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GRADE 9 TERM 4 MATHEMATICS
Mathematics Teaching Plan: Term 4 Grade 9 (ATP)
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Wee
k 1(
09O
ct-1
2Oct
)
LESSON 1: 1
Practice Exams in Number systems, financial contexts, including ratio and rate, integers, exponents 1 0.5LESSON 2: 1 Practice Exams in Number systems, financial contexts, including ratio and rate, integers, exponents 1 1.0 LESSON 3: 1 Practice Exams in Number systems, financial contexts, including ratio and rate, integers, exponents 1 1.6LESSON 4: 1 Practice Exams in Geometry of Straight lines, 2D Shapes, Pythagoras and Constructions 1 2.1LESSON 5: 1 Practice Exams in Geometry of Straight lines, 2D Shapes, Pythagoras and Constructions 1 2.6LESSON 6: 1 Practice Exams in Geometry of Straight lines, 2D Shapes, Pythagoras and Constructions 1 3.1LESSON 7: 1 Practice Exams in Expressions, Equations, Functions and Graphs 1 3.6LESSON 8 : 1 Practice Exams in Expressions, Equations, Functions and Graphs 1 4.2LESSON 9 Weekly Assessment
2
GRADE 9 TERM 4 MATHEMATICS
Wee
k 2
(15O
ct-1
9Oct
)
LESSON 1: 1
Practice Exams in Expressions, Equations, Functions and Graphs 1 4.7LESSON 2: 1 Practice Exams in Expressions, Equations, Functions and Graphs 1 5.2 LESSON 3: 1 Practice Exams in Number systems, Integers, Common Fractions, Decimal Fractions, Financial Contexts, including ratio and rate, 1 5.7LESSON 4: 1 Practice Exams in Number systems, Integers, Common Fractions, Decimal Fractions, Financial Contexts, including ratio and rate, 1 6.3LESSON 5: 1 Practice Exams in Number systems, Integers, Common Fractions, Decimal Fractions, Financial Contexts, including ratio and rate, 1 6.8LESSON 6: 1 Practice Exams in Geometric Patterns, Numeric Patterns and Functions 1 7.3LESSON 7: 1 Practice Exams in Geometric Patterns, Numeric Patterns and Functions 1 7.8LESSON 8 : 1 Practice Exams in Geometric Patterns, Numeric Patterns and Functions 1 8.3LESSON 9 SBA Assessment
Wee
k 3(
22O
ct-2
6Oct
)
LESSON 1: 1
Practice Exams in Data Handling and Probability 1 8.9LESSON 2: 1 Practice Exams in Data Handling and Probability 1 9.4LESSON 3: 1 Practice Exams in Data Handling and Probability 1 9.9LESSON 4: 1 Practice Exams in Area and Perimeter, Surface Area and Volume, 3-D objects and Transformations 1 10.4LESSON 5: 1
3
GRADE 9 TERM 4 MATHEMATICS
Practice Exams in Area and Perimeter, Surface Area and Volume, 3-D objects and Transformations 1 10.9LESSON 6: 1 Practice Exams in Area and Perimeter, Surface Area and Volume, 3-D objects and Transformations 1 11.5 LESSON 7: 1 Practice Exams in Area and Perimeter, Surface Area and Volume, 3-D objects and Transformations 1 12.0LESSON 8 : 1 Practice exams in Expressions and Equations 1 12.5LESSON 9 SBA Assessment - Project
Wee
k 4
(29
Oct
-02
Nov
)
LESSON 1: 1
Practice exams in Expressions and Equations 1 13.0LESSON 2: 1 Practice exams in Expressions and Equations 1 13.5 LESSON 3: 1 Practice Exams in Expressions, Equations, Functions and Straight line Graphs 1 14.1LESSON 4: 1 Practice Exams in Expressions, Equations, Functions and Straight line Graphs 1 14.6LESSON 5: 1 Practice Exams in Expressions, Equations, Functions and Straight line 1 15.1LESSON 6: 1 Practice Exams in Data Handling and Probability 1 15.6 LESSON 7: 1 Practice Exams in Expressions, Equations, Functions and Straight line 1 16.1LESSON 8: 1 Practice Exams in Expressions, Equations, Functions and Straight line 1 16.7LESSON 9 Weekly Assessment
4
GRADE 9 TERM 4 MATHEMATICS
Week 5 (05 Nov-09 Nov)
Lesson 1&2 : 1
Practice Exams on Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions 1 17.2Lesson 3&4 : 1 Practice Exams on Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions 1 17.7Lesson 5&6 : 1 Practice Exams on Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions 1 18.2Lesson 7&8 : 1 Practice Exams on Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions 1 18.8LESSON 9 Weekly Assessment
Wee
k 6
(12
Nov
-16
Nov
)
Lesson 1&2: 1
Practice Exams on Geometric and Numeric Patterns, Functions, Expressions and graphs 1 19.3Lesson 3&4: 1 : Practice Exams on Geometric and Numeric Patterns, Functions, Expressions and straight line graphs 1 19.8Lesson 5&6: 1 Practice Exams on Geometric and Numeric Patterns, Functions, Expressions and straight line graphs 1 20.3Lesson 7&8: 1 Practice Exams on Geometric and Numeric Patterns, Functions, Expressions and straight line graphs 1 20.8LESSON 9 Weekly Assessment
5
GRADE 9 TERM 4 MATHEMATICS
Wee
k 7
(19
Nov
-23
Nov
)
Lesson 1&2: 1
Practice exams on Constructions, Straight line Geometry and 2D shapes. 1 21.4Lesson 3&4: 1 Practice exams on Constructions, Straight line Geometry and 2D shapes. 1 21.9Lesson 5&6: 1 Practice exams on Area and Perimeter, 3-D objects, Surface Area and volume and Data handling including probability 1 22.4Lesson 7&8: 1 Practice exams on Area and perimeter, 3-D objects, Surface Area and volume and Data handling including probability 1 22.9LESSON 9 Weekly Assessment
Wee
k 8
(26
Nov
-30
Nov
)
Lesson 1&2: 1
Practice exams on Transformations and Straight line Graphs 1 23.4Lesson 3&4: 1 Practice exams on Transformations, Straight line Graphs exponents and Probability 1 24.0Lesson 5&6: 1 Practice exams on Expressions and Equations 1 24.5Lesson 7&8: 1 Practice exams on Expressions and Equations 1 25.0LESSON 9 Weekly Assessment
TOTAL OF SUB-TOPICS 48 Type of Assessment
Concepts & Skills Assessed Date to be completed
6
GRADE 9 TERM 4 MATHEMATICS
FORMAL ASSESSMENT: TEST (END OF THE TERM)Important considerations: • Include Multiple Choice Questions.• Ensure coverage of Cognitive levels as prescribed in CAPS p157.• Ensure that the questions are grade-appropriate.• The test and the memo should be moderated.
7
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 1 LESSON 1
TOPIC: Number systems, financial contexts, including ratio and rate, integers.
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
Define and apply rules for number systems
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Describe the real number system by recognising, defining and distinguishing properties of: natural numbers whole numbers integers rational numbers irrational numbers
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the definitions in the real number system to identify the different types of numbers by using their properties
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
This is the first lesson of the term thus there will be no homework
LESSON PRESENTATION/ DEVELOPMENT
20minThe following tables should be revised with the learners. They could present it to each other with some concepts blocked and fill in the blanks.
Natural Numbers(N ): The most basic type of number.
N = { 1; 2; 3; 4; 5; …}
CAPSTerm: 1Page reference:119
9
GRADE 9 TERM 4 MATHEMATICS
Even Numbers are a subset of Natural numbers or the numbers that are divisible by 2 or multiples of 2.
{2; 4; 6; 8; …}
Odd numbers are a subset of Natural numbers or any integer that cannot be divided exactly by 2.
{1; 3; 5; 7; 9; …}
Prime numbers are numbers greater than 1 which can only be divided by itself and 1, without a remainder. They have two factors, the number itself and 1
{ 2; 3; 5; 7; 11; …)
Composite numbers can be divided by 1, itself and at least one other number without a remainder. They have more than two factors.
{4; 6; 8; 9; 10; …}
1 is neither a prime number nor a composite numbers, but is a factor of every natural number
1 = 1 × 1; 2 = 1 × 2; 3 = 1 ×3; 201
=20
1 is the identity element of multiplication and division.15=1 ;√1=1 ; 3√1=1; ;etc .
Whole numbers (N 0): The set of natural numbers together with 0.Whole numbers also consist of odd, even and prime numbers, and 1 and 0
{0; 1; 2; 3; 4; 5; 6; …}
0 is neither a prime number nor composite. 4 + 0 = 4; 5 – 0 = 5; 0 is the identity element for multiplication 03=0 ;0×5=0 , but 4
0isundefined
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GRADE 9 TERM 4 MATHEMATICS
Integers (Z):The set of integers consists of the positive whole numbers, zero and the negative numbers
{…; -3; -2; -1; 0; 1; 2; 3; …}
Rational numbers (Q): Any number that can be
written in the form ab , where a and b are
integers but b≠0.Recurring decimal : a decimal fraction in which a figure or group of figures is repeated indefinitely, as in 0.666
Integernon−zeronumber ,
Finite decimals: 75100
=34=75 % ;
−1,5=−1510
=−32
;
Recurring decimals:
0 , 3=13;−0 , 8=−8
9;
Irrational numbers (Q'): They are numbers with infinite non-terminating decimals, whose numbers goes on forever.
In practice we use rounded off values: √2≈1,414 , which is a rational approximation of the real value of √2.
Pi (π ¿ , 227
=3,141592…
Real numbers (R): Consist of all the numbers that we use and include all the numbers
Real number system:
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GRADE 9 TERM 4 MATHEMATICS
NON-REAL NUMBERS: These numbers are generally powered roots of negative numbers.
Examples or non-real numbers are:√−3√−4 ; 10√−100 ; √−2 ; 4√−20 ;
UNDEFINED NUMBERS: Division by zero is undefined.
50 ;
00 ;
CLASSWORK 10 min Give the learners the following exercise to complete in class:Complete the following table of numbers:
Number N N0 Z Q Q' Non-Real Undefined15 Yes Yes Yes Yes No No No√3
0,14287
√ 14
−√1443√−1√−1
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GRADE 9 TERM 4 MATHEMATICS
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson
REFLECTION
13
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 1 Lesson 1
Class work
Number N N0 Z Q Q' Non-Real Undefined15 Yes Yes Yes Yes No No No√3 No No No No Yes No No
0,14287 No No No Yes No No No
√ 14
No No No Yes No No No
−√144 No No Yes Yes No No No3√−1 No No Yes Yes No No No
√−1 No No No No No Yes No
14
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 1 LESSON 2
TOPIC: Number systems, financial contexts, including ratio and rate, integers.
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
solve problems in contexts involving: Ratio and rate Direct and indirect proportion
by recognising and using calculation techniques.
FINANCIAL MATHS profit, loss, discount and VAT budgets accounts and loans rentals exchange rates and commission
by using the appropriate formulae
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
How to solve problems in contexts involving: Ratio and rate Direct and indirect proportion by recognising and using calculation techniques. FINANCIAL MATHS
profit, loss, discount and VAT budgets accounts and loans rentals exchange rates and commission by using the appropriate formulae
WHAT YOU SHOULD BE Use the appropriate formulae and conversion techniques to solve problems in contexts involving:
15
GRADE 9 TERM 4 MATHEMATICS
ABLE TO DO (skills) Ratio and rate Direct and indirect proportion FINANCIAL MATHS
profit, loss, discount and VAT budgets accounts and loans rentals exchange rates and commission exchange rates and commission
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT
20 min RateThe comparison of two amounts with different units. Notice that any rate uses the word per to indicate that it compares one quantity to one unit of another quantityWe use ratios to calculate rate.e.g: There are 96 boys and 120 girls in Grade 9. Write down, in the simplest form, the ratio of the number of boys to the number of girls in the grade.
Solution:96:120 = 8:10 = 4:5
Financial MathsKnow the following formulae:A=P(1+¿), where = final amount; = Initial amount, =interest rate and = number of periods.
Use this only for simple interest
CAPSTerm: 1Page reference:121
16
GRADE 9 TERM 4 MATHEMATICS
, where = final amount; = Initial amount, =interest rate and = number of periods.Use this only for compound interest
Exchange rates:Write the knowns under each other and solve for the unknown by cross multiplying. E.g. :
Make use of the exchange rate table below to calculate each of the given transactions
(a) Mr. D from Germany bought rands with 4500 euros from Mary.(b) Mr. H from South Africa bought Pula with R1 000 from Mary.(c) Mary sells R 4 000 worth of dollars to Ms. B
Solutions:a) If Mr. D bought rands with 4500 euros, it means that Mary bought 4500 euros. 4500 × 11,2780 = R50751,00 b) If Mr. H bought Pula with R1000, it means that Mary sold Pula. 1000 ÷ 0,8080 = 1237,62 P c) 4000 ÷ 8,4586 = $ 472,89
17
GRADE 9 TERM 4 MATHEMATICS
CLASSWORK 9 min 1. Divide R5 600 in the ratio 3: 4: 2.
2. A car travels a distance of 440 km at an average speed of 80 km/h. How long does it take the car to travel this distance? Round off your answer to the nearest hour.
3. Calculate the amount that will be in the bank after 5 years if R3500 was invested at 9% p.a. simple interest.
4. Calculate the interest if R10 000 is invested at 10 % per annum compound interest for
3 years.
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
1min 1. Simplify the ratio R250:R150:R1002. Divide 240g in the ratio 5 : 3 : 43. Calculate the interest if R6500 is invested for 3 years at 7,7% per annum compound
interest.4. Calculate the amount that will be in the bank after 5 years if R9500 was invested at
8% p.a. simple interest. 5. Mary works in a Foreign Exchange bank at OR Tambo airport. The various exchange
rates are shown on the electronic notice board below.
CurrencyBuy (R) Sell (R)
US Dollar $ 1 8,1090 8,4586
British Pound £ 1
12,7850 13,4767
Euro 1 11,2780 11,9060Botswana Pula P 1 0,9320 0, 8080
Mary buys $500 from a customer: How much did she pay in rand?
REFLECTION
18
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 1 Lesson 2Class work
1. Divide R5 600 in the ratio 3: 4: 2.39×R5600=R1866,67
49×R5600=R2488,89
29×R5600=R1244,44
2. A car travels a distance of 440 km at an average speed of 80 km/h. How long does it take the car to travel this distance? Round off your answer to the nearest hour.
time=distancespeed
= 440 km80km /h
∴time=6hours
3. Calculate the amount that will be in the bank after 5 years if R3500 was invested at 9% p.a. simple interest.
A=P(1+¿) and i= 9100
=0,09
∴ A=3500 (1+5×0,09 )=R5 075
4. Calculate the interest if R10 000 is invested at 10 % per annum compound interest for 3 years.
20
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 1 LESSON 3
TOPIC: Number systems, financial contexts, including ratio and rate, integers, exponents
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
Use laws and rules to do calculations involving integers and exponents
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
INTEGERS Commutative property
This law applies to addition and multiplication of numbers; it tells us that even if we change the order of the numbers we still get the same answer.
Associative propertyThis rule also applies to addition and multiplication; it allows us to group numbers when adding or multiplying and still get the same answer.
Distributive propertyWhen multiplying across addition or subtraction this property allows us to redistribute the numbers and still get the same answer.
Additive inverse: Is the number that is added to another to get 0 Examples: (1) 6 and -6, 6 + (-6) = 0 (2) –a and a, a + (-a) = 0 (3) 4b and -4b, 4b + (-4b) = 0
21
GRADE 9 TERM 4 MATHEMATICS
Order of operation (BODMAS):B – BracketsO – of/ other(exponents and surds)D – Division,M – multiplicationA – additionS – Subtraction
EXPONENTSProduct of powers: am×an=am+n , a > 0
Quotient of powers: am÷an=am−n , if m>n
Exponent zero a0=1 am÷am=am−m=a0 ,a>0
am
am=1
WHAT YOU SHOULD BE ABLE TO DO (skills)
Apply all the rules and laws above in order to do calculations
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
8min 1. Simplify the ratio R250:R150:R100
= 5:3:2
22
GRADE 9 TERM 4 MATHEMATICS
2. Divide 240g in the ratio 5 : 3 : 45 : 3 : 4
First mass :
Second mass :
Third mass : 3. Calculate the interest if R6500 is invested for 3 years at 7,7% per annum compound interest.
A=P¿A=6500 ¿A=R8120.08
4. Calculate the amount that will be in the bank after 5 years if R9500 was invested at 8% p.a. simple interest.
A=P(1+¿) and i=8
100=0,08
∴ A=9500 (1+5×0,08 )=R13 3005. Mary works in a Foreign Exchange bank at OR Tambo airport. The various exchange rates are
shown on the electronic notice board below.
CurrencyBuy (R) Sell (R)
US Dollar $ 1 8,1090 8,4586
British Pound £ 1
12,7850 13,4767
Euro €1 11,2780 11,9060Botswana Pula P 1 0,9320 0, 8080
Mary buys $500 from a customer: How much did she pay in rand?
23
GRADE 9 TERM 4 MATHEMATICS
500 × 8,1090 = R4 054,50 Mary sells £400 to a customer. How much did she receive in rand? 400 × 13,4767= R5390,68
LESSON PRESENTATION/ DEVELOPMENT/ CLASSWORK
15 min Place learners in groups and allow for the following exercises to be completed.Stop learners at intervals of 5 min and answer questions with them.
EXERCISE:1. The weather forecast for the world on TV shows the following temperatures:
Minimum MaximumJohannesburg -4 0C 15 0CBloemfontein -10 0C -1 0CLondon -3 0C 14 0C
(a) What is the difference between the minimum temperatures in Johannesburg and the minimum in Bloemfontein?
(b) What is the rise in temperature from minimum to maximum in Johannesburg?(c) What is the rise in temperature from minimum to maximum in Bloemfontein?
2. Simplify the following:a) 4m5×3m7×−2m3
b) a7×a6
a8×a3
c) ¿
d) (−2 x2)¿
e) 2n8n+2
43n2−2n
CAPSTerm: 1Page reference: 119- 122
CONSOLIDATION/CONCLUSION
2min 1. Calculate:a)– 3(-11 + 5)
24
GRADE 9 TERM 4 MATHEMATICS
AND OR HOMEWORK2. The minimum and maximum temperatures in Sutherland , Western Cape are shown in the table:
TEMPERATURES FOR SUTHERLAND:
January August October
Min 0C 120 -160 50
Max 0C 290 00 220
(a) What was the coldest temperature in Sutherland?
(b) What was the warmest temperature in Sutherland?
(c) What is the difference between the two temperatures?
3.a)
4 x2 y3
2x y5
b)
2 p8q4
8 p3qr÷ 16 p4
4 r
c)2x+1
3.2x−1
REFLECTION
25
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 1 Lesson 3Class work Homework
1.a) - 40C – (- 100C) = 6 0Cb) 150C – (-40C) = 19 0Cc) -10C – ( -100C) = 9 0C
2.a) 4m5×3m7×−2m3
b) a7×a6
a8×a3
c) ¿
d) (−2 x2 )¿
=−2x2
4 x2
¿ −24
=−12
1. Simplify the ratio R250:R150:R100
= 5:3:2 2. Divide 240g in the ratio 5 : 3 : 4
5 : 3 : 4
First mass :
Second mass :
Third mass : 3. Calculate the interest if R6500 is invested for 3 years at 7,7% per annum compound interest.
A=P¿A=6500 ¿A=R8120.08
4. Calculate the amount that will be in the bank after 5 years if R9500 was invested at 8% p.a. simple interest.
A=P(1+¿) and i=8
100=0,08
∴ A=9500 (1+5×0,08 )=R13 300
26
GRADE 9 TERM 4 MATHEMATICS
e) 2n8n+2
43n2−2n
¿2n (23 )n+2
(22 )3n2−2n= 2n23n+6
26n2−2n
¿ 2n+3n+6
26n−2n =24 n+6
24n
¿24n+6−4n=26=64
5. Mary works in a Foreign Exchange bank at OR Tambo airport. The various exchange rates are shown on the electronic notice board below.
CurrencyBuy (R) Sell (R)
US Dollar $ 1 8,1090 8,4586
British Pound £ 1
12,7850 13,4767
Euro €1 11,2780 11,9060Botswana Pula P 1 0,9320 0, 8080
Mary buys $500 from a customer: How much did she pay in rand?
500 × 8,1090 = R4 054,50 Mary sells £400 to a customer. How much did she receive in rand? 400 × 13,4767= R5390,68
27
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 1 LESSON 4
TOPIC: Geometry of Straight Lines, 2D shapes, Pythagoras and Constructions
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
Apply themselves using the theory of : Geometry of Straight Lines
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 2 Disc 1 ; Grade 9 Term 2 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Vertically opposite angles; Corresponding angles; alternate angles; co-interior angles
WHAT YOU SHOULD BE ABLE TO DO (skills)
Identify and apply the properties of: Vertically opposite angles are equal Corresponding angles are equal Alternate angles are equal Co-interior angles are supplementary
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
10 min 1. Calculate:a) – 3(-11 + 5) = - 3 × - 11 + - 3 × 5 = 33 +(-15) = 18
2. The minimum and maximum temperatures in Sutherland , Western Cape are shown in the table:
28
GRADE 9 TERM 4 MATHEMATICS
January August October
Min 0C 120 -160 50
Max 0C 290 00 220
(a) What was the coldest temperature in Sutherland? -16 0C in August
(b) What was the warmest temperature in Sutherland? 29 0C in January
(c) What is the difference between the two temperatures? 29 – (-16) = 45 0C
3.
a) 4 x2 y3
2x y5
¿2 x2−1 y3−5
¿ 2 xy2
b) 2 p8q4
8 p3qr÷ 16 p4
4 r
29
GRADE 9 TERM 4 MATHEMATICS
c) 2x+1
3.2x−1
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20 min Get learners into groups and ask them to do the following problems and have group leaders present to the class, while educator guides them. The educator should ensure that the notation for geometry is maintained at all times.Stop learners at 10 minute intervals to give feedback.
1.
CAPSTerm: 2Page reference:134-138
30
GRADE 9 TERM 4 MATHEMATICS
In the figure, AB//ED, Determine the size of and
2.
Calculate the values of and if
31
GRADE 9 TERM 4 MATHEMATICS
.
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson
REFLECTION Answers: Term 4 Grade 9 Week 1 Lesson 1
Class work
1.
In the figure, AB//ED, Determine the size of and
32
GRADE 9 TERM 4 MATHEMATICS
2.
Calculate the values of and if B2=x , D2= y , D1=44 ° ,C1=75 °∧AD‖BC
33
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 1 LESSON 5
TOPIC: Geometry of Straight Lines, 2D shapes, Pythagoras and Constructions
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
Apply themselves using the theory of : 2D shapes
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 2 Disc 1 ; Grade 9 Term 2 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Properties of and conditions for: Triangles Quadrilaterals Congruency and Similarity
WHAT YOU SHOULD BE ABLE TO DO (skills)
Identify and apply the properties of: Triangles Quadrilaterals Congruency and Similarity
35
GRADE 9 TERM 4 MATHEMATICS
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
10 Min Revise the conditions for congruency and similarity.Emphasise the notation for this section while doing the examples one at a time in class. Allow learners to write answers before assiting with corrections.
1. Determine whether the following are congruent, similar or neithera)
b)
CAPSTerm: 2Page reference: 134-138
36
GRADE 9 TERM 4 MATHEMATICS
1. Consider the triangles below. Prove Δ ABD≡ ΔCDB
2. Prove that
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework follows in the next lesson
REFLECTION
38
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 1 Lesson 5Class work
1.
a)
b) .c) Not congruent
d)2.
In
(common)
(given) (given)
( ;H; S)
3.
In
39
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 1 LESSON 6
TOPIC: Geometry of Straight Lines, 2D shapes, Pythagoras and Constructions
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
Apply themselves using the theory of : Pythagoras Constructions
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 2 Disc 1 ; Grade 9 Term 2 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
How to use a protractor and compass to construct angles and shapes Use the Theorem of Pythagoras to solve right angles triangles
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use a protractor and compass to construct angles and shapes Apply the Theorem of Pythagoras to solve right angles triangles
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT
10 minEnsure that learners know the following steps for constructions:
Bisecting a line segment with a ruler and a compass.
Step 1: Place the compass on one end point of the line segment (Point A).Draw an arc above and below the line. Step 2: Without changing the compass width place the compass on point
CAPSTerm: 2Page reference:134-138
40
GRADE 9 TERM 4 MATHEMATICS
B. Draw an arc below and above the line so that the arcs cross the first two.
Step 3: Use a ruler to join the points where the arcs intersect. This line segment known as BD is the bisector of AB.
*the perpendicular is a line that meets another line at 90˚.
Theorem of Pythagoras:In any right angled triangle:
41
GRADE 9 TERM 4 MATHEMATICS
Place learners in groups to complete the classwork.
CLASSWORK 10 min 1. Use a pair of compass and a ruler to make accurate constructions of the following:
2.
42
GRADE 9 TERM 4 MATHEMATICS
Calculate the value of the unknown side.
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
2 min 1. Use a pair of compass and a ruler to make accurate constructions of the following:
a) angle
2. Calculate the value of the unknown side.a)
b)
43
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 1 Lesson 6Class work
1. Use a pair of compass and a ruler to make accurate constructions of the following:
2.
45
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 1 LESSON 7
TOPIC: Expressions, Equations, Functions and graphs
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: manipulate expressions, solve equations, draw functions and graphs and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 2
47
GRADE 9 TERM 4 MATHEMATICS
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Factorisation ( all methods)
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the rules for expressions (BODMAS) to manipulate and simplify expressionsUse the rules for factorisation to simplify expressions and solve equations.
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
5min 1.Use a pair of compass and a ruler to make accurate constructions of the following:A angle
3. Calculate the value of the unknown side.c)
d)
48
GRADE 9 TERM 4 MATHEMATICS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
25min Educator should give learners this activity to do in pairs:1. Simplify:
a) 2a2(a−2)+2a(a2−3a )
2. If x=5 and y=−4 , find the value of
4 x2+3 y2
3. Calculate the value of :; if
4. If and ,calculate the value of
5. If , calculate the value of
6. Solve for x:a) 4 x−1=−9
b)
CAPSTerm: 2Page reference: 130-131
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GRADE 9 TERM 4 MATHEMATICS
c)
d)
e)
f)
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson
REFLECTION
50
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 1 Lesson 7Homework
1. 2a2 (a−2)+2a(a2−3a )
2. If x=5 and y=−4 , find the value of
3. ; if ¿−2¿¿−16−12−18+2¿−44
4. If and ,find the value of
51
GRADE 9 TERM 4 MATHEMATICS
5. If and ,calculate the value of
6. If and y = -3 ,calculate the value of
7. Solve for x:a) 4 x−1=−9
52
GRADE 9 TERM 4 MATHEMATICS
55
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 1 LESSON 8
TOPIC: Expressions, Equations, Functions and graphs
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: manipulate expressions, solve equations, draw functions and graphs and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Factorisation ( all methods)
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the rules for expressions (BODMAS) to manipulate and simplify expressionsUse the rules for factorisation to simplify expressions and solve equations.
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/ CLASSWORK
25 min Do the following examples with the learners, they should answer individually, one at a time, then the educator provides answers
1. Give the equation of the following:
CAPSTerm: 1,3Page reference: 130-131
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 1 Lesson 8Class work
1. Give the equations of the following:
y=x
2. Sketch the graph of y=−2
57
x
y
y
x
GRADE 9 TERM 4 MATHEMATICS
3. On the grid, draw the graphs defined by and . Label each graph and clearly mark the points where each graph cuts the axis and the axis.
58
GRADE 9 TERM 4 MATHEMATICS
4. Study the straight line graphs below and answer the questions that follow
Complete:a) The equation of line CD is b) The equation of line AB is … c) The length of CE = …
a)
b) c) CE = 6 units
59
GRADE 9 TERM 4 MATHEMATICS
Homework
1.Use a pair of compass and a ruler to make accurate constructions of the following:A angle
2. Calculate the value of the unknown side.a)
60
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 1 LESSON 9
TOPIC: WEEKLY ASSESSMENT AND REMEDIAL TEACHING
Grade 9
WEEKLY ASSESSMENT
QUESTION 1
In each of the questions below choose the correct answer.1.1 2a2 (a−2)+2a(a2−3a ) (2)
ABCD1.2 If x=5 and y=−4 , find the value of
4 x2+3 y2
(2)
A -148B 140C 148D -140
62
GRADE 9 TERM 4 MATHEMATICS
1.7
Choose a correct statement to describe the relationship between the above two triangles.
(2)
A
B
C They are not congruent
D They are neither congruent nor similar
1.8 Simplify : √ x8 + √ x16
A.B.C.D.
(2)
[16]
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GRADE 9 TERM 4 MATHEMATICS
QUESTION 2
2.1 Complete the following statements:
2.1.1 ABC is an acute angled triangle because_______________ (1)
2.1.2 DEF is a _____angled triangle because it has a 90° angle. (1)
2.1.3 GHI is an obtuse angled triangle because ______________ (1)
QUESTION 3
3.1 Calculate the interest if R1250 is invested for 3 years at 9% per annum compound interest. (4)
3.2 Calculate the amount that will be in the bank after 4 years if R6500 was invested at 5% p.a. simple interest.
(4)
[8]TOTAL 25
67
GRADE 9 TERM 4 MATHEMATICS
Grade 9WEEKLY ASSESSMENTMEMORANDUM
QUESTION 11.1 B (2)1.2 C (2)1.3 A (2)1.4 D (2)1.5 A (2)1.6 C (2)1.7 D (2)1.8 A (2)
[14]QUESTION 2
2.1 Complete the following statements:2.1.1 ABC is an acute angled triangle because all interior angles are smaller than 90° (1)2.1.2 DEF is a right angled triangle because it has a 90° angle. (1)2.1.3 GHI is an obtuse angled triangle because one of the interior angles is larger than 90° (1)
QUESTION 33.1 A=P¿
A=R1250 ¿A=R1618.79
(4)
3.2 A=P(1+¿) and i=
5100
=0,05
∴ A=6500 (1+4×0,05 )¿R7800
(4)
[8]TOTAL 25
68
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 2 LESSON 1
TOPIC: Expressions, Equations, Functions and graphs
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: manipulate expressions, solve equations.
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Factorisation ( all methods)
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the rules for expressions (BODMAS) to manipulate and simplify expressionsUse the rules for factorisation to simplify expressions and solve equations.
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
5min Revise the memo for the previous weeks test – only do the questions that were poorly answered or learners found difficult.
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20min The following must be done as individual examples, give learners 30 to 60 seconds to answer each question and then provide the answer, with explanation.
1. Factorise the following expressions:a) 2 x2−8 xb) mx−my+5x−5 yc) 3m−3d−4de+4med) tv−uv−tw+uw
2. Solve for
CAPSTerm: 1 and 3Page reference:130-131 and 141-145
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GRADE 9 TERM 4 MATHEMATICS
a)
b)
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework follows in the next lesson
REFLECTION
70
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 2 Lesson 11. Factorise the following expressions:
a)
b) mx−my+5x−5 y
c) 3m−3d−4de+4me
d) tv−uv−tw+uw
2. Solve for a)
71
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 2 LESSON 2
TOPIC: Expressions, Equations, Functions and graphs
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: manipulate expressions, solve equations, draw functions and graphs and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Types of Graphs Scale factor Identify dependent and independent variables
WHAT YOU SHOULD BE ABLE TO DO (skills)
Recognise and interpret graphs Draw conclusions from graphs regarding the dependent and independent variables
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
25min Use the following graph on the chalkboard. Ask learners for the dependant and independent variables and then ask learners the questions to interpret the graphs.
1. The graph below represents the charge per day from two car rental companies. Company A charges an initial fee of R120 and then charges R25 per day. Company B charges no initial fee, but charges R75 a day. According to the graph...
CAPSTerm: 1 and 3Page reference:130-131 and 141 - 145
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GRADE 9 TERM 4 MATHEMATICS
A.Company A is cheaperB. Company B is cheaper C. Company B is cheaper if you hire the car for two days.D.Company A is cheaper if you hire the car for more than two days
Solution: D.
2. A Businessman earns a basic salary of R1 000 plus R500 commission for every item he sells.
2.1 Write a function for calculating the salesman’s salary (y) if he sells x items.
74
GRADE 9 TERM 4 MATHEMATICS
2.2 Complete the table of values using your function from Question 1.
2.3
Draw a grid using a scale of 0 to 10 on the x-axis and 0 to 5 000 (with intervals of 500) on the y-axis, and plot a graph based on your table.
2.4 Use the graph to find out how much the salesman would be paid if he sold 7 items
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
5min 1. Draw the graph of 2. Find the equation of the graph passing through (2;3) and (-4;2)
REFLECTION
75
X1 2 3 4 5
Y
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 2 Lesson 2Class work
1. D- Company A is cheaper if you hire the car for more than two days 2.
2.12.2
2.3
2.4
76
x1 2 3 4 5
y 1500 2000 2500 3000 3500
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 2 LESSON 3
TOPIC: Number systems, financial contexts, including ratio and rate, integers.
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: calculate using number systems, integers, common fractions, decimal fractions.
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
The rules for the real number system Integers
WHAT YOU SHOULD BE ABLE TO DO (skills)
Apply the rules and simplify / solve using *integers*the real number system
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
5min 1.
77
GRADE 9 TERM 4 MATHEMATICS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
25min The following must be done by individual learners, one at a time, provide answers with explanations after each is completed. Revise defination of rational numbers as well.
1. Calculate, without the use of a calculator:
a)
b)c)
d)2. Write down any 5 rational numbers that will fit between the following integers:
a) -1 ; -2b) 2,3 ; 2,4
CAPSTerm: 1Page reference:122-126
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework follows in the next lesson
REFLECTION
79
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 2 LESSON 4
TOPIC: Number systems, financial contexts, including ratio and rate, integers.
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: calculate using number systems, integers, common fractions, decimal fractions, financial context, including ratio and rate
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Square roots , cube roots Decimal fractions Common fractions
WHAT YOU SHOULD BE ABLE TO DO (skills)
Apply the rules and simplify / solve using *integers*the real number system*common and decimal fractions*squares, cubes, square roots and cube roots
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
25min 1.a)
b)
c)
CAPSTerm: 1Page reference:122-126
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GRADE 9 TERM 4 MATHEMATICS
d)
2.Study the following table:A B C0,825 4,2367 3,452.1 Round off 0,825 to the nearest :
a) unit b) tenth c) hundredth
2.2 What is the place value of 2 in 0,825? 2.3 What is the number value of 2 in 0,825?2.4 What is the number value of 6 in 4,2367?
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
1. Calculate the following, without the use of a calculator:a)
b)
c)
d)
83
GRADE 9 TERM 4 MATHEMATICS
2. Calculate the following: (Round your answers off to 2 decimal places)a)
b)
c)
REFLECTION
84
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 2 Lesson 4Class work Homework
1.a)
b)
c)
1. a.
b.
c.
85
GRADE 9 TERM 4 MATHEMATICS
d)
2.a) 1,0b) 0,8c) hundredths (h)
d)
e)6
1000(6 thousandths)
d.
or
2. a.
b.
c.
86
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 2 LESSON 5
TOPIC: Number systems, financial contexts, including ratio and rate, integers.
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: calculate using number systems, integers, common fractions, decimal fractions, financial context, including ratio and rate
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Square roots , cube roots Decimal fractions Common fractions
WHAT YOU SHOULD BE ABLE TO DO (skills)
Apply the rules and simplify / solve using *integers*the real number system*common and decimal fractions*squares, cubes, square roots and cube roots
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
5min 3. Calculate the following, without the use of a calculator:
a)
87
GRADE 9 TERM 4 MATHEMATICS
4. Calculate the following: (Round your answers off to 2 decimal places)a)
b)
c)
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
25min 1. If 1 of petrol weighs 0,6798 . What will of petrol weigh? (round off your answer to 3 decimal places.
2. Mashudu bought a cooldrink for R7,50 ; a chocolate for R5,75 and a packet of chips for R6,00. He paid with a R50,00 note.
a) How much did he spend?b) How much change did he get?
3. The reading on a water meter at the beginning of the month was 322,573 .
CAPSTerm: 1Page reference:122-126
89
GRADE 9 TERM 4 MATHEMATICS
At the end of the month the reading is 332,523 . The municipality charges R1,25 per 200
a) How much water was used during this month?b) How much will be paid for this month’s water .
4. Water drips from a tap at a rate of 15 of water per minute. How many litres of water drips from the tap in a day?
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson.
REFLECTION
90
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 2 Lesson 5Class work Homework
1. 1 l=0 ,679 kg30 ,52l=xx=0 ,6798×30,52¿20 ,747 kg
2.a)
b)
3.a)
b)
1. Calculate the following, without the use of a calculator:a)
b)
c)
d)
91
GRADE 9 TERM 4 MATHEMATICS
4. 60 min in 1hr x 24 hrs = 1 440 minutes in a day
Water wasted in a day
2. Calculate the following: (Round your answers off to 2 decimal places)a)
b)
c)
92
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 2 LESSON 6
TOPIC: Geometric patterns; Numeric patterns and Functions
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to identify and use geometric patterns; numeric patterns and functions in calculations
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1 ; Grade 9 Term 3 Disc 2; Grade 9 Term 1 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Geometric patterns Numeric patterns Functions Equivalent forms Slow charts i.e. input and output values
WHAT YOU SHOULD BE ABLE TO DO (skills)
Apply the rules and simplify/ solve using Geometric patterns Numeric patterns Functions Equivalent forms Slow charts i.e. input and output values
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
25min Give learners time to discuss answers with a partner then give them opportunities to present their answers on the board, while guiding them.
1. a) Complete the table below described by the function , show only 2 calculations.
Input Value
-3 -2 -1 0 1 2
CAPSTerm: 1 and 3Page reference:126-129 and 141-145
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GRADE 9 TERM 4 MATHEMATICS
Output Value
b) draw a flow diagram to show the 2 calculations.
2. Find the output values in a flow diagram below for the rule
3. Use and to determine the corresponding output values ( values). Represent the input and output values in :a) A flow diagram
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
5min 1. Study the following diagram:
a) Draw the 4th diagramb) Complete the table:
Position 1st 2nd 3rd 4thValue 1
REFLECTION
94
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 2 Lesson 6Class work
1.Input Value
-3 -2 -1 0 1 2
Output Value
5 10 15 20 25 30
2
95
GRADE 9 TERM 4 MATHEMATICS
TOPIC: Geometric patterns; Numeric patterns and Functions
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to identify and use geometric patterns; numeric patterns and functions in calculations
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1 ; Grade 9 Term 3 Disc 2; Grade 9 Term 1 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Geometric patterns Numeric patterns Functions Equivalent forms Slow charts i.e. input and output values
WHAT YOU SHOULD BE ABLE TO DO (skills)
Apply the rules and simplify / solve using Geometric patterns Numeric patterns Functions Equivalent forms Slow charts i.e. input and output values
97
GRADE 9 TERM 4 MATHEMATICS
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
5min 1.a)
b)Position 1st 2nd 3rd 4thValue 1 4 9 16
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
25min Allow learners to complete individually and give different learners opportunity to present to class.
1. Copy and complete the table:Input Value
1 2 3 4 5 6
Output Value
4 7 10 19
2. Determine the rule for the relationship between the inputs and output values of the table
3. Find the values of and respectively-2 -1 0 1 12-7 -5 -3 -1 27
CAPSTerm: 1 and 3Page reference:126-129 and 141-145
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework to follow in the next lesson
REFLECTION
98
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 2 Lesson 7Class work
1.Input Value
1 2 3 4 5 6
Output Value
4 7 10 13 16 19
2. 3.
99
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 2 LESSON 8
TOPIC: Geometric patterns; Numeric patterns and Functions
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to identify and use geometric patterns; numeric patterns and functions in calculations
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1 ; Grade 9 Term 3 Disc 2; Grade 9 Term 1 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Geometric patterns Numeric patterns Functions Equivalent forms Slow charts i.e. input and output values
WHAT YOU SHOULD BE ABLE TO DO (skills)
Apply the rules and simplify / solve using Geometric patterns Numeric patterns Functions Equivalent forms Slow charts i.e. input and output values
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
25min 1. Determine the rule to describe the relationship between the input and
output values of the table below.
-2 -1 0 1 2-3 -1 1 3 5
2.
CAPSTerm: 1 and 3Page reference:126-129 and 141-145
100
GRADE 9 TERM 4 MATHEMATICS
In each of the following trms you can determine the next term by applying a rule to the previous term. Describe the rule in words in each case:
a)
b)
c)
d)3. Calculate the output values:
0 1 2 3 4-8
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
5min Prepare for the weekly assessment on*expressions; equations; functions and graphs*number systems; integers; common fractions; decimal fractions; financial contexts including ratio and rate* geometric patterns; Numeric patterns
REFLECTION
101
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 2 Lesson 8Class work
1.2.
a) Add three to the previous termb) Multiply the previous term by 2c) Subtract 4 from the previous term
d) Multiply the previous term by 3.
0 1 2 3 4-8 -12 -16 -20 -24
102
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 2 LESSON 9
TOPIC: WEEKLY ASSESSMENT AND REMEDIAL TEACHING
Grade 9
WEEKLY ASSESSMENT
QUESTION 11.1 Which of the following equations is equivalent to the equation (2)
ABCD1.2 Look at the first two patterns, how many sticks will Pattern 3 have? (2)
A 6B 9C 2D 151.3 Choose the function that represents the following graph: (2)
103
GRADE 9 TERM 4 MATHEMATICS
A.B.C.D.
[6]QUESTION 2Write down the next two terms of the following patterns:
2.12.2 (1)2.3 (2)2.4 (2)
[7]QUESTION 3
3.1 Complete the following pattern by drawing the next three terms: (3)
104
GRADE 9 TERM 4 MATHEMATICS
3.2 Complete the table :
x -2 -1 0 1 2 4 n
y 15 12 -9 -24
(8)
[11]
TOTAL 25
105
GRADE 9 TERM 4 MATHEMATICS
Grade 9
WEEKLY ASSESSMENT
MEMORANDUMQUESTION 1
1.1 B (2)1.2 B (2)1.3 C (2)
[6]QUESTION 2Write down the next two terms of the following patterns:
2.1 (2)2.2 (2)2.3 (2)2.4 (2)
[8]QUESTION 3
3.1 (3)
3.2 x -2 -1 0 1 2 4 7 12 n
y 18 15 12 9 6 0 -9 -24 -3x +12
(8)
[11]TOTAL 25
106
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 3 LESSON 1
TOPIC: Data handling and Probability
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should know and be able to organise data using a stem and leaf, calculate measures of central tendency and determine the probability of an event)
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 4 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Mean; mode; range Stem and leaf diagram Different graphs to represent data Probability definition and equation
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the definitions and formula as well as knowledge on graphs to work out problems related to data handling and probability
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
10min Review the previous weekly assessment. Do the examples that learners found difficult and/or the ones they struggled in after marking.
LESSON PRESENTATION/ DEVELOPMENT/ CLASSWORK
20min Using their previous knowledge and notes ask learners to answer the following questions individually and provide answers in between.
1. The given data set represents the weight to the nearest kg of a group of learners.82 73 6542 55 6265 58 6851 65 72
CAPSTerm: 4Page reference: 149-153
107
GRADE 9 TERM 4 MATHEMATICS
63 48 65a) Draw a stem and leaf diagram for the datab) Determine the range of the datac) Determine the moded) Determine the meane) Determine the median
2. An 8-sided die has the numbers 1 to 8 on its faces. When thrown, it has as equal chance of landing on any one of its facesa) How many possible outcomes are there?b) What is the probablility that it will land on a prime number?c) What is the probablility that it will land on a prime number?
1.a)
Stem Leaf8 27 2 36 2 3 5 5 5 5 85 1 5 84 2 8
b) Range ¿82−42=40
c) Mode ¿65
d) Mean
¿
e) Arrange data : 42 48 51 55 58 62 63 65 65 65 65 68 72 73 82
Media ¿ 65
2.
108
GRADE 9 TERM 4 MATHEMATICS
a) 8 possible outcomes
b) P(prime number) = c) P(number less than 0)= 0
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson
REFLECTION
109
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 3 Lesson 1
Classwork
1.a)
Stem Leaf8 27 2 36 2 3 5 5 5 5 85 1 5 84 2 8
b) Range ¿82−42=40
c) Mode ¿65
d) Mean ¿
e) Arrange data : 42 48 51 55 58 62 63 65 65 65 65 68 72 73 82 Media ¿65
2.a) 8 possible outcomesb) P(prime number) ¿c) P(number less than 0¿=0
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 3 LESSON 2
TOPIC: Data handling and Probability
110
GRADE 9 TERM 4 MATHEMATICS
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should know and be able to represent data using a scatterplot, analyse data, calculate measures of central tendency and determine the probability of an event)
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 4 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Mean; mode; range Stem and leaf diagram Different graphs to represent data Probability definition and equation
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the definitions and formula as well as knowledge on graphs to work out problems related to data handling and probability
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/ CLASSWORK
25min 1. A group of 14 learners measure their height and foot sizes and tabulate their results.Height 174 158 163 175 140 126 153 160 160Foot 27 24 24 26 23 23 22 25 24
Height 131 156 165 158 120Foot 20 23 25 24 20a) Draw a scatterplot for the data collected.b) According to the graph, do taller people have longer feet lengths and why?
2. There are eight balls in a basket. 2 are green, 3 are blue and the rest are white.a) Calculate how many white balls there are.b) What is the probability of picking a blue ball?c) What is the probability of picking a green ball?
CAPSTerm: 4Page reference: 149-153
CONSOLIDATION/CONCLUSION AND OR
5 min 1. A survey was conducted to test the relationship between the hand and shoe size. The table below shows 10 measurements of different hand lengths and shoe sizes.
Hand 5 7 2 9 6 7 4 9 8 5
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GRADE 9 TERM 4 MATHEMATICS
HOMEWORK lengthShoe size 12 13 10 15 12 15 11 16 15 11
a) Draw a scatter plot using the information in the table.b) Draw a line of best fit.c) What conclusion can you draw about the relationship between a hand length and a shoe size?d) Find the mode for the shoe size.e) Calculate the mean for the shoe size.f) Determine the range for the hand size.
2. There are 25 learners in a class. If a learner is chosen at random, what is the probability that a girl is chosen if there are 11 boys?
REFLECTION
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GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 3 Lesson 2
Classwork Homework1. a)
a) A positive correlation. Taller people do have longer feet length.
2.a) 8−(2+3)=3b) P(B)=¿c) P(G)=¿
1. a) and b)
1 2 3 4 5 6 7 8 9 10024681012141618
Relationship between hand and shoe size
Hand Length
Shoe
Size
c) The length of the hand is in direct proportion with the shoe size d) Mode ¿15
e) Mean ¿ 12+13+10+15+12+15+11+16+15+11
10=13
f) Range ¿9 –2=7
2. Girls: 25−11=14 P(G) ¿
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GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 3 LESSON 3
TOPIC: Data handling and Probability
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should be able to read the bar graph and scatterplot and answer related questions and be able to use a tree diagram to find possible outcomes of an event)
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 4 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Mean; mode; range Stem and leaf diagram Different graphs to represent data Probability definition and equation
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the definitions and formula as well as knowledge on graphs to work out problems related to data handling and probability
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GRADE 9 TERM 4 MATHEMATICS
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
10min a) and b)
1 2 3 4 5 6 7 8 9 10024681012141618
Relationship between hand and shoe size
Hand Length
Shoe
Size
c) The length of the hand is in direct proportion with the shoe size d) Mode ¿15
e) Mean ¿ 12+13+10+15+12+15+11+16+15+11
10=13
f) Range ¿9 –2=7
2. Girls: 25−11=14 P(G) ¿
LESSON PRESENTATION/ DEVELOPMENT/ CLASSWORK
20min 1. Study the bar graph below taken from the 2009 South African Census@School results. It shows the modes of transport to school from home of the learners who participated in the Census@School.
a) What is the graph about?b) What information is shown on the axes?
CAPSTerm: 4Page reference:
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GRADE 9 TERM 4 MATHEMATICS
c) Is the scale clear and easy to read?d) What conclusions can the graph help you make?
Stem Leaf1 1 2 5 7 2 0 1 3 4 83 2 9
149-153
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GRADE 9 TERM 4 MATHEMATICS
4 3 3 5 6 85 0 1 6
a) What is the range for the stem and leaf plot? b) What is the median value for the stem and leaf plot? c) What is the mode for the stem and leaf plot below? d) What is the mean value?
3. Represent the following 2-way table on a tree diagram:
T-shirt JeansBlack Blue Red
Green Black/green Blue/green Red/greenWhite Black/white Blue/white Red/white
1.a) In order to find out what the graph is about, we look at the title. The title tells us that the
graph shows how learners get to school each day.b) The axes are clearly labelled. The horizontal axis shows the different forms of transport:
walk, car, train, bus, bicycle, scooter, taxi and other. The vertical axis shows percentage.c) The scale is clear and easy to read. You cannot read exact percentages for the number of
learners walking to school, but it is easy to estimate that nearly 80% (or over 70%) walk to school.
d) You can immediately see that most of the learners in the census walk to school from home. The other learners mostly use car, bus or taxis to get to school
2. a) 56 – 11 = 45
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GRADE 9 TERM 4 MATHEMATICS
b)
39−322 = 3,5
c) 43 d) 624 ÷ 19 = 32,8
.
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson.
REFLECTION
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GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 3 Lesson 3
Class work
1.a) In order to find out what the graph is about, we look at the title.
The title tells us that the graph shows how learners get to school each day.
b) The axes are clearly labelled. The horizontal axis shows the different forms of transport: walk, car, train, bus, bicycle, scooter, taxi and other. The vertical axis shows percentage.
c) The scale is clear and easy to read. You cannot read exact percentages for the number of learners walking to school, but it is easy to estimate that nearly 80% (or over 70%) walk to school.
d) You can immediately see that most of the learners in the census walk to school from home. The other learners mostly use car, bus or taxis to get to school
2. a) 56 – 11 = 45
b)
39−322 = 3,5
c) 43 d) 624 ÷ 19 = 32,8
3.
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GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 3 LESSON 4
TOPIC: Area and Perimeter, Surface Area and Volume, 3-D objects and Transformations
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should be able to identify properties of solids, calculate the area, reflect and translate geometric figures, determine coordinates of images of transformation, compare and identify solids from their properties)
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 3; Grade 9 Term 4 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Formulae for: Area and Perimeter Surface Area Volume
3-D objects Conversions Transformations e.g. reflection and rotation
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use formulae and conversions to solve problems involving : Area and Perimeter Surface Area Volume
3-D objects Do any transformation of points and shapes and write down coordinates
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GRADE 9 TERM 4 MATHEMATICS
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/ CLASSWORK
25min First tell the learners what the topics for the lesson is then hand out the classwork and allow them to complete, question at a time. Give answers after each question revising some theory as you go along.
1. Complete the following table:
Platonic Solid Name of solid Number of edges
Number of vertices
Number of faces
a) b) c) d)
2. In the figure below, AP= 5m; AS = SB = 2m; PT = 12m and PS ⊥ AB
Calculate the area of the figure correct to 2 decimal places.
CAPSTerm: 3 & 4Page reference:146-148
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GRADE 9 TERM 4 MATHEMATICS
3. Reflect ∆≝¿ in the x-axis; y−¿axis and in the line y=x .
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
5min 1.a) Draw line segment PQ with P (2;3) and Q(5;5) on a Cartesian planeb) Translate line PQ 2 units to the right and 2 units upwards and label the image P 'Q'c) Write down the coordinates of P'∧Q '
2. Which of the following polyhedral are prisms
122
A B C D E F
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 3 Lesson 4
Class work
1.
Platonic Solid Name of solid Number of edges Number of vertices Number of facesa)Dodecahedron
b) 30 c) 20 d) 12
2. Area of kite
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GRADE 9 TERM 4 MATHEMATICS
Homework
1.
a) and b)
c ¿P ' (4 ;5) and Q '(7;7)
2. A, B, C are Prisms
D, E , F are pyramids
126
x
y
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 3 LESSON 5
TOPIC: Area and Perimeter, Surface Area and Volume, 3-D objects and Transformations
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should be able to reflect geometric figures, determine coordinates of images of transformation, identify prisms and calculate volume)
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 3; Grade 9 Term 4 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Formulae for: Area and Perimeter Surface Area Volume 3-D objects conversions Transformations e.g. reflection and rotation
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use formulae and conversions to solve problems involving : Area and Perimeter Surface Area Volume 3-D objects Do any transformation of points and shapes and write down coordinates
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GRADE 9 TERM 4 MATHEMATICS
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
10min 1. a) and b)
c) P '(4 ;5) and Q '(7 ;7)
2. A, B, C are Prisms D, E , F are pyramids
LESSON PRESENTATION/ DEVELOPMENT/ CLASSWORK
20min 1.a) Draw the Cartesian planeb) Draw rectangle JKLM with the following coordinates:
J (−5 ; 4) ,K (−3 ;4) , L(−3 ;1)∧M (−5;1)
CAPSTerm: 3Page reference:146-148
128
y
x
GRADE 9 TERM 4 MATHEMATICS
c) Shade half of the rectangled) Reflect the rectangle along the y-axis and label the image J ' ,K ' , L' , M ' and write down the
coordinates of each vertexe) Reflect the rectangle J ' ,K ' , L' , M ' along the x-axis and label the image J K L M and write
down the coordinates of each vertex.
2. What is a prism? 3. Calculate the volume of the following:
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework follows in the next lesson
REFLECTION
Answers: Term 4 Grade 9 Week 3 Lesson 5
Classwork
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GRADE 9 TERM 4 MATHEMATICS
1.
2. A prism is a polyhedral with two identical and parallel faces called bases.
3.
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 3 LESSON 6
TOPIC: Area and Perimeter, Surface Area and Volume, 3-D objects and Transformations
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GRADE 9 TERM 4 MATHEMATICS
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should be able to reflect geometric figures, determine coordinates of images of transformation, express the transformation algebraically, identify properties of solids and calculate volume)
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 3; Grade 9 Term 4 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Formulae for: Area and Perimeter Surface Area Volume
3-D objects conversions Transformations e.g. reflection and rotation
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use formulae and conversions to solve problems involving : Area and Perimeter Surface Area Volume
3-D objects Do any transformation of points and shapes and write down coordinates
131
GRADE 9 TERM 4 MATHEMATICS
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/ CLASSWORK
20min 1.a) Draw a Cartesian plane on the grid provided and label the axesb) Draw the figure SAMP with vertices S(1 ;−2) , A (2 ;−1) and
M (3 ;−2) and P(2 ;−5)c) Reflect the figure along the y-axis and label it S' A 'M ' P 'd) Write down the coordinates of S' A 'M 'P’ e) Compare the coordinates of SAMP and S' A 'M ' P 'f) What is the relationship between the coordinates of the object and the coordinates of the
image? g) Complete: (x ; y)→¿
2. Complete the table:
CAPSTerm: 3Page reference:146-148
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GRADE 9 TERM 4 MATHEMATICS
3. Calculate the volume of the following object:
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
1. Calculate the volume of the following, use π=3,14
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GRADE 9 TERM 4 MATHEMATICS
2. Describe the transformation if the coordinates of the original point and its image are:
a)
b)
c)
3.
a) Name the shapeb) What is the shape of its faces?c) How many faces does the shape have?d) How many edges does the shape have?e) How many vertices does the shape have?f) Draw the net of the shape.
REFLECTION
134
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 3 Lesson 6
Class work Homework
1. a) , b) and c)
d) S' (−1;−2 ) , A ' (−2 ;−1 ) , M ' (−3 ;−2 ) ,P '(−2;−5)
e) x−¿coorinates change a sign and y−¿coordiantes remain the same.
f) (x ; y) →(−x ; y)2.
1. V=π r2×h ¿3,14× ¿ ¿339,12 cm3
2. a) Translation 2 units downwardsb) Translation 10 units to the left and 7 units upwardsc) Translation 13 units to the right and 9 units upwards.
3. a) Dodecahedronb) Pentagonsc) 12 Facesd) 30 Edgese) 20 Vertices
f)
135
y
x
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 3 LESSON 7
TOPIC: Area and Perimeter, Surface Area and Volume, 3-D objects and Transformations
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should be able to enlarge geometric figures, determine scale factors of transformations, express, identify properties of solids and calculate area and volume)
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 3; Grade 9 Term 4 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Formulae for: Area and Perimeter Surface Area Volume
3-D objects Conversions Transformations e.g. reflection and rotation
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use formulae and conversions to solve problems involving : Area and Perimeter Surface Area Volume
3-D objects Do any transformation of points and shapes and write down coordinates
137
GRADE 9 TERM 4 MATHEMATICS
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
10min 1. V=π r2×h ¿3,14× ¿ ¿339,12 cm3
2. a) Translation of 2 units downwardsb) Translation of 10 units to the left and 7 units upwardsc) Translation of 13 units to the right and 9 units upwards.
3.a) Dodecahedronb) pentagonc) 12d) 30e) 20f)
LESSON PRESENTATION/ DEVELOPMENT/ CLASSWORK
20min 1. Study the diagram below: CAPSTerm: 3Page reference:146-148
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GRADE 9 TERM 4 MATHEMATICS
Complete the following:a) AB= 3cm A ' B' = 6cm therefore A ' B' = ------× ABb) BC= 2cm B' C ' = 4cm therefore B' C ' = ------× BCc) CD= 3cm C ' D ' = 6cm therefore C ' D ' = ------× CDd) AD= 2cm A ' B' = 4cm therefore A ' B' = ------× AD
2. Refer to question 1.a) Calculate the ratio of the area of Figure B to the area of Figure A.b) Simplify the ratio in question 2.a) above.
3. Complete the following table:
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GRADE 9 TERM 4 MATHEMATICS
Name Shape of faces
No of faces (F)
No of vertices (V)
No of edges (E)
F+V-E
4. The area of the base of a rectangular prism is 32mm2 and its height is 12mm. What is its volume?5. The volume of a cube is 216m3. What is the length of one of its edges?
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson.
REFLECTION
Answers: Term 4 Grade 9 Week 3 Lesson 7
140
GRADE 9 TERM 4 MATHEMATICS
Classwork Homework
1.a) AB= 3cm A ' B' = 6cm therefore A ' B' = --2----× ABb) BC= 2cm B' C ' = 4cm therefore B' C ' = --2----× BCc) CD= 3cm C ' D ' = 6cm therefore C ' D ' = --2----× CDd) AD= 2cm A ' B' = 4cm therefore A ' B' = --2----× AD
2.a) b)
Area of ABCD = 6cm2
Area of A ' B' C ' D'=24 cm2
Ratio of the area of figure B to the area of figure A = 24 cm2 : 6 cm2
The ratio in simplest form is:
4 : 1
22 : 1
Emphasise to learners that the area of the image = 4 times the area of an objectThis means that area of the image = 22× area of the objectIn general, if a shape enlarges by a factor of k, then the area of the image = k2 × area of the object
3. Complete the following table:
Homework will follow in the next lesson.
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GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 3 LESSON 8
TOPIC: Expressions, Equations
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to engage with problems related to data handling and probability. (leaners should be able to find products of algebraic expressions, factorise, simply algebraic expressions and solve algebraic equations)
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 4 Disc 1 GDE 16-01-2014 2014
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Factorisation ( all methods)
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the rules for expressions (BODMAS) to manipulate and simplify expressionsUse the rules for factorisation to simplify expressions and solve equations.
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/ CLASSWORK
20min Place the learners in groups with the classwork and allow them to do the exercises. Walk around and facilitate where necessary.
1. Expand and simplify:a) 2 (x2+4 x+8 )b) (x+2)( x+5)
2. Factorise:
CAPSTerm: Page reference:
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GRADE 9 TERM 4 MATHEMATICS
a) 25a2−9b) 1−16 x2
c) 2 x2−2d) ( x+ y )2−b2
e) 4 x6−19
f) −(x+ y )2+1g) x2+5 x+6h) x2−5 x+6i) 2 x2+10 x+12j) −2b2+6b−4
3. Simplify:
a) x2−9x2+x−6
÷ x2−3 xx+1
b)2
x2+4 x−12
−1x−2
4. Solve the following equations:
a) 4(2m – 5) = 5 – 2(m + 1) b) 3(x – 1) – 4x = 5 – 2(x+ 1)c) 2(x – 3) = x- 3(x+ 2)
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Learners must bring all materials for the SBA task – Project in the next lesson.e.g: cardboard; scissors; glue etc…
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GRADE 9 TERM 4 MATHEMATICS
REFLECTION
Answers: Term 4 Grade 9 Week 3 Lesson 8
Class work
1. Expand:a)
2 (x2+4 x+8 )
b)(x+2)( x+5)
2. Factorise:a)
25a2−9
b)1−16 x2
c)2 x2−2
d)
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GRADE 9 TERM 4 MATHEMATICS
( x+ y )2−b2
e) 4 x6−19
f) −(x+ y )2+1
g) x2+5x+6
h) x2−5 x+6(x−3)(x−2)
i) 2 x2+10 x+12
j) −2b2+6b−4¿−2 (b2−3b+2 )¿−2 (b−1 ) (b−2 )
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GRADE 9 TERM 4 MATHEMATICS
4. Solve the following equations:a) 4(2m – 5) = 5 – 2(m + 1)
8m−20=5−2m−28m+2m=5+20−210m=23
m=2310
¿2 310
b) 3(x – 1) – 4x = 5 – 2(x+ 1)3 x−3−4 x=5−2 x−2
3 x−4 x+2 x=5+3−2 x=6
c) 2(x – 3) = x- 3(x+ 2)
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GRADE 9 TERM 4 MATHEMATICS
Grade 9 Project Geometry of 3D Objects Marks: 48
1. Use the following nets to build 1.1 A rectangular prism1.2 A triangular prism1.3 A cylinder
2. Change all the dimensions by multiplying by 2 and build another rectangular prism in each – build again.3. Work out the surface area and volume of both sets of prisms and compare them.
a)
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GRADE 9 TERM 4 MATHEMATICS
Use the following rubric to allocate marks for learners’ objects:
1.1 A rectangular prism. Criteria
Neatness (3)
Accuracy (4) (original + enlarged)
Materials used (2)
Due date (2)
Answers (5)
Total [16]
1.2 A triangular prismCriteria
Neatness (3)
Accuracy (4) (original + enlarged)
Materials used (2)
Due date (2)
Answers (5)
Total [16]
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GRADE 9 TERM 4 MATHEMATICS
1.1.1.1.2.1.3. A cylinder
Criteria
Neatness (3)
Accuracy (4)(original + enlarged)
Materials used(2)
Due date ( 2 )
Answers (5 )
Total [16 ]
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GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 4 LESSON 1
TOPIC: Expressions, Equations
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
manipulate expressions, solve equations, draw functions and graphs and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Factorisation ( all methods)
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the rules for expressions (BODMAS) to manipulate and simplify expressions Use the rules for factorisation to simplify expressions and solve equations.
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
5min Give learners their SBA project marks and correct answers
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
25min Give the exercise and allow learners to explain to each other how to do them, also revise the examples given in term 4; week 3 lesson 8.1. Simplify:
a)b)c) ( 4a2+2b ) ( 4a−2ab+9c )
CAPSTerm: 1 and 3Page :130-131141 -145
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GRADE 9 TERM 4 MATHEMATICS
d) 9 x2( 13x+2x3)−4 x( 1
2x4−3 x2)
2. Solve the following equations:1. 4 ( x+2 )−3=2 (3−x )
2.
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson
REFLECTION
155
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 4 Lesson 1
Classwork
1.a)
b)
c)( 4a2+2b ) ( 4a−2ab+9c )
¿16a3−8a3b+36a2c+8ab−4ab2+18bc
d)9 x2( 1
3x+2x3)−4 x(1
2x4−3 x2)
¿3 x3+18 x5−2 x5+12x3
¿16 x5+15x3
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GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 4 LESSON 2
TOPIC: Expressions, Equations, Functions and Straight Lines
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
manipulate expressions, solve equations, draw functions and graphs and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Factorisation ( all methods) Drawing straight lines Interpreting straight lines
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the rules for expressions (BODMAS) to manipulate and simplify expressions Use the rules for factorisation to simplify expressions and solve equations. Use different methods to draw straight lines Interpret straight lines
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSSWORK
25min 1. Simplify:
a)
2. Solve for :
a)b)
CAPSCAPSTerm: 1 and 3Page :130-131141 -145
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GRADE 9 TERM 4 MATHEMATICS
a) Use the graph to calculate the gradient of the straight line.b) Determine the equation of the straight line.c) Write down the gradient of any other straight line which can be drawn parallel to the given
line
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GRADE 9 TERM 4 MATHEMATICS
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
5min 1. Solve for :
a) 2.
a) Write down the defining equation of each of the following straight line graphs.
b) What can you deduce about the lines AD and BC. Give a reason for your answer.
REFLECTION
160
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 4 Lesson 2
Classwork Homework
1.a)
OR x2−4 x+4−4¿ x2−4 x¿ x (x−4)
2.a)
b)
3.
1.a)
2.
a) mBC=−4−00−(−2 )
=−2
∴ y BC=−2 x−4
mAD=4−00−2
=−2
∴ y AD=−2 x+4
b) AD‖BC because the gradients are equal to each other
161
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 4 LESSON 3
TOPIC: Expressions, Equations, Functions and Straight Lines
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
manipulate expressions, solve equations, draw functions and graphs and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Factorisation ( all methods) Drawing straight lines Interpreting straight lines
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the rules for expressions (BODMAS) to manipulate and simplify expressions Use the rules for factorisation to simplify expressions and solve equations. Use different methods to draw straight lines Interpret straight lines
163
GRADE 9 TERM 4 MATHEMATICS
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
5min 1.a)
2. a) mBC=−4−00−(−2 )
=−2
∴ y BC=−2 x−4
mAD=4−00−2
=−2
∴ y AD=−2 x+4
b) AD//BC because the gradients are equal to each other
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
25min Allow learners to engage with each other in groups on methods of solving the exercise:1.Simplify the following expressions
a)b)
CAPSTerm: 1 and 3Page reference:130-131
141 -145
164
GRADE 9 TERM 4 MATHEMATICS
2. Solve the following equations:a) b)
3. Determine the gradient of the following straight line:
, as well as the intercept and the intercept
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework follows in the next lesson
REFLECTION
165
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 4 Lesson 3
Classwork Homework
1.a)
b)
2.a)
Homework follows in the next lesson
166
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 4 LESSON 4
TOPIC: Expressions, Equations, Functions and Straight Lines
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
manipulate expressions, solve equations, draw functions and graphs and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Factorisation ( all methods) Drawing straight lines Interpreting straight lines
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the rules for expressions (BODMAS) to manipulate and simplify expressions Use the rules for factorisation to simplify expressions and solve equations. Use different methods to draw straight lines Interpret straight lines
168
GRADE 9 TERM 4 MATHEMATICS
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
25min Do each example on the board after giving learners 30-60seconds to solve. Explain how the problems were solved using previous rules learnt.
1. Factorise the following expressions fully, using any suitable method:a) 3 x2 y−9x y2+12x3 y3
b)
2. Simplify the expression below:
a)
3. Draw the graph of
CAPSCAPSTerm: 1 and 3Page :130-131141 -145
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
1. Factorise the following expressions fully, using any suitable method:
a)b)
2. Simplify the expression below:
a)3. Find the equation of the graph
REFLECTION
169
x
y
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 4 Lesson 4
Classwork Homework
1.a)
b)
2. a)
1. a) (2 x− y )(2x+ y )
b) (x−2)(x−9)
2. 9 y2
7
3. y=−x+3
170
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 4 LESSON 5
TOPIC: Expressions, Equations, Functions and Straight Lines
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
manipulate expressions, solve equations, draw functions and graphs and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Factorisation ( all methods) Drawing straight lines Interpreting straight lines
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the rules for expressions (BODMAS) to manipulate and simplify expressions Use the rules for factorisation to simplify expressions and solve equations. Use different methods to draw straight lines Interpret straight lines
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
5min 1.a) 4 x2− y2
(2 x− y )(2x+ y )
b)
2.
172
GRADE 9 TERM 4 MATHEMATICS
a)
3. m=0−33−0
=−1
∴ y=−x+3
LESSON PRESENTATION/ DEVELOPMENT/CLASSSWORK
25min Do each example on the board after giving learners 30-60seconds to solve. Explain how the problems were solved using previous rules learnt.
1. Simplify:
a)
b)
c)
2. Factorise
a)
b)
3. Solve for :
a)
CAPSCAPSTerm: 1 and 3Page reference:130-131141-145
173
GRADE 9 TERM 4 MATHEMATICS
4. Study the graph below:
a) What type of graph is this?b) Is it an increasing or decreasing function?c) Approximately what ℉ is freezing point?
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework follows in the next lesson.
REFLECTION
174
x
y
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 4 Lesson 5Class work Homework
1.a)
b)
c)
2. a)
b)
1.a) 4 x2− y2=(2x− y )(2 x+ y )
b)
2.a)
3. m=0−33−0
=−1
∴ y=−x+3
176
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 4 LESSON 6
TOPIC: Expressions, Equations, Functions and Straight Lines
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
manipulate expressions, solve equations, draw functions and graphs and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Factorisation ( all methods) Drawing straight lines Interpreting straight lines
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the rules for expressions (BODMAS) to manipulate and simplify expressions Use the rules for factorisation to simplify expressions and solve equations. Use different methods to draw straight lines Interpret straight lines
178
GRADE 9 TERM 4 MATHEMATICS
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSSWORK
25min Allow learners to work in pairs to complete the exercise. Stop learners after 5 minutes and answer questions, allow for further questions from the learners as well.
1. Simplify:
a)
b)
2. Solve for
a) x2 = 25
3 What is the equation of the graph drawn below?
CAPSTerm: 1 and 3Page reference:130-131141-145
179
GRADE 9 TERM 4 MATHEMATICS
4.
a) At how many minutes do both companies charge the same rate?b) When is company T’s rates lower than that of Company S?
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
1. Simplify:
2. , calculate , when .
3. Complete the table below and draw the graph.-3 -2 -1 0 1 2 3
REFLECTION
180
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 4 Lesson 6
Classwork
1.a)
b)
2.a)
3.
4.a) At 20 minutesb) From 0 and 20 minutes
181
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 4 LESSON 7
TOPIC: Expressions, Equations, Functions and Straight Lines
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
manipulate expressions, solve equations, draw functions and graphs and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Factorisation ( all methods) Drawing straight lines Interpreting straight lines
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the rules for expressions (BODMAS) to manipulate and simplify expressionsUse the rules for factorisation to simplify expressions and solve equations. Use different methods to draw straight linesInterpret straight lines
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
5min 1. Simplify
2.
3.
182
GRADE 9 TERM 4 MATHEMATICS
-3 -2 -1 0 1 2 3-2 -1 0 1 2 3 4
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
25min Give learners exercise to complete individually for 15 min then answer with explanations.
1. Simplify:
a)
b)
c)
CAPSCAPSTerm: 1 and 3Page reference:130-131141-145
183
GRADE 9 TERM 4 MATHEMATICS
2. Solve for if :
3. , calculate , when
4. Use the given coordinates to find the equation of the straight line graphs passing through them.
a) (16; 5) and (7; 2)
b) (−12;8) and (-6; -3)
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework follows in the next lesson.
REFLECTION
184
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 4 Lesson 7
Class work
1.a)
b)
c)
2.a)
1.
a)
2.
3.
-3 -2 -1 0 1 2 3-2 -1 0 1 2 3 4
185
GRADE 9 TERM 4 MATHEMATICS
b)
3.a)
m=y2− y1
x2−x1
m= 5−216−7
m=13
∴ y=13x+c
∴5=13
(16 )+c
∴ c=−13
b)
m=y2− y1
x2−x1
m=8−(−3)−12
− (−6 )
∴m=2∴ y=2x+c
186
GRADE 9 TERM 4 MATHEMATICS
∴−3=2 (−6 )+c∴ c=9∴ y=2x+9
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 4 LESSON 8
TOPIC: Expressions, Equations, Functions and Straight Lines
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
manipulate expressions, solve equations, draw functions and graphs and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Factorisation ( all methods) Drawing straight lines Interpreting straight lines
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the rules for expressions (BODMAS) to manipulate and simplify expressions Use the rules for factorisation to simplify expressions and solve equations. Use different methods to draw straight lines Interpret straight lines
187
GRADE 9 TERM 4 MATHEMATICS
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
25min Learners should work at the exercise in pairs and assist each other with methodology. The educator should walk around the class to ensure that all the work is completed and understood.
1. Simplify
a)
b) 9 x2( 13x+2x3)−4 x( 1
2x4−3 x2)
c)12abc ( 14a2b
c+ 8ac3
b−22c3b3
a )2. Given that a=−1 ;b=7∧c=0 find the value for each of the following expressions:
a) 17abcb) 3a+2b−7 c
3. Solve for :
a) 4 ( x+2 )−3=2 (3−x )
b) 4 ( x−7 )+6 (2−3x )=5 (x−6 )
4. a) On the same Cartesian plane draw the graphs y = 4 and x = 4.
b) What is the gradient for each graph?
c) What do you notice about these two graphs?
CAPSCAPSTerm: 1 and 3Page :130-131141-145
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Learners must prepare for weekly test on expressions, equations, functions and straight line graphs
188
GRADE 9 TERM 4 MATHEMATICS
REFLECTION
Answers: Term 4 Grade 9 Week 4 Lesson 8
Classwork
1.a)
b)
9 x2( 13x+2x3)−4 x( 1
2x4−3 x2)
¿3 x3+18 x5−2 x5+12x3
¿16 x5+15x3
c)
12abc ( 14a2b
c+ 8ac3
b−22c3b3
a ) ¿7a3b2+4a2 c4−11b4 c4
2.a)
17abc ¿17 (−1 ) (7 ) (0 ) = 0
b)
189
GRADE 9 TERM 4 MATHEMATICS
3a+2b−7 c
¿3 (−1 )+2 (7 )−7 (0 )¿−3+14
3.a) 4 ( x+2 )−3=2 (3−x )
4 x+8−3=6−2x4 x+2 x=6−8+36 x=1
x=16
b) 4 ( x−7 )+6 (2−3x )=5 (x−6 )4 x−28+12−18 x=5 x−304 x−18 x−5x=−30+28−12
−19 x=−14
x=1419
4.
For y = 4, the gradient is 0
For x = 4, the gradient is undefined
They are perpendicular to each other
190
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 4 LESSON 9
Grade 9Weekly AssessmentTerm 4 - Week 4 15min
QUESTION 11.1 Calculate the intercept of the line (3)
[3]QUESTION 2
2.1 Simplify2.1.1 (2)
2.1.2 (2)2.1.3 (3)
2.2 Factorise:2.2.1
Solve for x :(2)
2.2.2 (3)[12]
TOTAL : 15
191
GRADE 9 TERM 4 MATHEMATICS
Grade 9Weekly AssessmentMEMORANDUMTerm 4 15min
QUESTION 11.1 intercept: Let :
intercept:
(3)
[4]QUESTION 2
2.12.1.1 (2)
2.1.2 (2)
2.1.3 (3)
2.22.2.1 (2)
2.2.2 (3)
[12]TOTAL : 16
192
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 5 LESSONS 1 & 2
TOPIC: Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
Define and apply rules for number systems
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Conversion between decimal and common fractions Financial maths formulae Percentage, ratio and rate Highest Common Factor and Lowest Common Multiple
WHAT YOU SHOULD BE ABLE TO DO (skills)
Apply all the knowledge when doing calculations Recall and apply formulae, where necessary.
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
10 min Revise the weekly assessment from the previous week
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20min Give learners the exercise to do in groups to revise the topics for this week, then allow them to present to the class.1. Which of the following numbers belong to each group below?
−2 13
9π √20 1,23 .. . −3 √16
CAPSTerm: 1Page reference:119-122
193
GRADE 9 TERM 4 MATHEMATICS
a) Integersb) Rational numbersc) Irrational numbers
2. List the following:a) The factors of 15b) The first four multiples of 6c) Find two rational numbers between -1,36 and -1,35
3. Calculate:
a) 1 12−1
6+5
3
b) 3 56−3 1
3
c) -9 – (21 – 4)d) 3 + 3 - (-7) – 8e) (450-349) x 2 + (-101)
4.US Dollar $8,4916 R11,78British Pound £13,7697 R7,26Euro €8,9 R11,24Jamie is travelling to Europe. She has R2 000 for spending.
a) How much will Jamie get in Euros?b) Will it be cheaper for her to go to London and use the British pound? Explain fully
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson.
REFLECTION
194
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 5 Lessons 1 & 2Classwork
1.
a) −3 ; √16
b) −2 1
3−3 √16
c) 9 π √20 1 ,23. . .
2.
a) 1 ; 3 ; 5 ; 15b) 6 ; 12; 18 ; 24c) −1 ,359 ; −1 ,358; −1 ,357 ; −1,356 ; −1 ,355 ; −1 ,354 ; −1,353 ; −1 ,352 ; −1 ,351
3.
a) 1 12−1
6+5
3
¿32– 1
6+ 5
3
¿ 9−1+106
¿ 186
¿3
b)3 56−3 1
3
¿ 236
−103
196
GRADE 9 TERM 4 MATHEMATICS
¿ 236
−10×23×2
¿ 236
−206
¿ 36=1
2a) -9 – (21 – 4)
= - 26
b) 3 + 3 - (-7) - 8=5
c) (450-349) x 2 + (-101)=101
4.a)
8,9=11 ,24x=200011 ,24 x=2000×8,9
x=2000×8,911 ,24
x=1583 ,63
b)
197
GRADE 9 TERM 4 MATHEMATICS
13 ,7697=7 ,26x=20007 ,26 x=2000×13 ,7697
x=2000×13 ,76977 ,26
x=3793 ,31She will get £3793,31Thus it will be cheaper.
198
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 5 LESSONS 3 & 4
TOPIC: Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
Define and apply rules for number systems
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Conversion between decimal and common fractions Financial maths formulae Percentage, ratio and rate Highest common factor and lowest common multiples
WHAT YOU SHOULD BE ABLE TO DO (skills)
Apply all the knowledge when doing calculations Recall and apply formulae, where necessary.
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
5 min Revise the weekly assessment from the previous week
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20minGive the exercise to learners in their groups to come up with solutions; assign group leaders to present to the class:
1. Simplify:
a) (3 12+3 1
2 )÷1 34
CAPSTerm: 1Page reference:119-122
199
GRADE 9 TERM 4 MATHEMATICS
b) 3 56−2 1
3
c) (-3)3
2. Calculate:a) 3 – (-9)b) -1 + 2 – 3 x 4c) 3 x 3 + 1 x 11 – 6d) √90−9
3. Don bought a music set for R199 and sold it to Tumi for R250. Thando bought a TV for R800 and sold it for R850.a) Calculate the profit that each one made.b) Calculate the percentage profit that each person made. (correct to one decimal place)c) Who made the larger profit?d) Who made the larger percentage profit?
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
REFLECTION
200
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 5 Lesson 3 and 4
Class work
1. Simplify:
a) (3 12+3 1
2 )÷1 34
¿( 72+ 7
2 )÷ 74
¿ 142× 4
7¿4
b) 3 56−2 1
3
¿ 236
−73
¿ 236
−7×23×2
¿ 236
−146
¿ 96=3
2=1 1
2
c) (-3)3
= -27
201
GRADE 9 TERM 4 MATHEMATICS
2. Calculate:a) 3 – (-9) =12
b) -1 + 2 – 3 x 4 =-11
c) 3 x 3 + 1 x 11 – 6 = 14
d) √90−9 = 93.a) Don: R250 –R199 = R51Thando R850-R800 =R50
b)Don:
51199
×100
=25 ,6 %
Thando:
50800
×100
=13 ,3 %
c) Dond) Thando
202
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 5 LESSONS 5 & 6
TOPIC: Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
Define and apply rules for number systems
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Conversion between decimal and common fractions Financial maths formulae Percentage, ratio and rate Highest common factor and lowest common multiples
WHAT YOU SHOULD BE ABLE TO DO (skills)
Apply all the knowledge when doing calculations Recall and apply formulae, where necessary.
203
GRADE 9 TERM 4 MATHEMATICS
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
5 min Do homework – previous lesson
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20min Learners work in pairs and educator assists with solutions individually, clarifying misconceptions when checking how learners are working out solutions
1. Simplify:
a) 3 37×(4 2
3−11
5 )b)
45+1 7
10c) -(3)2
d) 1,5 : 3
2. Calculate:a) 80 – 0
b)c) 11 + 12 + 13 + 14 + 115
3. Jabu deposits R2 000 into a savings account where the interest is 15% p.a. compounded annually.a) How much interest did he receive?
4. You receive R500 for your birthday. You decide to invest it for 15% p.a. for 3 years.a) Calculate the interest after 3 years.b) The final amount he will receive after 3 years.
CAPSTerm: 1Page reference:119-122
CONSOLIDATION/CONCLUSION AND OR
Homework will follow in the next lesson
204
GRADE 9 TERM 4 MATHEMATICS
HOMEWORK
REFLECTION Answers: Term 4 Grade 9 Week 5 Lesson 5 and 6
Class work Homework
1.
a) 3 37×(4 2
3−11
5 )
b)45+1 7
10
205
GRADE 9 TERM 4 MATHEMATICS
c) -(3)2
d) 1,5 : 3=1 : 2
2.a) 80 – 0 = 80
b)
c) 11 + 12 + 13 + 14 + 115=165
206
GRADE 9 TERM 4 MATHEMATICS
3.a)
A=P(1+ i)n
=2000 (1+15100
)12
=10700 ,50
b) Interest = R10 700 ,50 – 2 000 = R8 700,504.
a)
SI=Pr t100
=500×15×3100
=225
b) Interest : Initial amount + interest = R500 + R225 = R725
207
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 5 LESSONS 7 & 8
TOPIC: Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
Define and apply rules for number systems
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Conversion between decimal and common fractions Financial maths formulae Percentage, ratio and rate Highest common factor and lowest common multiples
WHAT YOU SHOULD BE ABLE TO DO (skills)
Apply all the knowledge when doing calculations Recall and apply formulae, where necessary.
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
5 min
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20minGive learners the exercise to work with in pairs, then provide answers, with explanations at intervals.
1. Complete the following table:
CAPSTerm: 1Page reference:119-122
208
GRADE 9 TERM 4 MATHEMATICS
2.Si
mplify:
a)23× 9
10
b)24+ 4
4
3. Calculate:
a) 4 × - 5 = - 20 b) (-135) +145c) 20 – (8)(0) ÷ 2(-10)(-1)
4. Johnny borrows R800 from his brother to buy a new i-pod. The agreement is that he will pay the money back together with 12% p.a. simple interest after two years. How much will he have to pay back?
5. A car costs R90 000. Calculate the value of the car after 10 years if the rate of depreciation is 12% p.a. on a reducing balance.
6. Your dad bought a laptop for R11000. It depreciates in value on a simple interest basis. Calculate
209
Number N N0 Z Q Q' Non-Real Undefined
0
√0,9
10
−3111
GRADE 9 TERM 4 MATHEMATICS
the value of the new computer after 3 years.
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Learners must prepare for the weekly assessment on : Whole numbers, Financial Mathematics, Integers, Common Fractions and Decimal Fractions
REFLECTION
210
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 5 Lesson 7 and 8
Class work Homework
1. Complete the following table:
2. Simplify:
a)23× 9
10
23× 9
10=18
30
211
Number N N 0 Z Q Q' Non-Real
Undefined
0 No Yes Yes Yes No No No
√0,9 No No No No Yes No No
10
No No No No No No Yes
−311
No No No Yes No No No
1 Yes Yes Yes Yes No No No
GRADE 9 TERM 4 MATHEMATICS
b)24+ 4
4
¿ 2+44
3. Calculate:a) 4 × - 5 = - 20 b) (-135) +145 =10c) 20 – (8)(0) ÷ 2(-10)(-1)
4.
SI=Pr t100
=800×12×2100
=192
Total= R800 +R192 = R992
212
GRADE 9 TERM 4 MATHEMATICS
5.
A=P(1−i)n
=90000(1−12100
)10
=25065 ,096.
Dep=P×r×t100
=11000×24×3100
=7920New value = R 11 000 – R7 920 =R3 080
213
GRADE 9 TERM 4 MATHEMATICS
GRADE 9 WEEKLY ASSESSMENTMAX: 25TIME: 30min
QUESTION 1Which of the following numbers belong to each group below?
−2 13
9π √20 1,23 .. . −3 √16
1.1.1 Integers (1)1.1.2 Rational numbers (2)1.1.3 Irrational numbers (2)
1.2 List the following:1.2.1 The factors of 15 (3)1.2.2 The first four multiples of 6 (2)1.2.3 The prime factors of 36 (1)1.2.4 Find two rational numbers between -1,36 and -1,35 (2)
[13]QUESTION 2Find the selling price if 2.1 cost price is R720 with a profit of 40% (2)2.2 Price marked at R85 with VAT included. (2)2.3 Jamie buys 10 pens and sells them for R5 each. If the 10 pens cost him R52
calculate his profit or loss per pen.(2)
[6]QUESTION 3
3.1 A flight from Durban to Cape Town takes 1 hour if an aeroplane flies at 800km/h. At what speed will it fly if the same flight takes 2 hours?
(2)
3.2 John and Jane are two brands of shoes. John sells for R7,20 for 8 pairs while Jane sells for R7,76 for 9 pairs. Which brand is the cheapest?
(4)
[6]TOTAL: 25
214
GRADE 9 TERM 4 MATHEMATICS
GRADE 9 WEEKLY ASSESSMENT - MemorandumMAX: 25
QUESTION 11.1.1 −3 ; √16 (1)
1.1.2−2 1
3−3 √16 (1)
1.1.3 9 π √20 1 ,23. . . (1)
1.21.2.1 1 ; 3 ; 5 ; 15 (2)1.2.2 6 ; 12; 18 ; 24 (2)1.2.3 2×2×3×3 (2)1.2.4 −1 ,359 ; −1 ,358; −1 ,357 ; −1,356 ; −1 ,355 ; −1 ,354 ; −1,353 ; −1 ,352 ; −1 ,351
[13]QUESTION 22.1 40
100×720
1=R288Selling Pr ice =R720+R288=R 1066
(2)
2.2 14100
×851
=R11 ,90Selling Pr ice =R85+R11 ,90=R 96 ,90
(2)
2.3 Cost Pr ice : R52÷10=R5 ,20R5−R5 ,20=−R 0 ,20He makes a loss of 20c .
(2)
[6]QUESTION 33.1
Speed=8002
km/h
=400km/h
(2)
3.2John=R7 ,20
8=90 c
Jane=R7 ,769
=86 cJane is the cheapest
(4)
[6]TOTAL: 25
215
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 6 LESSON 1 & 2
TOPIC: GEOMETRIC AND NUMERIC PATTERNS, FUNCTIONS, EXPRESSIONS AND GRAPHS
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
Define and apply rules for number systems Find the rule algebraically and in words for patterns Find output values, given input values and vice versa Be able to sketch and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1; Grade 9 Term 3 Disc 2; Grade 9 Term 1 Disc 2
PRIOR KNOWLEDGE Concepts and skills relating to Numeric and Geometric patterns, Input and Output values, Functions and graphs.
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
10 min Revise the weekly assessment form the previous week Page 126-129 &141-145
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20min Give the learners the exercise to do in pairs and exchange answers. Provide answers with explanations every few minutes.
1. Consider the following pattern:1; 4; 9; 16; ….a) Find the next 3 termsb) Write in words how you obtained the next term.c) Find the 10th term of the patternd) Write an algebraic expression for the pattern.
217
GRADE 9 TERM 4 MATHEMATICS
2. 7; 11; 15; 19; …a) Find the next 3 terms of the pattern
3.
a) Draw the next three patterns for the above.b) Describe in words the pattern.
3. If y=12 x−10 and x=−3 , x=−1 , x=0 , x=2 , x=4 , x=12. draw a graph to represent the above information. HINT: Draw a table of values first.
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson.
REFLECTION
Answers: Term 4 Grade 9 Week 6 Lesson 1& 2
Class work
1.a) 25; 36; 49b) The position of the term squaredc) 100
d)
218
GRADE 9 TERM 4 MATHEMATICS
2.a) 23; 27; 31
3.
a) b) Add one more circle than was added to the previous row, to the new row.
4.a)
x -3 -1 0 2 4 12
y 46 -22 -10 14 38 134
219
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 6 LESSON 3 & 4
TOPIC: GEOMETRIC AND NUMERIC PATTERNS, FUNCTIONS, EXPRESSIONS AND GRAPHS
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: Define and apply rules for number systems Find the rule algebraically and in words for patterns Find output values, given input values and vice versa Be able to sketch and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1; Grade 9 Term 3 Disc 2; Grade 9 Term 1 Disc 2
PRIOR KNOWLEDGE Concepts and skills relating to Numeric and Geometric patterns, Input and Output values, Functions and graphs.
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20min Give the learners the exercises to do in groups and then present to each other.Walk around the class, providing guidance where necessary.
1. Study the pattern below:
a) Draw the next three patterns for the above.b) Write down in words what the pattern is.
Page 126-129 &141-145
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GRADE 9 TERM 4 MATHEMATICS
2. Complete the following tables by filling in the missing input and output values and the formula for the pattern.a)
x-2 -1 0 1 2 7 n
y -7 -4 -1 26 44
b) Give the formula that defines the above table.c) Draw the graph of y=−3x+8.
3.Find the value of b 2 -6 3 b 4 ×(−3) -12 5 a
222
GRADE 9 TERM 4 MATHEMATICS
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
1. Find the next two terms of the pattern: 1; 2 ; 4; 8;….2. Find the equations of the following graphs:
a)
b)
REFLECTION
223
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 6 Lesson 3 & 4
Class work
1. a)
c) Add another E to the previous E’s.
2.a)
x -2 -1 0 1 2 7 10 16 n
y -10 -7-
4-1 2 17 26 44 3n – 4
b)T n=3n−4
224
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 6 LESSON 5 & 6
TOPIC: GEOMETRIC AND NUMERIC PATTERNS, FUNCTIONS, EXPRESSIONS AND GRAPHS
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: Define and apply rules for number system Find the rule algebraically and in words for patterns Find output values, given input values and vice versa Be able to sketch and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1; Grade 9 Term 3 Disc 2; Grade 9 Term 1 Disc 2
PRIOR KNOWLEDGE Concepts and skills relating to Numeric and Geometric patterns, Input and Output values, Functions and graphs.
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
10 min 1. 16; 322.
3.
Page 126-129 &141-145
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20min Allow learners to work in pairs and then provode answers after they have completed each example.
1. Consider the values in the following table. The rule for finding y is: divide x by −2 and subtract 4.
2 0 2 5-1 -3 -4 48
a) Use the rule to determine the missing values in the table, and write them in.
2. Sketch the graph of y=−x
226
GRADE 9 TERM 4 MATHEMATICS
3. Consider the following pattern: 7; 11; 15; 19; …a) Find the next 4 termsb) Write in words how you obtained the next term.c) Find the 10th term of the patternd) Write an algebraic expression for the pattern.
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson.
REFLECTION
227
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 6 Lesson 5 & 6Class work
1.
-6 2 0 2 5 -104-1 -3 -4 -5 -6,5 48
2.
3.a) 23; 27; 31 ; 23b) Add 4 to the previous termc) 4(10) + 3 = 43
228
x
y
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 6 LESSON 7 & 8
TOPIC: GEOMETRIC AND NUMERIC PATTERNS, FUNCTIONS, EXPRESSIONS AND GRAPHS
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to: Define and apply rules for number systems Find the rule algebraically and in words for patterns Find output values, given input values and vice versa Be able to sketch and interpret functions and graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 1; Grade 9 Term 3 Disc 2; Grade 9 Term 1 Disc 2
PRIOR KNOWLEDGE Concepts and skills relating to Numeric and Geometric patterns, Input and Output values, Functions and graphs.
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20min 1. Consider the following pattern: 8; 15; 22; 29; …a) Find the next 4 termsb) Write in words how you obtained the next term.c) Find the 10th term of the patternd) Write an algebraic expression for the pattern.
2. Complete the following table of values
3. If y=−2x+7 and
x=−4 , x=−2 , x=0 , x=1 , x=3 , x=8
Page 126-129 &141- 145
229
x-2 -1 0 1 2 4 n
y 0.
5
1 2 128 2048
GRADE 9 TERM 4 MATHEMATICS
a) Draw a table to represent the above values of yb) Draw a graph to represent the answers in your table.
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Learners prepare for the weekly assessment on Geometric and numeric patterns, functions, expressions and graphs
REFLECTION
230
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 6 Lesson 7 & 8
Class work
1.a) 36; 43; 50; 54b) Add 7 to the previous termc) 7(10) +1 = 71
d)
2.
x-2 -1 0 1 2 4 7 11 n
y 0.25 0.5 1 2 4 16 128 2048 2n
3.
x -4 -2 0 1 3 8
y 15 11 7 5 1 -9
231
GRADE 9 TERM 4 MATHEMATICS
Grade 9WEEKLY ASSESSMENTTerm 4Week6
QUESTION 11.1 Consider the following pattern:
1; 2; 4; 8; …1.1.1 Find the next 4 terms (3)1.1.2 Write in words how you obtained the next term. (2)1.1.3 Find the 10th term of the pattern (2)1.1.4 Write an algebraic expression for the pattern. (2)
[9]QUESTION 2Complete the following table of values
2.1 x -4 -2 -1 0 1 2 6 m
y -15 -
11
-7 -3 49
(6)
[6]TOTAL: 15
233
GRADE 9 TERM 4 MATHEMATICS
Grade 9WEEKLY ASSESSMENTMEMORANDUMTerm 4
QUESTION 11.11.1.1 16; 32; 64 ; (3)1.1.2 Double the previous term (2)1.1.3 512 (2)1.1.4 (2)
[9]QUESTION 2Complete the following table of values
2.1 x -4 -2 -1 0 1 2 6 14 m
y -23 -
15
-11 -7 -
3
1 17 49 4m-1
(6)
[6]TOTAL: 15
234
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 7 LESSON 1 and 2
TOPIC: Constructions, Straight line Geometry and 2D shapes
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
construct angles and shapes use the concept of FUN to find angles use the properties of triangles and quadrilaterals to solve for angles and sides
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 2 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
How to construct angles and shapes The theory behind straight line geometry Triangles and quadrilaterals
WHAT YOU SHOULD BE ABLE TO DO (skills)
construct angles and shapes use the concept of FUN to find angles use the properties of triangles and quadrilaterals to solve for angles and sides
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
10 min Revise the weekly assessment form the previous week
235
GRADE 9 TERM 4 MATHEMATICS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20min Learners work in groups and present their answers to the class. The educator emphasizes concepts and notation while answers are shared.
1.Refer to the diagram below and answer the questions that follow
a) Calculate the value ofx. Give a reason for your answerb) Determine the size of y. Give a reason for your answer
CAPSTerm: 2Page reference:134-138
236
P
Q
A
C
GRADE 9 TERM 4 MATHEMATICS
2. In the diagram below,prove that ∆PTQ≡∆PTR. Give reasons for your answer.
3. Use a pair of compasses and ruler to make accurate constructions of the following angle:
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson.
REFLECTION
237
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 7 Lesson 1and 2Class work
1.a) 2 x+3 °+137°+ x+52 °=360° (Rev. ∠) 3 x=360°−192°
3 x=168 ° x=56°
b) y= x+52 ° (alt. ∠’s, AB∥CD) y=108°
2.STATEMENT REASON
PT¿PT CommonQT¿TR Given
Given
∴∆PTQ≡∆PTR S∠S
3. Step 1: Place the compass on one end point of the line segment (Point A).Draw an arc above and below the line.
238
GRADE 9 TERM 4 MATHEMATICS
Step 2: Without changing the compass width place the compass on point B. Draw an arc below and above the line so that the arcs cross the first two.
Step 3: Use a ruler to join the points where the arcs intersect. This line segment known as BD is the bisector of AB.
*the perpendicular is a line that meets another line at 90˚
239
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 7 LESSON 3 and 4
TOPIC: Constructions, Straight line Geometry and 2D shapes
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
construct angles and shapes use the concept of FUN to find angles use the properties of triangles and quadrilaterals to solve for angles and sides
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 2 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
How to construct angles and shapes The theory behind straight line geometry Triangles and quadrilaterals
WHAT YOU SHOULD BE ABLE TO DO (skills)
construct angles and shapes use the concept of FUN to find angles use the properties of triangles and quadrilaterals to solve for angles and sides
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20min Learners must work individually and then present their answers to a partner across the room (make sure learners that share do not sit next to each other at first).
1. In the diagram below, A ¿ 70° quadrilateral ABCD is a rhombus extended to point E.
CAPSTerm: 2Page reference:134-138
240
GRADE 9 TERM 4 MATHEMATICS
a) Calculate the value of A BC , give reasons for your answer.b) Determine the size of BC D , give a reason for your answerc) Determine the size of C B E , give a reason for your answer
2. In the diagram below, PQ∥ST, SR¿ST, Q PR=¿ 55° andPQ S=¿27°.
a) Determine the size of Q ST . Give a reason for your answer.b) Determine the size of T S R. Give a reason for your answer.c) Calculate the value of x . Give a reason for your answer.
3. Use a pair of compasses and ruler to make accurate constructions of the following angle
241
GRADE 9 TERM 4 MATHEMATICS
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
1. Choose the correct answers:
1.1
Calculate the value of A. B. C.D.
1.2 Refer to the figure in 1.1. Calculate the value of A.B.C.D.
242
GRADE 9 TERM 4 MATHEMATICS
1.3
Calculate the size of T
A.B.C.D.
1.4 Refer to the diagram in 1.3. Give a reason why ∆PQR /// ∆ TMSA. All angles are equalB. All sides are in proportionC. A;A;SD. S;A;S
REFLECTION
243
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 7 Lesson 3 and 4
Classwork
1.a) is a rhombus A BC=18 00−700 ¿)¿1100
OR 2 A BC=3600−2¿ ¿)A BC=1100
b) BC D= A=700(opp .angles of arhombus)
c) C B E=700(corresponding angles AD ∥BC )
2.
a) (Alt. ∠s, QP∥TS )
b) (Cor. ∠s, QP∥TS¿
c) (sum of the ∠s ofa∆ ¿
x=180°−55°
2 ¿∠s opp. to equal sides)
x=¿ 62,5° 3. We know that:
So, to construct an angle of 30º, first construct a 60º angle and then bisect it. Often, we apply the following steps.Step 1: Draw the arm PQ.Step 2: Place the point of the compass at P and draw an arc that passes through Q.Step 3: Place the point of the compass at Q and draw an arc that cuts the arc drawn in Step 2 at R.
245
GRADE 9 TERM 4 MATHEMATICS
Step 4: With the point of the compass still at Q, draw an arc near T as shown.Step 5: With the point of the compass at R, draw an arc to cut the arc drawn in Step 4 at T.
Step 6: Join T to P. The angle QPT is 30º.
246
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 7 LESSON 5 and 6
TOPIC: Area and Perimeter, 3-D objects, Surface Area and volume, Data Handling and Probability
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
construct angles and shapes use the concept of FUN to find angles use the properties of triangles and quadrilaterals to solve for angles and sides
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, DVD Grade 9 Term 3 Disc 1; DVD Grade 9 Term 3 Disc 3; DVD Grade 9 Term 4 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Formulae for area and perimeter and volume Properties of 3D shapes Mean; mode Range Graphical representation of data Probability definition Tree diagrams; two way tables
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use formulae to calculate the area, perimeter and volume of 3D shapes Find the measures of central tendency, given data Represent and interpret data on and off a graph Draw and interpret tree diagrams and two way tables
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
10min 1.1 A1.2 B1.3 B1.4 A
LESSON PRESENTATION/
20min Learners must attempt these questions individually and the educator must present solutions as the class completes each example.
CAPSTerm: T3 and
247
GRADE 9 TERM 4 MATHEMATICS
DEVELOPMENT/CLASSWORK 1. The area of a parallelogram below is 156 mm2, MR¿12 mm and
NR¿5 mm. Calculate the length of TS.
2. PQRS is a square with inscribed circle O where r ¿7 mm. Calculate the area of the shaded part
correct to one decimal place. Take. π=227
3. Complete the table below:
T4Page reference:146-148 and 149-153
248
12 mm
5 mm
M T
SN R
P Q
O
RS
GRADE 9 TERM 4 MATHEMATICS
Platonic Solid Shape of faces Number of facesOctahedronIcosahedron
4.
Name the above shapes.
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson
REFLECTION
Answers: Term 4 Grade 9 Week 7 Lesson 5 and 6
249
GRADE 9 TERM 4 MATHEMATICS
Class work
1.
2. Area of shaded part ¿ (Area PQRS – Area of circle) ÷4
¿ {14mm×14mm−¿(227×7mm2)} ÷4
¿ (196 mm2−¿ 154mm2) ÷4 ¿ 42 mm2÷4 ¿ 10,5 mm
3.
250
GRADE 9 TERM 4 MATHEMATICS
Platonic Solid Shape of faces Number of facesOctahedron Equilateral triangles 8Icosahedron Equilateral triangles 20
4.A- TetrahedronB- OctahedronC- Icosahedron
251
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 7 LESSON 7 and 8
TOPIC: Area and Perimeter, 3-D objects, Surface Area and volume, Data Handling and Probability
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
construct angles and shapes use the concept of FUN to find angles use the properties of triangles and quadrilaterals to solve for angles and sides
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, DVD Grade 9 Term 3 Disc 1; DVD Grade 9 Term 3 Disc 3; DVD Grade 9 Term 4 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
Formulae for area and perimeter and volume Properties of 3D shapes Mean; mode Range Graphical representation of data Probability definition Tree diagrams; two way tables
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use formulae to calculate the area, perimeter and volume of 3D shapes Find the measures of central tendency, given data Represent and interpret data on and off a graph Draw and interpret tree diagrams and two way tables
252
GRADE 9 TERM 4 MATHEMATICS
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
25min 1. Given the circle below with right-angled triangle BCD. BD is 7cm and
DC is 5cm.
a) Find the diameter of the circle.b) Find the area of triangle BCD.c) Find the area in the circle that is not covered by ∆BCD.d) Find the circumference of the circle
2. If the perimeter of hexagon is 24 cm. The shape in Figure 2 is made of the hexagons of the same size as in Figure 1. What is the perimeter of the shape drawn in Figure 2?
CAPSTerm: T3 and T4Page reference:146-148 and 149-153
253
GRADE 9 TERM 4 MATHEMATICS
3. Complete the table beow:Platonic Solid Shape of faces Number of facesOctahedron Equilateral triangles
Equilateral triangles 20Hexahedron 4
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Prepare for the weekly assessment on :Area and Perimeter, 3-D objects, Surface Area and volume, Data Handling and Probability
REFLECTION
254
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 7 Lesson 7 and 8
Classwork Homework
1.a) BC2=B D2+C D2
BC2=(7 )2+ (5 )2
BC2=49+25
BC2=74
BC=√74
BC=8.6
b) Area=12b×h
Area=12×5×7
Area=17.5 cm2
c) Area of Circle ¿ π r2
¿ π (4.3 )2
¿58.09 c m2
Area not covered by ∆BCD = 58.09 – 17.5
= 40.59 cm2
d) Circumference ¿2πr
Prepare for the weekly assessment on :Area and Perimeter, 3-D objects, Surface Area and volume, Data Handling and Probability
255
GRADE 9 TERM 4 MATHEMATICS
¿2π ( 4.3 )
¿27.02 cm
2.
1 side = 24cm
6
¿ 4 cm P¿ 4 cm × 12 ¿ 48 cm
3.Platonic Solid Shape of faces Number of facesOctahedron Equilateral triangles 8Icosahedron Equilateral triangles 20Hexahedron Square 4
256
GRADE 9 TERM 4 MATHEMATICS
Grade 9WEEKLY ASSESSMENT 15 minTerm 4 Week 7
QUESTION 11.1 Study the diagram belown and answer the questions:
Determine, with reasons the sizes of the following:1.1.1 (2)
1.1.2 (2)
1.1.3 (2)
1.1.4 (2)
1.1.5 (2)
[10]QUESTION 2
2.1 A triangular prism is shown in the figure below. The base is a right-angled triangle with DF= 8 cm, FE = 6 cm and the height 15 cm. A B C
15cm F
8 cm 6 cm
D E
2.1.1 Calculate the area of ΔDEF. (2)
2.1.2 Calculate the volume of the prism.(3)
[5]
TOTAL: 15
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GRADE 9 TERM 4 MATHEMATICS
Grade 9WEEKLY ASSESSMENT 15 minTerm 4
QUESTION 11.1
1.1.1
(2)
1.1.2 (2)
1.1.3
(2)
1.1.4
(2)
1.1.5
(2)
[10]QUESTION 2
2.1.1
Area ΔDEF =1
2×8cm×6cm
=24 cm2
(2)
2.1.2 V =Area of base×height =24 cm2×15 cm
=360cm3 (3)
[5]TOTAL: 15
258
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 8 LESSON 1 and 2
TOPIC: Transformations and Straight Line Graphs
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
transform co-ordinates and shapes across quadrants draw and interpret straight line graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 3 Disc 1; Grade 9 Term 4 Disc 1
WHAT YOU SHOULD KNOW (Knowledge)
plotting points in the four quadrants transformations across the quadrants how to draw and interpret straight line graphs
WHAT YOU SHOULD BE ABLE TO DO (skills)
plot points in the four quadrants transform points and shapes across the quadrants, using reflections, rotations,
enlargements and reductions how to draw and interpret straight line graphs
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
10 min
Revise the weekly assessment form the previous week
259
GRADE 9 TERM 4 MATHEMATICS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20min
1. Draw the enlarged or reduced image of the following figure according to
the scale factor given. Scale factor =
2. Draw the graph of
CAPSTerm: 2 and 4Page reference:141-145147
260
GRADE 9 TERM 4 MATHEMATICS
3.Find the equation of the graph given below;
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson.
REFLECTION
261
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 8 LESSON 3 and 4
TOPIC: Transformations and Straight Line Graphs
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
transform co-ordinates and shapes across quadrants draw and interpret straight line graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 3 Disc 2; Grade 9 Term 4 Disc 1.
WHAT YOU SHOULD KNOW (Knowledge)
plotting points in the four quadrants transformations across the quadrants how to draw and interpret straight line graphs
WHAT YOU SHOULD BE ABLE TO DO (skills)
plot points in the four quadrants transform points and shapes across the quadrants, using reflections, rotations, enlargements and reductions how to draw and interpret straight line graphs
264
GRADE 9 TERM 4 MATHEMATICS
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20min Learners work in pairs and individuals are called to present answers with guidance of the educator.
1.
Translate PQR 5 units to the right and 3 units downTranslate PQR 5 units to the right and 3 units downAre all the triangles congruent?
2. Determine the equations of the straight lines passing through the following points:
a)
1 2 3 4 55 4 3 2 1
CAPSTerm: 2 and 4Page reference:141-145147
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GRADE 9 TERM 4 MATHEMATICS
b)-4 -2 0 2 42 0 -2 -4 -6
3. Draw the graphs of the following graphs on the same system of axes:
and
1.
1.3 Yes
266
GRADE 9 TERM 4 MATHEMATICS
3.
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
1. Draw the graphs of on the same system of axes.
268
GRADE 9 TERM 4 MATHEMATICS
a) State the rule for the transformation from A to B in the form b) Describe in words the transformations from G to Hc) Which of the transformations are:
i) Reflectionsii) Rotations
REFLECTION
269
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 8 Lesson 3 and 4Class work
1.
1.3 Yes
2.a)
b)
270
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 8 LESSON 5 and 6
TOPIC: Expressions and equations
272
GRADE 9 TERM 4 MATHEMATICS
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
transform co-ordinates and shapes across quadrants draw and interpret straight line graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Factorisation ( all methods)
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the rules for expressions (BODMAS) to manipulate and simplify expressions Use the rules for factorisation to simplify expressions and solve equations.
COMPONENTS TIME TASKS/ACTIVITIES CAPS
REVIEW AND CORRECTION OF HOMEWORK
10 min 1.
-2 0 22 0 -2
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GRADE 9 TERM 4 MATHEMATICS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20min Learners must be put in groups, they answer the exercise, then are shuffled around so that they can explain to other members of the class how to answer the questions. The educator facilitates the process by walking around and correcting misconceptions as they arise.
1. Simplify:
a)
b)
c)
d)
2. Solve for :
a)x2 = 25
b)
3. , calculate , when
4. Multiply by
CAPSTerm: 1 and 3Page reference:130-131141-145
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
Homework will follow in the next lesson.
REFLECTION
275
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 8 Lesson 5 and 6
Class work Homework
1.a)
b)
c)
d)
2.a)
2.
-2 0 22 0 -2
276
GRADE 9 TERM 4 MATHEMATICS
SUBJECT: MATHEMATICS GRADE 9 TERM 4 WEEK 8 LESSON 7 and 8
TOPIC: Expressions and equations
CONCEPTS AND SKILLS TO BE ACHIEVEDBy the end of the lesson, learners should know and be able to:
transform co-ordinates and shapes across quadrants draw and interpret straight line graphs
RESOURCES GDE ATP Fourth TermDBE workbook, Sasol-Inzalo workbook, textbook, calculator, Grade 9 Term 1 Disc 2; Grade 9 Term 3 Disc 1; Grade 9 Term 3 Disc 2
WHAT YOU SHOULD KNOW (Knowledge)
Rules for integers Factorisation ( all methods)
WHAT YOU SHOULD BE ABLE TO DO (skills)
Use the rules for expressions (BODMAS) to manipulate and simplify expressions Use the rules for factorisation to simplify expressions and solve equations.
COMPONENTS TIME TASKS/ACTIVITIES CAPS
LESSON PRESENTATION/ DEVELOPMENT/CLASSWORK
20min Learners must be put in groups, they answer the exercise, then are shuffled around so that they can explain to other members of the class how to answer the questions. The educator facilitates the process by walking around and correcting misconceptions as they arise.
1. Simplify:
a) 12x2 y−6 xy2
3 xy
b) (xa −¿3)(xa + 3)
c) √34 y6−9 y6
CAPSTerm: 1 and 3Page reference:130-131141-145
278
GRADE 9 TERM 4 MATHEMATICS
d) (2 x−3 )2−4 ( x−1 ) ( x+1 )
e)2(x+4)
2−2
f)p2q2×( p−2)2
p−2
2. Solve for :a)b) 3 ( x−1 )=2 x+5c) ( x−2 ) ( x−2 )=0
d)2x3
− x+14
=1
e) 2− x=64
3. If , then =…
CONSOLIDATION/CONCLUSION AND OR HOMEWORK
1min Learners prepare for the weekly assessment on expressions and equations
REFLECTION
279
GRADE 9 TERM 4 MATHEMATICS
Answers: Term 4 Grade 9 Week 8 Lesson 7 and 8
Class work Homework
1.a)
b) (xa - 3)(xa + 3)
c) √34 y6−9 y6
¿√25 y6
¿5 y3
d) (2 x−3 )2−4(x−1)(x+1)
¿4 x2−12x+9−4 (x2−1) ¿4 x2−12x+9−4 x2+4 ¿−12 x+5
Learners prepare for the weekly assessment on expressions and equations
280
GRADE 9 TERM 4 MATHEMATICS
e)2(x+4)
2−2
¿ x+4−2¿ x+2
f)p2q2×( p−2)2
p−2
¿ p2q2× p−4
p−2
¿ p2−4+2q2 ¿ p0q2
¿q2
2. a)
b)
281
GRADE 9 TERM 4 MATHEMATICS
c) ( x−2 ) ( x−2 )=0x=2
d)2x3
− x+14
=1
12×( 2 x3 )−12×( x+1
4 )=12×1
8 x−3 x−3=12 5 x=15x=3
e)2− x=642− x=26
x=−6
282
GRADE 9 TERM 4 MATHEMATICS
Grade 9WEEKLY ASSESSMENT 15 minTerm 4Week 8
QUESTION 11.1 How many values of satisfy the equation ?
A 0
B 1
C 2
D More than 2
[2]
QUESTION 22.1 The length of a rectangle is 4cm more than the width. If the perimeter is
32 cm, calculate the length and the width(5)
2.2 If I multiply a certain number by 5, I get the same answer as when I subtract the
number by 48. What is the number? (3)
[8]
QUESTION 2
2.1
Calculate if
(2)
2.2 Simplify the following expression
(3)
[5]TOTAL: 15
283
GRADE 9 TERM 4 MATHEMATICS
Grade 9WEEKLY ASSESSMENT MEMORANDUM15 minTerm 4
QUESTION 11.1 A (2)
[2]
QUESTION 22.1 Let the width be x, then length will be x +4
Let the width be then the length will be
Width is 6cm and the length is 10 cm. (5)
2.2
Let the number be
The number is 8. (3)
[8]
QUESTION 2
2.1
(2)
2.2
(3)
[5]TOTAL: 15
284
GRADE 9 TERM 4 MATHEMATICS
GRADE 9 CLASS TEST 1Functions and Relationships – Term 3MAX: 30TIME: 30 minutes
QUESTION 1
1.1 Determine the equations of the following graphs:
1.1.1 (2)
1.1.2 (2)
1.1.3 y
x
(2)
287
y
x
GRADE 9 TERM 4 MATHEMATICS
1.1.4 y(2)
1.1.5 (2)
[10]
QUESTION 2
2.1 Determine the x-intercept and gradient of the following graph:
(3)
288
x
GRADE 9 TERM 4 MATHEMATICS
2.2 Determine the gradient of the function passing through (2 ;2) and (−4 ;3). (3)
2.3 Determine equation of the straight line passing through (2 ;1) and perpendicular to y=3 x−5.
(4)
[10]
QUESTION 3
3.1 y=−x+33.1.1 Complete the table using the equation y=−x+3
x -3 -1 0 2 4y
(2)
3.1.2 Plot the graph on a Cartesian plane. (2)
3.2 Given: y=2x−13.2.1 Determine the x- and y−¿intercepts of the function. (4)
3.2.2 Plot the function on a Cartesian plane. (2)
[10]
TOTAL: 30
289
GRADE 9 TERM 4 MATHEMATICS
GRADE 9 CLASS TEST – MemorandumFunctions and Relationships – Term 3MAX: 30TIME: 30min
QUESTION 1
1.1 Determine the equations of the following graphs:
1.1.1
y=x
(2)
1.1.2
x=3
(2)
1.1.3
y=−4
(2)
290
y
x
x
y
GRADE 9 TERM 4 MATHEMATICS
1.1.4
x=−2
(2)
1.1.5
y=−x
(2)
[10]
QUESTION 2
2.1
x−int ercept : Let y=0x−2=0x=2(2 ;0)
(3)
291x
y
y
x
GRADE 9 TERM 4 MATHEMATICS
m=y2− y1
x2−x1
=(0−(−2 )(2−0 )
=22
=1
2.2m=
y2− y1
x2−x1
=(3−2)(−4−2)
=1−6
(3)
2.3m=−1
3; P(2 ;1)
y=mx+c
1=−13
(2)+c
c=53
y=−13x+5
3
(4)
[10]
QUESTION 3
3.1 y=−x+33.1.1 x -3 -1 0 2 4
y 6 4 3 1 -1(2)
3.1.2 (2)
292
xy
GRADE 9 TERM 4 MATHEMATICS
3.2
3.2.1x−int ercept : Let y=02x−1=02x=1
x=12
(12 ;0)y− int ercept : Let x=0y=2(0)−1y=−1(0 ;−1 )
(4)
3.2.2 (2)
[10]
TOTAL: 30
293
xy
GRADE 9 TERM 4 MATHEMATICS
GRADE 9 CLASS TEST 2GEOMETRY OF 2D SHAPESMAX: 20TIME: 30min
QUESTION 1
1.1 Name 2 properties of a parallelogram. (2)
1.2
Determine with reasons, without using a protractor, the size of:
1.2.1 x (3)
1.2.2 y (2)
1.2.3 z (2)
[9]
QUESTION 2Ín ∆ABC and ∆PQR is B = P = 90°; AB = PQ = 9cm and AC = QR = 34cm
2.1 Determine if the above pair of triangles is congruent. Give reasons. (4)2.2 Calculate the size of R with reasons if A=35° . (3)
2.3 Calculate the length of BC. (4)[11]
TOTAL: 20
294
GRADE 9 TERM 4 MATHEMATICS
GRADE 9 CLASS TEST – MemorandumGEOMETRY OF 2D SHAPESMAX: 20TIME: 30min
QUESTION 1
1.1 The opposite angles are equal The diagonals bisect each other The opposite sides are equal The opposite sides are parallel (any two)
(2)
1.2
1.2.1 3 x=58 °+ x ext. <s of ê 3 x−x=58 ° 2 x=58 ° x=29 °
(3)
1.2.2 y = 180°- (58° + 𝑥) sum of int. <s ∆ ¿180 °−87° = 93°
(2)
1.2.3 𝑧 = 𝑥 = 29° alt. <s (AE//DC) (2)
[9]QUESTION 2
2.1 ¿∆ ABC∧∆ PQRB=P=90 ° given AB = PQ given AC = QR given ∴∆ ABC≡∆PQR (RHS)
(4)
295
GRADE 9 TERM 4 MATHEMATICS
2.2 A=P ≡∆R=180°−( P+Q ) sum int < ∆¿180 °−(90 °+35° )¿180 °−125 °¿55 °
(3)
2.3 BC2 = AC2 – AB2
= 342 - 92
=1156 – 81BC = √1075 = 32,78719.... = 32,79cm
(4)
[11]TOTAL: 20
296
GRADE 9 TERM 4 MATHEMATICS
GRADE 9 CLASS TEST 3GEOMETRY OF 3D OBJECTSMAX: 20TIME: 30 min
QUESTION 1
1.1 Complete the table below:
Name Shape of faces
No of faces
No of vertices
No of edges
Triangles 4
6
Triangles 12
[10]
QUESTION 2
Draw the net shapes for the following 3D objects:
2.1 (2)
297
GRADE 9 TERM 4 MATHEMATICS
GRADE 9 CLASS TEST – MemorandumGEOMETRY OF 3D OBJECTSMAX: 20TIME: 30min
QUESTION 1
1.1
Name Shape of faces
No of faces
No of vertices
No of edges
Tetrahedron Triangles 4 4 6
Octahedron Triangles 8 6 12
Icosahedron Triangles 20 12 30
Cube/hexahedron
Squares 6 8 12
Dodecahedron Pentagons 12 20 30
[10]
QUESTION 2
2.1 (2)
299
GRADE 9 TERM 4 MATHEMATICS
GRADE 9 CLASS TEST 4GEOMETRY OF STRAIGHT LINESMAX: 20TIME: 30 min
QUESTION 11.1 Find the value of b in each of the following:1.1.1 a)
b)
(2)
1.1.2 (2)
301
GRADE 9 TERM 4 MATHEMATICS
1.1.3
(2)
1.2 Name the angle relationships between the following:
1.2.1 C and F (2)
1.2.2 F and D (2)
[10]QUESTION 22.1 Find the value of x in the following:
If AB // CD, A4=A3 and O2=60 °(6)
[6]
302
GRADE 9 TERM 4 MATHEMATICS
QUESTION 3Find the value of x in each of the following:
3.1 (2)
3.2 (2)
[4]TOTAL: 20
303
GRADE 9 TERM 4 MATHEMATICS
GRADE 9 CLASS TESTGEOMETRY OF STRAIGHT LINESMemorandumMAX: 20TIME: 30 min
QUESTION 11.11.1.1 b=180 °−50 °
=130° angles on a straight line
(2)
b=360 °−(209 °+96 ° )=55° angles around a point/revolution
1.1.2 b=43 ° vertically opposite angles (2)1.1.3 b=90 °−63 °
=27 ° complementary angles
(2)
1.21.2.1 C and F
alternate angles
(2)
1.2.2 F and DCo-interior angles
(2)
[10]QUESTION 22.1
AB // CD, A4=A3 and O2=60 ° (6)
304
GRADE 9 TERM 4 MATHEMATICS
O4=O2=60 ° (Vertically opposite angles)O4+ A4+ A3=180 ° ( Angles of triangle )
A4+ A3=180° −60 °=120 °
but : A4= A3 ( given )
A4= A3=120°2
=60 °
B2=A4 (alternate angles )B2=60 °
60 °+ { B 2
=180 ° ( straight line ) ¿ B2=180°−60 ° ¿ x=120° ¿¿
[6]QUESTION 33.1
2 x−50 °= x−30 °2 x−x=−30 °+50 °x=20 ° (vertically opposite angles)
(2)
3.2 x+44 °+107 °=180 ° (co−int erior angles)x=180 °−(44 °+107 )° }¿ =29 °
(2)
[4]TOTAL: 20
305
GRADE 9 TERM 4 MATHEMATICS
GRADE 9 CLASS TEST 5TRANSFORMATION GEOMETRYMAX: 20TIME: 30 min
QUESTION 11.1 ∆ABC with A(3;0), B(2;4) and C(0;2) is enlarged using the rule
(x ; y ¿→ (2x ;2 y ). The resulting image is A’B’C’ Draw ∆ABC and its image on the given grid.
(2)
1.2∆ABC is relfected in the y-axis. The reflection is A
} } B rSup { size 8{C} } } {¿ ¿¿. 1.2.1 Draw the image on the given grid A
} } B rSup { size 8{C} } } {¿ ¿¿ (2)
1.2.2What is the distance between A and A
} } } { ¿¿¿?(2)
[6]QUESTION 2
Give the coordinates of the following if:2.1 A ( -3 ;4 ) is reflected about the x−¿axis (2)
2.2 B ( 4 ; -12 ) is reflected about the line y=x (2)
2.3 C ( -2 ; 4 ) is translated 4 units down and 12 units to the left. (2)
2.4 D ( 3 ; -1 ) is reflected about the y−¿axis. (2)
2.5 E’ ( 16 ; 8 ) is enlarged by a factor of 4. (2)
2.6 F’ ( -2 ; 4 ) is translated 3 units up and 4 units to the right. (2)
[12]TOTAL: 18
306
GRADE 9 TERM 4 MATHEMATICS
QUESTION 1:
y
12
11
10
9
8
7
6
5
4
3
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
307
GRADE 9 TERM 4 MATHEMATICS
GRADE 9 CLASS TEST - MEMORANDUMTRANSFORMATION GEOMETRYMAX: 20TIME: 30 min
QUESTION 11.1 and 1.2.1
(4)
1.2.2 6 (units) (2)
[6]QUESTION 22.1 A’ (-3 ; -4 ) (2)2.2 B’ (-12 ; 4 ) (2)2.3 C’ ( 0 ; -14 ) (2)2.4 D’ (-3 ; -1 ) (2)2.5 E ( 4 ; 2 ) (2)2.6 F (-3 ; 2 ) (2)
[12]TOTAL: 18
308
GRADE 9 TERM 4 MATHEMATICS
TEMPLATE TO MARK QUESTION 1
𝑦9 B’8
7
6
B” 5 C’ B4
3
C”
C
2
A” 1 A A’ 𝑥-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
-7
-8
-9
309
GRADE 9 TERM 4 MATHEMATICS
Grade 9Project 1DATA HANDLING: FrequencyMax: 20
Conduct a survey at your nearest intersection for 1 hour.
Count the number of minibuses (taxis), buses, cars and vans that pass by in that interval that you observe.
1. Draw up a tally table for:
Minibuses (taxis)BusesCarsVans
2. Draw a bar graph to represent your information.
3. Answer the following questions:
3.1 Where is the intersection situated?3.2 Which are the most used type of vehicle?3.3 What could be the reason for this?
Use the following rubric to allocate marks for learners’ answers:
Criteria
Neatness (3)
Accuracy (4)
Bar graph (6)
Due date (2)
Answers (5)
Total [20]
311
GRADE 9 TERM 4 MATHEMATICS
Grade 9Project 2Financial MathsMax: 15
Find advertisements for 5 household items such as a fridge or a stove from a newspaper. (Do NOT use the internet!)Cut out and paste the adverts, then work out the interest you would pay on each item.
Answer the following questions:1. What other type of interest could be charged on the items you
chose?2. Which would be cheaper, to pay cash for the items or on hire
purchase?3. What do you think would be the most purchased item from the
items you chose?
Use the following rubric to allocate marks for learners’ answers:Criteria
Neatness (3)
Accuracy (4)
Due date ( 2 )
Answers (6 )
Total [15 ]
Note all learners’ answers will be unique to the advertisements they have chosen.
312
GRADE 9 TERM 4 MATHEMATICS
PROJECT 3 DATA COLLECTIONQuestionnaires
We can use different methods to collect data, for example questionnaires, face-to-face interviews or telephonic interviews. In this section, you will work with questionnaire questions that have multiple choice responses.
Here are two questions with multiple-choice responses from which a respondent will choose.
(A respondent is a person who responds to the questions)
How satisfied are you with our level of service? Not satisfied at all Fairly satisfied
Very satisfied
What is the colour of your eyes?
brown
green
blue
other
1. Write a suitable question with multiple-choice responses to find out the following information:
(a) What do teenagers spend their money on?
(b) How much time do Grade 8s spend on homework every day?
2. Choose one of the questions above. Write down what you think would be the best sample to use if you had to conduct this investigation.
____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
3. Use the multiple-choice question that you chose in question 2 to collect the data. Keep the results for the next section.
313
GRADE 9 TERM 4 MATHEMATICS
Organising data
The way we organise and summarise data depends on the kind of data that we have. It also depends on what we want to find out from the data. Work in groups to explore this. Don’t worry about getting the answers right at this stage. You will learn about the different ways to organise and summarise data in this chapter.
Look at the following sets of data. For each one, discuss with your group and write down what we want to find out and what you think we need to do to the data.
1. Data collected to find out which day would be best to have a soccer club practice:Twenty-five learners’ preferred day for soccer practice
Tuesday Tuesday Tuesday Wednesday Monday Thursday Tuesday Friday Friday Friday Tuesday Thursday Wednesday Wednesday Tuesday Tuesday Wednesday Monday Thursday Tuesday Tuesday Wednesday Monday Thursday Tuesday
__________________________________________________________________________________________________________________________________________________________________________________
2. Data collected to find out whether 5-year-old children in a certain village have healthy body weights:Body weights of twenty-five children in kilograms, rounded off to the nearest 0,5 kg
17 kg 16,5 kg 13,5 kg 14 kg 18 kg 18 kg 14 kg 21 kg 13,5 kg 15 kg 15 kg 14,5 kg
15,5 kg 19,5 kg 17 kg 17,5 kg 14 kg 14 kg 20 kg 14,5 kg 16 kg 18 kg 12 kg 16 kg 19 kg
_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
3. Data collected to find out how many learners answer a certain type of question in less than 20 seconds:Time taken (in seconds) by a group of learners to answer a question
20 25 24 33 13 26 10 19 39 31 11 16 21 17 11 34 14 15 21 18 17 38 16 21 25
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………..
314
GRADE 9 TERM 4 MATHEMATICS
4. Data collected to analyse the monthly salaries of employees of a small business:The monthly salaries of ten employees
R8 000 R2 500 R75 000 R6 000 R7 500 R5 200 R4 800 R10 300 R15 000 R9 500
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
315
GRADE 9 TERM 4 MATHEMATICS
PROJECT 3 MEMO – DATA
1. Write a suitable question with multiple-choice responses to find out the following information:(a) What do teenagers spend their money on?
(b) How much time do Grade 8s spend on homework every day?
Sample answers:
(a) On which of the following items do you spend most of your money?
food
clothing
air time
make-up or toiletries
entertainment
(b) How much time do you spend doing homework every day?
less than 1 hour
between 1 and 2 hours
between 2 and 3 hours
more than 3 hours
2. Choose one of the questions above. Write down what you think would be the best sample to use if you had to conduct this investigation.Sample answers:
(a) 50 teenagers from my school/50 teenagers from the local community
(b) All the Grade 8s in my school/20 Grade 8 learners from two schools in the area
3. Use the multiple-choice question that you chose in question 2 to collect the data. Keep the results for the next section.
Organising data
The way we organise and summarise data depends on the kind of data that we have. It also depends on what we want to find out from the data. Work in groups to explore this. Don’t worry about getting the answers right at this stage. You will learn about the different ways to organise and summarise data in this chapter.
Look at the following sets of data. For each one, discuss with your group and write down what we want to find out and what you think we need to do to the data.
1. Data collected to find out which day would be best to have a soccer club practice:Twenty-five learners’ preferred day for soccer practice
316
GRADE 9 TERM 4 MATHEMATICS
Tuesday Tuesday Tuesday Wednesday Monday Thursday Tuesday Friday Friday Friday Tuesday Thursday Wednesday Wednesday Tuesday Tuesday Wednesday Monday Thursday Tuesday Tuesday Wednesday Monday Thursday Tuesday
Sample answer: We want to know on which day the highest number of learners want to practise. We need to write down how many times each day appears.
2. Data collected to find out whether 5-year-old children in a certain village have healthy body weights:Body weights of twenty-five children in kilograms, rounded off to the nearest 0,5 kg
17 kg 16,5 kg 13,5 kg 14 kg 18 kg 18 kg 14 kg 21 kg 13,5 kg 15 kg 15 kg 14,5 kg
15,5 kg 19,5 kg 17 kg 17,5 kg 14 kg 14 kg 20 kg 14,5 kg 16 kg 18 kg 12 kg 16 kg 19 kg
Sample answer: We need to find out if these body weights are healthy compared to other children’s body weights. We could arrange the body weights in order and then summarise the whole set by using measures of central tendency and range. Grouping the data might be useful to show the number of body weights between 10 and 15 kg, 15 and 20 kg, and so on.
3. Data collected to find out how many learners answer a certain type of question in less than 20 seconds:Time taken (in seconds) by a group of learners to answer a question
20 25 24 33 13 26 10 19 39 31 11 16 21 17 11 34 14 15 21 18 17 38 16 21 25
Sample answer: We want to know how long different learners take to answer a question. We need to arrange the times in order and then look at a representation of the whole set. We could group the numbers to see how many are between 10 and 20 seconds, 20 and 30 seconds, etc. to answer the question.
4. Data collected to analyse the monthly salaries of employees of a small business:The monthly salaries of ten employees
R8 000 R2 500 R75 000 R6 000 R7 500 R5 200 R4 800 R10 300 R15 000 R9 500
Sample answer: This is a small data set of only ten values. We could arrange the data in order and then summarise it using measures of central tendency and range.
317
GRADE 9 TERM 4 MATHEMATICS
Grade 9 Project 4Geometry of 3D Objects Max: 48
1. Use the following nets to build 1.1 A rectangular prism1.2 A triangular prism1.3 A cylinder
2. Change all the dimensions by multiplying by 2 and build another rectangular prism in each – build again.
3. Work out the surface area and volume of both sets of prisms and compare them.
1.
2.
318
GRADE 9 TERM 4 MATHEMATICS
3.
Use the following rubric to allocate marks for learners’ objects:
1.3 A rectangular prism. Criteria
Neatness (3)
Accuracy (4) (original + enlarged)
Materials used (2)
Due date (2)
Answers (5)
Total [16]
1.4 A triangular prismCriteria
Neatness (3)
Accuracy (4) (original + enlarged)
Materials used (2)
Due date (2)
Answers (5)
Total [16]
319
GRADE 9 TERM 4 MATHEMATICS
2.2.1.2.2.2.3. A cylinder
Criteria
Neatness (3)
Accuracy (4)(original + enlarged)
Materials used(2)
Due date ( 2 )
Answers (5 )
Total [16 ]
320
GRADE 9 TERM 4 MATHEMATICS
Grade 9 Project 5Geometry of 3D Objects
Make a copy of the diagram below. Cut it out and fold it along the dotted lines. Attach the faces with sticky tape to make an open container with pentagonal faces.
Make another copy of the pentagon diagram, and make a second container.
321
GRADE 9 TERM 4 MATHEMATICS
Turn one of your containers upside down and put the two together to form a polyhedron.
Answer the following:
1. How many faces does your polyhedron have?2. Are the faces identical and what shape are they?3. Are the edges equally long, and how many edges are there?4. What is the common name for this polyhedron?
322
GRADE 9 TERM 4 MATHEMATICS
Grade 9 Project Geometry of 3D Objects Memorandum
ANSWERS1. 122. Identical regular pentagons3. 30 equally long edges4. Dodecahedron (5)
Use the following rubric to allocate marks for learners’ objects:Criteria
Neatness (3)
Accuracy (4)
Materials used (2)
Due date (2)
Answers (5)
Total [16]
323
GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 1 Lesson 1Class workGive the learners the following exercise to complete in class:Complete the following table of real numbers:Numbe
r N N 0 Z Q Q’ Non-Real
Undefined
15 Yes Yes Yes Yes No No No
√3
0,14287
√ 14
−√1443√−1
√−1
325
GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 1 Lesson 2Class work Homework
1. Divide R5 600 in the ratio 3: 4: 2.
2. A car travels a distance of 440 km at an average speed of 80 km/h. How long does it take the car to travel this distance? Round off your answer to the nearest hour.
3. Calculate the amount that will be in the bank after 5 years if R3500 was invested at 9% p.a. simple interest.
4. Calculate the interest if R10 000 is invested at 10 % per annum compound interest for 3 years.
1. Simplify the ratio R250:R150:R1002. Divide 240g in the ratio 5 : 3 : 43. Calculate the interest if R6500 is invested for 3 years at 7,7% per
annum compound interest.4. Calculate the amount that will be in the bank after 5 years if R9500
was invested at 8% p.a. simple interest. 5. Mary works in a Foreign Exchange bank at OR Tambo airport. The various exchange
rates are shown on the electronic notice board below.Currency Buy (R) Sell (R)US Dollar $ 1 8,1090 8,4586British Pound £ 1 12,7850 13,4767Euro €1 11,2780 11,9060Botswana Pula P 1 0,9320 0, 8080
Mary buys $500 from a customer: How much did she pay in rand?
326
GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 1 Lesson 3Class work Homework
1. The weather forecast for the world on TV shows the following temperatures:
Minimum MaximumJohannesburg -4 0C 15 0CBloemfontein -10 0C -1 0CLondon -3 0C 14 0C
a) What is the difference between the minimum temperatures in Johannesburg and the minimum in Bloemfontein?
b) What is the rise in temperature from minimum to maximum in Johannesburg?
c) What is the rise in temperature from minimum to maximum in Bloemfontein?
2. Simplify:a) 4m5×3m7×−2m3
b) a7×a6
a8×a3
c) ¿
d) (−2 x2)¿
e) 2n8n+2
43n2−2n
1. Calculate:a)– 3(-11 + 5)
2. The minimum and maximum temperatures in Sutherland , Western Cape are shown in the table:
January August OctoberMin 0C 120 -160 50
Max 0C 290 00 220
a) What was the coldest temperature in Sutherland? b) What was the warmest temperature in
Sutherland? c) What is the difference between the two
temperatures?
3. Simplify:
a¿ 4 x2 y3
2x y5
b¿ 2 p8q4
8 p3qr÷ 16 p4
4 r
c ¿ 2x+1
3. 2x−1
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 1 Lesson 4Class work
1.In the figure, AB//ED, Determine the size of and
2. Calculate the values of and if
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 1 Lesson 5Class work
1. Determine whether the following are congruent, similar or neither:
a)
b)
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GRADE 9 TERM 4 MATHEMATICS
2.Consider the triangles in the figure below. Prove∆ ABD≡∆CDB
3. Prove that ∆ ADE≡∆CFE
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 1 Lesson 6Class work
1. Use a pair of compass and a ruler to make accurate constructions of the following:
2.
Calculate the value of the unknown side.
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GRADE 9 TERM 4 MATHEMATICS
Homework 1. Use a pair of compass and a ruler to make accurate constructions of the following:a) angle
2. Calculate the value of the unknown side.a)
b)
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 1 Lesson 7
Homework1. Simplify:
a) 2a2 (a−2)+2a(a2−3a )
2. If x=5 and y=−4 , find the value of
4 x2+3 y2
3. Calculate the value of :; if
4. If and ,find the value of
5. If and ,calculate the value of
6. If and y = -3, calculate the value of 2×−2xy
7. Solve for x:a) 4 x−1=−9
b)
c)
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 1 Lesson 8Class work
1. Give the equation of the following:
2. Sketch the graph of y=−2
3. On the grid, draw the graphs defined by and . Label each graph and clearly mark the points where each graph cuts the axis and the axis.
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GRADE 9 TERM 4 MATHEMATICS
4. Study the straight line graphs below and answer the questions that follow
Complete:a) The equation of line CD is… b) The equation of line AB is … c) The length of CE = …
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GRADE 9 TERM 4 MATHEMATICS
Homework Revise for the weekly test: Topics:
1. Whole numbers i.e. number systems; financial maths; ratio and rate; integers2. Exponents3. Geometry of straight lines4. Geometry of 2D shapes5. Expression and equations
Functions and graphs
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GRADE 9 TERM 4 MATHEMATICS
Grade 9 week 1 lesson 9
WEEKLY ASSESSMENT
QUESTION 1
In each of the questions below choose the correct answer.1.1 2a2 (a−2)+2a(a2−3a ) (2)
ABCD1.2 If x=5 and y=−4 , find the value of
4 x2+3 y2
(2)
A -148B 140C 148D -140
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GRADE 9 TERM 4 MATHEMATICS
1.7
Choose a correct statement to describe the relationship between the above two triangles.
(2)
A
B
C They are not congruent
D They are neither congruent nor similar
1.8 Simplify : √ x8 + √ x16
A. x4+x8
B.C.D.
(2)
[16]
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GRADE 9 TERM 4 MATHEMATICS
QUESTION 2
2.1 Complete the following statements:
2.1.1 ABC is an acute-angled triangle because_______________ (1)
2.1.2 DEF is a _____angled triangle because it has a 90° angle. (1)
2.1.3 GHI is an obtuse-angled triangle because ______________ (1)[3]
QUESTION 3
3.1 Calculate the interest if R1250 is invested for 3 years at 9% per annum compound interest. (4)
3.2 Calculate the amount that will be in the bank after 4 years if R6500 was invested at 5% p.a. simple interest.
(4)
[8]TOTAL 27
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 2 Lesson 1Classwork
1. Factorise the following expressions:a) 2 x2−8 xb) mx−my+5x−5 yc) 3m−3d−4de+4med) tv−uv−tw+uw
2. Solve for
a)b)
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 2 Lesson 2Class work1. Use the following graph on the chalkboard. Ask learners for the dependant and independent variables and then ask
learners the questions to interpret the graphs.
The graph below represents the charge per day from two car rental companies. Company A charges an initial fee of R120 and then charges R25 per day. Company B charges no initial fee, but charges R75 a day. According to the graph...
A. Company A is cheaperB. Company B is cheaper C. Company B is cheaper if you hire the car for two days.D. Company A is cheaper if you hire the car for more than two days
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GRADE 9 TERM 4 MATHEMATICS
2. A Businessman earns a basic salary of R1 000 plus R500 commission for every item he sells.2.1 Write a function for calculating the salesman’s salary (y) if he sells x items.2.2 Complete the table of values using your function from Question 1.
X 1 2 3 4 5Y
2.3 Draw a grid using a scale of 0 to 10 on the x-axis and 0 to 5 000 (with intervals of 500) on the y-axis, and plot a graph based on your table.
2.4 Use the graph to find out how much the salesman would be paid if he sold 7 items2.5 Use the function you wrote in Question 1 to check your answer to Question4 .
Homework
1. Draw the graph of 2. Find the equation of the graph passing through (2;3) and (-4;2)
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 2 Lesson 3Class work1. Calculate, without the use of a calculator:
a)b)c)
d)2. Write down any 5 rational numbers that will fit between the following integers:
a) -1 ; -2b) 2,3 ; 2,4
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 2 Lesson 4Class work Homework
1.
a)
b)
c)
d)
2.Study the following table:A B C0,825 4,2367 3,45
2.1 Round off 0,825 to the nearest : a) unit b) tenth c) hundredth
2.3 What is the place value of 2 in 0,825? 2.3 What is the number value of 2 in 0,825?2.4 What is the number value of 6 in 4,2367?
1. Calculate the following, without the use of a calculator:
a)
b)c)d)
2. Calculate the following: (Round your answers off to 2 decimal places)
a)
b)c)
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 2 Lesson 5Class workHomework
1. If 1 of petrol weighs 0,6798 . What will of petrol weigh? (round off your answer to 3 decimal places.
2. Mashudu bought a cooldrink for R7,50 ; a chocolate for R5,75 and a packet of chips for R6,00. He paid with a R50 note.a) How much did he spend?b) How much change did he get?
3. The reading on a water meter at the beginning of the month was 322,573 . At the end of the month the reading is 332,523 . The municipality
charges R1,25 per 200a) How much water was used during this month?b) How much will be paid for this month’s water .
4. Water drips from a tap at a rate of 15 of water per minute. How many litres of water drips from the tap in a day?
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 2 Lesson 6Class work Homework
1. a) Complete the table below described by the function , show only 2 calculations.
Input Value
-3 -2 -1 0 1 2
Output Value
b) draw a flow diagram to show the 2 calculations.
2. Find the output values in a flow diagram below for the rule
3. Use and to determine the corresponding output values ( values). Represent the input and output values in :
b) A flow diagram
1. Study the following diagram:
a) Draw the 4th diagramb) Complete the table:
Position 1st 2nd 3rd 4thValue 1
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 2 Lesson 7Class work HomeworkAllow learners to complete individually and give different learners opportunity to present to class.
1. Copy and complete the table:Input Value
1 2 3 4 5 6
Output Value
4 7 10 19
2. Determine the rule for the relationship between the inputs and output values of the table
3. Find the values of and respectively-2 -1 0 1 12-7 -5 -3 -1 27
1. Study the following diagram:
a) Draw the 4th diagramb) Complete the table:
Position 1st 2nd 3rd 4thValue 1
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 2 Lesson 8Class work Homework
1. Determine the rule to describe the relationship between the input
and output values of the table below.-2 -1 0 1 2-3 -1 1 3 5
2.In each of the following terms you can determine the next term by applying a rule to the previous term. Describe the rule in words in each case:
a)
b)c)d)
3. Calculate the output values:
0 1 2 3 4-8
Prepare for the weekly assessment on expressions; equations; functions and graphs number systems; integers; common fractions;
decimal fractions; financial contexts including ratio and rate
geometric patterns; Numeric patterns
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 3 Lesson 1
QUESTION 11.1 Which of the following equations is equivalent to the equation (2)
ABCD1.2 Look at the first two patterns, how many sticks will Pattern 3 have? (2)
A 6B 9C 2D 151.3 Choose the function that represents the following graph: (2)
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GRADE 9 TERM 4 MATHEMATICS
A.B.C.D.
[6]QUESTION 2Write down the next two terms of the following patterns:
2.12.2 (1)2.3 (2)2.4 (2)
[7]QUESTION 3
3.1 Complete the following pattern by drawing the next three terms: (3)
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GRADE 9 TERM 4 MATHEMATICS
3.2 Complete the table :
x -2 -1 0 1 2 4 n
y 15 12 -9 -24
(8)
[11]
TOTAL 25
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 3 Lesson 1Classwork
1. The given data set represents the weight to the nearest kg of a group of learners.
82 73 6542 55 6265 58 6851 65 7263 48 65
a) Draw a stem and leaf diagram for the datab) Determine the range of the datac) Determine the moded) Determine the meane) Determine the median
2. An 8-sided die has the numbers 1 to 8 on its faces. When thrown, it has as equal chance of landing on any one of its faces
a) How many possible outcomes are there?b) What is the probablility that it will land on a prime number?c) What is the probablility that it will land on a prime number?
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 3 Lesson 2Class work Homework1. A group of 14 learners measure their height and foot
sizes and tabulate their results.
Height
174
158
163
175
140
126
153
160
160
Foot 27 24 24 26 23 23 22 25 24
2.Height 131 156 165 158 120Foot 20 23 25 24 20
a) Draw a scatterplot for the data collected.b) According to the graph, do taller people have longer
feet lengths and why?
3. There are eight balls in a basket. 2 are green, 3 are blue and the rest are white.a) Calculate how many white balls there are.b) What is the probability of picking a blue ball?c) What is the probability of picking a green ball?
1. A survey was conducted to test the relationship between the hand and shoe size. The table below shows 10 measurements of different hand lengths and shoe sizes.
Hand length
5 7 2 9 6 7 4 9 8 5
Shoe size 12
13
10
15
12
15
11
16
15
11
a) Draw a scatter plot using the information in the table.b) Draw a line of best fit.c) What conclusion can you draw about the relationship
between a hand length and a shoe size?d) Find the mode for the shoe size.e) Calculate the mean for the shoe size.f) Determine the range for the hand size.
2. There are 25 learners in a class. If a learner is chosen at random, what is the probability that a girl is chosen if there are 11 boys?
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 3 Lesson 3Class work
1. Study the bar graph below taken from the 2009 South African Census@School results. It shows the modes of transport to school from home of the learners who participated in the Census@School.
a) What is the graph about?b) What information is shown on the axes?c) Is the scale clear and easy to read?d) What conclusions can the graph help you make?
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GRADE 9 TERM 4 MATHEMATICS
2.Stem Leaf1 1 2 5 7 2 0 1 3 4 83 2 9 4 3 3 5 6 85 0 1 6
a) What is the range for the stem and leaf plot? b) What is the median value for the stem and leaf plot? c) What is the mode for the stem and leaf plot below? d) What is the mean value?
3. Represent the following 2-way table on a tree diagram:
T-shirt JeansBlack Blue Red
Green Black/green Blue/green Red/greenWhite Black/white Blue/white Red/white
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 3 Lesson 4Class work Homework
1. Complete the following table:
Platonic Solid Name of solid
Number of edges
Number of vertices
Number of faces
a) b) c) d)
2. In the figure below, AP= 5m; AS = SB = 2m, PT = 12m and PS ⊥ AB
Calculate the area of the figure correct to 2 decimal places.
1. a) Draw line segment PQ with P (2;3) and Q(5;5) on a Cartesian planeb) Translate line PQ 2 units to the right and 2 units upwards and
label the image P 'Q'c) Write down the coordinates of P'∧Q '
2. Which of the following polyhedral are prisms?
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 3 Lesson 5Class work1.
a) Draw the Cartesian plane𝐛) Draw rectangle JKLM with the following coordinates: J (−5 ; 4) ,K (−3 ;4) , L(−3 ;1)∧M (−5;1)c) Shade half of the rectangled) Reflect the rectangle along the y-axis and label the image J ' ,K ' , L' , M ' and write down the coordinates of each vertexe) Reflect the rectangle J ' ,K ' , L' , M ' along the x-axis and label the image J K L M and write down the coordinates of each vertex.
2. What is a prism? 3. Calculate the volume of the following:
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 3 Lesson 6Class work Homework1.
a) Draw a Cartesian plane on the grid provided and label the axes
b) Draw the figure SAMP with vertices S(1 ;−2) , A (2 ;−1) and M (3 ;−2) and P(2 ;−5)
c) Reflect the figure along the y-axis and label it S' A 'M 'P 'd) Write down the coordinates of S' A 'M 'P '’ e) Compare the coordinates of SAMP and S' A 'M 'P 'f) What is the relationship between the coordinates of
the object and the coordinates of the image? g) Complete: (x ; y)→¿
2. Complete the table:
1. Calculate the volume of the following, use π=3,14
2. Describe the transformation if the coordinates of the original point and its image are:a) (−2 ;−3)→(−2 ;−5)
b) (4 ;−7)→(−6 ;0)
c) (3 ;11)→(16 ;20)
3.
a) Name the shapeb) What is the shape of its faces?c) How many faces does the shape have?d) How many edges does the shape have?e) How many vertices does the shape have?f) Draw the net of the shape.
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 3 Lesson 7Class work
1. Study the diagram below:
Complete the following:a) AB= 3cm A ' B' = 6cm therefore A ' B' = ------× ABb) BC= 2cm B' C ' = 4cm therefore B' C ' = ------× BCc) CD= 3cm C ' D ' = 6cm therefore C ' D ' = ------× CDd) AD= 2cm A ' B' = 4cm therefore A ' B' = ------× AD
2. Refer to question 1.a) Calculate the ratio of the area of figure B to the area of Figure A.b) Simplify the ratio in question 2.a) above.
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GRADE 9 TERM 4 MATHEMATICS
3. Complete the following table:
Name Shape of faces
No of faces (F)
No of vertices (V)
No of edges (E)
F+V-E
4. The area of the base of a rectangular prism is and its height is 12mm. What is its volume?5. The volume of a cube is 216m3. What is the length of one of its edges?
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 3 Lesson 8Classwork
1. Expand and simplify:a) 2 (x2+4 x+8 )b¿ (x+2)(x+5)
2. Factorise:
a) 25a2−9b) 1−16 x2
c) 2 x2−2d) ( x+ y )2−b2
e) 4 x6−19
f) −(x+ y )2+1g) x2+5x+6h) x2−5 x+6i) 2 x2+10 x+12j) −2b2+6b−4
3. Simplify:a)
x2−9x2+x−6
÷ x2−3 xx+1
b) 2x2+4 x−12
−1x−2
4. Solve the following equations:a) 4(2m – 5) = 5 – 2(m + 1)
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GRADE 9 TERM 4 MATHEMATICS
b) 3(x – 1) – 4x = 5 – 2(x+ 1)c) 2(x – 3) = x- 3(x+ 2)
Worksheet: Term 4 Grade 9 Week 4 Lesson 1Classwork
1. Simplify:
a)
b)c) ( 4a2+2b ) ( 4a−2ab+9c )
d) 9 x2( 13x+2x3)−4 x(1
2x4−3 x2)
2. Solve the following equations:2.1 4 ( x+2 )−3=2 (3−x )
2.2
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 4 Lesson 2Classwork Homework
1. Simplify:a)
2. Solve for :
a)b)
3. (See next page)
1. Solve for :
a)
2.
a) Write down the defining equation of each of the following straight line graphs.
b) What can you deduce about the lines AD and BC. Give a reason for your answer.
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GRADE 9 TERM 4 MATHEMATICS
a) Use the graph to calculate the gradient of the straight line.b) Determine the equation of the straight line.c) Write down the gradient of any other straight line which can be drawn
parallel to the given line
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 4 Lesson 3Classwork
1.Simplify the following expressions
a)
b)
2. Solve the following equations:a)
b)
3. Determine the gradient of the following straight line:, as well as the intercept and the intercept
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 4 Lesson 4Class work Homework
1. Factorise the following expressions fully, using any suitable method:
a)b)
2. Simplify the expression below:
a)
3. Draw the graph of
1. Factorise the following expressions fully, using any suitable method:
a)b)
2. Simplify the expression below:
a)
3. Find the equation of the graph
375
x
y
GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 4 Lesson 5Class work
1. Simplify:a)b)c)
2. Factorisea)b)
3. Solve for :
a)
4. Study the graph :
a) What type of graph is this?b) Is it an increasing or decreasing function?c) Approximately what ℉ is freezing point?
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 4 Lesson 6Classwork Homework
3. Simplify:a)b)
4. Solve for
a) x2 = 25
What is the equation of the following:
a) At how many minutes do both companies charge the same rate?
b) When is company T’s rates lower than
1. Simplify:a)
2. , calculate , when .
3. Complete the table below and draw the graph.-3 -2 -1 0 1 2 3
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 4 Lesson 7Class work Homework
1. Simplify:a)b)c)
2. Solve for
a)3. , calculate , when
4. Use the given coordinates to find the equation of the straight line graphs passing through them.
a) (16; 5) and (7; 2)b) (−1
2;8) and (-6; -3)
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 4 Lesson 8Class work Homework
1. Simplifya)
b) 9 x2( 13x+2x3)−4 x( 1
2x4−3 x2)
c)12abc ( 14a2b
c+ 8ac3
b−22c3b3
a )2. Given that a=−1 ;b=7∧c=0 find the value for each of the following
expressions:
a) 17abcb) 3a+2b−7c
3. Solve for :
a) 4 ( x+2 )−3=2 (3−x )
b) 4 ( x−7 )+6 (2−3x )=5 (x−6 )
4. a) On the same Cartesian plane draw the graphs y = 4 and x = 4. b) What is the gradient for each graph? c) What do you notice about these two graphs?
Learners must prepare for weekly test on expressions, equations, functions and straight line graphs
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 5 Lesson 1 and 2Classwork1. Which of the following numbers belong to each group below?
−2 13
9π √20 1,23 .. . −3 √16
a) Integersb) Rational numbersc) Irrational numbers
2. List the following:a) The factors of 15b) The first four multiples of 6c) Find two rational numbers between -1,36 and -1,35
3. Calculate:a) 1 1
2−1
6+5
3
b) 3 56−3 1
3
c) -9 – (21 – 4)d) 3 + 3 - (-7) – 8e) (450-349) x 2 + (-101)
4.US Dollar $8,4916 R11,78British Pound £13,7697 R7,26Euro €8,9 R11,24
Jamie is travelling to Europe. She has R2 000 for spending. a) How much will Jamie get in Euros?b) Will it be cheaper for her to go to London and use the British pound?
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 5 Lessons 3 and 4Class work Homework
1. Simplify:a) (3 1
2+3 1
2 )÷1 34
b) 3 56−2 1
3
c) (-3)3
2. Calculate:a) 3 – (-9)b) -1 + 2 – 3 x 4c) 3 x 3 + 1 x 11 – 6d) √90−9
3. Don bought a music set for R199 and sold it to Tumi for R250. Thando bought a TV for R800 and sold it for R850.a) Calculate the profit that each one made.b) Calculate the percentage profit that each person
made. (correct to one decimal place)c) Who made the larger profit?d) Who made the larger percentage profit?
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 5 Lessons 5 and 6Class work1. Simplify:
a) 3 37×(4 2
3−11
5 )b) 4
5+1 7
10c) -(3)2
d) 1,5 : 3
2. Calculate:
a) 80 – 0
b)c) 11 + 12 + 13 + 14 + 115
3. Jabu deposits R2 000 into a savings account where the interest is 15% p.a. compounded annually.a) How much interest did he receive?
4. You receive R500 for your birthday. You decide to invest it for 15%p.a for 3 years.a) Calculate the interest after 3 years.b) The final amount he will receive after 3 years.
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 5 Lesson 7 and 8Class work
1. Complete the following table:
Number N N 0 Z Q Q' Non-Real Undefined0
√0,910
−3111
2. Simplify:
a) 23× 9
10
b) 24+ 4
4
3. Calculate:a) 4 × - 5 = - 20 b) (-135) +145
c) 20 – (8)(0) ÷ 2(-10)(-1)
4. Johnny borrows R800 from his brother to buy a new i-pod. The agreement is that he will pay the money back together with 12% p.a. simple interest after two years. How much will he have to pay back?
5. A car costs R90 000. Calculate the value of the car after 10 years if the rate of depreciation is 12% p.a. on a reducing balance.6. 6. Your dad bought a laptop for R11000. It depreciates in value on a simple interest basis. Calculate the value of the new computer after 3 years.
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 6 Lesson 1 & 2Class work
1. Consider the following pattern:1; 4; 9; 16; ….
a) Find the next 3 termsb) Write in words how you obtained the next term.c) Find the 10th term of the patternd) Write an algebraic expression for the pattern.
2. 7; 11; 15; 19; …a) Find the next 3 terms of the pattern
3.
a) Draw the next three patterns for the above.b) Describe in words the pattern.
4. If y=12 x−10 and x=−3 , x=−1 , x=0 , x=2 , x=4 , x=12. Draw a graph to represent the above information. HINT: Draw a table of values first.
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 6 Lesson 3 & 4Class work Homework
1. Study the pattern below:
a) Draw the next three patterns for the above.b) Write down in words what the pattern is.
2. Complete the following tables by filling in the missing input and output values and the formula for the pattern.
a)x -
2-1
0 1 2 7 n
y -7
-4
-1
26
44
b) Give the formula that defines the above table.c) Draw the graph of y=−3x+8.
1. Find the next two terms of the pattern: 1; 2 ; 4; 8;….2. Find the equations of the following:a)
b)
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 6 Lesson 5 & 6Class work
1. Consider the values in the following table. The rule for finding y is: divide x by −2 and subtract 4.
2 0 2 5-1 -3 -4 48
a) Use the rule to determine the missing values in the table, and write them in.
2. Sketch the graph of y=−x
3. Consider the following pattern: 7; 11; 15; 19; …a) Find the next 4 termsb) Write in words how you obtained the next term.c) Find the 10th term of the patternd) Write an algebraic expression for the pattern.
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 6 Lesson 7 & 8Class work Homework
1. Consider the following pattern: 8; 15; 22; 29; …a) Find the next 4 termsb) Write in words how you obtained the next term.c) Find the 10th term of the patternd) Write an algebraic expression for the pattern.
2. Complete the following table of valuesx -
2-1 0 1 2 4 n
y 0.5
1 2 128
2048
3.If y=−2x+7 and x=−4 , x=−2 , x=0 , x=1 , x=3 , x=8
a) Draw a table to represent the above values of y b) Draw a graph to represent the answers in your table.
Learners prepare for the weekly assessment on Geometric and numeric patterns, functions, expressions and graphs
390
GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 7 Lesson 1 and 2Classwork
1.Refer to the diagram below and answer the questions that follow
a) Calculate the value ofx. Give a reason for your answerb) Determine the size of ∠ y. Give a reason for your answer
2. In the diagram below,prove that ∆PTQ≡∆PTR. Give reasons for your answer.
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P
Q
A
C
GRADE 9 TERM 4 MATHEMATICS
3. Use a pair of compasses and ruler to make accurate constructions of the following angle:
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P
Q
T
T
R
GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 7 Lesson 3 and 4Class work Homework
1.In the diagram below, A ¿ 70° and quadrilateral ABCD
is a rhombus.
a) Calculate the value of A BC , give reasons for your answer.
b) Determine the size of BC D , give a reason for your answer
c) Determine the size of C B E , give a reason for your answer
1. In the diagram below, PQ∥ST, SR¿ST, Q PR=¿ 55° andPQ S=¿27°.
1. Choose the correct answers:
1.1
Calculate the value of A. B. C.D.
1.2 Refer to the figure in 1.1. Calculate the value of A.B.C.D.
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EBA
CD
GRADE 9 TERM 4 MATHEMATICS
a) Determine the size of Q ST . Give a reason for your answer.
b) Determine the size of T S R. Give a reason for your answer.
c) Calculate the value of x . Give a reason for your answer.
2. Use a pair of compasses and ruler to make accurate constructions of the following angle
1.3
Calculate the size of T
A.B.C.D.
1.4 Refer to the diagram in 1.3. Give a reason why ∆PQR /// ∆ TMS
A. All angles are equalB. All sides are in proportionC. A;A;SD. S;A;S
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27°
55°P
Q R
S
T
GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 7 Lesson 5 and 6Classwork
1. The area of a parallelogram below is 156 mm2, MR¿12 mm and NR¿5 mm. Calculate the length of TS.
2. PQRS is a square with Circle O where r ¿7 mm. Calculate the area of the shaded part correct to one decimal place. N.B. π=22
7
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12 mm
5 mm
M T
SN R
P Q
O
RS
GRADE 9 TERM 4 MATHEMATICS
3. Complete the table below:Platonic Solid Shape of faces Number of facesOctahedronIcosahedron
4.
Name the above shapes.
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 7 Lesson 7 and 8Classwork
1. Given the circle below with right-angled triangle BCD. BD is 7cm and DC is 5cm.
a) Find the diameter of the circle.b) Find the area of triangle BCD.c) Find the area in the circle that is not covered by ∆BCD.d) Find the circumference of the circle
397
GRADE 9 TERM 4 MATHEMATICS
2. If the perimeter of hexagon is 24 cm. The shape in Figure 2 is made of the hexagons of the same size as in Figure 1. What is the perimeter of the shape drawn in Figure 2?
3. Complete the table beow:
Platonic Solid Shape of faces Number of facesOctahedron Equilateral
trianglesEquilateral
triangles20
Hexahedron 4
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Figure 1
Figure 2
GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 8 Lesson 1 and 2Class work
1. Draw the enlarged or reduced image of the following figure according to the scale factor given. Scale factor =
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GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 8 Lesson 3 and 4Class work1.
Translate PQR 5 units to the right and 3 units downTranslate PQR 5 units to the right and 3 units downAre all the triangles congruent?
401
GRADE 9 TERM 4 MATHEMATICS
2. Determine the equations of the straight lines passing through the following points:
c)
1 2 3 4 55 4 3 2 1
d)-4 -2 0 2 42 0 -2 -4 -6
3. Draw the graphs of the following graphs on the same system of axes: and
402
GRADE 9 TERM 4 MATHEMATICS
Homework
1. Draw the graphs of on the same system of axes.
a) State the rule for the transformation from A to B in the form
b) Describe in words the transformations from G to Hc) Which of the transformations are:
i) Reflectionsii) Rotations
403
GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 8 Lesson 5 and 6Class work
1. Simplify:a)b)c)d)
2. Solve for :
a) x2 = 25
b)
3. , calculate , when
4. Multiply by
404
GRADE 9 TERM 4 MATHEMATICS
Worksheet: Term 4 Grade 9 Week 8 Lesson 7 and 8Class work
1. Simplify:a) 12x2 y−6 xy2
3 xy
b) (xa - 3)(xa + 3)
c) √34 y6−9 y6
d) (2 x−3 )2−4(x−1)(x+1)
e) 2(x+4)2
−2
f) p2q2×( p−2)2
p−2
2. Solve for :
a)b) 3 ( x−1 )=2 x+5c) ( x−2 ) ( x−2 )=0
d) 2x3
− x+14
=1
e) 2− x=64
3. Complete the following ,if then x=…
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