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Maths Workshop for Year 5 Parents and Carers Fractions, Decimals and Percentages 9 February 2015 Mrs Claire Searle Maths Leader

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What is a fraction? Talk to someone else what do you think?

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Why do children find fractions difficult? Difficulties with fractions often stem from the fact that they are different from natural numbers in that they are relative rather than a fixed amount - the same fraction might refer to different quantities and different fractions may be equivalent (Nunes, 2006). Would you rather have one quarter of 20 or half of 5? The fact that a half is the bigger fraction does not necessarily mean that the amount you end up with will be bigger. The question should always be, 'fraction of what?'; 'what is the whole?'. Fractions can refer to objects, quantities or shapes, thus extending their complexity.

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What do Year 5 pupils need to know and do with fractions, decimals and percentages?

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Numerators and Denominators A fraction is made up of 2 numbers. The top number is called the NUMERATOR and the bottom number is called the DENOMINATOR. In the fraction , 3 is the numerator and 4 is the denominator. DENOMINATOR This number shows how many equal pieces something has been divided into. In the fraction , 4 is the denominator showing that there are 4 equal pieces making up the whole. NUMERATOR This number shows how many of those pieces there are. In the fraction there are 3 pieces out of the total of 4.

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Numerators and Denominators For example, if a pizza is cut into 4 equal slices there will be 4 pieces on the plate. This makes a fraction of 4/4 (1 whole). If I eat one of those pieces, ( ) then there are 3 pieces left. ( ). The denominator stays the same, there are still 4 parts that made up the whole pizza, but the numerator has changed, as there are only 3 parts of the pizza left.

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Simplifying fractions Some fractions can be made simpler by finding the highest common factor. (The highest number that will go into both parts of the fraction.) Eg for 8/10 both the numerator and denominator can be divided by 2 to give 4/5. 16/24 Both the numerator and denominator can be divided by 2, 4 and 8. The highest common factor (HCF) is 8, so this fraction can be simplified to give 2/3. Try this! Simplify 16/36 These can be divided by 2 and 4. The HCF is 4, so the answer is 4/9

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What fraction is each part of the whole? What other fractions can you make? What equivalences can you find? Exploring equivalence using a tangram

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Equivalent fractions = 2/4 = 3/6 = 4/8 = 5/10 = 6/12 =... = 2/8 = 3/12 = 4/16 = 5/20 =... 1/3 = 2/6 = 3/9 = 4/12 = 5/15 =... Make fraction strips showing quarters, thirds, sixths, eighths, tenths

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Fraction strips Use your strips of paper to: Make some different fraction strips. What fractions can you find that are equivalent to 1/3? Which is larger, 5/8 or ?

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Fraction strips How can fraction strips help children make sense of problems like this?

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Comparing and ordering fractions Putting fractions in order of size can be difficult. Its easiest to convert them (temporarily) to fractions with the same denominator if you are unsure. Try putting these fractions in order: 3/4 1/3 9/10 4/5 1 15/8 5/16 1/3 4/5 9/10 1 15/8 5/16

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Addition and Subtraction Addition and subtraction need to be done with common denominators.

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Addition and subtraction Add or subtract these fractions. Remember to convert them into fractions with the same denominator first. Look for the smallest number that the denominators will all go into. Eg for 3/7 + 2/5 the smallest number that both 7 and 5 will go into is 35. For 3/7, there are 5 lots of 7 in 35, so multiply both parts of 3/7 by 5 = 15/35. For 2/5, there are 7 lots of 5 in 35, so multiply both parts of 2/5 by 7 = 14/35. Now you can add the fractions easily. 15/35 + 14/35 = 29/35. + = 2/4 + = 5/4 = 1 - 2/3 = 9/12 8/12 = 1/12 2/3 + 1/6 = 4/6 + 1/6 = 5/69/10 3/5 = 9/10 6/10 = 3/10 3/8 + 5/6 + = 9/24 + 20/24 + 18/24 = 47/24 = 1 23/24

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Multiplication by a whole number x 3 = To multiply a fraction by a whole number, first convert the whole number to an improper fraction. x 3/1 = Now multiply both numerators together and then both denominators giving 3/2. Finally divide the numerator by the denominator, giving a mixed fraction 1 So the answer to x 3 is 1 . You can also think of it as + + also giving 1 Try this: 2/3 x 6 = 2/3 x 6/1 = 12/3 = 4

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Multiplication by a fraction x = It is useful to imagine the multiplication sign means of so this calculation can be expressed as what is of ? and what is of ? Multiply the numerators together and the denominators together. x = 3/8 This answer is the same for both calculations above, as multiplications can always be done either way round and will give the same answer. Try this: of 5/8 = 15/32 This is a Year 6 objective but some children might be doing this in Year 5.

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Division Children need to be able to divide proper fractions by whole numbers, Eg 2 = 1/8. This is also a Year 6 objective To do this, turn the whole number into a fraction : 2/1 Then turn the fraction upside down: 1/2 Then multiply it by the first fraction x 1/2 = 1/8 2 = The denominator has been doubled, so the value has been halved. Try this! 1/3 4 = ? 1/3 4/1 1/3 x = 1/12

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Decimals In Year 5, children need to be able to round decimals with 2 decimal places (eg 17.36) to the nearest whole number and to 1 decimal place. To round to the nearest whole number, pupils need to decide whether the decimal fraction is larger or smaller than 0.5. Smaller than 0.5 rounds down. 0.5 or above rounds up. So 17.36 rounds down to 17 as 0.36 is less than 0.5 To round to one decimal place, pupils need to decide whether the hundredths part of the decimal is smaller than 0.05, (round down) or 0.05 and above (round up). So 17.36 rounds up to 17.4 as 0.06 is more than 0.05 Your turn! Try rounding 37.47 to the nearest whole number, and to 1 decimal place. 37 37.5

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Decimals Pupils in Year 5 also need to be able to read, write, order and compare numbers with up to 3 decimal places. This means they need to have a secure understanding of place value. So 6324.325 on a place value chart would be: Th H T U. 1 / 10 1 / 100 1 / 1000 6 3 2 4. 3 2 5 Put these numbers in order. 3.052 3.5 3.25 0. 352 32.5 0.035 0.035 0.352 3.052 3.25 3.5 32.5

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Decimal fractions In Year 5, pupils need to be able to read and write decimal numbers as fractions Eg 0.71 = 71 / 100 0.8 = 80 / 100 or 8 / 10 They also need to be able to express fractions with a denominator of 10, 100 and 1000 as decimal numbers 9 / 10 = 0.9 37 / 100 = 0.37 Try these! Express as a fraction or decimal number. 0.86 0.3 0.423 9 / 10 4 / 100 67 / 1000 86 / 100 3 / 10 and 30 / 100 423 / 1000 0.9 0.04 0.067

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Decimal fractions Finding harder decimal fractions (Year 6) What is 1/5 as a decimal? To convert a fraction to a decimal, simply divide the denominator (bottom part) into the numerator (top part). So to find 1/5 as a decimal, divide 1 by 5 which gives 0.2 1/5 = 1 5 = 0.2 = 3 4 = 0.75 Try this! What is 4/5 as a decimal? 4/5 = 4 5 = 0.8

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Converting decimals to fractions First make the fractions denominator (its bottom part) 10, 100, 1000 and so on for every digit after the decimal point. 0.75 75 3 Decimal number 100 4 with 2 places Count the Now divide both after the decimal decimal places;numbers by the point if there is 1 digit, thehighest number denominator is 10,that goes into both - if there are 2 then it25. is 100. The numerator is the number after. the decimal point. Have a go! Change 0.6 into a fraction. 0.6 6 3 10 5

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Percentages In Year 5, pupils need to recognise the per cent symbol (%) and understand that per cent relates to number of parts per one hundred. Your turn! Shade the dots activity

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Equivalences between fractions, decimals and percentages Converting between decimals and percentages is easy if the decimal number is below 1. Percentage just means out of 100. So 0.8 is 80% which is 8 tenths or 80 hundredths. 0.65 is 65% which is 65 hundredths. Children need to be sure about place value in decimals to be able to do this conversion easily. They also need to be able to know and use equivalences between fractions decimals and percentages. Which of these fractions are the same? 70% 4/5 3/40.55 8/10 80% 34% 0.45

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Finding percentages of whole numbers To find 10% of any number, divide by 10. 10% of 86 = 8.6 To find 5% of any number, divide by 10 and then halve that number. 5% of 86 - halve 8.6 to give 4.3 To find 15% of any number, add 10% and 5% together. So for 86, add 8.6 and 4.3 = 12.9 To find 1%, divide by 100. 1% of 18 is 0.18 Using these it is possible to find any percentage of a number. See how quickly you can do these: 30% of 60 Price reduced by 20%! Was 15, now ______ 15% of 20 25% off! Now 60! What was the price before 7% of 50 it was reduced? 110% of 75

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Example SATs questions

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Fraction terminology Numerator - the number on the top of a fraction showing the number of equal parts in the fraction eg 3/4 Denominator - the number on the bottom of the fraction showing the total number of equal parts in the whole eg 3/4 Proper fraction the number of parts examined, shown on the top, is less than the whole eg 2/3 Improper fraction the larger numerator indicates that the parts come from more than one whole (also called top-heavy fractions) eg 9/5 Mixed fraction has a whole number and a fraction eg 8 Equivalent fraction the same fraction written in different ways so each one gives the same answer in a calculation, even though they look different eg and 3/6 Common denominator a number that can be divided by the denominators of all of the fractions eg 2/3 5/8 7/12 all the denominators divide into 24 so 2/3 becomes 16/24, 5/8 becomes 15/24, 7/12 becomes 14/24. So 24 is the lowest common denominator as this is the smallest number that 3, 8 and 12 will divide into.

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Useful websites Fractions http://www.bbc.co.uk/skillswise/topic/fractions http://www.bbc.co.uk/skillswise/factsheet/ma17frac-l1-f-fraction-wall http://www.bbc.co.uk/bitesize/ks2/maths/number/fractions/read/1/ http://primarygamesarena.com/fractions http://resources.woodlands-junior.kent.sch.uk/maths/fractions/