Download Fractions, Decimals and Percentages

Fractions, Decimals and Percentages
Halving of sets of objects begins as early as
EYFS and Year 1.
It is vital that children know halves and quarters
must be equal in size.
In Year 2 children begin to use ½ and ¼ and find
these fractions of amounts
½ of £12 = £6
In Year 3 we begin to use the terms denominator
and numerator in writing proper fractions.
We identify fractions of shapes and compare and
order them.
In year 4 we read and write fractions, ordering
them and recognising equivalent fractions.
Children also find fractions of amounts.
3/5 of 25Kg = 15Kg
By Year 5 children simplify fractions by cancelling.
They relate fractions to decimals and
percentages, and find percentages of amounts.
In Year 6 we ask children to find common factors
in numerators and denominators. They use these
to simplify, order and make mixed numbers.
Children in Year 6 convert between F, D and P
and find proportions of amounts with all three
forms. A secure knowledge of their tables is
vital, as it helps them to see the links quickly.
Fractions, decimals and percentages are all parts
of a whole, and the concept can prove
confusing.
These next slides will explain the progression of
knowledge and how we can help children to
understand at each stage.
A huge focus is on what fractions, decimals and
percentages look and feel like.
A fraction is a part of a whole
Slice a pizza, and you will have fractions:

1/
2
1/
4
3/
8
(One-Half) (One-Quarter) (Three-Eighths)
The top number tells how many slices you have
The bottom number tells how many slices the
pizza was cut into.


We call the top number the Numerator, it is
the number of parts you have.
We call the bottom number the Denominator, it
is the number of parts the whole is divided
into.
Numerator Denominator You just have to
remember those names! (If you forget just
think "Down"-ominator)

Some fractions may look different, but are
really the same, for example:
 4/8
=
(Four-Eighths)
2/
4
(Two-Quarters)
=
1/
2
(One-Half)
It is usually best to show an answer using the
simplest fraction ( 1/2 in this case ). That is
called Simplifying the Fraction.

You can add fractions easily if the bottom
number (the denominator) is the same:
 1/4
+
1/
4
=
2/
4
=
1/
2

(One-Quarter) (One-Quarter) (Two-Quarters) (One-Half)

Another example:
 5/8
+
1/
8
=
6/
8
=
3/
4

But what if the denominators (the bottom
numbers) are not the same? As in this example:
 3/8

1/
+
= ?
4
You must somehow make the denominators the
same.

In this case it is easy, because we know that 1/4
is the same as 2/8 :
 3/8
+
2/
8
=
5/
8




In the number 327:
the "7" is in the Units position, meaning just 7
(or 7 "1"s),
the "2" is in the Tens position meaning 2 tens
(or twenty),
and the "3" is in the Hundreds position, meaning
3 hundreds



As we move right, each position is 10 times
smaller. From Hundreds, to Tens, to Units
But what if we continue past Units?
What is 10 times smaller than Units?
1/
10
ths (Tenths) are!


But we must first write a decimal point,
so we know exactly where the Units position is:
"three hundred twenty seven and four tenths“
but we usually just say "three hundred and
twenty seven point four"


The decimal point is the most important part
of a Decimal Number. It is exactly to the right
of the Units position. Without it, we would be
lost ... and not know what each position meant.
Now we can continue with smaller and smaller
values, from tenths, to hundredths, and so on,
like in this example:


When you say "Percent" you are really saying
"per 100"
So 50% means 50 per 100
(50% of this box is green)
And 25% means 25 per 100
(25% of this box is green)




Because "Percent" means "per 100" you should
think "this should always be divided by 100"
So 75% really means 75/100
And 100% is 100/100, or exactly 1 (100% of any
number is just the number, unchanged)
And 200% is 200/100, or exactly 2 (200% of any
number is twice the number)






Example:
100% of 80 is
Example:
50% of 80 is
100/
100
50/
100
× 80 = 80
× 80 = 40
Example:
5% of 80 is 5/100 × 80 = 4
Decimals, Fractions and Percentages are just
different ways of showing the same value:




A Half can be written...
As a fraction: 1/2
As a decimal: 0.5
As a percentage: 50%




A Quarter can be written...
As a fraction: 1/4
As a decimal: 0.25
As a percentage: 25%


Method 1
Try dividing both the top and bottom of the
fraction until you can't go any further (try
dividing by 2,3,5,7,... etc).
Example: Simplify the fraction 24/108 :
÷2
÷2
÷3
24
12
6
2
108
54
27
9


Method 2
Divide both the top and bottom of the fraction
by the Greatest Common Factor, (you have to
work it out first!).


Example: Simplify the fraction 8/12 :
1. The largest number that goes exactly into
both 8 and 12 is 4, so the Greatest Common
Factor is 4.
2. Divide both top and bottom by 4:
8
12
÷4
2
3
One of the most common SATs questions is
finding fractions of amounts, such as 1/5 of £20 =
As 1/5 is one of five equal parts, all we do is
divide £20 by 5, which equals £4.
4/5 of £50 =
Let’s find 1/5 of £50 = £10
Then x by 4 (for the 4 parts) = £40
As percent means ‘out of a hundred’ we can find
1% by dividing by 100, or 10% by dividing by 10.
30% of 18Kg =
10% of 18Kg is 1.8Kg, so 30% is...
1.8Kg x 3 = 5.4Kg
http://www.teachingideas.co.uk/maths/conten
ts_fractions.htm
http://www.primaryresources.co.uk/maths/ma
thsB6.htm
http://www.mathsisfun.com/numbers/index.ht
ml
I would like to discuss reasoning, problem solving
and the importance of vocabulary in future
sessions.
Any other ‘hot’ maths topics?