacher demonstrates how to plot points on the Cartesian plane.

Explanation:

· Cartesian plane – also called the co-ordinate plane, it is a plane made up of the x- and y-axis.

· To reflect about x-axis, is when points are flipped when the mirror line is the x-axis

Rule (A;B) reflect about x–axis (A;-B)

· To reflect about y-axis, is when a point is flipped when the mirror line is the y-axis

Rule (A;B) reflect about y–axis (-A;B)

· Place learners in pairs and instruct them to do the following activity.

Activity.

1. How many quadrants are there on the co-ordinate plane?

2. On the co-ordinate plane, plot the following points.

A (2; 2) B (0; 5) C (-1; 4) D (0; 0)

When learners are discussing the above in pairs, the teacher moves around the classroom and address errors.

SOLUTION

y-axis

x-axis

1.

Co-ordinate plane.

· Learners have to learn how to plot points on the co-ordinate plane.

· Learners have to know the conventions for writing ordered pairs ()

CLASS WORK

10min

1. Plot the following points on the co-ordinate system:

a) (5;2)

b) (-4;3)

c) (-5;1)

d) (-6;-2)

e) (-1;-1)

f) (3;-2)

g) (-5;-4)

2.

a) In which quadrant are both co-ordinates positive?

b) In which quadrants are both co-ordinates negative?

c) In which quadrants is x-co-ordinate negative and y-co-ordinate positive?

d) In which quadrants is y-co-ordinate negative and x-co-ordinate positive?


AND/OR HOMEWORK

2min

Activity : learners must complete the table below:

Given points

Reflection in the y-axis

Reflection in the x-axis

A(-3;3)

B(5;1)

C(-1;-2)

HOMEWORK

In each case, state whether the triangle was translated, reflected or rotated.

REFLECTION

Answers: Week 3 Lesson 5

ANSWERS TO MENTAL MATHS.

1. Cartesian plane – also called the co-ordinate plane, it is a plane made up of the x- and y-axis.

2. Origin – it is the point where the x- and y-axis meet (0; 0)

3. Transformation – when a figure /shape is moved from one position by sliding, turning or flipping.

4. Reflection – movement of figure by flipping.

5. Translation - movement of figure by sliding.

6. Quadrants – the four sections of the co-ordinate plane.

ANSWERS TO CLASS WORK.

1.

2.

a) Quadrant 1

b) Quadrant 3

c) Quadrant 2

d) Quadrant 4


WEEK 3: LESSON 6

TOPIC: TRANSFOMATION


By the end of the lesson, learners should know and be able to: recognise, describe and perform transformations with points on the co-ordinate plane, focusing on :

· Reflecting a point/triangle in the y-axis or x-axis.

· Translating a point/triangle within and across quadrants.

RESOURCES

ATP third term

Sasol–Inzalo workbook (47-74), DBE workbook (60-90), ruler, pencil, eraser, calculator, notebook, exercise books. DVDs (GDE 10 11 2014; GDE 12 11 2014).

PRIOR KNOWLEDGE

· Characteristics of the Cartesian plane.

· Ordered Pairs.

· Translating points.

· Reflecting points.

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTAL MATHS)

2 min

Discuss the following questions:

1. What is to reflect about x-axis?

2. What is to reflect about y-axis?

3. What is to translate?

Page 145

Learners should recognise that translation, reflections and rotations only change the position of the figure and not the shape or size.


3min

1. Rotation.

2. Reflection.

3. Translation.

4. Rotation.

5. Reflection.

6. Translation

LESSON


10 min

1. Copy and complete the table below:

Given points



A(-2;2)

B(1;2)

C(-2;-1)

ANSWERS TO LESSON DEVELOPMENT

Given points



A(-2;2)

A′(2;2)

A′′(-2;-2)

B(1;2)

B′(-1;2)

B′′(1;-2)

C(-2;-1)

C′(2;-1)

C′′(-2;1)

2. Copy and complete the table below.

Given points

Translated 3 units downward and 1 units to the left

Translated 2 unit downwards and 3 unit right

A(-2;2)

B(1;2)

C(-2;-1)

ANSWERS TO LESSON DEVELOPMENT

Given points

Translated 3 units downward and 1 units to the left

Translated 2 unit downwards and 3 unit right

A(-2;2)

A′(-3;-1)

A′′(1;0)

B(1;2)

B′(0;5)

B′′(4;0)

C(-2;-1)

C′(-3;-4)

C′′(1;-3)

CLASS WORK

10 min

Copy and complete the table below.

Given points

Translated 2 units upward and 2 units to the right

Translated 1 unit downwards and 1 unit left

A(-2;2)

B(1;2)

C(-2;-1)

Describe different transformations


AND/OR HOMEWORK

2min

Match words in Column A with words in Column B

Column A

Column B

Rotation

Flip

Translation

Turn

Reflection

Slide

REFLECTION

ANSWERS: WEEK 3 LESSON 6

MENTAL MATHS.

1. To reflect about x-axis is when points are flipped when the mirror line is the x-axis

Rule (A; B) reflect about x-axis (A;-B)

2. To reflect about y-axis is when a point is flipped when the mirror line is the y-axis

Rule (A; B) reflect about y-axis (-A;B)

3. Translate, is to change position of the point upward/downwards vertically or right/left horizontally

ANSWERS TO CLASS WORK

Given points

Translated 2 units upward and 2 units to the right

Translated 1 unit downwards and 1 unit left

A(-2;2)

A′(0;4)

A′′(-3;1)

B(1;2)

B′(3;4)

B′′(0;1)

C(-2;-1)

C′(0;1)

C′′(-3;-2)


WEEK 3: LESSON 7

TOPIC: TRANSFORMATION


By the end of the lesson, learners should know and be able to: recognise, describe and perform transformations with triangles on the co-ordinate plane, focusing on the co-ordinates of the vertices when:

· Reflecting a Triangle in the x-axis or y-axis.

RESOURCES

ATP third term


PRIOR KNOWLEDGE

· Plotting points on the Cartesian plane.

· Translating points.

· Reflecting points

· Relationship between object and image.

· Understanding the word: vertices.

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION/ MENTAL MATHS

1. Explain the and the axis and the Cartesian plane.

5min

1. Reflect the following along the y-axis to.

Page 145


3min

SOLUTION

Column A

Column B

Rotation

Turn

Translation

slide

Reflection

Flip

LESSON


12min

Learner activity:

a) Reflect the about the x-axis.

SOLUTION

Learners should recognise that reflection produces congruent figures.

CLASS WORK

5min

Complete the following table.

Vertices of triangle



A(-2;4)

B(0;2)

C(3;1)

CONSOLIDATION/

CONCLUSION

AND/OR HOMEWORK

5min

VERY IMPORTANTS POINTS TO ILUSRATE ARE:

· Reflection is a type of transformation along a mirror line, it’s either along x-axis or y-axis.

· When a figure is reflected or translated, the original shape is always congruency to the image.

· The x-axis is the horizontal line on the Cartesian plane.

· The y-axis is the vertical line on the Cartesian plane.

Homework

The points K, M and T are plotted on the coordinate system.

a) Write down the coordinates of points K, M and T.

b) Reflect each point in the x-axis and write down the coordinates of K', M' and T'.

c) Reflect points K, M and T in the y-axis and write down the coordinates of K'', M'' and T''.

d) Join points K, M and T to form a triangle. Do the same with points K', M' and T', and with points K'', M'' and T''.

REFLECTION

WEEK 3 LESSON 7

MENTAL MATHS

ANSWERS TO CLASS WORK

Vertices of triangle



A(-2;4)

A′(2;4)

A′′(-2;-2)

B(0;2)

B′(0;2)

B′′(0;-2)

C(3;1)

C′(-3;1)

C′′(3;-1)


WEEK 3: LESSON 8

TOPIC: TRANSFORMATION


By the end of the lesson, learners should know and be able to: recognise, describe and perform transformations with triangles on the co-ordinate plane, focusing on the co-ordinates of the vertices when:

· Rotating a triangle around the origin.

RESOURCES

ATP third term


PRIOR KNOWLEDGE

· Plotting points on the Cartesian plane.

· Rotation points of a triangle.

· The relationship between image and object.

· Centre of Rotation.

· Origin.

COMPONENTS

TIME

TASKS/ACTIVITIES

CAPS

INTRODUCTION

(MENTAL MATHS)

5min

1. What do you understand by the word Rotation and the origin?

2. Write down the co-ordinates of each image after these transformations:

a) Rotation 180 clockwise about the origin. A (1; 3) B (5; 4) C (4;-3).

b) Is the image and original congruent?

Page 145

Learners should recognize that rotation only change the position of the figure, and not its shape and size.


1.

a) Write down the co-ordinates of points A, B and C.

A(−1; 2); B(1; −4); C(4; 1)

b) Translate A, B and C, 6 units to the left and 4 units up.

c) Write down the co-ordinates of points A', B' and C'.

A'(−7; 6); B' (−5; 0); C' (−2; 5)

d) Join points A, B and C to form a triangle. Do the same with points

A', B' and C'.

e) Are ΔABC and ΔA'B'C' congruent? Yes

LESSON


10min

Class Activity (Teachers to do the activity with the learners, guiding learners to discover for themselves)

(N.B. Learners do not have to learn general rules for the transformations at this stage, but should explore the way the co-ordinates of points change when performing different transformations with lines or shapes.)

1. In the diagram below, point C has been rotated 90°clockwise about the origin.

a) Rotate points A and B 90° clockwise about the origin.

b) Write down the co-ordinat

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