math gr8 m3 magical world of - maths excellencemathsexcellence.co.za/books/e gd 8/mathematics/1...

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MODULE FRAMEWORK AND ASSESSMENT SHEET

FORMATIVE ASSESSMENT SUMMATIVE ASSESSMENT LEARNING OUTCOMES (LOS)

ASSESSMENT STANDARDS (ASS) ASs

Pages and (mark out of 4) LOs

(ave.out of 4) Tasks or tests

(%) Ave for LO

(% and mark out of 4)

LO 1 We know this when the learner: 1.2 recognises, classifies an represents the

following numbers to describe and compare them:

1.2.2 decimals, fractions and percentages;

1.2.5 additive and multiplicative inverses;

1.2.6 multiples and factors;

1.2.7 irrational numbers in the context of measurement (e.g. π and square and cube roots of non-perfect squares and cubes);

1.3 recognises and uses equivalent forms of the rational numbers listed above;

1.6 estimates and calculates by selecting and using operations appropriate to solving problems that involve:

1.6.1 rounding off;

1.6.2 multiple operations with rational numbers (including division with fractions and decimals);

1.7 uses a range of techniques to perform calculations, including:

1.7.1 using the commutative, associative and distributive properties with rational numbers;

NUMBERS, OPERATIONS AND RELATIONSHIPS

The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

1.7.2 using a calculator;





(%) Ave for LO


1.9 recognises, describes and uses: 1.9.1 algorithms for finding equivalent fractions;

1.9.2 the commutative, associative and distributive properties with rational numbers (the expectation is that learners should be able to use these properties and not necessarily to know the names of the properties).

LO 3 We know this when the learner: 3.2 in context that include those that may be used

to build awareness of social, cultural and environmental issues, describes and classifies geometric figures and solids in terms of properties, including:

SPACE AND SHAPE (GEOMETRY)

The learner will be able to describe and represent characteristics and relationships between two-dimensional shapes and three-dimensional objects in a variety of orientations and positions.

3.2.1 sides, angles and diagonals and their inter-relationships, with focus on triangles and quadrilaterals (e.g. types of triangles and quadrilaterals).

LO4 We know this when the learner: 4.2 solves problems involving:

4.2.1 length;

MEASUREMENT The learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts.

4.2.2 perimeter and area of polygonals and circles;





(%) Ave for LO


4.3 solves problems using a range of strategies including:

4.3.1 estimating;

4.3.2 calculating to at least two decimal positions;

4.3.3 using and converting between appropriate SI units;

4.4 describes the meaning of and uses π in calculations involving circles and discusses its historical development in measurement;

4.5 calculates, by selecting and using appropriate formulae:

4.5.1 perimeter of polygons and circles;

4.5.2 area of triangles, rectangles circles and polygons by decomposition into triangles and rectangles;

4.8 investigates (alone and / or as a member of a group or team) the relationship between the sides of a right-angled triangle to develop the Theorem of Pythagoras;

4.9 uses the Theorem of Pythagoras to calculate a missing length in a right-angled triangle leaving irrational answers in surd form (�);

4.10 describes and illustrates ways of measuring in different cultures throughout history (e.g. determining right angles using knotted string leading to the Theorem of Pythagoras).

LEARNING UNIT 1

The wonderful world of RATIONAL NUMBERS

..................................................................................................................ACTIVITY 1.1 Differentiating between rational and irrational numbers

LO 1.2.7 1. Can you remember what each of the following represents?

N = { ........................................................................... }

N0 = { ........................................................................... }

Z = { ........................................................................... }

R = { ........................................................................... }

2. Provide the definition for:

� a rational number:

............................................................................................................................................

� an irrational number:

............................................................................................................................................

3. How would you represent each of the following?

3.1 Rational number......................... 3.2 Irrational number .........................

4. Complete the following table by marking relevant numbers with an X:

2/7 0 1 3 3 9 3 8 2,47 45.1 84

916

Rasional

Irrasional

5. Select the required numbers from the list:

32− ; 1 + 4 ; 49 + ; -4 ; 5

112 ; 2

21+

5.1 Integers: ......................................................................................................................

5.2 Rational numbers: ......................................................................................................

5.3 Irrational numbers: ......................................................................................................

6. Explain what you know about an equivalent fraction.

............................................................................................................................................

7. Provide two equivalent fractions for the following: 72 = ............... = ...............

8. Provide the terms used to identify each of the following (e.g. proper fraction):

8.1 72

.....................................................................................................................

8.2 27

.....................................................................................................................

8.3 726 .....................................................................................................................

8.4 0,67 .....................................................................................................................

8.5 76,0 �� .....................................................................................................................

8.6 23 % .....................................................................................................................

Any of the above can be reduced to any of the others.

LO 1.2.7

..................................................................................................................ACTIVITY 1.2 Reduction of fractions to decimal numbers / recurring decimal numbers and vice versa

LO 1.2.2 LO 1.2.6 LO 1.3 LO 1.6.1 LO 1.9.1 1. Use your pocket calculator to reduce the following fraction to a decimal number:

2043 ..................................................

2. Explain how you would reduce this to a decimal number without the use of your pocket calculator. There are two methods:

Method 1: .................................................. (reduce denominator to 10 / 100 / 1 000)

Method 2: .................................................. (do division) (Let your educator assist you.)

� Do you see that the answer is the same – if the denominator cannot be reduced to multiples of 10 you have to apply the second method.

3. Now reduce each of the following to decimal numbers (round off, if necessary, to two

digits):

3.1 85 ..................................................

3.2 413 ..................................................

3.3 435 ..................................................

3.4 873 ..................................................

3.5 76 ..................................................

3.6 97 ..................................................

4. Write the following decimal numbers as fractions or mixed numbers: (N.B.: All fractions have to be presented in their simplest form.)

4.1 6,008 ..................................................

4.2 4,65 ..................................................

4.3 0,375 ..................................................

4.4 7,075 ..................................................

4.5 13,65 ..................................................

4.6 0,125 ..................................................

5. How do we reduce fractions to recurring decimal numbers?

E.g. 115

Step 1: place a comma after the 5, i.e. 5, 0000

Step 2: carry on dividing until a pattern becomes visible - the pattern will be indicated by the recurring numbers.

5, 50 60 50 60

11 = 0,4545…… (45 is repeated --- 4 and 5 therefore are recurring) = 54,0 ��

� Now try the following:

5.1 97 ........................................................................................................................

5.2 655− ........................................................................................................................

5.3 99133 ........................................................................................................................

6. What is noticeable about fractions that are recurring decimal numbers (with regard to the

denominator)?

............................................................................................................................................

7. Now, before we provide the steps for reducing a recurring decimal number to a common

fraction, see if you are able to write the following as fractions by making use of the information from no. 6.

7.1 3,0 � ....................................... 7.2 54,0 �� .......................................

7.3 320,0 �� ....................................... 7.4 300,0 � .......................................

8. The following provides complete steps for reducing a recurring decimal number to a common fraction:

e.g. 1,0 � = ????? Let 1,0 � = x 10x = 1,1111…..

− 1x = 0,1111….. 9x = 1 x = 9

1

Suggestion: Multiply by 10 (if you have one recurring figure). Multiply by 100 (if there are 2 recurring figures), etc.

9. Now try to do no. 7.2 in the way that is discussed in no. 8.

...........................................................................

...........................................................................

...........................................................................

...........................................................................

LO 1.2.2 LO 1.2.6 LO 1.3 LO 1.6.1 LO 1.9.9

..................................................................................................................ACTIVITY 1.3 Reducing percentages to fractions and vice versa

LO 1.2.2 LO 1.2.6 LO 1.6.1 LO 1.9.1

1. What is the meaning of % (percentage)? .....................................................................

2. If you have to reduce any fraction to a percentage, you have to reduce the denominator

to 100.

� If this is not possible, you have to x 1%100

(This principle can be applied in any situation, e.g. when you want to reduce a test that is marked out of 15 to a mark out of 50, you need to multiply by 1

50 )

� Reduce the following mathematics test marks from a grade 8 class to percentages (to one decimal figure, where necessary):

2.1 2017 ....................................... 2.2 40

19 .......................................

2.3 5038 ....................................... 2.4 60

45 .......................................

3. Reduce each of the following percentages to a common fraction (or a mixed number):

3.1 55 % ....................................... 3.2 15,5% .......................................

3.3 16 21 % ....................................... 3.4 3

26 % .......................................

4. Each South African citizen should have access to some means of transport.

� Bolokanang has a community of 25 500 people. Study the accompanying table indicating the number of people that use the given means of transport and answer the questions that follow.

Vehicle Number of users

Bicycle 814 %

Car 53

Motorbike 0,085

4.1 Indicate how many inhabitants make use of:

a) a bicycle .....................................................................................................

b) a car .....................................................................................................

c) a motorbike .....................................................................................................

4.2 Express the number of inhabitants that use a car as a fraction of those who travel by bicycle.

...................................................................................................................................

4.3 Which percentage of the inhabitants has no vehicle?

...................................................................................................................................

4.4 Which other means of transport do farm labourers use to get to the nearest town?

...................................................................................................................................

4.5 If the number of job opportunities in rural areas should increase, the fraction of citizens who use cars for transport will double. What fraction of the community will be using cars for transport under such conditions?

...................................................................................................................................

LO 1.2.2 LO 1.2.6 LO 1.6.1 LO 1.9.1

......................................................................................HOMEWORK ASSIGNMENT 1 1. Arrange the following decimal numbers in ascending order:

3,214 3,784 3,8 3,009 3,087 3,9

............................................................................................................................................

2. Arrange the following decimal numbers in descending order:

0,05 0,5 0,505 5,005 5,05

............................................................................................................................................

3. Fill in : = of > of <

3.1 2, 4 ......................... 2 2511 3.2 6,28 ......................... 6 400

108

4. Write each of the following as a decimal number:

4.1 00013

10013

100727 +++ ..................................................

4.2 85

25135,36 ++ ..................................................

5. Round the following decimal numbers as indicated:

5.1 72,284 .................. (interger) 5.2 24,342 .............. (one decimal place)

5.3 3,9998 .................. (3 decimal places) 5.4 17,8854 kg .................. ( 00011 kg)

6. Reduce each of the following to common fractions or mixed numbers:

6.1 0,085 .................. 6.2 17 21 % .................. 6.3 8,125 ..................

6.4 15,005 .................. 6.5 8 32 % ..................

6.6 51,0 �� (Show all steps.)

................................................................................................................

................................................................................................................

................................................................................................................

7. Reduce each of the following to decimal figures:

(Round to 1 decimal figure, where necessary.)

7.1 88,5 % ................................ 7.2 15 85 ................................

7.3 2416 ................................ 7.4 9

5 ................................

7.5 4019 ................................ 7.6 5 25

13 ................................

LEARNING UNIT 1 ASSESSMENT 1.1

MY ASSESSMENT: AS I SEE IT: EDUCATOR'S ASSESSMENT: I am able to… �� 1 2 3 4 CRITICAL OUTCOMES 1 2 3 4 differentiate between rational and irrational numbers (LO 1.2.2 ; 1.2.6; 1.2.7)

Critical and creative thinking

define a rational number (LO 1.2.2 ; 1.9.1) Collaborating

reduce fractions to mixed numbers (and vice versa) (LO 1.2.6; 1.3; 1.9.1)

Organising and manageing

reduce fractions to decimal numbers.(LO 1.2.6; 1.3; 1.9.1) Processing of information

reduce decimal numbers to fractions.(LO 1.2.6; 1.3; 1.9.1) Communication

reduce recurring decimal numbers to fractions (LO 1.2.6; 1.3; 1.6.1; 1.9.1)

Problem solving

�� good �� average �� not too good Independence

Learner's comments: ��

I am very satisfied with the standard of my work.. � �� Date:

I am satisfied with the steady progress I have made. �� Out of:

I have worked hard, but I am not satisfied with my performance. �� Learner:

I did not give my best. ��

Parents' Comments: Educator's comments: ............................................................................................................................ ......................................................................................................

............................................................................................................................ ......................................................................................................

............................................................................................................................ ......................................................................................................

Signature: --------------------------------------------------------- Date: ------------------- Signature: --------------------------------------- Date: --------------

..................................................................................................................ACTIVITY 1.4 Adding and subtracting rational numbers (fractions)

LO 1.2.2 LO 1.2.5 LO 1.2.6 LO 1.6.2 LO 1.7.1 LO 1.7.2 LO 1.9.1 LO 1.9.1 1. Reduce each of the following compound numbers to improper fractions.

This is very important in addition, subtraction, multiplication and division of fractions.

1.1 5 74 ................................ 1.2 7 9

7 ................................

2. What is of cardinal importance before attempting to add or subtract fractions?

............................................................................................................................................

3. Show whether you are able to do the following:

3.1 8 - 4 73 .......................................................................................................................

3.2 3 91 - 1 2

1 � ....................................................................................................................

� Note this: The denominators must be similar when you add fractions together or subtract them from one another.

� e.g. 2 74 - 1 7

6 2 – 1 = 1 and 7

4 - 76 ( 4 – 6 --- this is not possible. Carry one whole: 1 = 7

7 ) ( 4 + 7 = 11 --- yes, 11 – 6 = 5) Answer: 7

5

� You could also reduce compound numbers to improper fractions and make the denominators similar.

� e.g.. 75

713

718 =− (18 – 13 = 5: The denominators are the same. Subtract one

numerator from the other.)

4. Do the following:

4.1 4 71 + 4 42

16 .....................................................................................................

4.2 36 − 15 116 .....................................................................................................

4.3 83

81 625,0 −+ .....................................................................................................

4.4 43

21

105 674 ++

...................................................................................................................................

...................................................................................................................................

4.5 7 31 - 4 8

7 .....................................................................................................

4.6 7a - 4a a/4 .....................................................................................................

4.7 ( )baba369 −+ .....................................................................................................

4.8 - 6 + 2 76 .....................................................................................................

4.9 5 - (4 94 + 2 3

2 )

...................................................................................................................................

...................................................................................................................................

4.10 3 31 a - 2 2

1 a .....................................................................................................

LO 1.2.2 LO 1.2.5 LO 1.2.6 LO 1.6.2

LO 1.7.1 LO 1.7.2 LO 1.9.1 LO 1.9.2

..................................................................................................................ACTIVITY 1.5 Multiplication and division of rational numbers (fractions)

LO 1.2.6 LO 1.6.2 � You did this in grade 7 – let's refresh the memory.

1. Multiplication:

� Important: Write all compound numbers as fractions. Then do crosswise cancellation.

� Try the following:

� 1 41 × 2 2

1 × 4

......................................................................................................................................

......................................................................................................................................

2. Division:

� The reciprocal plays an important role in the division of fractions.

� Use an example to explain this term.

..........................................................................................................................................

..........................................................................................................................................

e.g. 32

31 ÷

� Both numbers are fractions

� Change ÷ to the × sign and obtain the reciprocal of the denominator (fraction following the ÷ sign).

� Do cancellation as with multiplication.

............................................................................................................................................

3. Do the following:

3.1 8 ÷ 118

.....................................................................................................

3.2 18 ÷ 87

.....................................................................................................

3.3 25

65 ÷ .....................................................................................................

3.4 -2 32 ÷ -1 9

7 .....................................................................................................

3.5 6 43 mn ÷ -6 m3 .....................................................................................................

3.6 ax

abxy

32

34 −− ÷ - .....................................................................................................

LO 1.2.6 LO 1.6.2

......................................................................................HOMEWORK ASSIGNMENT 2

SECTION A 1. Simplify each of the following:

(Use fractions.)

1.1 0,0049 ÷ 0,007 .....................................................................................................

1.2 7 + 0,5 ÷ 0,025 .....................................................................................................

1.3 1 + 0,001 x 0,4 ÷ 0,25

......................................................................................................................................

......................................................................................................................................

1.4 12 x 2,5 + 14,07 .....................................................................................................

2. 2

1 of 32 - (14 21 + 3 4

1 )

............................................................................................................................................

............................................................................................................................................

3. 20

2175 × ........................................................................................................................

4. 8

941

21

43

21 2421 ÷−×+

............................................................................................................................................

............................................................................................................................................

............................................................................................................................................

5. 12 x 4 4

3 ........................................................................................................................

6 21

41

41

21

58

11

−+

............................................................................................................................................

............................................................................................................................................

............................................................................................................................................

7. 6 76 x 2 3

1 ........................................................................................................................

8. 6

1214

43

21 212 +×+

............................................................................................................................................

............................................................................................................................................

............................................................................................................................................

9. 2 - ( 2

1 - 31 )

............................................................................................................................................

............................................................................................................................................

10. 4

3 + 83 × 2

............................................................................................................................................

............................................................................................................................................

11. Calculate 2 4

1 of two revolutions.

............................................................................................................................................

12. 158 + 16 x 4

3

............................................................................................................................................

13. (0,2)2 ÷ 0,002

............................................................................................................................................

14. 1 4

1 of ( 21 - 3

1 ) x 2 52

............................................................................................................................................

SECTION B 15. Show how you determine the answer and circle the correct answer.

15.1 21 - 2

1 x 21

...................................................................................................................................

a) 21 b) 4

1 c) 0 d) 81

15.2 =× 65

32 …

...................................................................................................................................

a) 97 b) 18

7 c) 95 d) 1 9

1

15.3 3221

1

1 is equal to:

...................................................................................................................................

a) 52 2 b) 2 2

1 c) 1 91 d) 10

9

15.4 1543

12852××

××× = …

...................................................................................................................................

a) 38

b) 34

c) 310 d) 3

16

15.5 237,50 % written as a compound number is:

...................................................................................................................................

a) 2 83 b) 2,735 c) 2 8

5 d) 23,750

15.6 Which of the following numbers is the smallest?

...................................................................................................................................

a) 41

b) 52 c) 7

2 d) 10

3

15.7 43

52 12 ÷ is equal to:

...................................................................................................................................

a) 74

512 ÷ b) 4

7125 × c) 4

7125 ÷ d) 7

45

12 ×

15.8 27,9 ÷ 0,9 = .....

...................................................................................................................................

a) 0,31 b) 3,1 c) 31 d) 310

16. Calculate 4 3

1 % of 279,36 kg

............................................................................................................................................

17. Write 30

14 as a percentage (accurate to one decimal figure).

............................................................................................................................................

18. Calculate 0,8 % of 0,05.

............................................................................................................................................

19. 3

261

41 4112 ÷÷

............................................................................................................................................

............................................................................................................................................

SECTION C � You may use your pocket calculator.

Show all operations that are entered on the pocket calculator.

1. If 30 % of a number is equal to 6060, the number is:

............................................................................................................................................

2. When a number has been increased by 14 % , the particular number is 587,6.

� Calculate the original number.

............................................................................................................................................

3. How many minutes make up 20% of 3 hours and 20 minutes?

............................................................................................................................................

4. Study the following pattern:

1 Row 1

2 3 4 Row 2

5 6 7 8 9 Row 3

10 11 12 13 14 15 16 Row 4

� What would the middle number in the 60th row be?

............................................................................................................................................

5. There are 400 learners in the Magnulate school. There are 325 girls.

� If 40 % of the boys are older than 14 years, how many boys are younger than 14 years?

............................................................................................................................................

............................................................................................................................................

6. A spring produces 9,375 litres of water per minute. This water flows into a tank. It takes 1 hour and 20 minutes to fill the empty tank.

� How much water will the tank contain when it is filled?

............................................................................................................................................

............................................................................................................................................


MY ASSESSMENT: AS I SEE IT: EDUCATOR'S ASSESSMENT: I am able to… �� 1 2 3 4 CRITICAL OUTCOMES 1 2 3 4 do addition of rational numbers (fractions) (LO 1.2.2; 1.2.5; 1.2.6; 1.3) Critical and creative thinking

do subtraction of rational numbers (fractions) (LO 1.2.2; 1.2.5; 1.2.6) Collaborating

do multiplication of fractions (LO 1.2.2; 1.2.6; 1.9.1; 1.9.1.9.2) Organising and manageing

do division of fractions with confidence (LO 1.2.2; 1.2.6; 1.9.1; 1.9.2) Processing of information

confidently execute these four operations with brackets (LO 1.2.2; 1.2.6) Communication

reduce decimal numbers to fractions and vice versa and can confidently execute four main operations (LO 1.2.2; 1.2.6; 1.7.1; 1.7.2; 1.9.1; 1.9.2)

Problem solving

reduce percentages to fractions and/or decimal numbers and vice versa, and can confidently execute four main operations (LO 1.2.2; 1.2.5; 1.2.6; 1.7.1; 1.7.2; 1.9.1; 1.9.2)

Independence

�� good �� average �� not too good





I did not give of my best. ��


............................................................................................................................ ......................................................................................................


TUTORIAL Module 3: Learning unit 1 (The wonderful world of RATIONAL NUMBERS)

Total: 60

1. Arrange in assending order:

52

31

153 10

5

................................................................................................................................... [2]

2. Determine the value of a in each of the following:

2.1 24128 a= 2.2 a

1283 =

............................................... ............................................... [2]

3. Simplify:

3.1 612 − ......................................................................................... [2]

3.2 816

721 − ......................................................................................... [2]

3.3 103

51

31 372 −+

..........................................................................................................................

.......................................................................................................................... [3]

3.4 31

32

41 112of4 ÷

..........................................................................................................................

.......................................................................................................................... [4]

3.5 ( ) 912

35 1÷−

..........................................................................................................................

.......................................................................................................................... [4]

3.6 aa 8132 +−

.......................................................................................................................... [3]

4. By how much is 6 3

1 more than -5 41 ?

...................................................................................................................................

................................................................................................................................... [3]

5. The product of two numbers is 6. Calculate what the second number would be if the first is - 2

1 ?

...................................................................................................................................

................................................................................................................................... [3]

6. Reduce the following to a recurring decimal number. Show how you do the division.

3383

...................................................................................................................................

................................................................................................................................... [3]

7. Reduce the following recurring decimal number to a common fraction or a compound

number.

7.1 2,2 �

..........................................................................................................................

..........................................................................................................................

.......................................................................................................................... [3]

7.2 320,0 ��

..........................................................................................................................

..........................................................................................................................

.......................................................................................................................... [3]

8. Complete the following table by placing an X in the appropriate space or spaces where

the number ought to be.

N N0 Z Q Q' R

3 27

94

3,0 �

[6]

9. The five numbers p, q, r, s and t provide an average of 23. The numbers p, q, r and s have an average of 21 only. Calculate the value of t.

.................................................................................................................................

................................................................................................................................. [2]

10. R 499,78 x 78 + 12 x R 499,78

...................................................................................................................................

................................................................................................................................... [2]

11. ( ) 18361 ×

...................................................................................................................................

................................................................................................................................... [2]

12. y

27 = 108 y = .......

................................................................................................................................... [1]

13. Which fraction is nearest to 2

1 �? Make use of percentages to calculate the answer. No marks will be awarded if you only provide an answer. Show all operations.

83 10

4 125 16

9

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... [4]

14. Calculate each of the following:

(You may use fractions throughout.)

14.1 0,7 ÷ 0,007

..........................................................................................................................

14.2 0,09 ÷ 4

..........................................................................................................................

14.3 (100 ÷ 0,01) + (0,01 ÷ 100)

..........................................................................................................................

[6]

TOTAL: 60

LEARNING UNIT 1 TUTORIAL ASSESSMENT 1.3

MY ASSESSMENT: AS I SEE IT: EDUCATOR'S ASSESSMENT: I am able to… �� 1 2 3 4 CRITICAL OUTCOMES 1 2 3 4 distinguish between rational and irrational numbers (LO 1.2.2 ; 1.2.7) Critical and creative thinking

reduce fractions (rational numbers) to decimal numbers and/or percentages and vice versa (LO 1.2.2 ; 1.9.1)

Collaborating

do addition with fractions with confidence (LO 1.2.5 ; 1.2.6) Organising and manageing

do subtraction with fractions with confidence (LO 1.2.5 ; 1.2.6) Processing of information

do multiplication with fractions with confidence (LO 1.6.2; 1.7.1; 1.9.2) Communication

do division with fractions with confidence (LO 1.2.6; 1.7.1; 1.9.2) Problem solving

confidently do all four main operations with fractions (LO 1.6.2; 1.7.1; 1.9.2)

Independence

use my pocket calculator confidently where necessary, and do the necessary rounding (LO 1.7.2; 1.6.1)

�� good �� average �� not too good







............................................................................................................................ ......................................................................................................


TEST 1 Module 3: Learning unit 1 (The wonderful world of RATIONAL NUMBERS)

Total: 40

SECTION A

1. 30 − 53 of 40 + 8 .........................

2. 12 21 % (Write as a common fraction and simplify.) .........................

3. 4 31 (reciprocal) .........................

4. 4 253 (Write as a decimal number.) .........................

5. 54 of ___ = 16 .........................

6. As 24 × 28 = 672, calculate the value of 48 × 14. .........................

7. 7,236 ÷ 9 .........................

8. 0,0698 ÷ 1 000 .........................

9. 7 ÷ 0,007 .........................

10. 10056,34 × 1 000 ......................... [10]

11. Which of the following numbers is greater than 50 %? Show how you thought it through.

0,04 0,26 157 22

11

...................................................................................................................................

Answer: ......................... [2]

12. 8 100

37 − 6,098 .................................................. .........................

13. 0,5 × 0,3 + 2,225 .................................................. ......................... [2]

14. Select the correct answer and mark a, b, c or d with an X:

14.1 103 × 10² − 1

a) 100 000 b) 99 999 c) 99 000 d) 9 999

14.2 2 52 as a percentage....

a) 120 % b) 40 % c) 300 % d) 240 %

14.3 8 of 5 − 4 ÷ 4 = y y =

a) 18 b) 39 c) 24 d) 4

14.4 8,5 x y = 0,0085 y =

a) 1 000 b) 0,01 c) 0,001 d) 100

14.5 12,12 ÷ 0,2 = y y =

a) 6,6 b) 6,06 c) 60,6 d) 66

14.6 Which number is the smallest?

a) 1001 b) 10

1 1 c) 2

1 d) 0

14.7 3 43 % =

a) 43 b) 4

15 c) 803 d) 0,375 [7]

15. Arrange in descending order:

15.1 0,079 ; 0,7 ; 0, 09 ....................; ....................; ....................

15.2 54 ; 8

7 ; 107 ; 20

17 ....................; ....................; ....................; ....................; [2]

16. Write each of the following as decimal numbers:

16.1 00019

1099300 +++ ..................................................

16.2 2 ÷ 3 ..................................................

16.3 85 .................................................. [3]

17. Round off as indicated:

17.1 28,685 litres (nearest litre) ..................................................

17.2 35,67324 (0,01) .................................................. [2]

18. Write each of the following as common fractions or as compound numbers:

18.1 15,34 .................................... 18.2 0,625 ....................................

18.3 2,02 % .................................... [3]

19. Calculate a in the following:

19.1. a x a x a = 0,027 a = ......................... [1]

20. Calculate:

20.1 5 x 3 53 ........................................................................................

20.2 54

54 × ........................................................................................

20.3 153

54 3+ .............................................................................................. [3]

21. Calculate:

21.1 ( ) 41

243 1×÷ aa

..........................................................................................................................

.......................................................................................................................... [3]

21.2 625142 p

.......................................................................................................................... [2]

21.3 dac

daabc

dcab

512

104

32

3

3

32

3

÷×

..........................................................................................................................

..........................................................................................................................

.......................................................................................................................... [4]

22. ( ) 55116 2

183

41 ÷+−

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... [4]

23. 5

4254 5489,2785 −+

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... [4]

24. Which of the following are irrational numbers between 2 and 10?

15 − 21 34 3 9 4,5 227

................................................................................................................................... [2]

25. Reduce the following recurring decimal number to a common fraction. Show all steps.

51,0 ��

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... [4]

26. Calculate your percentage for a mathematics test for a mark of 30

17 .

................................................................................................................................... [2]

27. BONUS MARK QUESTIONS [5]

27.1 If x * y = (x + y)² , then (1 * 4) * (3 * 2) = .......

.......................................................................................................................... [2]

27.2. 4

32a

aa +

..........................................................................................................................

.......................................................................................................................... [3]

TOTAL : 70

ENRICHMENT EXERCISE for the quick learner

Module 3: Learning unit 1

1. Prove that the product of three consecutive integers plus one will always be a perfect

square.

............................................................................................................................................

............................................................................................................................................

2. Study the given pattern and then attempt to answer the question.

4 Ö 3 = (4 x 3) + (4 + 3) = 12 + 7 = 19

2 Ö 5 = (2 x 5) + (2 + 5) = 10 + 7 = 17

� Calculate: 7 Ö 13

............................................................................................................................................

............................................................................................................................................

3. How many different four-digit numbers can be formed with the figures: 3; 5; 7 and 9 if

each figure may only be used once?

............................................................................................................................................

............................................................................................................................................

4. Determine the value of a and m. Show how you thought the problem through.

1 2 3 4 7 .... m

3 7 11 a 27 .... 59

............................................................................................................................................

............................................................................................................................................

LEARNING UNIT 2

The wonderful world of CIRCLES

.................................................................................................................ACTIVITY 2.1 Discovering the characteristics of a circle

LO 3.1 LO 4.2.1 LO 3.4 1. Try to copy the following design, using a pair of compasses only:

2. Draw a circle of any size. Refer to a textbook or any other source of information to help

you indicate the following on the circle:

2.1 Centre: T

2.2 Diameter (Name it PQ.)

2.3 Radius: TS

2.4 Any arc: FG

2.5 Sector: PTW (shade this portion.)

2.6 Chord: KL

2.7 Use a coloured pencil to indicate where you would determine the circumference of the circle.

3. Refer to your sketch to answer the following questions:

3.1 What is characteristic of TW, PT, TS and TQ? ..........................................................

3.2 Measure WTP ˆ . ..........................................................................................................

3.3 What is the size of QTP ˆ ? ........................................................................................

3.4 What do we call this type of angle? ............................................................................

4. Construct the following with the help of a pair of compasses:

4.1 a circle with a diameter measuring 4 cm

4.2 a circle with a radius of 1,5 cm

5. How would you go about constructing a circle of 4 m?

� Plan: ................................................................................................................................

..........................................................................................................................................

LO 3.1 LO 4.2.1 LO 3.4

..................................................................................................................ACTIVITY 2.2 Discovering the circumference of a circle and dealing with related problems

LO 4.2.2 LO 4.3.1 LO 4.3.2 LO 4.3.3 LO 4.4 LO 4.5.1 1. Make use of about four bottles / cups of different sizes. Use a length of string and

measure the diameter of each of the bottles to complete the following table:

circumference (O) diameter (m/d) O ÷ m/d

Bottle 1

Bottle 2

Bottle 3

Bottle 4

1.1 What is noticeable in the last column? .....................................................................

circumference ÷ diameter

1.2 What is the term used for the answer in the last column? ........................................

1.3 Name two values that can be used for π: ...................... or ......................

1.4 Which formula can therefore be used to calculate the circumference of any circle?

...................................................................................................................................

2. We could also deduce this formula from a circle by proceeding as follows:

2.1 Draw a circle with centre P and radius 25 mm on a sheet of paper.

2.2 Cut out the circle and place a mark anywhere on the edge of the cut circle.

2.3 Draw a line (use a ruler) across the remaining area of the sheet of paper. Roll the circle (cut out disk) on its edge along this line (place the mark on the edge of the circle at the beginning of the ruled line. Mark the spot where the rotation is completed on the line when the rolled circle has completed a full rotation.

2.4 Use your ruler to measure the marked distance.

� Distance: ......................... mm

2.5 What term would we use to describe the distance that was measured in 2.4? ..........

2.6 Use your calculator to calculate the following:

� circumference ÷ diameter = ..................... ÷ ..................... = ........................

2.7 What term do we use to describe the answer that you have obtained? ...................

3. What do we actually mean when we say that the wheel of a bicycle has completed a full

rotation?

............................................................................................................................................

4. Write the formula for calculating the circumference of a circle on the following line and

answer the questions that follow:

� Circumference = ..................................................

4.1 How would you calculate the radius of a circle when the circumference is provided?

� Radius (R) = ..................................................

4.2 How would you calculate the diameter of a circle when the circumference is provided?

� Diameter (d) = ..................................................

Now you should be able to answer any question dealing with the diameter, radius or circumference of a circle or wheel or any circular object.

5. Use your pocket calculator to calculate the circumference of each of the following circles:

Note this: Always write out the formula before you start. (π = 3,14).

5.1 r = 230 mm 5.2 r = 1,45 cm (answer to 2 decimal figures)

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

6. Determine the circumference of each of the following without the use of a pocket

calculator.

Note this: Always write out the formula before you start.

(π = 722

)

6.1 r = 14 cm 6.2 d = 35 cm

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

7. Calculate the radius of the following circle:

You may use your pocket calculator, but you have to show all the steps of the calculation.

(π=722

)

7.1 circumference 242 mm

...........................................................................

...........................................................................

...........................................................................

8. How many rotations will the wheel of a mountain bike complete over a distance of 7,5 m

if the diameter of the wheel is 67 cm?

...........................................................................

...........................................................................

...........................................................................

LO 4.2.2 LO 4.3.1 LO 4.3.2 LO 4.3.3

LO 4.4 LO 4.5.1

......................................................................................HOMEWORK ASSIGNMENT 1 1. Draw a circle and illustrate the following, using different colours:

1.1 radius 1.2 diameter

1.3 circumference 1.4 sector

1.5 arc

� Draw the circle in this space:

2. Construct three circles with the same centre P, and radii of 30 mm, 45 mm and 65 mm.

2.1 What would these circles be called?

...................................................................................................................................

3. Determine the circumference of each of the following circles without the use of a pocket calculator:

� (π= 722

)

3.1 r = 28 cm 3.2 d = 5,6 m

........................................................... ...........................................................

........................................................... ...........................................................

4. Determine the circumference of each of the following circles with the help of a pocket

calculator (accurate to one digit):

� (π = 3,14).

4.1 r = 315 mm 4.2 d = 25,7 cm

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

5. The wheel of a motorbike rotates 834 times over a distance of 2 km. Calculate the radius

of this wheel.

............................................................................................................................................

............................................................................................................................................

6. Calculate (to the nearest centimetre) both the diameter and the radius of a bicycle wheel

that completes a distance of 275 cm in one rotation.

............................................................................................................................................

............................................................................................................................................

7. How many times bigger that the circumference of A is the circumference of B?

Error! A: B:

............................................................................................................................................

............................................................................................................................................

P mm 3 P mm

8. Calculate the circumference of the shaded points:

8.1 8.2

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

45 mm

45 mm 14 cm


MY ASSESSMENT: AS I SEE IT: EDUCATOR'S ASSESSMENT: I am able to… �� 1 2 3 4 CRITICAL OUTCOMES 1 2 3 4 use π in a formula (LO 4.4) Critical and creative thinking

identify different parts of a circle (LO 4.2.2) Collaborating

calculate the circumference of a circle without the help of a pocket calculator (LO 4.2.2; 4.5.1; 4.2.1)


calculate the circumference of a circle with a pocket calculator (LO 4.2.2; 4.5.1; 4.2.1)

Processing of information

solve any problem involving diameter, radii and circumference (LO 4.3; 4.5.1)

Communication

�� good �� average �� not too good Problem solving

Independence







............................................................................................................................ ......................................................................................................

............................................................................................................................ ......................................................................................................


..................................................................................................................ACTIVITY 2.3 Discovering the area of a circle and solving related problems

LO 4.2.1 LO 4.2.1 LO 4.5.1 LO 4.3 1. Can you remember the formula for calculating the area of a rectangle?

............................................................................................................................................

2. Draw a circle with centre O and a radius of 60 mm on a sheet of paper. Divide the circle into 32 equal sectors. Use red for colouring 16 sectors and blue for the remaining 16 sectors.

3. Cut out all 32 sectors and arrange them in line in such a way that the segments eventually form a rectangular paving design.

� Paste your triangles in the following space

4. Measure both the length and breadth of the rectangle. Use the formula from no. 1 to

calculate the area of the rectangle.

............................................................................................................................................

5. What do you deduce with regard to the rectangle and the circle that you have drawn in no. 2?

............................................................................................................................................

6. Which unit of measurement is used for calculating area? .................................................

7. Provide the formula for calculating the area of any circle.

............................................................................................................................................

8. Calculate the area of the circle you have drawn in no. 2 with the help of the formula from no. 7.

............................................................................................................................................

What do you notice? ..........................................................................................................

9. Calculate the area of each of the following circles without making use of a pocket calculator.

� (π = 722

)

9.1 r = 14,7 cm 9.2 d = 56,49 cm

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

10. Calculate the area of the shaded parts. � You may use your pocket calculator for this. (π = 3,14)

A: B:

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

11. Calculate the area of the shaded parts.

............................................................................................................................................

............................................................................................................................................

............................................................................................................................................

............................................................................................................................................

............................................................................................................................................

LO 4.2.1 LO 4.2.2 LO 4.5.2 LO 4.3

5 cm

14,5 cm

14,5

cm

A

D

H

G

B

C

E

F

BE = FC = 15 cm EF = 10 cm

40 cm

......................................................................................HOMEWORK ASSIGNMENT 2 1. Complete the following table: (You may make use of your pocket calculator.)

� Show all operations in the spaces that are provided for this purpose.

Circumference Area Radius Diameter

1 568 cm

2 590,43 cm²

3 5,4 cm

4 138 mm

1: Area: ....................................................................................................................................

............................................................................................................................................

1: Radius: ................................................................................................................................

............................................................................................................................................

1: Diameter: .............................................................................................................................

............................................................................................................................................

2: Circumference: ...................................................................................................................

............................................................................................................................................

2: Radius: ...............................................................................................................................

............................................................................................................................................

2: Diameter: ............................................................................................................................

............................................................................................................................................

3: Circumference: ...................................................................................................................

............................................................................................................................................

3: Area: ...................................................................................................................................

............................................................................................................................................

3: Diameter: ............................................................................................................................

............................................................................................................................................

4: Circumference: ...................................................................................................................

............................................................................................................................................

4: Area: ...................................................................................................................................

............................................................................................................................................

4: Radius: ...............................................................................................................................

............................................................................................................................................

2. Calculate the area of the shaded parts:

2.1 2.2

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

3. Study the map of the Theewaterskloof Dam and environment and answer the questions

that follow.

3.1 Which types of trees might be found in this area and which part of these trees relate to the theme of this learning unit?

...................................................................................................................................

3.2 Sketch a cross section of the trunk of a pine tree and supply it with a suitable radius.

3.3 Now calculate the area of the cross section.

...................................................................................................................................

...................................................................................................................................

3.4 What part of this trunk is important for determining the age of the tree?

...................................................................................................................................

3.5 Indicate (3.4) in your sketch and determine the area of one of these (3.4).

...................................................................................................................................

...................................................................................................................................

3.6 Circles obviously play a role in helping us to execute some calculations concerning nature. Trees also form part of a natural circle (cycle). Discuss this “circle” with regard to trees.

...................................................................................................................................

...................................................................................................................................


MY ASSESSMENT: AS I SEE IT: EDUCATOR'S ASSESSMENT: I am able to… �� 1 2 3 4 CRITICAL OUTCOMES 1 2 3 4 use π in a formula (LO 4.4); Critical and creative thinking

calculate the circumference of a circle without using a pocket calculator (LO 4.2.2; 4.5.1)

Collaborating

calculate the circumference of a circle with a pocket calculator (LO

4.2.1; 4.2.2; 4.5.1) Organising and manageing

calculate the area of a circle without using a pocket calculator (LO

4.2.1; 4.2.2; 4.5.1) Processing of information

calculate the area of a circle with a pocket calculator (LO 4.3; 4.5.2) Communication

solve any problem involving circles (LO 4.2.2; 4.3; 4.5.1; 4.5.2) Problem solving

Independence �� good �� average �� not too good


I am very satisfied with the standard of my work.. � �� Date





............................................................................................................................ ......................................................................................................

............................................................................................................................ ......................................................................................................


....................................................................................... CLASSWORK ASSIGNMENT for continuous assessment – Portfolio

Date: .........................

Question 1

� Write the formula for each of the following:

1.1 circumference of a circle ..........................................................................

1.2 area of a circle ..........................................................................

1.3 area of a square ..........................................................................

1.4 area of a rectangle ..........................................................................

Question 2

� Calculate the area of the shaded parts: You may use a pocket calculator. π = 3,14

2.1 2.2

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

4 cm

4 cm

A

B

C AC = CB 6,5 cm

288o

2.3 2.4

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

2.5 2.6

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

40 m

60 m

3 cm

8 cm

15cm

15cm

3. Bonus mark question

� Calculate the area of the shaded part.

� Given: PQ = QR = ST = 23 cm en RS = 1 cm

............................................................................................................................................

............................................................................................................................................

............................................................................................................................................

............................................................................................................................................

............................................................................................................................................

Q P R

S T

PQ = QR = ST = 3 cm

RS = 1 cm

TUTORIAL Module 3: Learning unit 2 The wonderful world of circles

Total: 35

INSTRUCTIONS:

1. All calculations are to be shown fully.

2. You may use a pocket calculator.

QUESTION 1 [15]

� Complete the following table: (You may use your pocket calculator.)

� Show all operations in the spaces allowed for this purpose.

Circumference Area Radius Diameter

1 286,5 mm

2 378,65 cm²

3 2,31 cm

4 234 mm

1: Area: ....................................................................................................................................

............................................................................................................................................

1: Radius: ................................................................................................................................

............................................................................................................................................

1: Diameter: .............................................................................................................................

............................................................................................................................................

2: Circumference: ...................................................................................................................

............................................................................................................................................

2: Radius: ...............................................................................................................................

............................................................................................................................................

2: Diameter: ............................................................................................................................

............................................................................................................................................

3: Circumference: ...................................................................................................................

............................................................................................................................................

3: Area: ...................................................................................................................................

............................................................................................................................................

3: Diameter: ............................................................................................................................

............................................................................................................................................

4: Circumference: ...................................................................................................................

............................................................................................................................................

4: Area: ...................................................................................................................................

............................................................................................................................................

4: Radius: ...............................................................................................................................

............................................................................................................................................

QUESTION 2 [10]

� Calculate the area of the shaded parts:

2.1 2.2

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

QUESTION 3 [5]

� A circle fits exactly into a square with 8-cm sides. A second square is drawn inside the circle, as in the sketch. Determine the total area of the shaded section.

............................................................................................................................................

............................................................................................................................................

............................................................................................................................................

0,13 m

40 mm

QUESTION 4 [5]

� The circumference of a circle is equal to the circumference of a square. Calculate:

area of circle area of square

............................................................................................................................................

............................................................................................................................................

............................................................................................................................................

TOTAL: 35


MY ASSESSMENT: AS I SEE IT: EDUCATOR'S ASSESSMENT: I am able to… �� 1 2 3 4 CRITICAL OUTCOMES 1 2 3 4 use π in a formula (LO 4.4); Critical and creative thinking

differentiate between the different parts of a circle (LO 4.3) Collaborating

calculate the circumference of a circle (with and without a pocket calculator (LO 4.2.2; 4.3; 4.4; 4.5.2)


calculate the area of a circle without using a pocket calculator (LO 4.2.1; 4.2.2; 4.5.1) Processing of information

solve any problem involving circles (LO 4.2.2; 4.3; 4.5.1; 4.5.2) Communication

Problem solving �� good �� average �� not too good Independence







............................................................................................................................ ......................................................................................................

............................................................................................................................ ......................................................................................................


TEST 1 Module 3: Learning unit 2 The wonderful world of circles

Total: 35

� Instructions : You may use your pocket calculator.

QUESTION 1

� Identify the following parts of a circle:

1.1 AF .........................................................

1.2 OB .........................................................

1.3 Q .........................................................

1.4 AB .........................................................

1.5 shaded section BF ............................................. [5]

QUESTION 2

� Complete.... (formula)

2.1 Circumference of circle .....................................................................................

2.2 Area of circle ..................................................................................................... [2]

QUESTION 3

� Calculate:

3.1 circumference

..................................................................

.................................................................. [3]

3.2 area

..................................................................

.................................................................. [3]

3.4 Calculate the radius of a circle with a circumference of 158 cm. (1 decimal)

..........................................................................................................................

.......................................................................................................................... [3]

3.5 Calculate the radius of a circle with area 346 cm². (1 decimal)

..........................................................................................................................

.......................................................................................................................... [3]

A

B Q

F

O

AB = 11 cm

A

11 cm

B

QUESTION 4

� Calculate the area of the shaded parts of each of the following.

4.1

..................................................................

..................................................................

..................................................................

..................................................................

.................................................................. [5]

4.2

..................................................................

..................................................................

..................................................................

..................................................................

.................................................................. [5]

4.3

..................................................................

..................................................................

..................................................................

..................................................................

.................................................................. [6]

TOTAL : 35

QUESTION 5: BONUS

� Calculate the area of the shaded part to the nearest mm. [3]

............................................................................................................................................

............................................................................................................................................

............................................................................................................................................

7 cm

10 cm

20 cm

ENRICHMENT EXERCISE for the quick learner

Module 3: Learning unit 2

1. A father is four times as old as his son is. In 20 years he will be twice as old as his son

will be. What is his present age?

............................................................................................................................................

............................................................................................................................................

2. Seven tenths of a rod measures 210 mm. What is the total length of the rod?

............................................................................................................................................

............................................................................................................................................

3. Consider the following pattern:

First row: 1

Second row: 2 3

Third row: 4 5 6

Fourth row: 7 8 9 10

� What will the last number in the 100th row be if the pattern is continued? [2]

............................................................................................................................................

............................................................................................................................................

4. 7 does not fit in the group 3; 7; 12; 18; 42 because 7 is the only number that is not

divisible by 3. Find another number that does not fit in the following group for another reason.

1; 9; 25; 48; 64

............................................................................................................................................

............................................................................................................................................

LEARNING UNIT 3

The wonderful world of TRIANGLES

..................................................................................................................ACTIVITY 3.1 Classifying triangles, discovering important theorems about triangles and constructing triangles

LO 3.1 LO 3.3 LO 3.4 LO 4.2.1 � By the end of this learning unit, you will be able to do the following:

� understand how important the use of triangles is in everyday situations;

� explain how to find the unknown sides of a right-angled triangle (Pythagoras);

� calculate the area of a triangle;

� enjoy the action in geometry;

� use mathematical language to convey mathematical ideas, concepts, generalisations and mental processes.

1. When you classify triangles you can do it according to the angles or according to the

sides.

1.1 Classification on the basis of the angles of a triangle: Are you able to complete the following?

a) Acute-angled triangles are triangles with ............................................................

b) Right-angled triangles have ................................................................................

c) Obtuse-angled triangles have .............................................................................

1.2 Classification on the basis of the sides of the triangle: Are you able to complete the following?

a) An isosceles triangle has ....................................................................................

b) An equilateral triangle has...................................................................................

c) A scalene triangle's .............................................................................................

2. Are you able to complete the following theorems about triangles? Use a sketch to

illustrate each of the theorems graphically.

THEOREM 1:

� The sum of the interior angles of any triangle is.........................

� Sketch:

THEOREM 2:

� The exterior angle of a triangle is......................................................................................

..........................................................................................................................................

� Sketch:

3. Constructing triangles:

� Equipment: compasses, protractor, pencil and ruler

REMEMBER THIS: � Begin by drawing a rough sketch of the possible appearance.

� Begin by drawing the base line.

3.1 Construct ∆ PQR with PQ = 7 cm, PR = 5 cm and P = 70°.

a) Sketch:

b) Measure the following:

1. QR = ........ 2. R = ........ 3. Q = ........ 4. =++ RQP ˆˆˆ ........

3.2 Construct ∆ KLM , an equilateral triangle. KM = 40 mm, KL=LM and K = 75°. Indicate the sizes of all the angles in your sketch.

� Sketch:

LO 3.1 LO 3.3 LO 3.4 LO 4.2.1

......................................................................................HOMEWORK ASSIGNMENT 1

1. Construct ∆ ABC with BC= 75 mm, B = 105° and C = 35°.

� Measure: 1.1 A = .............. 1.2 AC = ..............

2. Can you remember what a parallelogram is like?

2.1 Draw a sketch of this kind of quadrilateral:

2.2 What are the characteristic features of a parallelogram? Indicate it on your sketch.

2.3 Now try to construct parallelogram ABCD as in the sketch.

3. Calculate the sizes of the unknown angles and provide reasons. (You have done this in Module 2, Learning unit 3. Refer to this if you cannot remember all the details.)

3.1 3.2

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

3.3 3.4

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

// // 40°

65° y x

x – 60°

4x – 10° 5x + 50°

c a

b

// // /

/

»

»

b

a

55° »

»


MY ASSESSMENT: AS I SEE IT: EDUCATOR'S ASSESSMENT: I am able to… �� 1 2 3 4 CRITICAL OUTCOMES 1 2 3 4 classify triangles according to sides and angles (LO 3.2); Critical and creative thinking

calculate the sizes of angles in triangles with the help of theorems 1 and 2 (LO 3.2);

Collaborating

construct triangles from given measurements (LO 3.2). Organising and manageing

Processing of information �� good �� average �� not too good Communication Problem solving Independence







............................................................................................................................ ......................................................................................................

............................................................................................................................ ......................................................................................................


..................................................................................................................ACTIVITY 3.2 Discovering the Pythagorean theorem of Pythagoras and calculating unknown sides with the help of this theorem

LO 4.2.1 LO 4.8 LO 4.9 LO 4.10 � The following could be done in groups.

Practical exercise: Making you own tangram.

1. Cut out a cardboard square (10 cm x 10 cm).

2. Draw both diagonals, because they form part of the bases of some figures.

3. Divide the square in such a way that the complete figure consists of the following:

3.1 two large equilateral triangles with bases of 10 cm in length;

3.2 two smaller equilateral triangles, each with base 5 cm in length;

3.3 one medium equilateral triangle with adjacent sides 5 cm in length;

3.4 one square with diagonals of 5cm;

3.5 one parallelogram with opposite sides of 5 cm.

� Make two of these. Cut along all the lines so that you will have two sets of the above shapes.

LO 4.2.1 LO 4.8 LO 4.9 LO 4.10

4. Now trace the largest triangle of your tangram

in your workbook as a right-angled triangle.

5. Arrange the seven pieces to form a square and place this on the hypotenuse of the traced triangle.

6. Now arrange the two largest triangles to form a square and place this on one of the sides adja-cent to the right angle of the traced triangle.

7. Arrange the remaining pieces to form a square and place this on the other adjacent side.

8. Calculate the area of each square.

9. What can you deduce from this exercise?

10. Deduction: Write out Pythagoras’ theorem in the space below by making use of the triangle that is provided.

..............................................................................................

..............................................................................................

..............................................................................................

11. Solve x in each of the following triangles:

(You may make use of your calculator.)

11.1 11.2

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

11.3 11.4

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

12. Do the calculations to determine whether the following is a right-angled triangle or not:

12.1 ∆ DEF with DE = 8 cm, EF = 10 cm, DF = 6 cm

.....................................................................................

.....................................................................................

.....................................................................................

.....................................................................................

P

R Q

q r

p

12 cm x cm

5 cm

20 cm 8 cm

x cm

13. AREA OF TRIANGLES

13.1 Construct rectangle ABCD with AB = 45 mm and AD = 25 mm on a sheet of paper and cut it out. Draw diagonal AC.

13.2 Calculate the area of rectangle ABCD.

...................................................................................................................................

13.3 Cut out ∆ ABC. What is the area of ∆ ABC? Paste it here.

� Area of ∆ ABC = ................. mm²

13.4 Are you able to develop a formula for determining the area any triangle?

Write it here: ............................................................................................................

13.5 Calculate the area of ∆ ABC.

.......................................................................

.......................................................................

.......................................................................

.......................................................................

13.6 In the figure SQ = 15 cm, QR = 7 cm and PR = 9 cm.

Important: Provide all necessary information on your sketch. Check to see what you may need to complete the instructions fully.

(a) Calculate the area of ∆ PSQ (accurate to 2 decimals).

............................................................................................................................

............................................................................................................................

(b) Now calculate the area of ∆ PSR. Suggestion: You will first have to calculate the area of another triangle.

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

13.7 Calculate the area of ABCD.

...........................................................................

...........................................................................

...........................................................................

...........................................................................

...........................................................................

...........................................................................

...........................................................................

14. Calculate the length of the unknown sides of each of the following:

14.1 14.2

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

14.3 ................................................................

................................................................

................................................................

................................................................

................................................................

................................................................

................................................................ S

U

R

V

T

7

14 5

12

y

15. Playing in a park is a necessary aspect of the development of a child.

� You have been asked to supply slides. The problem that is involved requires calculating the length of the poles that are needed. Make use of the knowledge that you have accumulated to supply a plan to erect the slides.

� The following is required:

15.1 a sketch

15.2 a scale, e.g. 1 cm = 1 m

15.3 Calculations must be completed fully.

LO 4.2.1 LO 4.8 LO 4.9 LO 4.10

......................................................................................HOMEWORK ASSIGNMENT 2 1. Determine the value of x in each instance:

1.1 1.2

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

1.3 1.4

........................................................... ...........................................................

........................................................... ...........................................................

80 x

R Q

P

21

12

x

D

F

E

24

D

43

C x

A

B

40 8,7 cm x

G F

E

9 cm

3,7 cm H

........................................................... ...........................................................

1.5 ............................................................

............................................................

............................................................

............................................................

............................................................

2. Calculate the length of PQ and PR.

2.1 PQ : ..................................................

............................................................

............................................................

............................................................

2.2 PR: ...................................................

............................................................

............................................................

............................................................

3. Do a calculation to determine whether the following represent right-angled triangles or

not. If they do, indicate the right angle.

3.1 ∆ PQR with PQ = 4 cm ; PR= 5 cm ; QR = 3 cm

..............................................................................................

..............................................................................................

..............................................................................................

..............................................................................................

3.2 ∆ ABC with AB = 8 cm ; AC = 5 cm ; BC = 12 cm

..............................................................................................

..............................................................................................

..............................................................................................

..............................................................................................

P

S

Q

R

30 cm

T

9 cm

x

TR = x

R 4,5 cm S

16,3

cm

Q

P

/ /

6 cm

4. Calculate the area of each of the shaded parts. You may use a pocket calculator. All answers have to be accurate to one decimal.

4.1 4.2

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

4.3 4.4

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

........................................................... ...........................................................

A

D

B

C

8 cm

9 cm

6 cm A

//

/

B

E F D C

30 m

m

25 mm

//

/

/ /

A

C B D

16

25

8

7 cm


MY ASSESSMENT: AS I SEE IT: EDUCATOR'S ASSESSMENT: I am able to… �� 1 2 3 4 CRITICAL OUTCOMES 1 2 3 4 prove the Pythagorean theorem (LO 4.8); Critical and creative thinking

use the Pythagorean theorem to calculate unknown lateral lines of triangles (LO 4.8; 4.9; 4.10);

Collaborating

calculate the area of a triangle (LO 4.5.2); Organising and manageing

determine the area of any shaded section (LO 4.5.1; 4.5.2). Processing of information

Communication �� good �� average �� not too good Problem solving Independence







............................................................................................................................ ......................................................................................................

............................................................................................................................ ......................................................................................................


TUTORIAL Module 3: Learning unit 3 (The wonderful world of TRIANGLES)

Total: 20

INSTRUCTIONS:

� You may use a pocket calculator.

1. Calculate the value of a, x or y in each instance, providing reasons.

1.1 1.2

.................................................. ....................................................

.................................................. ....................................................

.................................................. ....................................................

.................................................. [2] .................................................... [2]

1.3 1.4

.................................................. ....................................................

.................................................. ....................................................

.................................................. ....................................................

.................................................. [2] .................................................... [2]

\\

y 120°

a //

y 2x + 20°

\\

70°

5y

5x + 10°

80°

45° 55°

x

a

80°

40° »

»

»

»

1.5 1.6

.................................................. ....................................................

.................................................. ....................................................

.................................................. ....................................................

.................................................. [3] .................................................... [3]

2. Calculate the areas of the following figure:

2.1 2.2

.................................................. ....................................................

.................................................. ....................................................

.................................................. ....................................................

.................................................. [3] .................................................... [3]

TOTAL 20

40 mm

// //

/

/

21 m

m

x

x

2x

4x

3x

2x

1

2

3

5

4


MY ASSESSMENT: AS I SEE IT: EDUCATOR'S ASSESSMENT: I am able to… �� 1 2 3 4 CRITICAL OUTCOMES 1 2 3 4 prove the Pythagorean theorem (LO 4.8); Critical and creative thinking

use the Pythagorean theorem to calculate unknown lateral lines of triangles (LO 4.8; 4.9; 4.10);

Collaborating

calculate the area of a triangle (LO 4.5.2); Organising and manageing

determine the area of any shaded section (LO 4.5.1; 4.5.2). Processing of information

Communication �� good �� average �� not too good Problem solving Independence







............................................................................................................................ ......................................................................................................

............................................................................................................................ ......................................................................................................


TEST Module 3: Learning unit 3 (The wonderful world of TRIANGLES)

Total: 30

INSTRUCTIONS:

� You may use your pocket calculator.

1. Calculate the value of x in each of the following instances:

1.1 1.2

.................................................. ....................................................

.................................................. ....................................................

.................................................. ....................................................

.................................................. [3] .................................................... [4]

1.3

.............................................................................................................................

.............................................................................................................................

.............................................................................................................................

............................................................................................................................. [4]

2. An aeroplane flies directly north from point B to point A, a distance of 530 km. Then it

turns and flies directly east from A to C, a distance of 415 km. How far from C is B?

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... [3]

S

U

R

V

T

7

14 5

12

y

3. Calculate the area of each of the following figures: 3.1 3.2

.................................................. ....................................................

.................................................. ....................................................

.................................................. ....................................................

.................................................. [4] .................................................... [5]

3.3

.....................................................................

.....................................................................

.....................................................................

.....................................................................

.....................................................................

..................................................................... [3]

4. Calculate the area of the shaded part of the following:

(π = 3,14)

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... [4]

TOTAL 30

/

=

100 cm

140

cm

\

= 60 c

m

3 cm

6 cm

4 cm

Mathematics Project: Grade 8

DATE: .........................

LO: 5.1 – 5.9

Start working on this today!!!!

STATISTICS � Statistics is the field of study that deals with methods for collecting, processing and

analysing numerical facts. In this project we are going to collect, process and analyse specific numerical data.

A. Study the following terms and their definitions, as well as your mathematics textbook.

Making use of any additional sources will be to your advantage.

TERMS DEFINITIONS

1. Data numerical facts of values that are read or measured

2. Frequency table use a source.

3. Average = sum of data counts number of counts

4. Median of the middle, the middle number

5. Modus count occurring most frequently

6. Variation range (compass, scope)

highest value - (minus) lowest value

7. Graphs Pie chart

Pictogram

Bar graph

Broken line graph

B. Instructions

1. Choose one of the following as topic for data collection (or a topic of your own) and collect 40 numerical readings on this subject. These 40 readings comprise your data.

� Suggested topics:

� Height of learners

� Amount of pocket money

� Test marks

� Daily temperature at 16:00

� Number of hours that you sleep each night

� Copy down your data.

2. Compile a frequency table for the data.

3. Use the frequency table and design TWO WAYS of representing your data graphically.

(This means that you may choose any TWO methods from no. 7 in A.)

4. Refer to your frequency table to calculate the following:

4.1 average

4.2 modus

4.3 median

4.4 variation range

5. Deduction:

� Write a brief paragraph, using your own words, on what you see as the purpose of statistics and list some examples.

� Use a computer to set out your work neatly and logically.

� This project must be presented as your individual effort and may not simply be taken from a book or off the Internet. Your parents should certify that this is your own work on the attached evaluation form.

Project evaluation

CRITERIA POSSIBLE MARK ACTUAL MARK

Frequency table 2

Graphs: 1 : 2

2: 2

CALCULATION

Average 2

Modus 1

Median 1

Variation range 1

GENERAL

Neatness 1

Explanation 1

DEDUCTION 2

TOTAL 15

Educator's comments: .............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

Educator: ------------------------------------------------------- Date: -------------------------

CERTIFICATION:

I, .......................................................................... , as the parent of

........................................................................... hereby declare that this

project represents his/her original and independent effort.

math gr8 m3 magical world of - maths excellencemathsexcellence.co.za/books/e gd 8/mathematics/1...

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