Transcript Longfield Primary School

Maths Workshop for Year 5
Parents and Carers
Fractions, Decimals and Percentages
9 February 2015
Mrs 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 5 pupils need to know and do with
fractions, decimals and percentages?
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 ¾, 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 ¾, 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
¾ 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, ( ¼) then there are 3 pieces
left. ( ¾ ). 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 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
Exploring equivalence using a tangram
What fraction is each part of
the whole?
What other fractions can
you make?
What equivalences can you
find?
Equivalent fractions
½ = 2/4 = 3/6 = 4/8 = 5/10 = 6/12 = ...
¼ = 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
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 ¾?
Fraction strips
How can fraction strips help children make sense of problems like this?
Comparing and ordering fractions
Putting fractions in order of size can be difficult. It’s easiest to convert them
(temporarily) to fractions with the same denominator if you are unsure.
Try putting these fractions in order:
3/4
9/10
1/3
4/5
15/8
5/16
1/3
¾
4/5
9/10
1¼
5/16
1¼
15/8
Addition and Subtraction
Addition and subtraction need to be done with common denominators.
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.
½+¾=
2/4 + ¾ = 5/4 = 1 ¼
2/3 + 1/6 =
4/6 + 1/6 = 5/6
¾ - 2/3 =
9/12 – 8/12 = 1/12
9/10 – 3/5 =
9/10 – 6/10 = 3/10
3/8 + 5/6 + ¾ =
9/24 + 20/24 + 18/24 = 47/24 = 1 23/24
Multiplication by a whole number
½x3=
To multiply a fraction by a whole number, first convert the whole number to
an improper fraction. ½ 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 ½
•So the answer to ½ x 3 is 1 ½ .
•You can also think of it as ½ + ½ + ½ also giving 1 ½
Try this: 2/3 x 6 =
2/3 x 6/1 = 12/3 = 4
Multiplication by a fraction
This is a Year 6 objective but some children might be doing this in Year 5.
½x¾=
•It is useful to imagine the multiplication sign means ‘of’ so this
calculation can be expressed as ‘what is ½ of ¾?’ and ‘what is ¾ of
½?’
• Multiply the numerators together and the denominators together.
½ x ¾ = 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:
¾ of 5/8 = 15/32
Division
Children need to be able to divide proper fractions by whole numbers,
Eg ¼ ÷ 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
¼ 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 ¼ = 1/12
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!
place.
Try rounding 37.47 to the nearest whole number, and to 1 decimal
37
37.5
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
6 3 2 4 . 3
1/
100
2
1/
1000
5
Put these numbers in order.
3.052
3.5
0.035
0.352
3.25
3.052
0. 352
3.25
32.5
3.5
0.035
32.5
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
86/
100
0.3
3/
10
0.423
and
30/
100
423/
1000
9/
10
0.9
4/
100
67/
1000
0.04
0.067
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
¾ = 3 ÷ 4 = 0.75
Try this!
What is 4/5 as a decimal?
4/5 = 4 ÷ 5 = 0.8
Converting decimals to fractions
First make the fraction’s denominator (its bottom part) 10, 100, 1000 and so
on for every digit after the decimal point.
0.75
Decimal number
with 2 places
after the decimal
point
75
3
100
4
Count the
decimal places;
if there is 1 digit, the
denominator is 10,
if there are 2 then it
is 100. The numerator
is the number after
the decimal point.
Now divide both
numbers by the
highest number
that goes into both 25.
.
Have a go!
Change 0.6 into a
fraction.
0.6
6
10
3
5
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
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
80%
3/4
0.55
0.45
8/10
34%
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
15% of 20
7% of 50
110% of 75
Price reduced by 20%! Was £15, now ______
25% off! Now £60! What was the price before
it was reduced?
Example SATs questions
Example SATs questions
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 ½
•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 ½ 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.
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/