Year 3 Teaching Sequence 12 - Ordering and finding fractions of shapes and numbers (three days)
Prerequisites:
 Know doubles to double 20 by heart (see oral and mental starter bank 12)
Overview of progression:
Children fold paper in half and half again to find ¼, ½ and ¾ of shapes and see the equivalence between two quarters and one
half. They do the same with paper strips of objects to find ½, ¼, and ¾ of numbers (all multiples of 4) and then half of odd
and even numbers to 30 using strips or cubes to help. Children then move onto finding thirds and two thirds of shapes, and
one third of multiples of 3 by folding strips as for quarters.
Note that children will probably find folding the strips of objects into thirds more difficult but reminding them that each
part must have the same number of objects should help to overcome some inaccurate folding.
Watch out for children who do not realise that fractions are equal parts, and so for example divide a shape into three or
four parts, but not equal parts. This is not surprising as we use the fraction words inexactly in everyday language: “Give your
cousin the larger half!”
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y3 Maths TS12 – Aut – 3days
Objectives:
 Understand and use fraction notation
 Find ½, ¼, ¾, 1/3 and 2/3 of shapes, strips of objects and numbered strips
 Recognise equivalence between ½ and 2/4 by folding shapes and using diagrams
 Find half of odd and even numbers to 40, using notation such as 13½
Whole class
Group activities
Paired/indiv practice
Resources
Give each child a rectangular sheet of paper. Ask them
to fold it in half in a different way to their maths
partner. What’s special about each half? How do we
write one half? Fold it into four equal parts; try to do
this in a different way to your partner. What do we call
each part? How do we write one quarter? Collect in a few
differently folded sheets of paper (e.g. diagonal folds),
and quickly shade ¾ of each one. How much is shaded?
And on this one? How do you know? Show me one half of
your sheet of paper. What do you notice? Discuss how
one half is the same as two quarters.
Give chn strips of 8 objects (see resources). Fold your
strip in half. How many in each half? Now fold it in half
again, so you have four equal parts. What do we call
these? How many in each quarter? How many in two
quarters? What do you notice? Discuss how two quarters
have the same quantity as one half. How many in three
quarters? Together write sentences about fractions of
objects of the strip:
½ of 8 is 4
¼ of 8 is 2
2/4 of 8 is 4
¾ of 8 is 6.
Rpt with a strip of 16 objects, asking chn to work in pairs
to write their own sentences on their whiteboards.
Group of 4-5 children
Give each pair six strips of objects (see
resources). I’m thinking of one of your
strips. I fold it in half, and see ten
objects in each half. Which strip do you
think I’m thinking of?
I’m thinking of one of your strips. I
fold it into quarters and can see four
objects in each quarter. Which strip do
you think I'm thinking of? Fold it in
quarters to check.
Repeat with other strips.
Easier: Focus more on halves to begin
with. Ask chn to fold each strip into
quarters before describing quarters.
Harder: Also include descriptions such
as I can see 15 objects on three
quarters of the strip.
Give each pair of chn strips of
objects, which they fold in half to
find ½, ¼, 2/4, and ¾ of numbers
(all multiples of 4). They write
sentences about halves and
quarters as in the whole class
teaching.
Harder: Challenge chn also to
work in pairs to halve 10, and then
find a quarter of ten.
 A4 paper
 Activity sheets
of strips of 8
objects and 16
objects
 Activity sheet
of six strips of
objects (see
resources)
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y3 Maths TS12 – Aut – 3days
Give each child a strip of seven objects (see resources).
Fold the strip in half to find half of seven. Take
feedback about what happens. Agree that there are
three objects in each half and one split down the middle,
so 3 and a half in each half. Write ½ of 7 is 3 ½ on the
board.
Give each pair of chn 26 cubes and ask them to make a
tower. Break the tower in half to find half of 26. Agree
that half of 26 is 13 and record the on the board. What
is half of 20? And half of 6? Record
Half of 26
20
6
10
3
10 + 3 = 13
What is double 13? What is double 10? Double 3? So
double 13 is 26.
What do you think half of 27 might be? Talk to your
partner. Take feedback and discuss that 27 is one more
than 26, and so there would be one more cube to split
between the two groups giving and answer of 13½. Also
discuss that half of 20 is 10 and they agreed earlier that
half of 7 is 3½, so half of 27 is 13½.
Half of 27
Group of 4-5 children
Give each pair strips of objects from
the activity sheet (see resources). I’m
thinking of one of your strips. I fold it
in half, and see five objects in each
half. Which strip do you think I’m
thinking of?
I’m thinking of one of your strips. I
fold it in half, and see five and a half
objects in each half. Which strip do you
think I’m thinking of?
Repeat with other strips.
Easier: Use the first six strips from
the easier version of the Activity
sheet.
Chn work in pairs to draw lines to
show how to cut strips of objects
in half. They then use cubes to
help them to find half of each
number from 20 to 30.
Discuss what they have found out
about halving odd and even
numbers in the plenary.
Easier: Chn work in pairs to cut
strips of objects in half (see
resources).
Harder: Chn work in pairs to find
of half of each number from 20
to 40. They use cubes to help
where necessary.
 Strips of seven
objects (see
resources)
 Strip of 15
objects (see
resources)
 Activity sheets
of strips of
objects
20
7
10
3½
10 + 3½ = 13½
Work with a partner to find half of 15. Use your cubes
to help. Agree that half of 14 is 7, and if they were to
cut the remaining cube in half, they would have 7½ cubes
in each half.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y3 Maths TS12 – Aut – 3days
Show a strip of 15 objects on the board (see resources).
If you were to cut this strip of objects in half, where
would you cut it? Ask a child to come up and draw a line
to show you. Is there the same amount on each side of
the line?
Give each child a rectangular sheet of paper. I want you
to fold it into three equal parts; this is a bit more
difficult than folding into two or four! Share examples
of chn’s folded rectangles (some may have folded
horizontally, and some vertically), say that we call each
part a third and stress the importance of each part
being of equal size. Write 1/3 on each of three parts of
one rectangle. Draw a square on your whiteboards, and
divide it into thirds. Repeat with a circle, if necessary
showing how to divide like a cake, and finally a regular
hexagon. Share different ways of doing this.
Sketch oblongs, squares, circles and hexagons on the
board, and shade one or two thirds. Ask chn how much is
shaded in each case, showing how to record 2/3.
Ask chn to draw two smiley faces on each third of their
paper rectangles. How many smiley faces altogether?
What is 1/3 of 6? What number sentence can we write?
Draw another two smiley faces on each third. How many
faces altogether? What fraction number sentence could
we write?
Group of 4-5 children
Give each pair six strips of objects (see
resources). I’m thinking of one of your
strips. I fold it into thirds, and see
three objects in each third. Which
strip do you think I’m thinking of?
I’m thinking of one of your strips. I
fold it into thirds and can see four
objects in each third. Which strip do
you think I'm thinking of? Fold it in
thirds to check.
Repeat with other strips.
Easier: Ask chn to fold each strip into
thirds before describing thirds.
Harder: Also include descriptions such
as I can see 10 objects on two thirds of
the strip.
Give each pair of chn strips of
paper, which they fold into thirds.
They draw the same amount of
simple objects on each third and
write sentences about them as in
the whole class teaching.
Easier: Draw one, then two, then
three… five objects on each third
of the strips.
Harder: After drawing five strips
ask chn to discuss what might be
one third of 30 and 300!
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 A4 paper
 Strips of paper
 Activity sheet
of six strips of
objects (see
resources)
Y3 Maths TS12 – Aut – 3days