Common fractions with different denominators and numerators

COMMON FRACTIONS WITH DIFFERENT DENOMINATORS AND NUMERATORS Activity 1: To recognise common fractions with different denominators and numerators [LO 1.3] When we break whole things into equal parts, we obtain fractions. Fractions are parts of wholes. 1. Read the following and fill in any missing number of parts: Number of equal parts into which the whole is broken Name of fraction 2 equal parts Halves …….equal parts Thirds 4 equal parts Quarters 5 equal parts Fifths …….equal parts Sixths 7 equal parts Sevenths 8 equal parts Eighths 9 equal parts Ninths …….equal parts Tenths

2. Name the parts or COMMON FRACTIONS into which each bar has been divided: Example:

It has been divided into quarters. 2.1

It has been divided into 2.2

It has been divided into 2.3

It has been divided into 2.4

It has been divided into 2.5

It has been divided into 2.6

It has been divided into TEST YOUR SKILL (Exercises 1 and 2 above) 1. 1.1 Divide the circle into two halves:

1.2 Divide it into halves another way:

1.3 In how many different ways can a circle be divided in half? 2. 2.1 Divide the rectangle into 3 thirds

2.2 Divide it into thirds another way:

2.3 How many equal parts are there if something has been divided into thirds? 3. How many equal parts are there in each of the following diagrams and what are the parts called?

3.1 parts; called

3.2 parts; called 4. Now shade in one half of 3.1 on the previous page, and one third of 3.2. Which is bigger: one half or one third? 5. Now look at the two bars below. The top bar shows because there are equal parts.

The bar below it shows because there are equal parts. 3. HANDS ON! INDIVIDUAL WORK: RECOGNISING AND REPRESENTING NUMERATORS The work on this page is for cutting out and folding. In this module you have a separate page containing shapes. Cut out all the shapes and follow the instructions below: 3.1 Cut out the triangle on your extra page. Fold it in half. Now open it out. Draw dotted lines on the fold. The dotted lines divide the triangle into two equal parts, or halves. Colour in one half. Now paste your cutout on top of the triangle printed below. Name the part that you coloured in.

3.2 Cut out the circle on your extra copy. Fold it in half. Fold it in half again. Now open out the circle. Draw dotted lines on the folds. The dotted lines should divide the circle into four equal parts, quarters. Shade in three of them. Now paste your cutout on top of the circle printed below. Name the part that you coloured in.

3.3 Has this circle been divided into quarters? Your answer: 3.4 Cut out the rectangle. Fold it to make thirds. Now open it out. Draw dotted lines on the folds. The dotted lines should divide the rectangle into thirds. Shade in two of them. Do the same with the second rectangle, but try to fold it to make sixths. Also shade in two of them. Now paste your cutout on top of the rectangles printed below. Name the parts that you coloured in. 3.5 Cut out the bar. Fold it to make eighths. Now open it out. Draw dotted lines on the folds. The dotted lines should divide the bar into eight equal parts. Check that this is correct. Shade in two of them. Do the same with the second bar but fold it to make quarters. Also shade in two of them. Now paste your cutout on top of the bars printed below. Name the parts that you coloured in. 3.6 Now look at the bars, and use the signs: < and  to complete the following on the page in your module: Two-eighths ___________two quarters Three-eighths ___________one-quarter One-eighth ___________one-quarter Five-eighths ___________three-quarters Six-eighths ___________two-quarters Three-eighths ___________two-quarters SHAPES TO CUT OUT

Activity 2: To recognise and describe reciprocal relationship, equivalence of division and fractions, and the properties of whole numbers [LO 1.12] What are fractions? We have said fractions are equal parts of a whole. Fractions are numbers. Twenty-five is a number; half is also a number. 25 is not a 2 and a 5! 25 is twenty and five. Similarly we must think of a half as a number. It does not consist of a 1 and a 2; it is a half, a number. All the bits of 12 size 12{ { {1} over {2} } } {} form a number. We learnt that twenty-five could be written in words or with digits: 25. Fractions can also be written in words or with digits: half or 12 size 12{ { {1} over {2} } } {}. What is a half? We take a whole and divide it into two equal parts. We could take an apple and divide it equally between two girls: 12 =half 12 size 12{ { {1} over {2} } } {} The line in the middle could mean  so 1  2 Half or 12 size 12{ { {1} over {2} } } {} means 1  2 When we write fractions as numbers, the digit below tells us into how many parts the whole has been divided. The top digit tells us how many of those parts we are using. 1 2 size 12{ { {1} over {2} } } {} How many of those parts are being used (Numerator) How many parts the whole is divided into (Denominator)

1. Each of the following bars represents one whole. 1.1 This bar has been divided into fifths. a) Draw coloured lines on it to show tenths:

Shade 310 size 12{ { {3} over {"10"} } } {} of it. 1.2 This bar shows twelfths. a) Draw coloured lines on it to show quarters.

b) Shade 34 size 12{ { {3} over {4} } } {} of it. 1.3 This bar shows fourteenths. a) Draw coloured lines on it to show sevenths.

b) Shade 47 size 12{ { {4} over {7} } } {} of it. Activity 3: To solve problems involving equal sharing with remainders [LO 1.8] To recognise and use equivalent forms of common fractions [LO 1.5] To recognise and represent common fractions in order to describe and compare them in writing and diagram form [LO 1.3

GROUP WORK 1. Read the following little story, then complete the questions and instructions about it. You may work in a group or with a friend if your educator agrees. When the bell rang for break, Khanyi and Reyhana ran to their favourite sunny corner of the playground. They sat down and opened their lunch boxes. “Oh my!” said Khanyi, “I’ve got six Marie biscuits today! I can’t eat six biscuits! I tell you what, Reyhana, let’s share our lunches equally.” “That’s a good idea,” said Reyhana “I’ve got those bits of dried fruit. You know, they mash up the dried fruit, roll it in sugar and cut it into bite size. My mother has given me nine pieces!” Just then two of their friends ran up and asked if they might join them. “Of course!” said Reyhana. “We’re going to share our lunches equally. This will be fun. What have you got?” Jill sat down and opened her box. “I’ve got two of those cheeses that come in a round box,” she said. “You know, they are triangles of cheese done up in silver paper.” Themba said, “I think my mother was in a hurry today! She cut up an apple into eight pieces and gave them to me for my lunch.” “That’s good,” said Khanyi, “There are four of us, so each of us can have two pieces of your apple. Now let’s share my six biscuits.” Questions and instructions concerning the story. There were four girls. Colour in how much biscuit ONE girl received.

1.2 How much biscuit did each girl receive? 1.3 Khanyi said each girl could have two pieces of apple. Discuss with a friend or group: how much of the whole apple did each girl receive? Now write your answer. 1.4 There were nine pieces of sugared fruit. How many whole pieces did each girl receive? 1.5 How many pieces of dried fruit were left? Make a drawing to show how the girls would share this equally. 1.6 Altogether, how much dried fruit did each girl receive? 1.7 There were two triangular cheeses and four girls. Discuss with a friend or group how the girls would share these equally and draw in dotted lines on the diagrams below to show how they did it.

1.8 What fraction of one cheese did each girl receive? 1.9 What fraction of all the cheese (two cheeses) did each girl receive? Just then the bell rang for the end of break. When they were settled in the classroom, their educator said, “Today we are going to consider ‘Equal Sharing’ and you may draw how to share things equally.” Of course, our four friends found the lesson very easy and their educator was pleased with them. She wondered how they were able to do the work so quickly and correctly. Only after the lesson did they explain how they had spent their break-time! TEST YOUR SKILLS: FRACTIONS IN DIAGRAMMATIC FORM; EQUAL SHARING [LO 1.3, 1.5, 1.8] See if you can complete the work that the educator gave her class: Share 2 Marie biscuits equally amongst 5 learners. Draw lines on the circles below to show how you would do this and then write down how much each learner received altogether.

Answer: _____________________ Share 5 Provita biscuits equally between 2 girls. Draw lines on the rectangles below to show how they were shared equally between the 2 girls. Then write down how much each girl received altogether. Answer:________________________ Three learners want to share a tin of Coke equally. They each have a paper cup. How much of the Coke will each learner receive? Draw dotted lines on the can below to show how much each learner will get. Then write down what part of the Coke each learner will receive. Answer: ……………………………………………. 4. Share 2 loaves of bread equally amongst 3 workers. How much will each worker receive? (You may draw if it helps.) 5. Share 7 sausage rolls equally amongst 6 boys. How much sausage roll will each boy receive? (You may draw if it helps.) 6. Share 8 sandwiches equally amongst 3 boys. How much will each boy receive? (You may draw if it helps.) 7. Share 8 bananas equally amongst 7 boys. How much will each boy receive? (You may draw if it helps.) 8. Share 17 slices of polony equally amongst 8 boys. How much will each boy receive? (You may use the drawing if it helps.)

Answer: ………………………………….

Assessment Learning outcomes(LOs) LO 1 Numbers, Operations and RelationshipsThe learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems. Assessment standards(ASs) We know this when the learner: 1.1 counts forwards and backwards in a variety of intervals; 1.3 recognises and represents the following numbers in order to describe and compare them: common fractions with different denominators, common fractions in diagrammatic form, decimal fractions and multiples of single-digit numbers; 1.3.2 common fractions with different denominators, including halves, thirds, quarters, fifths, sixths, sevenths and eighths; 1.3.3 common fractions in diagrammatic form; 1.3.4 decimal fractions of the form 0,5; 1,5 and 2,5; etc., in the context of measurement; 1.3.6 multiples of single-digit numbers to at least 100; 1.5 recognises and uses equivalent forms of the numbers including common fractions and decimal fractions; 1.5.1 common fractions with denominators that are multiples of each other; 1.5.2 decimal fractions of the form 0,5; 1,5 and 2,5, etc., in the context of measurement; 1.7 solves problems that involve comparing two quantities of different kinds (rate); 1.7.1 comparing two or more quantities of the same kind (ratio); 1.8 estimates and calculates by selecting and using operations appropriate to solving problems that involve addition of common fractions, multiplication of at least whole 2-digit by 2-digit numbers, division of at least whole 3-digit by 1-digit numbers and equal sharing with remainders; 1.8.3 addition of common fractions in context; 1.8.6 equal sharing with remainders; 1.9 performs mental calculations involving: 1.9.2 multiplication of whole numbers to at least 10 x 10; 1.12 recognises, describes and uses:, and 1.12.1 the reciprocal relationship between multiplication and division (e.g. if 5 x 3 = 15 then 15 ÷ 3 = 5 and 15 ÷ 5 = 3; 1.12.2 the equivalence of division and fractions (e.g. 1 ÷ 8 = ⅛); 1.12.3 the commutative, associative and distributive properties with whole numbers.