Maths Workshop for Year 6 Parents and Carers 12 January 2015
Mrs Claire Searle Maths Leader
Slide 2
What is a fraction? Talk to someone else what do you
think?
Slide 3
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.
Slide 4
What do Year 6 pupils need to know and do with fractions?
Slide 5
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.
Slide 6
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.
Slide 7
Slide 8
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
Slide 9
Slide 10
What fraction is each part of the whole? What other fractions
can you make? What equivalences can you find? Exploring equivalence
using a tangram
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 ?
Slide 13
Fraction strips How can fraction strips help children make
sense of problems like this?
Slide 14
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
Slide 15
Addition and Subtraction Addition and subtraction need to be
done with common denominators.
Slide 16
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
Slide 17
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
Slide 18
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
Slide 19
Division Children 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 : 2/1 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
Slide 20
Decimal fractions Finding 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
Slide 21
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
Slide 22
Slide 23
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
Slide 24
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
Slide 25
Example SATs questions
Slide 26
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.
Slide 27
Ratio and Proportion
Slide 28
Ratio 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 written like this 6:2
This 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?
Slide 29
Tomato soup! 6 tomatoes make 1 bowl of soup. How would you
write the ratio? 6:1 How 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. 12 18 36 8 20 1 million! multiplying by 6 Dividing by 6
Slide 30
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? 3:2
Slide 31
Fish 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?
Slide 32
From the Nrich website
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Example SATs questions
Slide 34
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 Proportion
http://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/
