MODULE FRAMEWORK AND ASSESSMENT SHEET

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2 MODULE FRAMEWORK AND ASSESSMENT SHEET LEARNING OUTCOMES (LOS) ASSESSMENT STANDARDS (ASS) FORMATIVE ASSESSMENT ASs Pages and (mark out of ) LOs (ave. out of ) SUMMATIVE ASSESSMENT Tasks or tests Ave for LO (%) (% and mark out of ) NUMBERS, OPERATIONS AND RELATIONSHIPS LO We know this when the learner: The learner is able to recognise, describe and represent numbers and their relationships, and counts, estimates, calculates and checks with competence and confidence in solving problems.. counts forwards and backwards fractions;. describes and illustrates various ways of writing numbers in different cultures (including local) throughout history;. recognises and represents the following numbers in order to describe and compare them:.. common fractions to at least twelfths;. recognises and uses equivalent forms of the numbers listed above, including:.. common fractions with denominators that are multiples of each other;. solves problems in context including contexts that may be used to build awareness of other Learning Areas, as well as human rights, social, economic and environmental issues such as:.. financial (including buying and selling, profit and loss, and simple budgets);

3 LEARNING OUTCOMES (LOS) ASSESSMENT STANDARDS (ASS) FORMATIVE ASSESSMENT ASs Pages and (mark out of ) LOs (ave. out of ) SUMMATIVE ASSESSMENT Tasks or tests Ave for LO (%) (% and mark out of ). estimates and calculates by selecting and using operations appropriate to solving problems that involve:.. addition and subtraction of common fractions with the same denominator and whole numbers with common fractions (mixed numbers);.. finding fractions of whole numbers which result in whole numbers;.9 performs mental calculations involving:.9. addition and subtraction;.9. multiplication of whole numbers to at least 0 x 0;.0 uses a range of techniques to perform written and mental calculations with whole numbers including:.0. rounding off and compensating;.0. using a calculator.

4 LEARNING OUTCOMES (LOS) ASSESSMENT STANDARDS (ASS) FORMATIVE ASSESSMENT ASs Pages and (mark out of ) LOs (ave. out of ) SUMMATIVE ASSESSMENT Tasks or tests Ave for LO (%) (% and mark out of ) PATTERNS, FUNCTIONS AND ALGEBRA LO We know this when the learner: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.. describes observed relationships or rules in own words;. writes number sentences to describe a problem situation, including problems within contexts that may be used to build awareness of human rights, social, economic, cultural and environmental issues;. determines, through discussion and comparison, the equivalence of different descriptions of the same relationship of rule presented:.. in flow diagrams;.. by number sentences. DATA HANDLING LO We know this when the learner: The learner will be able to collect, summarise, display and critically analyse data in order to draw conclusions and make predictions, and to interpret and determine chance variation.. organises and records data using tallies and tables;. draws a variety of graphs to display and interpret data (ungrouped) including:.. a pie graph.

5 In this module you will do the following: Activity number Details Learning Outcome.. Question on fractions (competition) Colouring in of certain fractions Recognising, classifying and representing fractions Adding of common fractions Recognising and using equivalent forms Writing equivalent fractions like the Egyptians Mental arithmetic Relationship signs Simplifying Rounding off to the nearest integer Comparing methods for addition of fractions Problem solving Subtraction of fractions Calculation of sums with fractions (multiplication) Task for portfolio Division with fractions Fractions on the pocket calculator Brain-teasers Test,, Writing fractions as decimal fractions: tenths Fractions and decimal fractions on a number line Counting in decimal fractions Counting in decimal fractions, using a pocket calculator Matching of common and decimal fractions Mental arithmetic Writing cents as rand

6 Activity number Details Writing fractions as decimal fractions: hundreds Writing fractions as decimal fractions on the pocket calculator Filling in hundredths on a number line Relationship signs Measuring your friends length Writing fractions as decimal fractions: thousandths Writing down the value of the underlined digit Circling of smallest decimal fraction Subtraction of decimal fractions Task for portfolio Brain-teasers Test Learning Outcome

7 To recognise, classify and represent fractions (positive numbers) in order to describe and compare them LO... How much do you still remember of what you learnt about fractions in Gr.? Let us start with a competition girls against boys! Take turns and see if you can answer the following questions. Your educator will tell you who must answer first and will also award points ( points for every correct answer and points if the boys can answer a question that the girls can t, and vice versa).. What is a fraction? If I write what do I call the?.... What operation sign can replace the in?.... What is the function of the denominator? If I cut up a whole into more and more sections, each section becomes.... What do I call the in?.... Fractions of the same size are called fractions.. The fewer the number of sections the whole is divided into, the they are..9 What is the function of the numerator? How do we simplify our fractions? WHO WON?...!

8 A fraction is an equal part of a whole. : Counts how many equal parts I am working with and is called the numerator. : The denominator says how many equal parts the whole has been divided into.. Let us test your knowledge by means of a few practical activities. Look at the following and answer the questions:. Colour in the figures that show halves: (a) (b) (c) (d). Colour in only the figures that show quarters: (a) (b) (c) (d) (e)

9 . Neatly colour in the figures that show sixths: (a) (b) (c) (d). Why didn t you colour in the other figure c?. What fraction is cut out in each of the following figures? i) ii) iii) iv) v) vi) vii) viii) ix) x) xi)

10 To recognise, classify and represent fractions (positive numbers) in order to describe and compare them LO.. To use tables to sort and record data LO.. In the next activity we are going to find out whether you can recognise and then record the fractions correctly. Look at the figures and then complete the table. A B C D E F G H I J K Diagram Number of equal parts Number of parts coloured in Fraction coloured in Number of parts not coloured in Fraction not coloured in E.g. A B C D E F G H I J K

11 Did you know? 9 is a proper fraction. The numerator is smaller than the denominator. is an improper fraction. The numerator is bigger than the denominator. is a mixed number. A mixed number is always bigger than and consists of a whole number () plus a fraction ( ). To calculate by means of computations that are suitable to be used in adding ordinary fractions LO... Can you still remember how to add fractions? Let us see. Work together with a friend. Take turns to say the answers. Choose any two fractions and add them. Give your answer first as an improper fraction and then as a mixed number. Ask your teacher s help if you struggle...

12 To count forwards and backwards in fractions LO.. If you are good at adding fractions, it will also help you to understand mixed numbers and improper fractions better. You will also find it easier to add and subtract fractions. Count in tenths and join the correct dots. In this way you will be able to find out which animal is hiding here. Let us count Count backwards in halves and see who or what is hiding away

13 . Work together with a friend and take turns:. Use improper fractions and: 9 a) count in quarters from to 9 b) count backwards in tenths from 0 to 0. Use mixed numbers and: a) count in tenths from 0 to b) count backwards in quarters from to To recognise and use equivalent forms LO... Look carefully at the following questions and then complete them as neatly as possible. EQUIVALENT FRACTIONS. Colour of the figure in blue:. Colour of the figure in green:. Colour of the figure in yellow:. Colour of the figure in red:. What do you notice?.... Complete: Did you know? We call fractions that are equal in size, equivalent fractions. The word equivalent means the same as. Thus the fractions are equal.

14 Do you remember? unit The following activity will prepare you for the addition and subtraction of fractions. Use your knowledge of equivalent fractions and answer the following. Where you are in doubt, use the diagram above

15 Did you know? We can form equivalent fractions by multiplying the numerator and denominator by the same number: ; 9 ; If you divide the numerator and denominator of any fraction by the same number, you will also get equivalent fractions. ;. If you are able to correctly apply the rules that we have just discussed, you will never find it difficult to add or subtract fractions. Apply the rules and complete the following: Let us look for some more equivalent fractions. Try to find the boot that will complete each pair below. Connect them and colour them in the same colour. e.g

16 Did you know? The Egyptians only used the fraction and other fractions with as a numerator. Some of their fractions looked like this: 0 To describe and illustrate different ways of writing in different cultures LO.. Look carefully at the following ways of writing given above. How would you write equivalent fractions for the following if you were an Egyptian? BRAIN TEASER! + looked like this: How would the Egyptians have written the following? a)... b) 0... c)... d)...

17 To recognise and use equivalent forms LO... Play a game Let us test your ability to find an equivalent fraction for another given fraction. Divide a folio sheet into twentieths. Play with a friend. Choose one of the following by closing your eyes, then letting your pencil point to one of these sections Then colour in this fraction on your page. Take turns. The one whose page is coloured in first, wins! CHECKLIST Before we go any further, it is important for you to check whether you understand everything that we have done so far and whether you are able to apply it correctly. Mark the following with a tick in the applicable box. If you are uncertain about any section, mark the no box and ask your teacher to help you. (That means that you are only allowed to indicate yes if you are quite sure you understand and know how to do it!) Time for self-assessment I did well in the competition. (LO.) Tick the appropriate block: YES NO I could fill in the table at Act.. correctly. (LO.)

18 I can explain the following concepts: * proper fraction * improper fraction * mixed number * equivalent fraction I can count forwards and backwards in fractions. (LO.) I know how to form equivalent fractions. (LO.) I can write fractions like the Egyptians. (LO.) I could play the game at Act... (LO.) To be able to do mental arithmetic LO.9 By now you know how important it is to calculate an answer very quickly. Write down the answers only and then we will see how well you have done in this mental arithmetic test Complete: I got... correct! 0

19 To recognise and classify ordinary fractions in order to compare them LO.. RELATIONSHIP SIGNS (< ; > ; ). Look at the diagram on p. 0 again. Compare the following fractions and then fill in <, > or Compare the following fractions and draw a circle around the one that is the greatest in each of the following:. ;. ;. ; 0 9. ;. ;. ; 0 Class discussion HOW can we determine the answers for no. and if we don t have a diagram to help us? In the following activity you will see how important your knowledge of equivalent fractions is. Once you have mastered it, you will find that it is child s play to compare the fractions with each other. Use the rule as determined during your class discussion and fill in >, < or

20 . Now use your knowledge and fill in >, < or To calculate by selecting and using operations LO... Split up into groups of three. See if you know how to solve the problems.. Gizelle and her twin brother, Donovan, receive pocket money every month. Gizelle saves two sixths of her pocket money. Donovan saves four ninths of his. Who saves most if they get the same amount of pocket money?

21 . Mom likes making pancakes. She gives Jake and his friends three quarters to eat. Then Mom makes the same number of pancakes. She sends four fifths of the pancakes to school for Dimitri and his friends to enjoy. Who got the most pancakes from Mom?. Vusi and Sipho wrote the same test. Vusi answered four sevenths of the questions correctly. Sipho had five eighths right. Who did better in the test?

22 . Two identical taxis transport passengers between Johannesburg and Pretoria. The one taxi is two thirds full, while the other one is three quarters full. Which taxi transports the most passengers? GROUP ASSESSMENT Assess your work on a scale of - by drawing a circle around the appropriate number: CRITERIA SCALE All group members participated in the activities. Members of the group listened to each other. Group members helped and encouraged each other in the group. Group members kept to the assignment. Each one had a turn to speak. The group s work was done neatly. The answers were calculated correctly.

23 . Each group now has the opportunity to share their solutions to the problems with the rest of the class.. Have a class discussion on the best method to solve this kind of problem. Arrange the following fractions from biggest to smallest: ; ; ; SIMPLIFYING Did you know? In order to write a fraction in its simplest form we divide the numerator and denominator by the same number. The value of the fraction does not change because we are actually dividing the fraction by. E.g. 0 and To simplify common fractions LO... Now that you know how to simplify a fraction, see whether you can complete the following table: Fraction by Simplified E.g

24 ROUNDING OFF Let us round off to the nearest whole number. Look carefully at 0 the number line: Can you see that 0 is nearer to than to? The answer is thus. If I have to round off 0 to the nearest whole number, my answer will be because 0 is much closer to than to. To use a series of techniques to do calculations LO.0.. In the previous modules you often rounded off whole numbers. Now we are going to round off mixed numbers to the nearest whole number. Connect the number in column A to the correct answer in column B. A Number B Rounded off to the nearest whole number E.g

25 Time for self-assessment Tick the appropriate column: I did well in my mental test. (LO.9) I can fill in relationship signs correctly. (LO.) I can simplify fractions correctly. (LO.) I can round off fractions correctly to the nearest whole number. (LO.0) BRAIN TEASER! In how many different ways can you colour in ( ) of this square?... To calculate through selection and use of suitable computations LO... In the following number of activities we are going to use all the knowledge that you have acquired. Let us begin! ADDITION:. Fill in the missing numbers on the number line: Now answer the following questions: a) +... b) +... c) +... d) +...

26 . Let us calculate +. Work through the following methods with a friend: a) I use a number line to help me. I know My answer is thus or b) I must calculate +. It is easier for me to draw the sum: 9 + c) I calculate + in this way: I convert the quarter to eighths: Thus: 9 + d) According to you, which method is the easiest?... e) Which method is the quickest?...

27 f) Use the method at (c) to calculate:

28 To calculate through selection and the use of suitable computations To recognise and use equivalent forms of fractions To write number sentences in order to describe a problem situation LO.. LO.. LO.. Split up into groups of three. Work through the following problems and see if you can find solutions: a) A farmer transports his fruit to the market by lorry. On arrival he discovers the following: one quarter of the bananas, one eighth of the apples and three eighths of the pears have become spoiled. Which fraction of the fruit could not be off-loaded to be sold at the market? b) The learners of the Khayelitsha Primary School decided to add some colour to the informal settlement nearby. They painted two fifths of the shacks yellow. Later three tenths of the remaining shacks were painted blue. i) What fraction of all the shacks was painted?

29 ii) What fraction still had to be painted? iii) Which colour would you paint them and why? c. Mrs Johnny decided to start a soup kitchen in her area. i) If she gives and seven ninths of the pea soup, and and two thirds of the bean soup to less privileged people on a certain day, what fraction of the soup is eaten altogether on that specific day? ii) What is your favourite kind of soup?

30 d. It takes and a half hours to fly from Cape Town to Johannesburg. A flight from Johannesburg to London takes 9 and three quarters of an hour. How long will it take you altogether to fly to London if you depart from Cape Town? Give your answer as a mixed number. e. Mrs Zuma makes delicious fruit juices to give to the learners at school during break. She mixes and three quarters of orange juice with and a half litre of pineapple juice. What is the difference between these two quantities? f. Mrs Sonn helps her friend to bake cakes for the learners. She buys kg of sugar and uses and a third of this quantity. How many kilograms of sugar are left?. Your teacher will now ask you to explain one of the above-mentioned problems to the rest of the class.. Compare your solutions to those of other groups in the class.. Discuss the differences and / or similarities between the different methods that were used.

31 Did you know? Here are two ways in which we can add mixed numbers: a) first add the whole numbers and then the fractions: b) or convert the mixed numbers to improper fractions, e.g. + en Thus: + + To determine the equivalence and validity of different representations of the same problem through comparison and discussion LO... Work with a friend. Work through the solutions given above and explain the difference between the two methods to one another.. Which method do you prefer?... Why?

32 SUBTRACTION Did you also know? When we want to subtract fractions from each other we must first make the denominators the same, e.g. ( ) When we subtract mixed numbers from each other, it is easier to change them first to improper fractions: e.g. ( ) To calculate through selection and by using suitable computations To describe observed relationships and rules in your own words LO.. LO.. Look carefully at the following problems and explain to a friend what your approach would be in calculating the various answers

33 . 0. Now calculate the answers.. Check your answers with your friend. To calculate through selection and by using suitable computations LO.. To determine, through comparison and discussion, the equivalence and validity of different representations of the same problem LO.. To describe observed relationships and rules in your own words LO.. Sometimes one can use a pie graph to represent fractions. A survey was done of the extramural activities of a Grade class and the results were represented by using a pie graph. See whether you can read it, and then complete the table. Activity Netball Tennis Rugby Choir Chess Swimming Fraction It is important for us to be able to interpret the pie graph, otherwise we will not be able to make meaningful deductions from it and solve the problems. Work through the following problem with a friend and find out how many methods can be used to solve it.

34 If there are 0 learners in the class, how many learners play netball?. The question is 0 of 0 I can draw it: of 0 0 of 0 will be. I must calculate 0 of 0. I find out what 0 is by dividing 0 by If one tenth is, then tenths will be. There are thus pupils who play netball.. Girls 0 of 0 Thus: (0 0). 0 of 0 0 of 0

35 . What would you say is the rule for these of sums? Which of these methods do you prefer?... Why? Look again at the methods at. and.. What do you notice? Can you say how many learners in Act.. participate in: rugby?... swimming?... Now calculate:. of. of. of 0. of 000 m. litre 000 litre k 000 g kg 000 kg t 000 mm m 000 m km

36 To calculate through selection and by using suitable computations LO... Let us see whether you are able to successfully apply the knowledge that you have acquired up to now. Work on your own and calculate:. Five learners share litre of cool drink equally. How many m does each learner get?. Zane lives km from the school. He has already covered of the distance. How far has he walked? (Give your answer in m).. The mass of a bag of flour is kg. Mom needs 0 of this to bake a cake. How much flour will she use?. Joy buys m of material but only uses of this to make a dress. What fraction of material is left over?... How much material is left over? Time for self assessment I can add fractions correctly. (LO.) Tick the appropriate block: I can subtract fractions correctly. (LO.) I can correctly calculate a fraction of an amount. (LO.)

37 To use tables and graphs to arrange and record data LO. To draw and interpret a graph LO... The following activity is for your portfolio. Look carefully at the assessment table before you begin your teacher will allocate a code from - for the different sections. Challenge!. Carry out a survey in your class and find out how many learners read which magazines. Write you information down in a table, e.g. Magazine You Time SA Runner Fair Lady Number of learners Now show the information by means of a pie diagram (see p. 9).

38 . Answer the following questions: a) Which magazine is the most popular?... b) Which magazine is read the least?... c) Which magazine is YOUR favourite?... Why? ASSESSMENT: MAGAZINES CRITERIA The assignment was done neatly. The assignment was handed in on time. All the instructions were carried out. The circle diagram was completed correctly. The answers were correct. To do mental arithmetic LO.9 Let us see if you can improve on the result of your previous mental test! of m... mm of m... mm..... (9 ) Double: 09: Halve: 0: of of of Did you improve?...

39 BRAIN TEASER! Who am I? a) If you subtract me from, you will get... b) If you cut me into sixths, you will have... c) If you double me, you will get... d) If you halve me, you will get... e) If you calculate of me, you will get... To solve problems in context LO.. Split up into groups of three. You will be given the necessary paper to work on. Remember to discuss the solutions amongst yourselves beforehand and then you can do them neatly on paper.. Mrs Mvusi buys metres of material. If she wants to make each one of her four children a bright cushion for his or her room, how many metres of material can she use for each one? (All the cushions are of the same size.) Give each answer as a fraction Mr Muruvan buys 9 pieces of dry sausage that he wants to share equally among himself, his wife and their five children. What fraction of the sausage will each one get?

40 . Grandpa Ben would like to divide R0 equally among his four grandchildren. What is the amount each one will get? CHECKLIST As a group, complete the following list. Mark the applicable space.. needs attention. very good. reasonably good. excellent CRITERIA Each one had a turn to speak. We listened to one another s opinions. We worked neatly. Give the following checklist and your solutions to another group for assessment. Mark the applicable space. YES NO. The group s work was neat.. All the questions were answered.. Al the answers were correct.

41 To solve problems in context LO.. Let us do some more division. Work with a friend. Look carefully at the following:. Mom buys chocolates and must divide them equally between children: I intend doing it this way: Mom Dad I think she should do it this way: a) Who is right? Mom or Dad?... b) Why? Dad buys equally long pieces of biltong. He wants to divide the biltong equally among Mom, two children and himself. Zita thinks she can do it like this: Mom Dad Ben Me Mom Dad Ben Me a) Did she divide it fairly?... b) What fraction does each person get?... c) Write your answer as an improper fraction:...

42 . Sketch the solutions to the following: a) Divide eight fizzers equally between five children b) Divide five milk tarts equally between guests Calculate the following: a) Divide R,00 equally between four children b) Divide pies equally between eight learners

43 To use a series of techniques to do calculations LO.0.. It is important for us to know how to key in ordinary fractions on a pocket calculator. This will help us find the answers to problems in no time. Did you know? If you want to show a fraction on the calculator, e.g. you must key in.. How does the calculator show the following fractions? Write down what you key in. a)... b)... c)... d)... e)... BRAIN TEASER! There are seven cows in a camp. Isolate them by means of three fences so that each cow is in its own small camp. Indicate with a coloured pencil crayon where you would put the fences.

44 . Fill in the missing words: 0. Look at the fraction. is called the... and the... (). Fill in the missing numbers: (). Complete the following number patterns:. ;... ; ; ;... (). 0 ; ; ;... ;... (). Fill in: < ; > or :. 9. of of (). Calculate:. of. of 9 (). Calculate:. d ()

45 (). Gina wants to divide berries equally among people. How many berries must each person get? (). of Sam s fishing rod is 0,m long. How long is the whole rod? () 9. What must you key in if you want to show 9 on the calculator?... () TOTAL: 0