Embed Size (px)
Citation preview
����������������������������
�����������������������������������������������������������������������������������
��������������������������������������
����������������
������� �����
�������
�����������������������������������������
����������������
�������������������������������������
����������������
OVERVIEW: GRADE 4 MODULE 3
CONTENTS
1
2
3
4
5
Introduction and Phase Overview
Learning Programme Overview
Time Schedule – an approximation
Step-by-step through each module
Memorandum
INTRODUCTION
The understanding and use of mathematics is a life skill. Mathematics enables members of society to function as useful, integral parts of society. In teaching mathematics we aim to make the learner see how mathematical relationships are used in all the aspects of everyday life; develop in the learner a confidence and competence and lack of fear when coping with mathematical situations; help the learner to be aware of the beauty and elegance of mathematics; and develop in the learner a questioning attitude and a love of mathematics.
INTERMEDIATE PHASE OVERVIEW
The mathematics learning area includes interrelated knowledge and skills:
Knowledge Skills
Numbers, operations and relationships Representation and interpretation
Patterns, functions and algebra Estimation and calculation
Space and shape (geometry) Reasoning and communication
Measurement Problem posing
Data handling Problem solving and investigation
Describing and analysing
The knowledge and skills are reflected in the learning outcomes, as indicated in the table
below.
Learning Outcomes Main focus in each outcome
LO1 Numbers, operations and relationships To be able to recognize, describe and represent numbers and their relationships and to count, estimate, calculate and check with competence and confidence in solving problems.
The learner moves from counting correctly to calculating with all four operations; learns to use the calculator as an effective tool as and when it’s needed; knows tables to 12 x 12 and can calculate mentally effectively.
LO 2 Patterns, functions and algebra To be able to recognize, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.
Numeric and geometric patterns are studied, especially the relationships between the terms in a sequence and between the number of a term and the term itself.
LO 3 Space and Shape (Geometry) To be able to describe and represent characteristics and relationships between two-dimensional shapes and three-dimensional shapes in a variety of orientations and positions.
The learner deals with a more detailed description of 2-D shapes and 3-D objects.
LO 4 Measurement To be able to use appropriate measuring units, instruments and formulae in a variety of contexts.
Learners use standardized units of measurement and measuring instruments and must be able to estimate and prove results through accurate measurement.
LO 5 Data handling To be able to collect, summarize, display and critically analyse data in order to draw conclusions and make predictions, and to determine chance variation.
Learners gain skills in gathering and summarising data so that the data can be interpreted and used to make predictions.
ASSESSMENT STANDARDS The assessment standards are closely related. Activities should, wherever possible, cover more than one assessment standard within one learning outcome. Activities may cover related assessment standards across learning outcomes within the grade. LEARNER ASSESSMENT At the end of each activity there is an assessment sheet. Both the learner and the educator complete this. The assessment of both may then be compared. The educator’s assessment will serve to provide marks for the portfolio.
Codes for assessment sheets
4 = Learner’s performance has exceeded the requirements of the learning outcome for the
grade.
3 = Learner’s performance has satisfied the requirements of the learning outcome for the
grade.
2 = Learner’s performance has partially satisfied the requirements of the learning outcome
for the grade.
1 = Learner’s performance has not satisfied the requirements of the learning outcome for
the grade.
Continuous assessment: learner’s portfolio Each learner will have a portfolio. A portfolio is “a method of assessment that gives the learner and teacher together an opportunity to consider work done for a number of assessment activities” (Revised National Curriculum Statement, May 2002, p. 99). A learner’s portfolio gives a full picture of his/her achievements concerning knowledge, skills, attitudes and values. To be effective, continuous assessment should include various forms of assessment. For moderation purposes, proof of the following assessed activities must be kept and may be placed in the portfolio, which should include the following*:
Forms of assessment Minimum requirements Year
Tests/Examinations 2 per term for the first 3 terms 6 per year
Class work/Homework 2 per term 8 per year
Projects (in a group) 1 before the end of the second
term
1
Tasks (individual) 1 per semester / 2 per year 2
Investigations 1 per semester / 2 per year 2
Total number of items
enclosed in the portfolio
for moderation purposes
19
*(This is for the senior phase, i.e. grades 7 – 9, and is also to be applied to grade 4.) The link between outcomes and forms of assessment The aim of outcomes-based education is to enable learners to realise their potential. This is done by setting learning outcomes (goals). These learning outcomes are explained to the learners before they begin each activity. To help them to achieve the learning outcomes there are detailed minimum assessment standards. Thus the approach is learner-centred and activity-based. Each module comprises a variety of tasks, the required number of assignments, projects, tests, investigations and class work. In completing these adequately, the learner will fulfil the minimum assessment standards; in achieving the minimum assessment standards,
the learner will achieve the desired learning outcome and also the critical outcomes (life skills) and developmental outcomes (what the learners must be able to use to acquire life skills). The activities in the modules are designed to relate to “real life” situations and problems in everyday life. There are activities to create an awareness of the relationship between social justice, human rights, a healthy environment and inclusivity. Learners are also encouraged to develop knowledge and understanding of the rich diversity of this country, including the cultural, religious and ethnic components of this diversity.
LEARNING PROGRAMME OVERVIEW
“Education is to be learner-centred and activity-based” (Revised National Curriculum
Statement – May 2002).
Module 3 deals with measurement of time, capacity, length and mass as well as space and shape, stressing how these are needed in everyday life. Time Schedule � Each of the four modules should take approximately ten weeks. A detailed time
schedule is presented below: NOTE: this is merely a suggested schedule.
MODULE ACTIVITY CONTENTS TIME (an approximation)
THREE
1; 2; 3; 4 Time: using various clocks/ watches;
recording time; problems; history of
measuring time
4 weeks
5; 6 3-D objects; 2-D objects 2 weeks
7; 8 Estimating, measuring and recording
shapes and objects; problems:
measurement
3 weeks
9 Perimeter 1 week
Approach
Seeing that education is to be learner-centred and activity-based
Discussion Discussion amongst the learners after and even during an activity is very important. It must take place, as it is through discussion that the learner clarifies his/her thoughts. The teacher has the exciting and difficult task of initiating discussion, controlling it but NOT dominating it. The use of calculators is to be integrated in the activities where necessary.
STEP BY STEP THROUGH THE ACTIVITIES
The teacher should begin with module 1, activity 1 and work through each activity up to the last activity of module 4. Having said this, oral activities (e.g. the examples in activity 1 and in other activities) should be done daily, for 5 minutes each day from the beginning of the year to the end of the year, and should be varied so that learners are kept on their toes. Speed tests cannot be used to replace oral activities, as their aims are totally different and opposing to those of oral activities.
........................................... ACTIVITIES 1 to 4 inclusive – time!
� Learners seem to struggle with this. Try to establish the “basics” very firmly by doing as much practical work as possible. Let learners read the different types of clocks and watches; see it on the T.V. and on computers, discuss it. Luckily Athletics and Swimming have become very time conscious. The sums given in the exercises are “real” times of children. Let learners time each other when doing little activities. E.g. How long do you think it would take to walk round the school; down the corridor; to the Tuck-shop?” When they have written down estimations, let them walk, and time them. It makes it meaningful and interesting. (Of course, we can only do this if everyone is self-controlled…Life skills!)
............................................. ACTIVITY 5 – space and shape
� A complete change, on purpose. Do as much practical work as possible; let them see and hold the objects. Take them to a road and show them road signs. The instructions in the module are explicit.
............................................. ACTIVITIES 7 and 8 – measurement
� Once more the secret is to make it interesting by including as much practical measurement as possible. After they have done the practical activities in the module, you may wish to add an activity concerning conversion, e.g. from mm to m; from g to kg, etc. Please do so. The jump from the practical to the abstract/ theoretical is the dangerous part. It is strongly advised that enough practical measurement be done, even if it does take time. It’s worth it in the long run. It makes the concept meaningful.
� The word sums in activity 8 are from “real-life” situations. One might extend the rainfall exercise by recording rainfall at the school, and comparing it with that of the region.
............................................. ACTIVITY 9 – an introduction to perimeter
� Instructions are explicit. The teacher will have to keep control and see that they have the
necessary equipment and that nobody gets hurt with it! Note that the learners are not told to make a square or rectangular hen-run, but there is mention of a “length” and a “width”. It’s a fun, “real life” experience for the learners and can be a powerful learning tool.
MEMORANDUM GRADE 4 MODULE 3
............................................. ACTIVITY 1
1.1 2 1.2 5 1.3 7 Practical work TEST YOUR SKILLS
1.1 20 to 11 or 10.40 1.2 9.25 or 25 past 9 2 Drawing hands on clock faces (see module)
............................................. ACTIVITY 2
1.1 05:10 1.2 16:20 1.3 21:45 1.4 00:57 of 24:57 1.4 20:00 1.5 09:59
2.1 06:45 2.2 16:10
3.1 Drawing on clock-face: ten to two in the afternoon
3.2 Drawing on a clock-face: ten past nine in the morning
4. Morning; the hour hand is on the right side of the clock-face; in the afternoon it would be
on the left side of this clock-face.
5.1 1 min. 17,53s 5.2 5 min. 56,01s
............................................. ACTIVITY 3 problems involving time
1.1 Kathleen 1.2 Her time is the shortest 1.3 0,9s 2. 13:00 or 1 p.m
3.1 Flight 502: afternoon; Flight 504: evening 3.2 Flight 504 was 5 min. faster.
4. 7 h 40 min.
5.1 8 April 2003 5.2 5 December 2003 5.3 10 days 5.4 3 weeks 3 days 5.5 1 weeks 2 day
6.1 The time from one morning high tide to the next increases; the increase varies from
one minute to four minutes 6.2 The time from one afternoon high tide to the next increases; the increase varies
from one minute to 3 minutes. (Note: from morning high tide to afternoon high tide on the same day the time seems to decrease by 1min.each day, but not on 3 July.)
6.3 04:14 6.4 12 h 26 min.
7.1 1h 8 min. 22 s. 7.2 6 h 49 min.
............................................. ACTIVITY 4 assignments
1. Read 2. Look up information
3.1 Drawings 3.2 Practical and oral 3.3 Own – practical and oral 3.4 Own – complete table
4. They could not measure seconds and parts of seconds; outside conditions (e.g. wind)
influenced the instruments. 5. hour-glass; egg-timer
............................................. ACTIVITY 5 3D objects
1. Study 2. Drawings; sphere; cube; cylinder; cone; cuboid/ rectangular prism; cuboid; pyramid
3.1 and 3.2
Sphere Cylinder Cube Cuboid Pyramid Cone Orange Spaghetti Ice block Book Box of
chocolates Ice-cream
cone All balls Candle Dice Brick Paper hat
Rake handle margarine
4.1 cuboid 4.2 cylinder 4.3 cone 4.4 cone 4.5 cuboid
5. Table
Object Number of surfaces Flat or curved surfaces
Shape of surfaces
Box 6 flat Rectangle
ball 1 curved Sphere
cube 6 flat Square
candle 3 Sides: curved Cylindrical
pyramid 3 or 4 flat Sides: triangular; Base: triangular or
square
............................................. ACTIVITY 6 2D shapes
1. Polygons: own 2.1 Circles: polygons have straight edges; circles are curved 2.2 It has a curved edge.
3.1 to 3.5 own
4.1 to 4.4 own
5.1 and 5.2
Triangle Sides Corners/ Angles
3
all the same 3
all the same 3
2 the same 3
2 the same 3
2 the same 3
2 the same 3
none the same 3
none the same 3
none the same 3
none the same 3
none the same 3
none the same
5.1 Own
6.1 Own
6.3 (a) yes (b) yes (c) yes
(d) It is a closed, flat 4-sided figure with straight sides. TEST YOUR PROGRESS
1.1 05:35 1.2 45 min. past 3 in the afternoon or quarter to 4 in the afternoon or 3.45 nm.
2. 6 h 45 min. 3. 13,4 s
4.1 freestyle 4.2 2 min. 25,07 s
5.1 hexagon 5.2 rectangle 5.3 triangle 5.4 octagon
6. 3 7. An octagon has straight sides; a circle is curved 8. A circle does not have straight sides.
9.1 cuboid/ rectangular prism 9.2 cylinder 9.3 phere 10. 6 11. curved 12. curved 13. 4 (base + 3 sides)
............................................. ACTIVITY 7 measuring
1 Mass
1.1 500 g (or other sizes) 1.2 (a) 500 g (b) cornflakes (c) depends on size (d) 250 g 1.3 (a) own (b) own (2,5 g) (c) 2,5 g (d) own 1.4
Object My estimation Actual measured mass
Tea-bag own 2,5 g
Margarine own 500g (or other)
Brick own About 3 kg
Me own Own
2. Length and Distance
2.1 to 2.7 Recordings:
Item Estimation Actual Measurement
Head own Own
Friend’s head “ “
Foot “ “
Height “ “
Tall person: height “ “
Eye-lash “ “
Thumb-nail: width “ “
Longest finger: length “ “
2.8 Item Estimation Actual Measurement
Height of door own 2m
Width of window “ They vary
Length of corridor “ “
Distance to Office “ “
Length of rugby-field “ “
Width of soccer-field “ “ (The size of school sports-fields are smaller than ones for adults.)
3. Measuring Capacity
Item Estimation Actual Measurement
Bucket own Usually 5 or 10 or 15
Cool drink tin “ Depends on size of tin
Cool drink tins in a litre packet
“ “
Tea-spoon “ 5 ml
Tea-spoons in a titre packet “ 200
Baby’s bath “ Depends
My bath “ “
School swimming-pool “ “
Pools differ in size
3.7 Practical (colouring matter does not give flavour)
............................................. ACTIVITY 8 problems using S.I. units
1.1
Month Rainfall in ml that month Total for that month
January 17,4
February
March 58,6
April 30,5
May
June 17,0
July 60,4
1.2 oral 1.3 yes 1.4 5 ml 1.5 half 1.6 February and May 1.7 autumn according to these figures – 89,1ml then; 77,4ml in winter so far, but the
rainfall for August has not been included. (It is actually a winter rainfall area.) 1.8 123,5 ml 2.1 Gary 2.2 4,6 m is the longest jump.
3. 5 958 km 4. 380,9 km 5. 7,17 kg
.......................................... ACTIVITY 9 perimeter – practical investigation
1 to 6 Own practical measurement and recording
TEST YOUR PROGRESS
1.1 6,578 kg 1.2 5 703 m 1.3 6,712 liter 1.4 0,768 m 1.5 3,4 cm
1. 5,905 m 2. 73 cm 3. 600 ml 4. 2 490 kg 5. 1,5 kg End of Module 3
OVERVIEW: GRADE 5 MODULE 3
FRACTIONS AND DECIMAL FRACTIONS (LO 1, 2 AND 5)
LEARNING UNIT 1 FOCUSES ON ORDINARY FRACTIONS
� Ensure that the learners master the terminology: numerator; denominator; proper fraction improper fraction; mixed number; equivalent fractions; simplify. It is also important that learners should be able to count backwards and forwards in fractions correctly.
� Place a great deal of emphasis on simplifying fractions as well as on forming equivalent fractions, as this is the foundation of the work in the following grades.
� Learners must be allowed to follow their own methods in the addition and subtraction of fractions. It is best to do the section on division (Activity 1.21 and 1.22) slowly and thoroughly and to make sure that all learners understand the work fully.
� This module links very well with critical outcome 4 (Learners collect, analyse, organise and critically evaluate information), critical outcome 5 (Learners communicate effectively by using visual, symbolic and / or language skills in various modes) and critical outcome 7 (Learners demonstrate an understanding of the world as a set of related systems by recognising that problem-solving contexts do not exist in isolation).
� Learners usually find “fractions” more difficult than the other work, therefore 4 - 5 weeks can be allocated to this module.
� For the portfolio: Activity 19 is an assignment for the portfolio. Teachers must make sure that learners know exactly what is expected of them. The matrix for the assessment must also be given to the learners in advance, and it must be explained in detail.
LEARNING UNIT 2: FOCUS ON DECIMAL FRACTIONS�
� This module covers tenths, hundredths, and thousandths, adding and subtracting decimal fractions and writing fractions as decimal fractions.
� The correct method of adding and subtracting should be emphasised right from the start, as learners’ own, often totally incorrect, methods can create a great deal of confusion. Make sure that learners are also able to write ordinary fractions as decimal fractions, and the other way around. Learners often find this very confusing and “difficult”.
� The themes Social Justice: Human Rights and Inclusively can quite easily be incorporated here (the role of money in our society, and the different monetary systems in the world). Critical outcomes 7 (Learners demonstrate an understanding of the world as a set of related systems by recognising that problem-solving contexts do not exist in isolation) and developmental outcomes 2 (Learners participate as responsible citizens in the life of local, national and global communities) can also be made applicable here.
� This module should be completed within 3 - 4 weeks.
� For the portfolio: Activity 21 is an assignment for the portfolio. Teachers must make sure that learners know exactly what is expected of them. The matrix for assessment must also be supplied and explained to the learners in advance.
STEP BY STEP THROUGH MODULE 3
LEARNING UNIT 1: COMMON FRACTIONS
............................................. ACTIVITY 1.1
� In this activity the purpose is to test the prior knowledge of the learners. Ensure that learners know and understand the answers to all of the questions, because they constitute the basic knowledge that is necessary to master this learning unit.
� Insist on NEAT colouring in work by the learners!
............................................. ACTIVITY 1.2
� This activity is a practical application of the learners’ prior knowledge. Learners must be perfectly able to distinguish between “number of parts” and “fraction”.
............................................. ACTIVITY 1.3
� Learners now have the opportunity of adding two different fractions without using pencil and paper. Encourage them to use as many combinations as possible! Also make sure that they know the difference between “improper fraction” and “mixed number”.
............................................. ACTIVITY 1.4
� Learners must be able to add forwards and backwards in fractions in this activity. More “drilling” can be done here if necessary, as this forms the basis of addition and subtraction.
............................................. ACTIVITY 1.5
� It is very important for learners to know what “equivalent fractions” are and how to do these calculations, as it is of paramount importance for addition and subtraction of fractions. Give them many exercises to do on this aspect, and insist that they colour in NEATLY (no. 4).
............................................. ACTIVITY 1.6
� This activity is mainly for added interest and to expand the learners’ general knowledge. Learners can compare our notation of fractions to the Egyptians’ manner of writing them.
............................................. ACTIVITY 1.7
� Learners are again given an opportunity to find equivalent fractions. They can adapt/change the game by using other fractions.
............................................. ACTIVITY 1.8
� The mental calculation test is meant to enhance the learners’ ability to do tables, and also to “test” their knowledge of the work done in the previous activities. A time limit (2 - 4 minutes) can be allocated for the test – teachers can determine the time to suit the learners’ abilities.
............................................. ACTIVITY 1.9
� In this activity fractions must be recognised and classified so that they can be compared to each other. Make sure that learners know which way the greater than and smaller than signs point. If learners find it difficult to find the answers, “equivalent fractions” must be given extra attention.
............................................. ACTIVITY 1.10
� In this activity learners are expected to read with understanding/insight so that they will be able to solve the problems. The emphasis is still on equivalent fractions so that fractions with different denominators can be compared with each other. If learners still have difficulty doing this, you can go back to Activities 1.5, 1.7 and 1.9 and give them similar exercises.
............................................. ACTIVITY 1.11
� Make sure that learners know how to simplify. Give them many additional exercises here, seeing that this aspect is of cardinal importance in the multiplication and division of fractions that learners have to do in the higher grades.
............................................. ACTIVITY 1.12
� Learners must be able to round off to the nearest whole number. The number line is a good aid to use, seeing that it enables learners to physically “see” the logic (of how to determine the correct answer).
............................................. ACTIVITY 1.13
� This activity is a revision of the previous activities. Make sure that all the learners have mastered the work before starting with the next activity!
............................................. ACTIVITY 1.14
� Learners must solve the problems in context in this activity. Note that they may use any method, but they must be capable of explaining it! Give the learners the opportunity to demonstrate their solutions on the board so that they will all be exposed to a variety of different methods. It is important that there should be plenty of social interaction and that differences and similarities between the various methods should be pointed out.
............................................. ACTIVITY 1.15
� With reference to Activity 1.14, learners now have the opportunity to examine two different solutions to the same problem. Although learners will probably prefer one of the methods to the other, it is important that they understand both methods.
............................................. ACTIVITY 1.16
� A class discussion on how to subtract fractions can be held before attempting this activity. If it seems necessary, the conversion of mixed numbers to improper fractions should also be done again. However, learners may use their preferred method to calculate the answers in no. 3.
............................................. ACTIVITY 1.17
� In this activity the learners must be able to interpret given information. Various methods to solve a problem are also looked at. It is important for learners to discover the “rule” for finding the answers. They must also be able to write it down in no. 3.
............................................. ACTIVITY 1.18
� This activity is a consolidation (further revision) of the previous activity. More examples can be given if necessary.
............................................. ACTIVITY 1.19
� This is an activity for the learner’s portfolio. It must be read through thoroughly with the learners and explained to them. The assessment matrix must also be given to the learners beforehand.
............................................. ACTIVITY 1.20
� Learners now have the opportunity of improving their mental calculation skills. They can be required to complete the exercise within a set time.
............................................. ACTIVITY 1.21
� Learners must work in groups and use their own methods to “divide” with fractions. It is important that they should demonstrate their methods to the rest of the class, so that the learners will be exposed to a variety of methods.
............................................. ACTIVITY 1.22
� This activity serves as a further consolidation of activity 1.21. Insist that the learners make neat drawings in no. 1.3!
............................................. ACTIVITY 1.23
� It is important for learners to know how to key in fractions on a pocket calculator. More examples can be given so that the learners can practise doing this properly.
� The test at the end of the learning unit can be used as a summative mark.
LEARNING UNIT 2: DECIMAL FRACTIONS
............................................. ACTIVITY 2.1
� This activity tests the learners’ ability to distinguish between parts of fractions that are coloured in and those that are not. It tests the learners’ prior knowledge to determine whether they are able to write common fractions as decimal fractions. The number line is used to enable the weaker learners to “see” the correlation between ordinary and decimal fractions. Number 1.5 is an important exercise, and more of these examples can be given, especially where learners find it difficult to complete the number patterns.
............................................. ACTIVITY 2.2
� Make sure that the learners know how to program the pocket calculator to “count”. This activity will assist learners with the correct notation when decimal fractions are added (inserting the comma in the correct place).
............................................. ACTIVITY 2.3
� In this activity learners practise their skills in writing ordinary fractions as decimal fractions and vice versa. If they should find it difficult, you could use a number line to explain it further.
............................................. ACTIVITY 2.4
� The mental calculation test shows whether the learners know their tables, but it will also indicate whether they have mastered the work done in the previous activities. A time limit of 2 - 3 minutes can be imposed here.
............................................. ACTIVITY 2.5
� In this activity the focus is on hundredths. Emphasise the use of the 0 as a place holder, as well as the fact that hundredths are the second number after the decimal comma.
............................................. ACTIVITY 2.6
� This activity can serve as a consolidation of the previous work.
............................................. ACTIVITY 2.7
� Learners must know where hundredths fit in on a number line. More such examples can be given if necessary.
............................................. ACTIVITY 2.8
� In this activity learners learn through play about the place value and value of each figure in a decimal number. At the same time they practise “breaking open” a decimal number. This is an exercise that will be helpful in the next activity.
............................................. ACTIVITY 2.9
� At this point learners must be able to determine the value of each figure. If any of the learners find this difficult, simplify the decimal fractions to common fractions first.
............................................. ACTIVITY 2.10
� This is a practical activity that can be done in class. See to it that you have enough measuring tapes beforehand.
............................................. ACTIVITY 2.11
� In this activity the emphasis shifts to thousandths. Learners must be able to recognise the numbers that are represented, and then to convert them to ordinary fractions.
............................................. ACTIVITY 2.12
� This is a consolidation of activity 2.2, but now thousandths are used. Make sure that the correct notation has been consolidated before moving on to no. 12.2.
............................................. ACTIVITY 2.13
� Here the value of each figure is examined again. Learners who still find it difficult, can convert the numbers to ordinary fractions/mixed numbers first.
............................................. ACTIVITY 2.14
� Learners are given another opportunity to improve their mental calculation skills.
............................................. ACTIVITY 2.15
� In this activity the learners must discover for themselves that the problems can be solved through addition. They must also be allowed to use any method. However, it is important that the learners must be able to explain how the answers have been calculated. They can use the pocket calculator to check their answers.
............................................. ACTIVITY 2.16
� Make sure that the learners understand all the methods perfectly well (although they will choose only one to solve the problems)!
............................................. ACTIVITY 2.17
� If learners are not capable of calculating the answers it will be necessary to examine the method(s) they used. Indicate to them where they made mistakes, e.g. commas that are not properly aligned, and so on.
............................................. ACTIVITY 2.18
� In this activity the learners must discover for themselves that the problems can be solved by means of subtraction. Learners may use their own methods and techniques, but they must be able to explain how the answers have been calculated!
............................................. ACTIVITY 2.19
� Make sure that the learners understand all the methods perfectly (although they will choose only one to solve the problems)!
............................................. ACTIVITY 2.20
� If learners choose the vertical method, teachers must insist that they align the figures and the commas properly!
............................................. ACTIVITY 2.21
� This is an assignment for the portfolio. Learners must know exactly what is expected of them, and also how they will be assessed.
� The test at the end of the learning unit can be used as a summative mark.
MEMORANDUM GRADE 5 MODULE 3
LEARNING UNIT 1
............................................. ACTIVITY 1.1
1.1 Equal parts of a whole 1.2 Nominator 1.3 ÷ 1.4 Say in how many equal parts the whole is divided 1.5 Smaller 1.6 Nominator 1.7 Equivalents 1.8 Larger 1.9 Say with how many equal parts I work / are coloured in 1.10 Divide the nominator and denominator by the same number
2. 2.1 b and c
2.2 c and e 2.3 a en b 2.4 Not equal parts
2.5 (i) 41
(ii) 82 / 4
1
(iii) 84 / 2
1
(iv) 83
(v) 21
(vi) 81
(vii) 102 / 5
1
(viii) 104 / 5
2
(ix) 103
(x) 52
(xi) 51
............................................. ACTIVITY 1.2
1. B 8 1 8
1 7 87
C 6 1 61 5 6
5
D 8 1 81 7 8
7
E 3 1 3
1 2 32
F 12 6 126 / 2
1 6 126 / 2
1
G 16 8 168 / 2
1 8 168 / 2
1
H 16 4 164 / 4
1 12 1612 / 4
3
I 8 2 82 / 4
1 6 86 / 4
3
J 12 6 126 / 2
1 6 126 / 2
1
K 8 2 82 / 4
1 6 86 / 4
3
............................................. ACTIVITY 1.4
1. Seal 2. Dog (Sledge dog)
............................................. ACTIVITY 1.5
1.5 Fractions all equal 1.6 2
1 = 42 = 8
4 = 168
2. 2.1 10
5 2.6 52
2.2 64 2.7 9
3
2.3 108 2.8 2
1
2.4 123 2.9 12
6
2.5 1210 2.10 9
6 3. 3.1 1
122 3.4 18
51
3.2 6141 3.5 10
9
3.3 54 3.6 27
12 4. 12
10 = 65 3
2 = 96 3
2 = 64
43 = 8
6 108 = 5
4 103 = 20
6
............................................. ACTIVITY 1.8
1. 1.1 28 1.11 72 40 1.12 75 6 1.13 6 5 1.14 8
4 1.15 43
7 1.16 79 / 1 7
2
54 1.17 1 41
1.8 8 1.18 3 83
1.9 8 1.19 5 64 / 5 3
2
1.10 42 1.20 5 65
............................................. ACTIVITY 1.9
1. 1.1 < 1.2 > 1.3 > 1.4 < 1.5 = 1.6 < 1.7 = 1.8 < 1.9 > 1.10 = 2. 2.1 4
3 2.2 32
2.3 109 2.4 2
1
2.5 21 2.6 5
4
CLASS DISCUSSION
First make both nominators the same by finding the smallest common denominator OR
First simplify the fraction, if you can 3. 3.1 > 3.2 > 3.3 = 3.4 = 4. 4.1 < 4.2 < 4.3 > 4.4 >
Another BRAIN-TEASER!
65 ; 9
7 ; 32 ; 2
1
............................................. ACTIVITY 1.11
1. 1.1
55 9
8
1.2 55 5
3
1.3 44 4
3
1.4 66 5
4
1.5 66 9
8
............................................. ACTIVITY 1.12
1. 3 6
1 → 3 1.2 3 85 → 4
1.3 4 97 → 5 1.4 2 5
2 → 2
1.5 6 81 → 6 1.6 7 4
1 → 7
BRAIN-TEASER! 9
............................................. ACTIVITY 1.13
1.1 53 ; 5
4 ; 1 52 ; 1 5
4 ; 2
1.2 a) 54 ; b) 1 5
3 ; c) 1 51 ; d) 1 5
2
1.3 f) (i) 1 94 (ii) 1 10
7 (iii) 1 2
1 (iv) 1 85
(v) 811 (vi) 8
7
............................................. ACTIVITY 1.16
1. 1.1 81 1.2 12
3 = 41
1.3 123 = 4
1 1.4 106 = 5
3
1.5 1051 = 2
11 1.6 831
............................................. ACTIVITY 1.17
1. a)
103 10
2 102 10
1 101 10
1
5. It is the same 6. 10 ; 5
7. 1.7 21 7.2 20
7.3 300 7.4 168
............................................. ACTIVITY 1.18
1. 1.1 200 ml 1.2 1 500 m 1.3 300 g 1.4 6
5
1.5 2 500 mm
or 2,5 m or 2 2
1 m
............................................. ACTIVITY 1.20
1. 1.1 22 1.11 1 1.2 9 991 1.12 1 1.3 14 1.13 100 1.4 6 1.14 10 1.5 7 1.15 14 1.6 49 1.16 618 1.7 1 200 1.17 253 2
1
1.8 1 52 1.18 440
1.9 21 + 8
4 1.19 180
1.10 1 62 + 1 3
1 1.20 540
BRAIN-TEASER!
a) 8
1 b) 4 c) 2 4
1 d) 4 6
1 e) 16
............................................. ACTIVITY 1.22
1.1 a) Both b) Each gets 3
2
1.2 a) Yes
b) 1 21
c) 23
a)
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
1 2 3 4 5 1 2 3 4 5
b)
1.4 a) R1,25 / 125c
b) 1 85
............................................. ACTIVITY 1.23
1.1 a) 3 ÷ 5 = 0,6 b) 6 ÷ 7 = 0,8571428 c) 5 ÷ 8 = 0,625 d) 1 ÷ 12 = 0,0833333 e) 3 ÷ 4 = 0,75
BRAIN-TEASER!
TEST 1. 1.1 nominator
denominator
2. 2.1 126 2.2 5
3 3. 3.1 8 4
2 ; 7 43
3.2 3 122 ; 3 12
6
4. 4.1 = 4.2 < 5. 5.1 462 5.2 4 130 6. 6.1 4 12
5
6.2 1 87
7. 9 2
1 8. 1,5 m 9. 8 ÷ 9 =
LEARNING UNIT 2
............................................. ACTIVITY 2.1
1. 1.1 103
1.2 106
1.3 109
2. 2.1 0,03
2.2 0,6 2.3 0,9
3. 104 ; 10
5 ; 106 ; 10
8 ; 1011 ; 10
31 ; 1041 ; 10
51 0,3; 0,7; 0,9; 1,2; 1,3 4. 4.1 31,5
4.2 312,4 4.3 402,6 4.4 650,2
5. 5.1 0,8; 1; 1,2; 1,4; 1,6 5.2 4,1; 3,9; 3,7; 3,5; 3,3
5.3 2,5; 3,5; 4,5; 5,5; 6,5 5.4 2,8; 2,4; 2; 1,6; 1,2 5.5 9; 8,9; 8,8; 8,7; 8,6
............................................. ACTIVITY 2.2
1.1 4,3; 4,9; 5,5; 6,1; 6,7; 7,3; 7,9; 8,5; 9,1; 9,7 1.2 8,9; 8,5; 8,1; 7,7; 7,3; 6,9; 6,5; 6,1; 5,7; 5,3
............................................. ACTIVITY 2.3
1. 1.1 105 / 2
1
1.2 17 106
1.3 8 104
1.4 152 107
1.5 1 105 / 1 2
1
2. 2.1 0,8 2.2 0,1 2.3 0,6 2.4 0,35 2.5 0,6 2.6 0,8
3. Change denominator to 10 or 100 (equivalent fractions)
4. Numerator + denominator =
............................................. ACTIVITY 2.4
12. 1.1 57 1.11 40 1.2 300 1.12 9 1.3 995 1.13 72 1.4 98 1.14 13,4 1.5 510 1.15 124,7 1.6 28 1.16 1,8 1.7 24 1.17 2,7
1.8 9 1.18 4 109
1.9 7 1.19 12 108
1.10 6 1.20 09 102
............................................. ACTIVITY 2.5
1. 1.1 R0,04 1.2 R0,38 1.3 R0,02 1.4 R3,03 1.5 R4,60
2. 2.1 100
86 = 0,86 2.2 10072 = 0,72 2.3 100
44 = 0,44
2.4 1003 = 0,03 2.5 100
10 = 0,10 2.6 10070 = 0,70
............................................. ACTIVITY 2.6
1. 1.1 10036 = 0,36
1.2 100
71 = 1,07 1.3 10
63 = 3,6 / 3,60
1.4 100
8542 = 42,85 1.5 100
347 = 47,03 BRAIN-TEASER!
1. 0,03 2. 0,09 3. 0,4 4. 0,8 5. 0,37 6. 0,59 Only one digit after the comma. Pocket calculator does not show the last nought.
............................................. ACTIVITY 2.7
1.
A B C D
............................................. ACTIVITY 2.9
1. 1.1 > 1.2 > 1.3 < 1.4 < 1.5 < 1.6 =
BRAIN-TEASER!
a) 0,75 a) 0,04 b) 0,15 c) 0,34
............................................. ACTIVITY 2.11
1. 1.1 5,026 1.2 2,603 1.3 0,359
2. 2.1 5 1000
26
2.2 2 1000603
2.3 1000
359
............................................. ACTIVITY 2.12
1. 4,003; 4,006; 4,009; 4,012; 4,018; 4,021; 4,024; 4,027 2. 2,998; 2,996; 2,994; 2,992; 2,990; 2,988; 2,986; 2,984
............................................. ACTIVITY 2.13
1. 1,523; 1,52; 2,5; 2,146; 1,7; 1,510; 3,5 2. 2.1 100
3 2.2 10
9
2.3 107
2.4 20 2.5 1000
6 2.6 100
9 3. 3.1 0,006
3.2 0,032 3.3 1,101
BRAIN-TEASER!
0,125; 0,375; 0,625; 0,875 0,448 0,7
Change denominator to 1 000 (equivalent fractions)
............................................. ACTIVITY 2.14
1. 1.1 72 1.11 72 1.2 1000
736 1.12 84
1.3 10,08 1.13 5 1.4 007 1.14 49
1.5 100028 1.15 7
1.6 29 1.16 5 1.7 9 888 1.17 0,1 1.8 9,997 1.18 0,01 1.9 4,2 1.19 0,001
1.10 1000609 1.20 09
............................................. ACTIVITY 2.16
3. Actually the same
............................................. ACTIVITY 2.17
1. 1.1 157,727 1.2 44,519 1.3 142,498 1.4 290,126
2. 4,5 m
BRAIN-TEASER!
0,8 2,4 1,9 0,7 0,3 2,5 2,1 0,2 0,9 2,7
............................................. ACTIVITY 2.20
1. 1.1 3,44 1.2 2,66 1.3 4,578 1.4 5,779
BRAIN-TEASER! 3,574
TEST 1. 1.1 149,3
1.2 38,17 1.3 2,468
2. 2.1 1000
7 2.2 100
38 2.3 246 10
1 3. 3.1 100
4 3.2 10
8 3.3 1000
3 4. 4.1 <
4.2 = 4.3 >
5. 5.1 2,5; 3,5; 4,5
5.2 9,5; 8,5; 7,5 6. 83,044 7. 6, 0 0 0 - 2, 4 5 3 3, 5 4 7 8. x = 4,735 + 2,894 = 7,629 kg 9. y = 50,3 – 37,344 = 12,956 m
OVERVIEW: GRADE 6 MODULE 3
The learning programme for grade six consists of five modules:
1. Number concept, Addition and Subtraction
2. Multiplication and Division
3. Fractions and Decimal fractions
4. Measurement and Time
5. Geometry; Data handling and Probability
� It is important that educators complete the modules in the above sequence, as the
learners will require the knowledge and skills acquired through a previous module to be able to do the work in any subsequent module.
3. COMMON AND DECIMAL FRACTIONS (LO 1; 2 AND 5)
LEARNING UNIT 1 FOCUSES ON COMMON FRACTIONS
� This module continues the work dealt with in grade 5. Addition and subtraction of fractions are extended and calculation of a fraction of a particular amount is revised.
� Check whether the learners know the correct terminology and are able to use the correct strategies for doing the above correctly.
� Critical outcome 5 (Communicating effectively by using visual, symbolic and /or language skills in a variety of ways) is addressed.
� It should be possible to work through the module in 3 weeks.
� ** Activity 17 is designed as a portfolio task. It is a very simple task, but learners should do it neatly and accurately. They must be informed in advance of how the educator will be assessing the work.
LEARNING UNIT 2 FOCUSES ON DECIMAL FRACTIONS
� This module extends the work that was done in grade 5. Learners should be able to do rounding of decimal fractions to the nearest tenth, hundredth and thousandth. Emphasise the use of the correct method (vertical) for addition and subtraction. Also spend sufficient time on the multiplication and division of decimal fractions.
� As learners usually have difficulty with the latter, you could allow 3 to 4 weeks for this section of the work.
� ** Activity 19 is a task for the portfolio. The assignment is fairly simple, but learners should complete it neatly and accurately. They must be informed in advance of how the educator will be assessing the work.�
�
STEP BY STEP THROUGH MODULE 3 �
LEARNING UNIT 1: COMMON FRACTIONS
............................................. ACTIVITY 1
� In this activity it is important for learners to recognise the fractional values in a figure. The exercise becomes slightly more complicated when learners have to add two parts of the figure, but they should be able to do this. The learners should also be able to distinguish between proper numbers, improper numbers and mixed numbers. It they cannot do this, the educator should do revision of the relevant Grade 5 work.
............................................. ACTIVITY 1.2
� The focus is on equivalent fractions. Learners should not experience problems with the completion of the exercise. If necessary, the educator should do revision of the relevant work and explain it.
............................................. ACTIVITY 1.3
� The focus is still on equivalent fractions. A number line is used to represent this visually. If learners need to, they could make use of the number line to complete the assignments.
............................................. ACTIVITY 1.4
� This is a fairly uncomplicated test in mental calculation. Expect learners to complete it in a predetermined period of time, but limit the time to suit the capabilities of the learners.
............................................. ACTIVITY 1.5
� In this activity, learners need to be able to apply simplification correctly. If it is necessary, educators should do revision of the Grade 5 work.
............................................. ACTIVITY 1.6
� Learners work in groups of three to solve problems involving fractions in context. Educators should allow the learners to use any preferred method for finding the answers. The class discussion that should follow this activity will be of cardinal importance, as it will expose the learners to a variety of methods/operations. Ensure that they understand all the different operations and are able to apply them.
............................................. ACTIVITY 1.7
� This activity involves proper consolidation of the completed work. Learners now have to calculate their answers individually.
............................................. ACTIVITY 1.8
� Learners have to know how to find a common denominator (the smallest common multiple). They will have to gain much additional practice before they attempt the exercise.
............................................. ACTIVITY 1.9
� Learners are given another opportunity to solve problems in context. The given examples are more complicated and learners are required to add mixed numbers. Provide additional examples, if necessary.
............................................. ACTIVITY 1.10
� This is an exercise in performing mental calculation with the help of a number line.
............................................. ACTIVITY 1.11
� Although learners are free to use preferred operations, it is advisable for educators to guide them to convert the mixed numbers to improper fractions because this simplifies the process of subtraction considerably.
............................................. ACTIVITY 1.12
� The learners may be expected to complete this test within a fixed period of time.
............................................. ACTIVITY 1.13
� Learners work in groups of three in this activity. They have to be able to solve problems concerning fractions of quantities in context and may use any method. It will be important to demonstrate the different methods on the writing board so that learners can discover which method is the easiest to use.
............................................. ACTIVITY 1.14
� In this activity the learners are presented with different methods that can be used for solving a particular problem. Ensure that they understand each of the methods and are able to apply them.
............................................. ACTIVITY 1.15
� This is an activity aimed at providing proper consolidation of the work of the previous two activities to ensure. If learners struggle to do the last two sums you should help them to convert metre to millimetres and kilolitre to litres before attempting to calculate the answer.
............................................. ACTIVITY 1.16
� These puzzling problems are intended for learners who have completed the above work and have to "wait" while the educator attends to learners who experience problems.
............................................. ACTIVITY 1.17
� ** This activity is planned for inclusion in the portfolio. It is an uncomplicated assignment, but the educator must attend to the accuracy of the table and the pie graph in particular. (Learners may have some difficulty in doing the latter accurately.) Be sure to provide the learners with the assessment grid before they start the activity.
............................................. ACTIVITY 1.18
� The test could be used for the summative mark.
LEARNING UNIT 2: DECIMAL FRACTIONS
............................................. ACTIVITY 2.1
� Learners should be able to recognise and know the value of each digit in a number by now. This will be of cardinal importance when the four operations have to be used. If learners have problems, they should do many more exercises to consolidate the required knowledge.
............................................. ACTIVITY 2.2
� Learners need to be able to recognise the different fractions and classify them as common and decimal fractions. This should not present problems, provided that Activity 1 is properly understood.
............................................. ACTIVITY 2.3
� It is not possible to overemphasise the importance of knowing the different values of each digit in a number, and it is also relevant in this activity. Additional practice can be given in the writing out of extended notation. Learners should also be able to deduce what the number is that is represented in the illustrations provided for 3.2.
............................................. ACTIVITY 2.4
� This activity will help learners to form a visual impression of where some numbers fit into a larger whole. If this is difficult for them, the numbers should be converted to hundredths before carrying on with the operation.
............................................. ACTIVITY 2.5
� Here learners have to be able to write common fractions as decimal fractions, and vice versa. Guide the learners to first convert the denominator to 10, 100 or 1000, because this helps them to immediately arrive at a decimal fraction.
............................................. ACTIVITY 2.6
� The learners may be expected to complete this test within a fixed period of time.
............................................. ACTIVITY 2.7
� The pocket calculator could be used very effectively for checking answers in this activity. Learners will need to have sound knowledge of place values to do the exercise successfully.
............................................. ACTIVITY 2.8
� This activity is aimed at consolidating the learners' knowledge of the values and place values of numbers. They also need to be able to recognise patterns. If learners have problems with this, educators have to repeat the explanation of how a pattern is discovered. The pocket calculator can than be used to check answers (Programme it for using the constants.)
............................................. ACTIVITY 2.9
� This is another exercise for consolidation and for checking the learners' knowledge of values and place values.
............................................. ACTIVITY 2.10
� Educators must ensure that learners understand the principles of rounding off decimal fractions. Let them have plenty of exercise in rounding to the nearest tenth because grasping this will enable them to also round off to the nearest hundredth and thousandth quite easily when they get to it.
............................................. ACTIVITY 2.11
� This activity tests the learners' ability to write common fractions as decimal fractions and vice versa. Learners may use either method, but have to be able to classify/order numbers correctly
............................................. ACTIVITY 2.12
� For this activity learners have to be able to do rounding correctly to the nearest whole number. First allow them to practise doing this before letting them attempt to complete the table.
............................................. ACTIVITY 2.13
� The learners may work in groups to solve these problems. Any method may be followed, provided that they are able to explain how they go about finding the solution. The class discussion and comparison of methods will therefore be important. Grade 6 learners, however, need to be able to do addition and subtraction in columns. Educators should give additional attention to learners who have not mastered this method.
............................................. ACTIVITY 2.14
� Learners apply what has been discussed and explained in the preceding activity. The pocket calculator may be used to check work.
............................................. ACTIVITY 2.15
� This mental calculation test assesses the learners' ability to add and subtract small decimal numbers. Learners can be expected to complete the test in a set period of time. If learners do not cope well, it will be necessary to do revision of the value and place value of each digit in a number.
............................................. ACTIVITY 2.16
� The activity deals with multiplication of decimal fractions with multiples of 10. Learners may calculate the answers with the help of a pocket calculator, but have to try to identify the rules that are applicable in this.
............................................. ACTIVITY 2.17
� After the earlier activity, learners should be able to grasp the rules for dividing decimal fractions with multiples of 10 quite easily. Educators should guide the learners to make the necessary deductions and thereby "discover" the rules for themselves.
............................................. ACTIVITY 2.18
� This activity is not complicated, but accuracy (correct keying in of numbers and operators) is very important.
............................................. ACTIVITY 2.19
� ** This activity is planned for inclusion in the portfolio. Ensure that the learners know how they will be assessed before they start.
� The test mark can be used as a summative mark.
MEMORANDUM GRADE 6 MODULE 3
LEARNING UNIT 1
A B
Numerator Indicates how many equal parts are coloured in/ taken
Denominator Numerator is smaller than the denominator
Equivalent fractions Consists of a whole number and a proper fraction and is always bigger than 1
Proper fraction Indicates the number of equal parts into which the whole has been divided
Improper fraction Fractions of equal size
Mixed (fractional) number
The numerator is bigger than the denominator and the fraction is always bigger than 1
............................................. ACTIVITY 1.1
1. A : B : C : 81
162
A + C : 21
168
B + C : C + D : 83
166
A + D : 85
1610
A + B : B + D :
2. Proper 3.
166
161
163
167
165
4. IMPROPER FRACTION MIXED NUMBER
4.1 414
3 21
4.2 619
3 61
4.3 715
2 71
4.4 811
1 83
4.5 29
4 21
............................................. ACTIVITY 1.2
1.1 63
= 105
= 21
1.2 1510
= 128
= 32
1.3 106
= 53
1.4 1210
= 65
2.
............................................. ACTIVITY 1.3
1.1 a) 811
1 b) 84
c) 816
d) 46
e) 86
1.2 a) 41
b) 86
c) 42
84
d) 45
e) 23
46
f) 814
g) 48
816
2. BRAIN TEASER!
2.1 126
2.2 1512
2.3 76
2.4 98
2.5 105
3. 3.1 > 3.2 < 3.3 = 3.4 < 3.5 First make denominators the same 4.
5. 5.1 < 5.2 > 5.3 First find common denominator 6. 6.1 63 6.2 20 6.3 18 6.4 40 6.5 10 7.
7.1 52
7.2 94
7.3 74
............................................. ACTIVITY 1.4 1.1 48 1.9 33 1.2 5 1.10 951 1.3 6 1.11 9995 1.4 6 1.12 49
1.5 96
1.13 33
1.6 2820
1.14 108
1.7 3624
1.15 12
1.8 2016
............................................. ACTIVITY 1.5
1.1 32
1.2 2013
1.3 85
1.4 32
............................................. ACTIVITY 1.7
1.1 87
1.2 914
= 1 95
1.3 1418
= 1 72
1.4 1014
= 52
............................................. ACTIVITY 1.8
1.1 20158+
= 2023
1.2 643+
= 67
= 1 61
= 1 203
1.3 24206+
= 2426
1.4 15125+
= 1517
= 1 152
CLASS DISCUSSION
Whole number + fraction
First add whole numbers
First change all to improper fractions
............................................. ACTIVITY 1.9
1.1 5 432+
= 5 45
= 1 41
1.2 1 85
+ 2 32
3 241615+
= 3 2431
= 4 87
1.3 3 41
+ 2 51
5 2045+
= 5 209
2.
2.1 4 21
2.2 5 2019
2.3 5 2110
BRAIN TEASER!
1 + 21 = 1
21
1 + 21 +
41 = 1 4
3
1 + 21 +
41 +
81 = 1 8
7
1 + 21 +
41 +
81 +
161 = 1 16
15
1 + 21 +
41 +
81 +
161 +
321 = 1 32
31
25
3 21
0 2 4
321
1 121
CLASS DISCUSSION
� Make denominators the same � Find lowest common multiple � Make all improper fractions � First subtract whole numbers
............................................. ACTIVITY 1.10
1.1 59
– 57
or 1 54
– 1 52
1.2 613
– 69
or 2 61
– 1 63
1.3 711
– 77
or 1 74
– 1
............................................. ACTIVITY 1.11
OWN METHOD
1.1 1 83
1.2 3 21
1.3 1 107
1.4 2 127
............................................. ACTIVITY 1.12
1.1 70 1.9 65
1.2 983 1.10 27 1.3 438 1.11 29
1.4 354 21
1.12 87
1.5 9 1.13 1 81
1.6 132 1.14 43
1.7 8 1.15 10 000
1.8 65
............................................. ACTIVITY 1.14
1. To use a range of strategies to control solution
2. Own answer 3. 1.1 and 1.3 ; 1.2 and 1.4
............................................. ACTIVITY 1.15
1.1 402 1.2 312 1.3 695 1.4 665 1.5 1,236 1.6 1,5
BRAIN TEASER! 1.1
1.2 23
> 1 2.
2.1 41
2.3 209
2.2 256
2.4 187
3.
3.1 126
3.3 ( )123
3.2 ( )124
3.4 ( )122
TEST 1
1. Fill in the missing words:
1.1 Improper 1.2 Mixed number
2.1 2820
2.2 65
3. Fill in: < ; > or = :
3.1 = 3.2 > 4. Simplify:
4.1 1916
4.2 43
5. Calculate:
5.1 = 10 32
+ 95
5.2 1 87
= 10 911
5.3 2 476
6. x = 61
+ 94
= 183
+ 188
x = 1811
7. y = 53
x 11025
= 615 km
25
LEARNING UNIT 2
HOW WELL DO YOU REMEMBER THIS?
decimals
comma
tenths
second
thousand
point
............................................. ACTIVITY 2.1 1. 300
2. 107
3. 10009
4. 1005
............................................. ACTIVITY 2.2
SQUARE AMOUNT FRACTION DECIMAL FRACTION
10 101
0,1
12 10012
or 253
0,12
60 10060
or 53
0,6
9 1009
0,09
7 1007
0,07
............................................. ACTIVITY 2.3
1.1 8 + 104
+ 1007
+ 10002
1.2 10 + 3 + 108
+ 1003
1.3 400 + 20 + 6 + 109
2. 2.1 204,35 2.2 21,739 2.3 20,405 2.4 32.041
............................................. ACTIVITY 2.4
1,35 1,53 1,77 2,09
............................................. ACTIVITY 2.5
COMMON FRACTION 21
41
43
54
81
204
83
85
DECIMAL FRACTION 0,5 0,25 0,75 0,8 0,125 0,2 0,375 0,625
BRAIN TEASER!
0,6 repeating
0,16 (6 repeating)
0,1 repeating
............................................. ACTIVITY 2.6
1.1 45 1.9 7 1.2 18 1.10 7 1.3 1 984 1.11 8 1.4 8 1.12 125 1.5 10 1.13 3
1.6 12 1.14 10075
1.7 45 1.15 10093
1.8 9
............................................. ACTIVITY 2.8
1.1 0,0009 ; 0,01 ; 0,011 ; 0,021 1.2 0,024 ; 0,023 ; 0,022 ; 1.3 0,75 ; 1 ; 1,25 ; 1,5 1.4 0,015 ; 0,02 ; 0,025 ; 0,03 1.5 4,25 ; 4 ; 3,75 ; 3,5 1.6 2,65 ; 2,475 ; 2,3 ; 2,125
............................................. ACTIVITY 2.9
1.1 False 1.2 True 1.3 False 1.4 False 1.5 True 1.6 True 1.7 True 1.8 False 1.9 False 1.10 True
............................................. ACTIVITY 2.10
1.2 a) 6,4 b) 2,6 c) 1 d) 5,3 e) 4,3 f) 3,9
1.3 thousandths
hundredth a hundredth 1.4 0,261 = 0,26 0,935 = 0,94 3,478 = 3,48 0,955 = 0,96 4,227 = 4,23 2,132 = 2,13
BRAIN TEASER! 1.5 a) 4,263
b) 5,145 c) 2,512 d) 6,329 e) 1,835 f) 3,490
............................................. ACTIVITY 2.11
2.1 = 2.6 = 2.2 < 2.7 < 2.3 < 2.8 < 2.4 < 2.9 < 2.5 = 2.10 <
............................................. ACTIVITY 2.12
1.1 15,549 1.2 23,866 1.3 25,909 1.4 121,301 1.5 149,869
............................................. ACTIVITY 2.13
1. 165,2 � 2. 372,564 3. 56,42 kg 4. 147,431 m 5. and 6. Own explanation
............................................. ACTIVITY 2.14
1.1 374,019 1.2 613,44 1.3 78,721 1.4 388,76
BRAIN TEASER!
2.4 200 ; 290 ; 3 ; 10,02 ; 2,1 ; 2,5 ; 3,02 3. Numbers whithin the square are equal to double those in the cicle
............................................. ACTIVITY 2.15
1.1 12 1.9 0,87 1.2 8 1.10 0,77 1.3 4 000 1.11 0,808 1.4 1 186 1.12 2,62 1.5 254,5 1.13 2,25 1.6 1 350 1.14 0,514 1.7 9 900 1.15 9,45 1.8 132
............................................. ACTIVITY 2.16
1. 10,2 ; 9 ; 3 ; 4,5 ; 20,41 ; 34,8 ; 3,68
2. 2.1 shifted one position to the left 2.2 shifted one position to the right
3. 3.1 30 90 45 348 102 36,8
204,1 3.2 shifted two positions to the right 3.3 shifted two positions to the left 4.1
NUMBER 0,3 0,9 0,45 3,48 0,368 2,041
x 1 000 300 900 450 3 480 368 2 041
4.2 shifted three positions to the right
............................................. ACTIVITY 2.17
DECIMAL FRACTION ÷ 10 ÷ 100 ÷ 1 000
0,3 0,03 0,003 0,0003
0,9 0,09 0,009 0,0009
0,45 0,045 0,0045 0,00045
3,48 0,348 0,00348 0,000348
1,02 0,102 0,0102 0,00102
0,368 0,0368 0,00368 0,000368
2,041 0,2041 0,02041 0,002041
2.1 one position to the left 2.2 two position to the left 2.3 three position to the left
............................................. ACTIVITY 2.18
1.1 34,38 1.7 52,627 1.2 23,4 1.8 36,432 1.3 4 562 1.9 4,3256 1.4 10,168 1.10 349,81 1.5 35,68 1.11 451,262 1.6 3 4871,1 1.12 0,2395
TEST
1.1 0,95 1.2 0,625 3.1 4,7 3.2 7,9 4.1 4,67 4.2 21,39 5.1 4,977 5.2 2,676 6.1 > 6.2 < 6.3 = 7.1 0,975 7.2 42 390 8.1 434,499 8.2 159,265 9. x = 3,782 + 2,879 +6,45 = 13,111 kg 10. y = 68,59 – 42,38
= 25,31 kg
25
OVERVIEW: GRADE 7 MODULE 3
3. PREDICTIONS, COMPARISONS AND VARIABLES
� Learners now become acquainted with squared and cubed numbers. They learn to replace numbers with letters of the alphabet, i.e. to work with variables and to solve algebraic equations. Learners also have an opportunity to work with variables.
� All the “import and export” tables can easily be related to a class discussion on South African imports and exports and the conditions under which these take place. This can be linked to “A Healthy Environment”. In turn this links with critical outcome number 6.
� It should not take longer than 2 - 3 weeks to complete this module.
MEMORANDUM GRADE 7 MODULE 3
1. (b) quadrate number 2. (a) (b) No not quadrate of number (c) No 1 + 2 + 3 + 4 ÷ 4 ÷ 5 ≠ 3. (b) 64; 125; 216; 343 (c) 64 (d) 64 000 (e) 274 625
(f) K4: + 64 K5: + 64 + 125 = 225
(g) 1 + 8 + 27 + 64 + 125 + 216 = 441 (h) all square number 4. OWN ATTEMPTS 5. (a) 202 (i) 470 (b) 485 (j) 18 400 (c) 8 (k) 40 (d) 8 (l) 64 (e)` 7 (m) 10 000 (f) 56 (n) 64 (g) 820 (o) 1 000 000 (h) 96 6. 12 7 (a) 18 (d) 19 (b) 13 (e) 12 (c) 17
Sum: 45 2.1
8.
1
14
7
12
15
4
9
6
10
5
16
3
8
11
2
13 Sum: 34 9. (a) 48 (d) 90 (b) 10 (e) 108 (c) 64 10. (a) true (d) false
(b) true (e) true (c) false 11.
12.
9 969
9 699
6 669
6 966
9 669
6 696
6 699
6 969
9 666 13. LEARNERS OWN ASSESSMENT 14. (a) 100 (b) 12 (c) 124 (d) 8 15. (a) 10 99 75 5 (c)
8
21
39
74
16.2 (a) 5� + 7 = 22
(b) 8� - 10 = 46 (c) 5 + 9� = 59 (d) � - 13 = 6 16.3 (a) 21 (b) 17 (c) 34 18 (a) 72 (j) 30 (b) 12 (k) 5 (c) 7 (l) 57 (d) 141 000 (m) 9
(e) 900 (n) 9 987 (f) 47 (o) 125
(g) 135 (h) 336 (i) 7
20. (a) � > 10 (b) y < 2 000 (c) (c+8) > 6 (d) y < 50 (e) k – (k ÷ 2) < 20 21. (a) Days 5 49
Boxes 150 200 600 1 750
22. (b) Sketch
Number of squares 4 7 10 13 25 40 (c) Squares = 1 + (Sketch No. x 3) (d) (i) 1 + (25 x 3) = 76
(ii) 1 + (37 x 3) = 112 (iii) 1 + (101 x 3) = 304
(e) (i) 43
(ii) 55 (iii) 80
23. (a) u = i ÷ 4 (b) u = (i x 2) + 1
24. (a) Input
money
24. (a) Input money
R1 R5 R30 R50 R100
Output : flower bulbs
3 15 90 150 300
(b)
(c)
Input
Nights
1
7
10
15
31
Output
Cost
R280
R1 960
R2 800
R4 200
R8 680
Input
Kg
1
2½
4
5¼
19
Output
Amount
R6,20
R17
R27,70
R35,70
R129,78
