Lower Key Stage 2
West Sussex
Teacher Assessment
Exemplification:
End of Lower Key
Stage 2
(Non-statutory)
Mathematics
Working at expected standard
Spring 2017
© West Sussex County Council 2017
Page 1
Lower Key Stage 2
Key principles
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The non-statutory West Sussex Interim Framework is to be
used only to make a teacher assessment judgement at the
end of lower Key Stage 2, following the completion of the year
3/4 curriculum. It is not intended to be used to track progress
throughout the Key Stage. The West Sussex Interim Framework does not include full
coverage of the content of the national curriculum and focuses
on key aspects for assessment. Pupils achieving the different
standards within this interim framework will be able to
demonstrate a broader range of skills than those being
assessed. The West Sussex Interim Framework is not intended to guide
individual programmes of study, classroom practice or
methodology. Individual pieces of work should be assessed according to a
school’s assessment policy and not against this Interim
Framework. Teachers must base their teacher assessment judgement on a
broad range of evidence from across the curriculum for each pupil.
This evidence should reflect the National Curriculum aims of
fluency, reasoning and problem solving.
© West Sussex County Council 2017
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West Sussex non-statutory interim teacher assessment framework at the end of
Lower Key Stage 2 (Year 4)
Working at expected standard (EXS)
The pupil can use the following procedures or skills to solve a variety of problems.
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Recognise the place value of each digit in Th H T U numbers, within a range of contexts, including
rounding, ordering, comparing
Round decimals with one decimal place to the nearest whole number
Add/subtract numbers up to 4 digits using formal written methods, within the context of a twostep problem, deciding which operation to use and why
Estimate and use inverse operations to check answers to a calculation
Use place value knowledge and known and derived facts to multiply and divide mentally (factor
pairs)
Use mathematical reasoning to solve problems involving multiplying and adding (e.g. area and
perimeter) and including the distributive law, HTU x U, TU x U
Solve problems using an understanding of the connections between hundredths, tenths, place
value and decimal measures e.g. money and decimals to 2 decimal places
Use factors and multiples to recognise equivalent fractions and simplify where appropriate
Solve problems by making connections between fractions of a length, of a shape and as a
representation of one whole or a set of quantities
Measure and calculate using different metric units of measure in a range of contexts e.g. time,
distance, money
Use mathematical reasoning to compare and classify geometric shapes (incl. quadrilaterals and
triangles), identify and compare acute and obtuse angles and complete simple symmetric figures
in different orientations
Plot specified points and draw sides to complete a given polygon and describe movements
between positions as translations
Interpret and present discrete and continuous data using appropriate graphical methods including
bar charts and time graphs
© West Sussex County Council 2017
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Working at the expected standard: Year 4 collection
This collection demonstrates evidence that the pupil is able to meet the
statements for the “working at the expected standard” of the West Sussex
Interim end of lower Key Stage 2 framework across a range of tasks.
The tasks within the collection come from a range of curriculum
experiences including topic work, science, English and pure mathematics.
All of the pieces highlight pupil voice and the conversations had whilst the
children were working, or, after they had completed a task. All of the
thinking, calculating and representing is independent.
Purposeful tasks enable the pupil to develop fluency and see the links
between the different areas of mathematics. The teacher’s accurate use of
vocabulary during the lessons is evident, as the pupil often uses it when
discussing their mathematics.
Throughout the year the pupil has used a range of concrete resources to
develop their understanding and enable them to move to pictorial and
abstract representations.
This collection meets the requirements for ‘working at
the expected standard’ using the West Sussex lower Key
Stage 2 interim statements.
© West Sussex County Council 2017
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West Sussex End of Lower Key Stage 2 (Year 4)
Interim Assessment Framework: Maths
Key Principles
This interim assessment framework for Y4 does not include full
coverage of the content of the National Curriculum.
Pupils achieving the standard within this interim assessment
framework will be able to demonstrate a broader range of skills
than those being assessed.
Teachers should base their judgements on a broad range of
evidence that reflects the National Curriculum aims of fluency,
reasoning and communication.
Working at expected standard

The pupil can recognise the place value of each digit in Th H T
U numbers, within a range of contexts, including rounding,
ordering, comparing
 The pupil can round decimals with one decimal place to the
nearest whole number
 The pupil can add/subtract numbers up to 4 digits using
formal written methods, within the context of a two-step
problem, deciding which operation to use and why
 The pupil can estimate and use inverse operations to check
answers to a calculation
 The pupil can use place value knowledge and known and
derived facts to multiply and divide mentally (factor pairs)
 The pupil can use mathematical reasoning to solve problems
involving multiplying and adding (e.g. area and perimeter)
and including the distributive law, HTU x U, TU x U
 The pupil can solve problems using an understanding of the
connections between hundredths, tenths, place value and
decimal measures e.g. money and decimals to 2 decimal
places
 Use factors and multiples to recognise equivalent fractions
and simplify where appropriate
 The pupil can solve problems by making connections between
fractions of a length, of a shape and as a representation of
one whole or a set of quantities.
 The pupil can measure and calculate using different metric
units of measure in a range of contexts e.g. time, distance,
money
 The pupil can use mathematical reasoning to compare and
classify geometric shapes (incl. quadrilaterals and triangles),
identify and compare acute and obtuse angles and complete
simple symmetric figures in different orientations
 The pupil can plot specified points and draw sides to complete
a given polygon and describe movements between positions
as translations
 The pupil can interpret and present discrete and continuous
data using appropriate graphical methods including bar charts
and time graphs
© West Sussex County Council 2017
Page 5
WORKING AT THE EXPECTED STANDARDS (EXS)
The pupil can use the following procedures or skills to
solve a variety of problems.

Recognise the place value of each digit in
Th H
T U numbers, within a range of contexts, including
rounding, ordering, comparing

Round decimals with one decimal place to the
nearest whole number

Add/subtract numbers up to 4 digits using formal
written methods, within the context of a two-step
problem, deciding which operation to use and why
Estimate and use inverse operations to check
answers to a calculation
Use place value knowledge and known and derived
facts to multiply and divide mentally (factor pairs)
Use mathematical reasoning to solve problems
involving multiplying and adding (e.g. area and
perimeter) and including the distributive law, HTU x
U, TU x U
Solve problems using an understanding of the
connections between hundredths, tenths, place value
and decimal measures e.g. money and decimals to 2
decimal places
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Use factors and multiples to recognise equivalent
fractions and simplify where appropriate

Solve problems by making connections between
fractions of a length, of a shape and as a
representation of one whole or a set of quantities
EVIDENCE
(Tick the box each time a piece of evidence relating
to the statement is seen)
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Measure and calculate using different metric units of
measure in a range of contexts e.g. time, distance,
money

Use mathematical reasoning to compare and classify
geometric shapes (incl. quadrilateral triangles),
identify and compare acute and obtuse angles and
complete simple symmetric figures in different
orientations

Plot specified points and draw sides to complete a
given polygon and describe movements between
positions as translations

Interpret and present discrete and continuous data
using appropriate graphical methods including bar
charts and time graphs
Comments and reasons for any changes to teacher assessment judgements, if applicable:
© West Sussex County Council 2017
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Overall
Statement
The pupil can recognise the place value of each digit in Th H T U numbers, within a range of
contexts, including rounding, ordering, comparing.
To start with I thought of odd
and even numbers to make as
this seemed the best system to
me.
Next time I could use the
numbers in a problem or
find a fraction.
I think half of 64.5 is 32.25
but I’m not quite sure. I
need to see if I can find and
use some fraction
resources to help me.
If I think of it as £64.50,
then £32.25 would be
correct.
Context
This was given as a morning starter activity for the children to do as they came into school at the
beginning of the day. The children had a set of number cards to use if needed. The children
generated their own numbers to work with and decided on what to do with the numbers. They
were encouraged to explore a range of ideas. Word prompts on a working wall encouraged the
pupil to think of all the different areas of place value we have visited during the half term.
This pupil demonstrated they have a clear understanding of place value, comparing, rounding and
ordering 4 digit numbers. In the first part they show they know the difference between odd and
even numbers by looking at the ones digit. They are able to compare largest to smallest showing
an awareness of the relationship between the numbers and a sense of the size of the number.
They are aware of the value of each digit and the relationships between them and can round up to
the nearest 10, 100 and 1000. The pupil is able to break a number down into parts showing how
a number can be made up. They show an understanding of the relationship between a number
and landmark numbers, plotting them on a number line and can work out the difference between
them using appropriate language to explain. They have explored what happens when you keep
halving a number and were able to do this until they stopped getting a whole number answer.
They show a curiosity for finding out something they are unsure of as when questioned about
what happens if you half the number again they gave an informed answer but asked to go and
find out for sure. The pupil is aware of halving numbers and fractions of the amount of the
number. Finally they have explored doubling the number and noticed the relationship between the
2x, 4x and 8x table.
© West Sussex County Council 2017
Page 7
Statement
The pupil can recognise the place value of each digit in Th H T U numbers, within a range of
contexts, including rounding, ordering, comparing.
I partitioned the number then
looked at other ways of
showing what it was made
up of. I can prove I’m correct
using dienes to help me show
my thinking.
Context
The pupil was asked to demonstrate different ways they could write a given number.
The pupil demonstrated they not only understand the value of each digit but also how the number
is made up into different parts. They also found a way to prove their thinking to the teacher.
© West Sussex County Council 2017
Page 8
Statement
The pupil can recognise the place value of each digit in Th H T U numbers, within a range of
contexts, including rounding, ordering, comparing.
I started with the largest
number I could make and
worked backwards each time.
Having this system made it
easier.
I know that this is the less than sign, so I had to
have the smallest number first and largest
number at the end. It got harder when all the
numbers started with 5000. I started by making
the largest number with the 5 in the 1000
column, then in the 100s, then in the 10s and
finally in the 1s.
Context
This was a quick starter activity for the beginning of a maths session. The pupil started off solving
it independently before working with a partner to peer mark the numbers they generated. The
children had to explain to each other how they solved the problem.
The pupil demonstrated they understood the value of each digit and can compare a set of
generated numbers to make a blank statement with given symbols read true. They are aware of
the size of 4 digit numbers explaining that they made the largest number possible first and then
worked backwards. This also shows they are able to order them and explain how they generated
each set of numbers. The pupil had their own approach which they could justify.
© West Sussex County Council 2017
Page 9
Statement
The pupil can recognise the place value of each digit in Th H T U numbers, within a range of
contexts, including rounding, ordering, comparing.
Context
The children were given an ‘nrich’ problem called ‘The Thousands Game’ and asked to explain
their thinking as they solved the problem.
The pupil demonstrated they have a clear understanding of place value, comparing and ordering 4
digit numbers. They also demonstrated their ability to use mathematical reasoning.
© West Sussex County Council 2017
Page 10
(Typed version of page 10 showing children’s response to the nrich ‘Thousands
Game’ problem)
Class 3 were playing a game. There were ten cards with the digits 0 to 9 on them.
These cards were put into a bag and players took out four cards and made a number out of them.
At first they made the highest number they could. Sinita took out
Zero is a place holder so he has
made a 3 digit number - 457
and made
Then they made the lowest number they could. Jamie took out
and made
"You can't put zero at the beginning of a number," objected Paul. The class discussed this and
decided that Jamie had made four hundred and fifty-seven.
Next they played to make the highest even number. Jill took out
and Vincent took out
Who won?
Then they played to make the highest odd number. Belinda took out
and Ali took out
Who won?
Next they played to make the lowest even number. Rohan took out
and Ben took out
Who won?
The last game they played was to make the closest number to 5000.
Alice took out
and
Chloe took out
who won?
Alice can make 4987 and Chloe can
make 5013. Both are 13 away from
5000 so both win. It’s a draw!
© West Sussex County Council 2017
Jill’s number has to
end in a 6 or 8 to
be even. 8 is the
largest digit so has
to go in the ‘Th’
place to make the
largest number –
8736
Vincent has to end
in 2 or 4. The 9
needs to go in the
‘Th’ so he makes
9412. This wins as
9000 is more than
8000.
Belinda needs a 9 in the
units to be odd. She can
make 6409.
Ali can choose to end in
1,5 or 7 to be odd. She
needs to put the 7 first
though to make the
highest 4 digit number.
She makes 7521.
Ali wins.
Rohan needs an 8 or 4 in
the units to make this
even. If he puts 1 first he
can make 1458 which will
win as Ben can’t put 0
first so 3790 is the
smallest number he can
make.
Page 11
Statement
The pupil can round decimals with one decimal place to the nearest whole number.
I just looked at the
number cards and
found which digit
cards could be put
with 45 to round
up. Only the 6
digit card could go
in the tenths
column with 45 to
round up to 46. I
then knew there
were going to be
less numbers. But
then I made a
mistake. I saw that
I can’t have 46.5 as
that would round
up to 47. So I was
right after all, it
was less
combinations.
Context
Following work on rounding numbers with one decimal place to the nearest whole number, the
children were given this challenge task and asked to solve the given problem and show their
findings.
The pupil clearly demonstrated that they understand how to round numbers with one decimal
place to the nearest whole number. It shows they have an understanding of what the decimal
numbers mean as they can generate them from a limited set of number choices. The pupil
shows that they have a good grasp of the concept of rounding as they were aware when
making numbers for 46, it should have had fewer numbers generated than the first. They could
then see where they had made an error and were able to self-correct without prompting.
© West Sussex County Council 2017
Page 12
Statement
The pupil can round decimals with one decimal place to the nearest whole number.
I put each child’s jumps in order from
shortest to longest to see who had jumped
the furthest out of the three jumps.
I just remember
to round .5 and
above up to the
next whole
number and .4
and below
down to the
lower whole
number. The
whole number
doesn’t change
when you round
down! You can
check on a
number line.
Mia has jumped 0.4m further
than Imran did.
Context
This lesson was part of a series of lessons following sports day. Length was focused upon
to explore the children’s understanding of decimals. Decimals was a concept that had
been taught the previous half term. The children were given a table which had the results
of a long jump competition. They had to find out who would get first (gold), second
(silver) and third (bronze) place. They had a statement from one of the children in the
competition to discuss and explain. Their next step was to show an understanding of how
to round decimals with one decimal place to nearest whole number.
The pupil demonstrated that they were able to successfully order the jumps from shortest
to longest to work out who had won. They were then able to make a judgement about
the given statement showing an understanding that although for that round Imran had
jumped the furthest overall his best jump was beaten by someone else’s jump from a
previous round. They were able to say by how much they had won by too. Finally they
could round each number to the nearest whole number and give an explanation to how
they worked out who would have won.
As a quick fire plenary activity they were given two lists of numbers and had to order
them against the clock. The pupil has a secure understanding of how to round decimals
with one decimal place to the nearest whole number and can clearly explain how they
know when to round up or down.
© West Sussex County Council 2017
Page 13
Statement
The pupil can add/subtract numbers up to 4 digits using formal written methods, within the context
of a two-step problem, deciding which operation to use and why.
The pupil can estimate and use inverse operations to check answers to a calculation.
1) A new local football stadium has been built. What is the total capacity that the stadium
can hold? Estimate first and then calculate your answer.
To estimate I am going to round
the numbers to the nearest 100
because it will be easier to
calculate and more accurate than
just rounding to the nearest 1000.
2) The home team have been allowed to use 3 sections, which 3 sections will give them
the maximum capacity?
3) If 2068 seats belong to season ticket holders how many home tickets are available to
buy on match day?
4) From the section left, the away team are bringing 1269 supporters. How many spare
seats will be left?
© West Sussex County Council 2017
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For question 2, to work out how
many the home team can have, I
can subtract the smallest number
from the total. This will be quicker
as I have already calculated the
total. To check if my answer is
correct I can use the inverse
operation and add the three
largest totals.
For question 3 I used my answer from
question 2 and just subtracted the
number of season tickets. You don’t
have to start again for each question,
you can just use the information you
already have.
Question 4
Context
This work was generated from a unit planned during the football European Championships
(Euros) 2016. It began with the children looking at the capacity of football stadiums both locally
and internationally. Following on from this the children had to plan a stadium that met certain
criteria.
The pupil was able to give clear reasons for the methods they had chosen to use.
© West Sussex County Council 2017
Page 15
Statement
The pupil can use place value knowledge and known and derived facts to multiply and divide
mentally (factor pairs).
I wrote down my fact family first
and noticed that 126 was
double 63.
What about 252 ÷ 9 = ?
I knew this because 4 lots of 60 is
4x6x10 which is 240. I then
added the 12 from 4x3.
It’s also double 126!
7x4 can be worked out quickly
by doubling and doubling again.
I did this to check.
I did 30 x 9 and then subtracted
18.
Context
The group of children were given a fact and asked to explain how it would help to answer a
different calculation. They were asked to write down on whiteboards their thinking as they
solved the problem. The teacher then scribed some of the responses during the discussion that
followed.
This pupil demonstrated that they were able to work in a systematic way and use their place
value knowledge and multiplication facts to work out how the first fact helped solve the next
one. As a next step they were given a third problem that related to a different part of the fact
family. They noticed this and could clearly explain their reasoning.
© West Sussex County Council 2017
Page 16
Statement
The pupil can use place value knowledge and known and derived facts to multiply and divide
mentally (factor pairs).
For this one I would use
near doubles. 13x3 = 39.
Double 40 is 80. Double
80 is 160. Subtract 4 =
156
Context
The pupil was given a calculation and asked to show different ways it could be solved.
This pupil demonstrates an understanding of factor pairs and can use them to multiply. They also
show they are confident in using written methods of calculations.
The pupil demonstrated their understanding of factor pairs and can use them to multiply two 2
digit numbers. They confidently calculate in a variety of ways.
© West Sussex County Council 2017
Page 17
Statement
The pupil can use place value knowledge and known and derived facts to multiply and divide
mentally (factor pairs).
Context
The children were asked to derive facts from the starting calculation in the centre box (5 x 7 = 35)
Questions included:
What strategies are you using?
Which are easiest to calculate?
How can you check what you think?
What do you notice?
It’s easy when you think
that it is 5 x 7 in different
sizes like 5 x70 which is
10 times bigger, 5 x 700
which is 100 times bigger
and 5 x 7000 which is
1000 times bigger.
I’m using my place value
knowledge because I
know how the digits shift
when you multiply or
divide by 10, 100 or 1000.
I can check using a place
value grid.
5 x 35 is half of 5 x 70.
This is an easier way to
work it out.
If you double an answer
in the five times table it’s
then the same as an
answer in the ten times
table. Double a multiple
of 5 gives you a multiple
of 10.
© West Sussex County Council 2017
Page 18
Statement
The pupil can use mathematical reasoning to solve problems involving multiplying and adding and
including the distributive law.
Context
The children have been developing their mental mathematical skills and were asked to use these
to solve a range of problems that linked to their ‘chocolate’ topic. The children were taught the
term ‘distributive’ and looked for the connections between the numbers e.g. number bonds,
partitioning. Much of the reasoning came through when discussing the strategies they were using.
Tasks:
a) A group of children were selling chocolates at the Christmas fair. One child sold 23, another
sold 45 and the third child sold 77. How many chocolates did they sell altogether?
b) The teachers in year 4 received a lot of chocolate as Christmas presents this year from the
children in their classes. One teacher received a total of 1300g, the second received a total of
280g and the third received a total of 700g. How much chocolate did the year 4 teachers receive
altogether in grams?
The teachers got 2280 grams
altogether, which is the same as
2kg and 280 grams. That’s a lot
of chocolate!
c) In a box, chocolate bars are stacked so that there are 5 bars across, 3 bars high and 8 bars
deep. How many bars in the box?
The children reasoned that they
needed to use multilink cubes to
represent the problem before
transferring this concrete idea into
a calculation. This was necessary
as they couldn’t picture the box
clearly in their heads.
© West Sussex County Council 2017
Page 19
d) In a box of Maltesers there were 52 chocolates. How many are there in 7
boxes?
It is easier to partition 52. To
work out 50 x 7 I did 5 x 7 and
then made the answer 10 times
bigger.
e) At a local theatre 619 tubs of chocolate ice cream were sold during the interval
of the pantomime. The O2 sold 8 times more than this. How many tubs of ice
cream did they sell?
Again, I partitioned 619. To
work out 600 x 8 I did 6 x 8 and
then made the answer 100
times bigger.
© West Sussex County Council 2017
Page 20
Statement
The pupil can solve problems using an understanding of the connections between hundredths,
tenths, place value and decimal measures e.g. money and decimals to 2 decimal places.
Context
The children have been looking at the largest and smallest numbers they can make using only 3
digits. This has been linked to money and they have been using coins to make the connections
between tenths and hundredths.
Using the digits 2, 3 and 7 and a decimal place, how many different
numbers can you generate? What is the largest and what is the
smallest number?
If you think of it as
money the most you
would have is £73.20
and the least is £2.37
Continue this sequence…
0.05, 0.06, 0.07, ____, _____, _____, _____, _____
Explain what happens.
0.1 is the same as 0.10
which is 10p. 1p is one
hundredth of a pound
which is 0.01 and the
one is in the
hundredth column.
When you get to 0.09, it
then goes 0.10, like 9p
then 10p. If you went into
the thousandths column
and put 0.010 the number
would be smaller.
© West Sussex County Council 2017
Page 21
Statement
The pupil can solve problems using an understanding of the connections between hundredths,
tenths, place value and decimal measures e.g. money and decimals to 2 decimal places.
Context
In Geography the children have been studying the local area and in particular were looking at the
different shops in the local shopping parades. The following questions were based around the fish
and chip shop.
These are some prices in a fish and chip shop.
Fish £2.30
Curry sauce 40p
Sausage £1.85
Peas 35p
Chips (small bag) 70p
Can of drink 55p
Chips (large bag) 95p
Pickled onion 28p
1) Charlie buys one fish, a large bag of chips and a pickled onion.
How much does he pay?
2) Emily buys a sausage and a can of drink.
Matthew buys a small bag of chips and a curry sauce.
How much more does Emily pay than Matthew?
1.
This is 95p which can also be
written as £0.95. This means no
pounds, 9 tens and 5 ones.
10p is one tenth of a pound.
© West Sussex County Council 2017
Page 22
2.
The child was asked to
discuss the methods they
had used to present their
calculation.
I did do it in my head but then I
decided to check by writing it
down just in case I had got the
decimal point mixed up. It must
stay in the right place.
3. Olivia only has silver coins. Is there anything on the menu she does not
have the exact money for?
She can buy everything on the menu except a
pickled onion as the prices are all multiples of 5 and
10.
5p and 10p are silver coins as are 20p and 50p. If she
got 5 picked onions she would be able to pay exactly
for them as it would cost 140p or £1.40 and this is a
multiple of 10.
© West Sussex County Council 2017
Page 23
Statement
Use factors and multiples to recognise equivalent fractions and simplify where appropriate.
To keep the fraction the same,
what you do to the numerator you
have to do to the denominator. So
6/16 – if you multiply by 2 you get
12 / 32. It’s still the same fraction.
You can see which ones belong
together. 3/4, 6/8, 12/16. I just
kept halving the numerator then if
half of the denominator was the
same too, they are equivalent.
I recognised the numbers were
multiples of 3 so looked to see if it
worked. So for 12 /15, you divide
12 by 3 and divide 15 by 3. 3 X 4
= 12 and 3 X 5 = 15. So 12/15 is
equivalent to 4/5
I did the same thing with these
fractions.
Context
In pairs, children sorted a range of fraction cards, some of which were equivalent. One pupil
chose to put them in columns with the lowest form at the top.
She explained how she had recognised equivalence and recorded some of the equivalent
fractions.
The pupil started by using her knowledge of multiplication and division to find equivalent
fractions and lowest common denominators.
© West Sussex County Council 2017
Page 24
Statement
Use factors and multiples to recognise equivalent fractions and simplify where appropriate.
1/2 is easy. As long as
you know the halves or
the doubles of numbers.
Here, the pupil became
more adventurous in linking
both their understanding of
multiples and place value to
create chains of equivalent
fractions.
I just know that
3/4 can be 6/8
or 9/12. I then
used my times
tables.
2/5 is harder. I mostly
used place value and my
times tables.
Context
The children were asked to demonstrate how to generate equivalent fractions from a given
starting point.
© West Sussex County Council 2017
Page 25
Statement
The pupil can solve problems by making connections between fractions as a representation of one
whole or a set of quantities.
I had to work out how many 2/3
of 24 is. First I worked out what
1/3 of 24 is. It’s 8, so 2/3 is 16.
So they had 4 each.
I found the next bit hard to work
out at first because they only had
16 to share not 24. Then I saw it
was easy because 16 divided by 4
is 4 so each friend had 4/24 which
is the same as 1/6.
To find a quarter you half the
amount and then halve it
again.
I know that £1.00 is 1/2 of
£2.00, and 50p is 1/4, so
£1.50 is 3/4 of £2.00
4/10 of £1.00 was easy because
1/10 is 10p so 4/10 is 40p.
Then I just multiplied that by 3.
Context
This work linked in with our chocolate topic and the buying and selling of ingredients. Once the
children understood fractions as equal parts of a whole, the problems were set in contexts where
the children needed to calculate and compare fractions of a quantity.
© West Sussex County Council 2017
Page 26
Statement
The pupil can solve problems by making connections between fractions of a length.
Yellow is ½. You can only write the fractions as
tenths and fifths and half. 1 brown is 4/5 of
the orange. One purple is 2/5. If you double
this, two purples is 4/5 too, so two purples are
equivalent to a brown.
Purple
Brown
If the orange is 1,
what colour is 1/2?
What else can you
tell us?
If brown is 1, the purple is 1/2.
Yellow is 5/8 of the brown as it is
more than half and the white is
worth 1/8. Five white pieces are
equivalent to the yellow which
makes 5/8.
Context
The children were exploring fractions of a whole related to length. They starting by viewing the
orange as one whole. Work followed where the children were asked to choose a different rod as
1 whole. For instance, using the brown as 1, the purple became half and the children gave
reasons for their thinking.
© West Sussex County Council 2017
Page 27
Statement
The pupil can solve problems by making connections between fractions of a length.
I started by working out the length
of the pool. 4 lengths is 100
metres, so one length must be 25
metres (100 ÷ 4).
Next I had to work out what 2/5
of 25 is. I used my multiples
knowledge here or I could have
divided 25 by 5, which is the
denominator, and then multiplied
the answer by the numerator
which is 2. Both ways show that it
is 10 metres, so more than the
judge said.
The swimmer was not right. He
thought he was 10 metres ahead
but it was only 9 metres. He led by
a smaller fraction of the length of
the pool.
Context
This lesson was part of a series of lessons following sports day. This was a 2-step problem, following
work on fractions of length. The work was independent but the children were reminded to pick out
and underline the important information for the first step of the calculation.
The pupil has identified the various steps needed to solve the problem and shown two strategies for
finding the fraction of the length of the pool.
© West Sussex County Council 2017
Page 28
Statement
The pupil can solve problems by making connections between fractions of length and shape.
For a pentagon the total
length is a multiple of 5
because each side is 1/5 of
the total length. So it can’t be
a pentagon. It can’t have 7, 9
or 10 sides either because 24
is not a multiple of these.
Context
Before devising a plan for a garden that had specific measurement requirements, the children had
the opportunity to make connections between their knowledge of fractions and multiplication and
apply this to their knowledge of regular shapes. Here, the length of each side compared to the
perimeter was used to determine what the shape could be.
© West Sussex County Council 2017
Page 29
Statement
The pupil can measure and calculate using different metric units of measure in a range of contexts.
I just knew
that 100 x 4
is 400 and
25 x 4 is 100
but I wrote it
down to
show how I
worked it
out in my
head.
I multiplied the
ingredients for the giant
by 3. I nearly forgot to
add the milk on so I had
to do it again.
To work out £1.45 x 3, I
did £1 x 3 and kept one
lot of 45p. Then I added
the other two 45ps
together to get 90p
which I added to the
£3.45 to get the total
cost for the milk. My
strategy for adding was
to add £1.00 to £3.45
and then subtract 10p.
Context
The children had previously worked on applying multiplication to scaling up (using
resources to make connections). They had also worked with a range of metric units,
using all four operations.
The context of this task was linked to work in both science and English.
Once the children had calculated, they made the pancakes and were assessed on their
ability to measure out the ingredients accurately using weighing scales and measuring
cylinders.
© West Sussex County Council 2017
Page 30
Statement
The pupil can measure and calculate using different metric units of measure in a range of contexts.
The tickets for four people to go and see
the show are £180 which is £45 x 4. To
work this out I doubled 45 and then
doubled the answer again.
When choosing how to get there it’s
important to think about which
information I need. Not everything here
is going to help me solve the problem. I
need to think about time and cost.
The car journey is 86 miles there and
back again. I only need parking for up to
5 hours as the show is 2 ½ hours long.
For the train you don’t have to worry
about miles as you just pay for one ticket
price per adult. There are two adults and
two children. The children travel for free.
© West Sussex County Council 2017
Page 31
This is without any traffic, which may not
happen!
These are the costs plus the ticket prices.
Context
This is an extended word problem set in a real life context which the children worked on over 2
days. It linked to a cross-curricular topic and encouraged the children to think about a problem
that everyone may consider when going on a journey.
The children were presented with a range of information and had to think about what was
relevant in order to solve the problem. They worked in small groups to discuss the information
and to prioritise what they needed to consider. The children then calculated the answers
independently.
© West Sussex County Council 2017
Page 32
Statement
The pupil can use mathematical reasoning to compare and classify geometric shapes, identify and
compare obtuse and acute angles and complete simple symmetrical figures in different
orientations.
Before the children could begin the project they had to have a
secure understanding of acute and obtuse angles. We used a right
angle checker initially to help us spot different types of angles in
our school environment. The children were then asked if they
could identify the different angles drawn on squared paper.
We could have sorted
them into the 4
different types of
triangle by looking at
the length of their
sides and their angles.
Context
This work was
contextualised as
part of a project on
improving the local
environment. The
children had
explored a range of
triangles and
quadrilaterals.
They had identified
obtuse, acute and
right angles and
named shapes by
recognising their
specific properties.
The children had
previously worked
on rotation and
symmetry and
applied their
knowledge to this
project.
These quadrilaterals
all have two sets of
parallel sides
Looking at the
six
quadrilaterals
you can see
acute, obtuse
and right
angles.
These have been
sorted to show
those with a
right angle and
those without.
These
quadrilaterals
all have one
set of parallel
sides
None of the
triangles have an
obtuse angle.
I made a
vertical
line of
symmetry
down the
centre
then drew
my
planters.
You also
have to
think about
what it
looks like as
the council
will want it
to look nice.
© West Sussex County Council 2017
IMPROVING THE
ENVIRONMENT
Can you explore and design
three different shaped
planters and identify where,
on The Quadrangle, you
would like to place them.
The Council have asked for
the planters to be limited to
3 or 4 sided shapes and
would like the area to have
a line of symmetry. They
would also like the planters
to include all three types of
angle in order to prevent
everything from looking the
same.
I used the dots to help me
rotate the triangles. This
helped me to see what they
looked like when they had
been rotated.
Page 33
Statement
The pupil can use mathematical reasoning to compare and classify geometric shapes.
A pentomino is a shape made up of 5 identical squares.
How many different
arrangements can
you make?
Is it true that both the area and the
perimeter are always the same?
Explain your reasoning and give
examples.
Lots of the ones I have made are the
same but rotated or reflected.
3 and 6 are the same – like a reflection
if the mirror was horizontal. So are 9
and 11.
9 and 10 are also a reflection going
sideways where the mirror would be
vertical.
1, 3, 6 and 8 all have at least one line of
symmetry.
The area is always 5 square
centimetres because we
used 5 squares. That is true.
The perimeter is not always
the same and I have used
two examples to prove it.
Number 7 is different
because there are 3 shared
sides for one square. The
perimeter is 10cm
For number 1 and 8 none of
the squares share 3 sides
and the perimeter is 12
square centimetres.
Context
The pupils used tiles to make a few different pentominoes and saw that there were several
different ways. The children then went on to record as many solutions as they could find. This is
not a complete set as the child chose to just stop at 12 examples because another child told her
there were 12 ways. She did, however, identify and discuss the properties using logical
reasoning.
© West Sussex County Council 2017
Page 34
Statement
The pupil can use mathematical reasoning to compare and classify geometric shapes. The pupil can
identify and compare acute and obtuse angles.
I like my last one the
best because I used a
diagonal line for part
of the way. Each half
has 7 sides and it has
an obtuse angle, a
right angle and acute
angles.
I started with the four easy ones then I didn’t know how
to work it out so I drew some but that didn’t help. Next I
cut some squares out of paper. I folded the square in half
then started to draw from opposite ends I cut them out
and matched them to check I was right.
I thought there were more than
four ways but I can see from
cutting them out that 1 and 2
are the same but just turned to
the left. This is the same for 3
and 4. Numbers 5 and 6 are just
reflections of each other and
these are repeated for 7 and 8.
You could then say I only have
four ways.
Context
Following on from a line of enquiry using pentominoes, the children were asked if it was true that
there were four different ways to cut a square in half so that each half was identical. They had also
previously worked on finding half of a shape by counting squares.
This child thought they had more than four ways from their drawings. They then used reasoning to
explain why this may not be true using their knowledge of rotation. They concluded that it depends
on whether rotations are ‘allowed’ as to whether they had more than four ways.
© West Sussex County Council 2017
Page 35
Statement
The pupil can plot specified points and draw sides to complete a given polygon and describe
movements between positions as translations.
Context
The children had explored a unit of work about pirates and had spent time drawing large scale
grids out on the playground. They made ships and moved them to different positions on the grid,
describing these movements using the language of ‘left, right, up and down’. The children moved
onto plotting their movements on smaller scale maps and describing the movements between
points as translations. In addition they were given some points of different pirate polygons and
had to identify the missing point to complete it.
The children then transferred this knowledge back in class and described the movement and
translation of set points on a grid. A few weeks later challenge tasks were set at the beginning of
each maths session over the period of a week. The children were given a selection of key
questions for them to be able show a range of skills. The questions focus on developing fluency,
reasoning and problem solving when describing movement and direction.
The pupil demonstrated that they were able to successfully describe movements, complete a
given polygon and explain their results in a variety of ways. The teacher and teaching assistant
scribed the children’s responses during discussion.
What do you
notice? Can you
make any
predictions?
I saw that both shapes had two sets
of numbers that were the same (2, 9)
and (5, 9) so I kind of knew it would
overlap and that one of the sides was
going to be the same size. I could also
see the other two numbers both
started the same (2) and (5) so it was
going to be a smaller rectangle of
some kind or a square.
© West Sussex County Council 2017
Page 36
It is a quadrilateral but Aisha has not
looked at the length of the sides
carefully enough.
This looked hard at first as all the points
were everywhere but then I
remembered a pirate game we did on
the grid outside where we moved
pirate ships about. I then looked for
different size squares and squares at
different angles. The tricky one was the
one where the square had turned and
was standing on its corner, not on a
side.
© West Sussex County Council 2017
Page 37
Statement
The pupil can interpret and present discrete and continuous data using appropriate graphical
methods, including bar charts and time graphs.
Context
In science the children were testing which material was the best insulator. They cooked Jacket
Potatoes and then choose three different materials to wrap them in. Every 10 minutes they
recorded what the temperature was and plotted it on a graph. The children then answered
questions about their graph.
Before you begin
drawing, what do
you think the graph
will look like?
I think the lines will go down because
the temperature of the potato is
decreasing.
I also think it will be easy to spot the
‘air’ line as the temperature drops very
quickly at the beginning.
© West Sussex County Council 2017
Page 38
The lines do all go down as I predicted
they would. After 30 minutes three of
the points were very close together.
The cotton wool worked well for 20
minutes and was almost the same
temperature as the tin foil at this point
before the potato got a lot cooler in the
following 10 minutes.
The pink line seems to be the
smoothest line because the potato
dropped 8 degrees in the first 10
minutes and then 8 degrees again in
the second 10 minutes. For the last 20
minutes it dropped 5 degrees and then
7 degrees. There wasn’t a sudden drop
in temperature like the air, greaseproof
paper and cotton wool.
© West Sussex County Council 2017
The tin foil was the best insulator at
every time interval.
Page 39