Maths – Suggested task.
This task allows you to assess the children’s current understanding of fractions, enabling you to
evaluate what pupils need to experience next in order to develop a broader and deeper
understanding. This task also looks at a ‘whole’ which is divided into pieces which are not the same
size. The more that children can physically play with different concepts of the ‘whole’ and ‘parts’
(including parts which look different but are equivalent) the deeper their conceptual understanding
of fractions will be.
Throughout the activities, encourage pupils to devise their own questions by saying ‘What questions
do you have about this so far? Is there anything else you are wondering about?’ This will help you
assess against the reasoning section of the ‘Working Mathematically Document’
You will need:
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Sets of tangrams (at least one between two, see attached pdf- cut up in sets, plus a few
extra sets)
Sugar paper
Marker pens
Getting Started:
You may wish to share the background story of tangrams to the children, if they haven’t seen them
before.
http://www.youtube.com/watch?v=X5mc-dkYLfI
This is a simple story of the tangram – all the characters in the video are made from the tangram
pieces.
Familiarisation
Allow them to explore and play with the shapes:
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What do you notice about the shapes?
Which shapes can you name?
Can you sort the shapes? Can you sort them in another way?
Can they make any of the characters/ objects/ shapes from the story?
Can you make a different picture with your tangram? Can you explain to your friend how to
make the picture (using shape and positional language)?
Warning: most children will try to make the large square out of the seven shapes, some will be
successful, others not so. Please limit the time for this and provide an image of the solution so that
all the children know how the shapes fit together to make the square. This prevents children
becoming overly frustrated with making the ‘whole’ rather than thinking about fractional parts.
Introduction:
Ask the children to find the small triangle and the small square. What is the relationship between
these two shapes? Allow time for discussion, encourage the children to rotate the shapes and place
them on top of each other etc.
The small triangle is …… (half) …….. of the small square
Or
The small square is ….. (double)…… the small triangle
If the small square is worth ….. (4), what is the small triangle worth? (2)
If the small triangle is worth 6, what is the value of the small square?
Ask the children to work in pairs to order the shapes.
Assessment point:
Watch the children carefully to see how they do it – do the children put shapes on top of each other,
rotating them etc. Possibly ask some children to explain their methods and reasoning focusing on
the parallelogram.
Task 1: Understanding fractions
1) The children need to find out the fractional value of each shape in the tangram if the small square
is worth 1, so the small triangle is worth …(half) - model this for the children if needed.
2) They are then going to order them on a number line (border roll stuck on to sugar paper, or a line
drawn on sugar paper) and write the fractional values for each of the shapes and explain how they
found out. Model with the small square and small triangle.
The small square is worth 1.
What is the value of the other shapes?
Place your shapes on the number line and write their
values.
How did you work it out? Explain your thinking.
What about the original large square (all seven
pieces), what would that be worth?
Independent/ paired/ small group learning: Depending on how confident the children are (some
children may stay with the original modelled task above)
The large triangle is now worth 1.
What is the value of the other shapes?
Place your shapes on the number line and write their
values.
How did you work it out? Explain your thinking, how
do you know?
Think about the original large square (all seven
pieces), what would that be worth?
1
The small square is now worth .
4
What is the value of the other shapes?
Place your shapes on the number line and write their
values.
How did you work it out? Explain your thinking, how
do you know?
Think about the original large square (all seven
pieces), what would that be worth?
1
The parallelogram is now worth .
8
What is the value of the other shapes?
Place your shapes on the number line and write their
values.
How did you work it out? Explain your thinking, how
did you work it out?
What about the original large square (all seven
pieces), what can you say about that?
Encouraging further exploration questions:
Can
If the parallelogram is 1/8 – can you find any combinations of shapes that are equivalent to 1/8?
Show me how you knew.
What fraction of the whole square would 2 parallelograms be?
Can you find a shape that also represents ¼? Are there any more?
Going deeper and broader ideas
If you need something more challenging start by telling the children the value of the original large
square, for example, is 2 ½ . What are the values of the other shapes?
Alternatively, there are many different forms of tangram available on the internet. Allow the
children to explore the fractional possibilities in the more complex ones (some have very intriguing
names such as the Tormentor, the Cross Breaker) – attached.
Task 2: Finding fractional quantities
In each case, ask the children to calculate with the fractions they have been working on, for
example. They can add this to sugar paper/number lines diagrams – stressing that you want to know
how they have worked it out.
If you have been using the small square = 1
Task then…
Imagine that the Medium triangle sells for £2.
What is the value of all the other shapes, including the original large square?
If you have been using the large triangle = 1
Task then…
Imagine that the large triangle sells for £8.
How much would I have to pay for the large square?
If you have been using the small square = ¼
Task then…
Imagine the original large square sells for £1.60p.
What is the value of each shape?
Extension suitable for all:
Ask the children to give a value to one of the shapes. Calculate the total for the large square. Then
challenge a friend to find the value of the shapes given their total for the large square.
Assessment points:
Working Mathematically
This activity provides opportunities to assess a number of strands within ‘Working Mathematically.’
Can the children explain their thinking and the steps they took to solve the puzzles? Some children
might be able to show you how they solved it, but may need support in writing this down.
NOTE: it doesn’t have to be written sentence explanations, drawings/images etc. are acceptable –
allow them to explain it in their own way, some children may only be able to verbally explain –
using the tangram and number line to support them (try to capture these conversations and support
them in written/diagrammatic explanation’s)
Including:
Does the pupil make suggestions of ways to tackle the problems? Possible evidence for - Ideas,
questions and lines of enquiry
Did the pupil raise further questions themselves or as a part of a group that they wanted to explore?
Possible evidence for - Ideas, questions and lines of enquiry/ Reasoning
How securely was the pupil able to make connections to prior learning? E.g. did they begin to refine
predictions based on knowledge of former tasks during the sequence? Possible evidence for - Ideas,
questions and lines of enquiry/ Reasoning
How effectively was the pupil able to justify responses made? How well do they support their
justification using the tangram shapes to convince others? How accurately are they able to use
mathematical language when explaining? Possible evidence for – Reasoning / Represent and
communicate
Is the pupil beginning to check for accuracy? Possible evidence for - Represent and communicate
Understanding of fractions
Write the fractions correctly? Possible evidence for F1 – recognise, find, write, name and count
fractions.
Order them ? Possible evidence for F3 – comparing and ordering fractions
Do they put the shapes along the number line in approximately proportionally accurate places? If
you ask them to, can they (this is 0 and this is 1, where do they go?)? Possible evidence for F3 –
comparing and ordering fractions
How do the children manage shapes that have the same value but look different? Can they explain
it? Do they use the language of equivalence/equal? Possible evidence for F2 – equivalent fractions
Can they think of another way of saying 1/2, do they know the equivalents? Do they know 2/4? Can
they take it further? Do they know another way, and another etc…. Possible evidence for F2 –
equivalent fractions
How are pupils using the size of other pieces to discover the size of the one they are working on? Are
the children seeing the relationship of the sizes in the pieces? Possible evidence for F3 – comparing
and ordering fractions
How do they get to the value of the large square? Possible evidence for F4 – add/subtract fractions
How do they calculate the value of the shapes when they are given a monetary value? Possible
evidence for F10 solve problems with fractions and decimals and/or F1 recognise, find, write, name
and count fractions, particularly with reference to year 2 – write simple fractions (e.g. ½ of 6 = 3)
and year 3 - find fractions of a discrete set, but do consider year 4 (non-unit fractions where the
answer is a whole number).
Strand
EYFS 40-60+
months
ELG 11 they
solve problems,
including
doubling,
halving and
sharing
F1
Recognise,
find, write,
name and
count fractions
National
curriculum
reference Year
1
1F1a
Recognise, find
and name a half
as one of two
equal parts of
an object,
shape or
quantity
National
curriculum
reference Year
2
2F1a
Recognise, find,
name and write
fractions 1/3,
1/4, 2/4 and ¾
of a length,
shape, set of
objects or
quantity
1F1b
Recognise, find
and name a
quarter as one
of four equal
parts of an
object, shape or
quantity
2F1b
Write simple
fractions [e.g.:
½ of 6 = 3]
F2
Equivalent
fractions
F3
2F2
Recognise the
equivalence of
2/4 and 1/2
National curriculum
reference Year 3
National curriculum
reference Year 4
3F1a
Count up and down in
tenths; recognise that
tenths arise from
dividing
an object into 10
equal parts and in
dividing one-digit
numbers or quantities
by 10
3F1b
Recognise, find and
write
fractions of a discrete
set
of objects: unit
fractions
and non-unit fractions
with small
denominators
3F1c
Recognise and use
fractions as numbers:
unit fractions and
non-unit fractions with
small
denominators
3F2
Recognise and show,
using diagrams,
equivalent fractions
with small
denominators
4F1
Count up and down in
hundredths; recognise
that hundredths arise
when dividing an
object by a hundred
and dividing tenths by
ten
4F2
Recognise and show,
using diagrams,
families of common
equivalent fractions
National curriculum
reference Year 5
National curriculum
reference Year 6
5F2a
Recognise mixed
numbers and improper
fractions and convert
from one form to the
other; write
mathematical
statements >1 as a
mixed number [e.g.:
2/5 + 4/5 = 6/5= 1 1/5]
5F2b
Identify name and
6F2
Use common factors
to simplify fractions;
use common multiples
to express fractions in
the same
denomination
Comparing
and ordering
fractions [KS2]
write equivalent
fractions of a given
fraction, represented
visually, including
tenths and hundredths
3F3
Compare and order
unit fractions and
fractions with the
same denominators
F4
Add / subtract
fractions [KS2]
F10
Solve
problems with
fractions and
decimals [KS2]
3F4
Add and subtract
fractions with the
same denominator
within one whole
[e.g.: 5/7 + 1/7= 6/7]
4F4
Add and subtract
fractions with the
same denominator
3F10
Solve problems that
involve 3F1–3F4
4F10a
Solve problems
involving increasingly
harder fractions to
calculate quantities
and fractions to divide
quantities, including
non-unit fractions
where the answer is a
whole number
4F10b
Solve simple
measure and money
problems involving
fractions and
decimals to two
decimal places
5F3
Compare and order
fractions whose
denominators are all
multiples of the same
number
5F4
Add and subtract
fractions with the
same denominator
and denominators that
are multiples of the
same number
6F3
Compare and order
fractions, including
fractions >1
5F10
Solve problems
involving
numbers up to three
decimal places
6F10
Solve problems which
require answers to be
rounded to specified
degrees of accuracy
6F4
Add and subtract
fractions with different
denominators and
mixed numbers, using
the concept of
equivalent fractions
Answers:
Small square = 1
Small triangle = ½
Parallelogram = 1
Medium triangle = 1
Large triangle = 2
Large triangle = 1
Small square = ½ or 2/4 or …
Parallelogram = ½ or 2/4 or …
Medium Triangle = ½ or 2/4 or …
Small triangle = ¼
Large Square = 3 ¾
Small square = ¼ or 2/8, ….
Small triangle = 1/8
Parallelogram = ¼
Medium triangle = ¼
Large triangle = ½
Large square = 2
The parallelogram is worth 1/8. What is the value of the large square?
If you need something more challenging start by telling the children the value of the original large
square, for example 2 ½ .