Fractions, decimals, percentages, ratio and proportion
Year 5 Spring 5
Recognise the equivalence between the decimal and fraction forms of halves, quarters, tenths and hundredths
Previous learning
Core for Year 5
Extension
Use, read and begin to write these words:
Use, read and begin to write these words:
Use, read and write these words:
fraction, numerator, denominator, decimal, equivalent, …
fraction, numerator, denominator, decimal, equivalent, …
fraction, numerator, denominator, decimal, equivalent, …
Recognise equivalent decimal and fraction forms of halves,
fifths and tenths.
Recognise equivalent decimal and fraction forms of halves,
quarters, tenths and hundredths.
Recognise equivalent decimal and fraction forms of halves,
quarters, eighths, tenths, hundredths and thousandths.
On a line with 10 divisions, or a counting stick from 0 to 1,
label the tenths in decimal and fraction form, then the fifths
and then the halves.
• Identify equivalent points representing halves, quarters and
tenths on a line with 100 divisions.
Explore equivalences of fractions and decimals by converting
fractions to decimals using division and a calculator, e.g.
• Use a calculator to enter
Repeat with
5
10
1
2
• Use a calculator to enter
as 1 ÷ 2.
50
100
as 5 ÷ 10, then
as 50 ÷ 100.
Repeat with
125
1000
1
8
as 1 ÷ 8.
as 125 ÷ 1000.
0.5
Recognise that
1
2
is equivalent to
5
10
0.125
Note the decimal in the display. What do you notice?
Note the decimal in the display. What do you notice?
Repeat with 1 ÷ 4 and 25 ÷ 100, and 3 ÷ 4 and 75 ÷ 100.
Repeat with 3 ÷ 8 and 375 ÷ 1000, 5 ÷ 8 and 625 ÷ 1000,
and 7 ÷ 8 and 875 ÷ 1000.
or 0.5.
Recognise that :
–
10
100
=
1
10
= 0.1
50
100
=
5
10
= 0.5 =
1
2
20
100
=
2
10
25
100
=
1
4
= 0.2, etc.
= 0.25
• Now enter
75
100
=
3
4
= 0.75
Respond to question such as:
• Write four fifths as a decimal number.
• Which of these means
• Circle the fraction that is the same as nought point five.
1
2
1
3
1
4
3
4
A 70
7
10
B 7
2
8
,
25
100
250
1000
and
. What do you notice?
125
1000
=
1
8
= 0.125
250
1000
=
2
8
=
1
4
= 0.25, etc.
Respond to question such as:
• Write
?
C 0.7
D 0.07?
3
4
as a decimal.
• Write 0.23 as a fraction.
• Write the fraction which is equal to 0.8.
• 0.4 is the same as:
A four
,
Recognise that :
–
Respond to question such as:
1
4
B four tenths
C four hundredths
D one quarter
• Write
7
100
as a decimal.
• Which number represents the shaded part of the figure?
A 2.8
© 1 | Year 5 | Spring TS5 | Fractions, decimals, percentages, ratio and proportion
B 0.5
C 0.2
D 0.02
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Use equivalence to help order fractions, e.g.
72
100
, 0.76 and
Previous learning
3
4
Core for Year 5
Extension
Use equivalence to order fractions, e.g. change halves,
quarters and tenths to hundredths to compare them.
Use equivalent fractions to compare two fractions, e.g.
• Which is larger: 0.76 or
• Which is smaller: 0.5 or
3
4
3
5
? Explain how you know.
Reduce a fraction to an equivalent fraction by dividing both
numerator and denominator by the same number, e.g.
5
20
? Explain how you know.
=
5 ÷5
20 ÷ 5
=
1
4
Change a fraction to an equivalent fraction by multiplying
both numerator and denominator by the same number, e.g.
3
10
Order fractions by comparing them with one half, e.g.
• Here are four fractions.
3
4
1
8
1
3
3
5
Write each fraction in the correct box on the number line.
=
3 × 10
10 × 10
=
30
100
Compare and order simple fractions by converting them to
fractions with the same denominator, and place them on a
number line, e.g.
• Which is larger,
1
3
or
2
5
? Explain how you know.
• Mark each of the fractions
1
3
and
5
6
on the number line.
Begin to understand percentage as the number of parts in every 100 and find simple percentages of shapes
Previous learning
Core for Year 5
Extension
Use, read and begin to write:
Use, read and begin to write:
Use, read and write:
tenth, hundredth, …
percentage, per cent (%), …
percentage, per cent (%), discount, increase, decrease, …
Recognise the equivalence of tenths and hundredths, e.g.
Understand percentage as the number of parts in every 100.
Understand percentage as the number of parts in every 100.
Understand the relationship between fractions and
percentages, and know that::
Understand the relationship between fractions and
percentages, and know that:
3
10
=
30
100
.
one whole = 100%
one half = 50%
• What fraction is the small square of the large square?
How many of the small squares are in a long strip?
What fraction is the long strip of the large square.
So
10
100
of the big square is equivalent to
1
10
one quarter = 25%
one tenth = 10%
• Recognise the percentage of 100 Multilink cubes that are
red, yellow, blue, green, …
of the big square.
© 2 | Year 5 | Spring TS5 | Fractions, decimals, percentages, ratio and proportion
1
10
1
20% =
5
1
1% =
100
23
23% =
100
10% =
25% =
50% =
75% =
1
4
1
2
3
4
• Work out the percentage of the numbers 1 to 100 that are
even, are multiples of 5, have a digit 3, are greater than 40,
lie between 60 and 70, …
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Previous learning
Core for Year 5
Extension
Find fractions of shapes, e.g.
Find simple percentages of shapes, e.g.
Find percentages of shapes, e.g.
• What fraction of each shape is shaded?
• What percentage of each shape is shaded?
• What percentage of this grid is shaded?
Calculate simple percentages of whole number quantities by
using fractions, e.g.
Calculate simple percentages of whole number quantities by
using fractions, e.g.
• To find 50% of £300,
find one half of £300
• To find 50% of £300,
find one half of £300
• To find 25% of £300,
find one quarter of £300, i.e. half of one half of £300
• To find 75% of £300,
find one quarter of £300, and add it to half of £300
• To find 10% of £300,
find one tenth of £300
• To find 20% of £300,
find one tenth of £300 and double it.
Without a calculator, find percentages of quantities such as:
Without a calculator, find percentages of quantities such as:
25% of £40
50% of £30
10% of £5
25% of £800
60% of £3
30% of 3 m
10% of 2 kg
25% of 1 kg
20% of 80 cm
75% of £30
40% of 5 kg
75% of 2 litres
Using a calculator, find percentages of quantities such as:
• 24% of 525
Solve problems involving percentages such as:
Solve problems involving percentages such as:
• 70% of the children in a school have a school lunch.
What percentage do not have a school lunch?
• A coat costs £35. It has a 10% discount in a sale.
What is its sale price?
• 35% of the children in a class are boys.
What percentage are girls?
• A football team played 15 games. They won 60%.
How many games did they lose?
• A bottle holds 500 ml of juice.
A larger bottle holds 30% more juice.
How much juice does the larger bottle hold?
© 3 | Year 5 | Spring TS5 | Fractions, decimals, percentages, ratio and proportion
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Use ratio to describe relationship between two quantities, e.g. there are twice as many boys as girls
Previous learning
Core for Year 5
Extension
Use, read and begin to write these words:
Use, read and begin to write these words:
Use, read and write these words:
for every, to every, in every, out of every, …
one/two/three times as many as, …
for every, to every, in every, out of every, …
one/two/three times as many as, … proportion, …
for every, to every, in every, out of every, …
one/two/three times as many as, … ratio, proportion, …
Describe the relationship between two quantities using
statements such as:
Describe the relationship between two quantities using
statements such as:
Revise describing the relationship between two quantities
using statements such as:
• 1 out of every 3 squares is red in this pattern.
• In this bead pattern:
• In this bead pattern:
Out of every 6 squares, 2 are red.
Out of every 9 squares, 3 are red.
Out of every 12 squares, 4 are red.
• In every week I spend 5 days at school. So:
in every 2 weeks I spend 10 days at school,
in every 3 weeks I spend 15 days at school.
• For every 2 bags of crisps you buy you get 1 sticker.
For every 4 bags of crisps you get 2 stickers.
To get 3 stickers you must buy 6 bags of crisps.
To get 4 stickers you must buy 8 bags of crisps.
1 bead in every 3 beads is red,
2 beads in every 6 beads are red, …
• 2 out of every 5 beads is red, and
3 out of every 5 beads are blue, so:
2 beads in every 3 beads are blue,
4 beads in every 6 beads are blue, …
the proportion of red beads is 2⁄5;
One third of all the beads are red.
Two thirds of all the beads are blue.
There are half as many red beads as blue beads.
There are twice as many blue beads as red beads.
There is:
1 red bead to/for every 2 blue beads,
2 red beads to every 4 blue beads, …
the proportion of blue beads is 3⁄5.
• There are:
2 red beads to/for every 3 blue beads,
4 red beads to/for every 6 blue beads,…
so the ratio of red beads to blue beads is 2 : 3.
Use ratio to solve problems, e.g. adapt a recipe for 6 people to 3 people or 12 people
Previous learning
Core for Year 5
Extension
Solve simple problems involving ‘in every’ or ‘out of every’, e.g.
Solve problems involving ratio or proportion, e.g.
Solve problems direct proportion by scaling quantities up or
down, e.g.
• 1 in every 4 of these squares is red.
• 1 in every 4 of these squares is red.
• In this diagram, 2 out of every 3 squares are shaded.
Which diagram has 3 out of every 4 squares shaded?
Complete these statements.
Complete these statements.
A
B
For every red square, there are … blue squares.
… in every 8 squares are red.
C
D
The number of blue squares is … times the number of red
squares.
… in every 16 squares are red.
3 in every … squares are red.
10 in every … squares are red.
• Make a tile pattern where 1 in every 5 tiles is blue.
© 4 | Year 5 | Spring TS5 | Fractions, decimals, percentages, ratio and proportion
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Previous learning
Core for Year 5
Extension
Solve problems involving adapting recipes, e.g.
Use ratio or direct proportion to solve simple problems, e.g.
• Deirdre is going to make some lemonade.
The finished drink should be 1⁄3 lemon juice and 2⁄3 water.
Jenny puts 100 ml of lemon juice in a glass.
How much water should she put with it?
• Peanuts cost 60p for 100 grams.
What is the cost of 350 grams of peanuts?
• This is what you need to make 4 pancakes.
100 g flour
150 ml of milk
2 small eggs
What do you need to make 12 pancakes?
• Here is a recipe for pasta sauce.
300 g
120 g
75 g
tomatoes
onions
mushrooms
Jamie makes the pasta sauce using 900g of tomatoes.
What weight of onions should he use?
• Chicken must be cooked for 50 minutes for every kg.
How long does it take to cook a 3 kg chicken?
• This map has a scale of 1 cm to 6 km.
Altburn
Ridlington
Carborough
The road from Ridlington to Carborough measured on the
map is 6.6 cm long.
What is the length of the road in kilometres?
• There are 30 children, in a class.
There are 3 boys for every 2 girls.
How many boys are there?
© 5 | Year 5 | Spring TS5 | Fractions, decimals, percentages, ratio and proportion
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999