Longfield Primary School

Longfield Primary SchoolMaths Workshop for Year 6 Parents and Carers9 December 2015Mrs Claire Searle Maths Leader

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

What do Year 6 pupils need to know and do with fractions?What do Year 6 pupils need to know and do with fractions ? - continued

Numerators and DenominatorsA 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.

DENOMINATORThis 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.

NUMERATORThis number shows how many of those pieces there are. In the fraction there are 3 pieces out of the total of 4.

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.

Simplifying fractionsSome 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 16/36These can be divided by 2 and 4. The HCF is 4, so the answer is 4/9

What fraction is each part of the whole? What other fractions can you make?What equivalences can you find?Exploring equivalence using a tangramEquivalent 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, tenthsFraction stripsUse your strips of paper to:Make some different fractionstrips.

What fractions can you find that are equivalent to 1/3?

Which is larger, 5/8 or ?Fraction stripsHow can fraction strips help children make sense of problems like this?

See Primary Magazine Essentials maths to share link click on calculation Issues 23 and 24 cover structures for addition and subtraction https://www.ncetm.org.uk/resources/38453

Comparing and ordering fractionsPutting 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:3/41/39/104/51

15/85/16 1/3 4/5 9/10 1 15/8 5/16

Addition and SubtractionAddition and subtraction need to be done with common denominators.Addition and subtractionAdd 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 = 1/122/3 + 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 23/24Multiplication 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

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 =15/32DivisionChildren need to be able to divide proper fractions by whole numbers,Eg 2 = 1/8 .

To do this, turn the whole number into a fraction : 2/1Then turn the fraction upside down: 1/2Then 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 Decimal fractionsFinding decimal fractions

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 Converting decimals to fractionsFirst 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 4with 2 places Count the Now divide bothafter the decimal decimal places;numbers by thepoint 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

Equivalences between fractions, decimals and percentagesConverting 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%4/53/40.558/1080%34%0.45Finding percentages of whole numbersTo find 10% of any number, divide by 10. 10% of 86 = 8.6To find 5% of any number, divide by 10 and then halve that number. 5% of 86 - halve 8.6 to give 4.3To find 15% of any number, add 10% and 5% together. So for 86, add 8.6 and 4.3 = 12.9To 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

Example SATs questionsExample SATs questions 2016 SATs20% of 3500 =5/7 3/7 =1/3 x 1/695% of 360 =11 x 2 =1 - 1/3 =2/3 + 5/6 =5/7 2 =On Saturday Ella read 1/3 of her book. On Sunday she read the other 80 pages to finish the book. How many pages are there in Ellas book?

Fraction terminology

Numerator - the number on the top of a fraction showing the number of equal parts in the fraction eg 3/4Denominator - 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 2/3Improper fraction the larger numerator indicates that the parts come from more than one whole (also called top-heavy fractions) eg 9/5Mixed 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 3/6Common 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.

Ratio and Proportion

Ratio and ProportionRatio compares the size of quantities.

Proportion compares the relationship between 2 sets of quantities.Ratios show how much bigger one thing is than another.Two things are in proportion when a change in one causes a related change in the other.

A fruit bowl with a ratio of 6 apples to 2 bananas can be writtenlike this 6:2This can be divided by 2 and simplified to 3:1 meaning that for every 3 apples there is 1 banana.

How many apples would there be if there were 6 bananas in the fruit bowl?

Tomato soup!

6 tomatoes make 1 bowl of soup.How would you write the ratio?6:1How many tomatoes do you need to make 2 bowls of soup? 3 bowls of soup? 6 bowls of soup?

What operation did you use to find the answers?

How many bowls of soup could you make with 48 tomatoes?What about with 120 tomatoes?6 million tomatoes?

What operation did you use this time?

The tomatoes and the bowls of soup are in direct proportion. The ratio between them is always the same. 1218368201 million!multiplying by 6Dividing by 6

Proportion

What proportion of the stick is blue?Proportion means fraction or percentage.6/10 or 3/5 or 60% of the stick is blue.For every 6 blue cubes there are 4 yellow cubes.If the stick had 9 blue cubes, how many yellow cubes would there be?If the stick had 60 blue cubes how many yellow cubes would there be?What is the ratio of blue cubes to yellow cubes?3:2Fish Pie

Omar makes fish pie for 3 people.How many grams of fish should he use?

Mary used 2kg of potato to make a fish pie.How many people did her fish pie feed?How much butter was in her fish pie?How much fish was in her fish pie?

From the Nrich websiteExample SATs questions

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

Ratio and Proportionhttp://www.bbc.co.uk/education/topics/zsq7hyc

http://www.11plusforparents.co.uk/Maths/ratio1.html

http://nrich.maths.org/8959

http://resources.woodlands-junior.kent.sch.uk/maths/fractions/