Fractions, ratio and proportion
Year 5 Autumn 5
Revise finding fractions of shapes
Previous learning
Core for Year 5
Use, read and begin to write these words:
Use, read and begin to write these words:
part, fraction, whole, equivalent, …
proper fraction (e.g.
3
4
Extension
Use, read and write these words:
fraction, part, whole, equivalent, …. proper fraction (e.g.
), mixed number (e.g.
3
1
4
)…
Understand the terms numerator and denominator.
improper fraction (e.g.
7
4
), mixed number (e.g.
3
1
4
3
4
),
)…
fraction, part, whole, equivalent, cancel, ….
numerator, denominator, …
proper fraction, improper fraction, mixed number,…
Understand the terms numerator and denominator.
2
5
5
8
The top number is the numerator. It shows that 2 parts of the
shape are shaded blue.
The top number is the numerator. It shows that 5 parts of the
shape are shaded blue.
The bottom number is the denominator. It shows that the
shape is divided into 5 equal parts.
The bottom number is the denominator. It shows that the
shape is divided into 8 equal parts.
Find fractions of shapes, paper strips, and sets of objects, e.g.
Revise finding fractions of shapes, e.g.
Revise finding fractions of shapes, e.g.
• Find eighths or sixths of a variety of paper shapes by
folding them in different ways into equal parts.
• What fraction of this shape is shaded?
• What fraction of this shape is shaded?
Write your answer as simply as possible.
• What fraction of this shape is shaded?
• Shade
• Shade
1
2
1
5
of this shape.
• Shade one third of the diagram.
of this shape.
• Shade more triangles so that
• Shade more squares so that
7
8
2
3
of the hexagon is shaded.
•This rectangle has 13 identical shaded squares inside it.
of the shape is shaded.
• If
3
8
of a shape is shaded, what fraction is not shaded?
What fraction of the rectangle is shaded?
© 1 | Year 5 | Autumn TS5 | Fractions, ratio and proportion
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Recognise the equivalence between quarters and eighths, thirds and sixths, fifths and tenths
Previous learning
Core for Year 5
Extension
Recognise simple equivalences between halves, quarters
and eighths, or thirds and sixths.
Recognise the equivalence between quarters and eights,
thirds and sixths, and fifth and tenths.
Recognise the equivalence between sixteenths, eighths,
quarters and halves, and hundredths, tenths and halves.
Use folded strips or diagrams such as a fraction wall to
identify equivalent fractions.
Use a fraction wall to identify equivalent fractions, e.g.
Use a fraction wall with 16 intervals to identify equivalences
between sixteenths, eighths, quarters and halves.
Use a number line with 100 intervals to identify equivalences
between hundredths, tenths, quarters and halves.
Recognise that :
Identify pairs of fractions with a total of 1, e.g.
• If
1
6
and
–
–
.
2
of a shape is shaded, what fraction is not shaded?
3
Recognise from diagrams that:
1
2
1
4
5
6
is equivalent to
is equivalent to
2
4
2
8
or
3
6
and
or
3
4
4
8
is equivalent to
6
8
Identify fractions with a total of 1, e.g.
• Think about the fraction
1
8
.
How many of them add to make 1?
10
100
=
1
10
50
100
=
5
10
=
1
2
20
100
=
2
10
25
100
=
1
4
75
100
3
4
=
Recognise simple equivalent fractions.
Reduce a fraction to its simplest form.
Recognise from diagrams that:
Recognise patterns in equivalent fractions, e.g. for one half,
one third, one quarter, one fifth and one tenth.
–
–
–
–
1
2
1
4
1
3
2
3
is equivalent to
is equivalent to
is equivalent to
is equivalent to
2
4
2
8
2
6
4
6
or
3
6
and
or
or
4
8
or
3
4
is equivalent to
Recognise that a fraction can be:
6
8
• reduced to an equivalent fraction by dividing both
numerator and denominator by the same number (i.e. by
cancelling), e.g.
4
12
8
12
5
20
Recognise patterns in equivalent fractions, e.g.
1
2
=
2
4
=
3
6
=
4
8
5
10
=
=
6
12
=
7
14
3
10
1
2
• What fractions are equivalent to
3
4
? To
. To
2
3
1
3
? To
1
4
.
=
4
2
4
=
8
=
1
4
=
3 × 10
10 × 10
=
30
100
3
4
=
8
?
• Write the fraction
5
20
as simply as possible.
• Write a different fraction that is equivalent to
• Fill in the missing numbers in the boxes.
1
2
5 ÷5
20 ÷ 5
Respond to questions such as:
Respond to questions such as:
• Find a fraction equivalent to
=
• changed to an equivalent fraction by multiplying both
numerator and denominator by the same number, e.g.
…
and similar patterns for one fifth and one third.
© 2 | Year 5 | Autumn TS5 | Fractions, ratio and proportion
= 0.2, etc.
4
5
.
• Fill in the missing numbers in the boxes.
1
2
=
6
2
12
=
6
1
2
=
1
24
=
6
24
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Previous learning
Core for Year 5
Extension
Use a fraction wall to compare fractions, e.g.
Use a fraction wall to compare fractions, e.g.
Use equivalent fractions to compare two fractions, e.g.
• Which fraction is bigger, three eighths or five eighths?
One half or three eighths? Three quarters or five eighths?
• Which fraction is bigger, one half or one third?
One eighth or one sixth?
• Show that
• Amy says: ‘one eighth of 40 is bigger than half of 10’.
Is she correct? Explain how you know.
• How much of each square grid is shaded? For each grid,
write ‘More than half’ or ‘Half’ or ‘Less than half.’
1
3
>
• Which is larger,
1
4
1
3
by changing them both to twelfths.
or
2
5
? Explain how you know.
• Circle the two fractions that are greater than one half.
1
8
7
8
3
8
3
4
Relate finding fractions to division and use to find simple fractions of quantities, e.g. thirds, fifths, sixths and tenths
Previous learning
Core for Year 5
Extension
Relate finding one quarter to dividing by 4, or to finding half
of one half, e.g.
Relate finding fractions to division and use division to find
simple fractions of quantities, e.g.
Relate finding fractions to division and find fractions,
including several tenths and hundredths, of quantities, e.g.
1
2
1
4
of 8 = 4
of 8 = 2
zzzz
{{{{
zz{{
{{{{
8÷2=4
•
8÷4=2
Use division to find simple fractions, e.g.
• Find
1
2
of 24 by dividing 24 by 2.
Recognise from diagrams and use relationships such as:
•
•
1
4
1
8
is half of
is half of
1
2
1
4
Use halving to find quarters, e.g.
• What is one quarter of 24? Of 60?
• One quarter of a number is 3. What is the number?
•
1
4
Understand that:
of 32 pupils like milk. How many of the pupils like milk?
© 3 | Year 5 | Autumn TS5 | Fractions, ratio and proportion
12
3
• Find
is another way of writing 12 ÷ 3;
1
5
2
5
• when 3 whole cakes are divided equally into 4, each
person gets three quarters, or 3 ÷ 4 =
3
4
;
• Find
• finding one fifth is equivalent to dividing by 5, so find
1
of 30 by working out 30 ÷ 5.
5
of
1
is
8
1
10
half of
1
4
Use halving to find halves, quarters and eighths, e.g.
• What is
1
4
of 64?
• One eighth of a number is 2. What is the number?
of 20
20 ÷ 5 = 4
of 20
4×2=8
of 90
90 ÷ 10 = 9
of 90
9 × 7 = 63
Recognise from diagrams and use relationships such as:
1
4
1
10
1
2
1
of
5
is half of
is half
1
8
1
5
is half of
is double
1
4
1
10
1
1
is half of
6
3
1
is one tenth
100
of
1
10
Find hundredths by finding one tenth of one tenth, e.g.
• What is
• What is one eighth of 64? Of 120?
of 20
3
of 90
10
1
10
7
10
Recognise from diagrams and use relationships such as:
1
1
is half of
4
2
1
is one tenth
100
2
5
3
100
of £650?
1
of £650
10
1
of £650
100
3
of £650
100
£650 ÷ 10 = £65
£65 ÷ 10 = £6.50
£6.50 × 3 = £19.50
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 such as:
Solve problems such as:
Without using a calculator, respond to questions such as:
• What is one third of 18? Of 27?
• A book has 60 pages. I have read
• What is half of this amount?
1
5
of the pages.
How many pages have I read?
• What is
• What is
• One quarter of a number is 3. What is the number?
1
3
3
4
of 27?
3
5
• Work out
• What is
2
3
• Calculate
of 24? Of 200?
• Find
• Joe has some pocket money.
He spends three-quarters of it. He has 50p left.
How much pocket money did he have?
3
10
of £40.
of 66?
3
4
of £15.
of 80 metres.
Using a calculator, respond to questions such as:
• Calculate
3
8
of 980.
Change an improper fraction to a mixed number, e.g.
7
4
Previous learning
Core for Year 5
Extension
Change an improper fraction to a mixed number, e.g.
Change an improper fraction to a mixed number, e.g.
1
2
Interpret mixed numbers, e.g. 5 .
to 1 34
change
7
4
to
3
1
4
change
.
33
8
to 4
1
8
Understand the term mixed number.
Understand the terms proper fraction, improper fraction,
mixed number.
Understand the terms vulgar fraction, proper fraction,
improper fraction, mixed number.
Use diagrams to illustrate a mixed number, e.g. 2 3 ,
10
Count along a counting stick:
Change a mixed number to an improper fraction, e.g.
recognising that this represents two wholes and three tenths.
• Change 2 3 to an improper fraction.
10
• from 0 to 5 in steps of one half;
Use diagrams to illustrate the mixed number 2 3 and
10
• from 0 to 2 1 in steps of one quarter;
recognise that this represents 23 tenths or
• from 0 to 3
Make a line from 0 to 10 to 10 showing whole, half and
quarter numbers. Count on or back along sections of the line
in steps of one half, one quarter.
4
1
3
23
.
10
in steps of one third.
Label the divisions on the stick with equivalent proper and
improper fractions and mixed numbers.
3 =
2 10
Change an improper fraction to a mixed number, e.g.
• Change
23
10
to a mixed number.
Use base 10 materials to represent a mixed number such
as 2 3 , showing that this is equivalent to 23 tenths.
2 × 10 + 3
10
=
23
10
Change an improper fraction to a mixed number, e.g.
• Change
33
8
to a mixed number.
33
8
= 33 ÷ 8 = 4
1
8
10
23
10
© 4 | Year 5 | Autumn TS5 | Fractions, ratio and proportion
= 23 ÷ 10 = 2 3
10
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Order mixed numbers on a number line
Order mixed numbers involving halves and quarters on a
number line, e.g.
Order mixed numbers on a number line, e.g.
Order mixed numbers on a number line, e.g.
Respond to questions such as:
Respond to questions such as:
Respond to questions such as:
• What number is half way between 3 and 4?
Between 2
1
2
• Draw an arrow on this number line to show 1
and 3?
3
4
.
• Here is part of a number line.
Write in the two missing numbers.
1
4
• Tell me any number between 6 and 7.
• Write the two missing numbers in this sequence.
1
4
1
2
3
4
1
1
1
2
1
• Mark each of these fractions on a line from 0 to 2.
3
4
3
4
1
2
7
4
3
2
5
4
• Write these in order, smallest first:
1
2
Use fractions to describe a proportion, e.g.
1
5
11
2
2
1
4
13
4
of the beads are yellow
Previous learning
Core for Year 5
Extension
Find fractions of shapes or sets of objects when the fraction
is several parts of a whole, including tenths, e.g.
Use fractions to describe a proportion, e.g.
Use fractions to describe a proportion, e.g.
• What fraction/proportion of £1 is 10p?
• What fraction of this
shape is shaded?
• What fraction/proportion
of the beads are blue?
• Shade three tenths of
this rectangle in different
ways.
• What fraction/proportion
of the container is filled
with water.
• Ring
7
10
of this set of
buttons.
• What fraction of these
squares is ringed?
• What fraction/proportion of 1 metre is 25 cm?
• What fraction of the
larger bag of flour is the
smaller bag?
• Here is a chocolate bar.
Tom eats 4 pieces and
Aysha eats 1 piece.
What fraction of the
chocolate bar remains?
• What fraction of these
buttons is ringed?
© 5 | Year 5 | Autumn TS5 | Fractions, ratio and proportion
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999