Year 4/5
Mastery Overview
Autumn
Year 4/5
Mixed Year Overview
Guidance
Since our Year 1 to Year 6 Schemes of Learning and
overviews have been released we have had lots of requests
for something similar for mixed year groups. This document
provides the yearly overview that schools have been
requesting. We really hope you find it useful and use it
alongside your own planning.
The White Rose Maths Hub has produced these long term
plans to support mixed year groups. The mixed year groups
cover Y1/2, Y2/3, Y3/4, Y4/5 and Y5/6. These overviews are
designed to support a mastery approach to teaching and
learning and have been designed to support the aims and
objectives of the new National Curriculum.
We had a lot of people interested in working with us on this
project and this document is a summary of their work so far.
We would like to take this opportunity to thank everyone who
has contributed their thoughts to this final document.
The overviews:
•
have number at their heart. A large proportion of time is
spent reinforcing number to build competency.
•
ensure teachers stay in the required key stage and
support the ideal of depth before breadth.
•
provide plenty of time to build reasoning and problem
solving elements into the curriculum
These overviews will be accompanied by more detailed
schemes linking to fluency, reasoning and problem solving.
Termly assessments will be available to evaluate where the
children are with their learning.
If you have any feedback on any of the work that we are
doing, please do not hesitate to get in touch. It is with your
help and ideas that the Maths Hubs can make a difference.
The White Rose Maths Hub Team
© Trinity Academy Halifax 2016
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This document fits in with the White Rose Maths Hub Year 1 –
6 Mastery documents. If you have not seen these documents
before you can register to access them for free by completing
the form on this link http://www.trinitytsa.co.uk/maths-hub/freelearning-schemes-resources/
Once registered you will be provided with a Dropbox link to
access these documents; please be aware some school IT
systems block the use of Dropbox so you may need to access
this at home.
Year 4/5
Mixed age planning
Using the document
Progression documents
The overviews provide guidance on the length of time that
should be dedicated to each mathematical concept and the
order in which we feel they should be delivered. Within the
overviews there is a breakdown of objectives for each
concept. This clearly highlights the age related expectations
for each year group and shows where objectives can be
taught together.
We are aware that some teachers will teach mixed year
groups that may be arranged differently to our plans. We are
therefore working to create some progression documents that
help teachers to see how objectives link together from Year 1
to Year 6.
There are certain points where objectives are clearly separate.
In these cases, classes may need to be taught discretely or
incorporated through other subjects (see guidance below).
Certain objectives are repeated throughout the year to
encourage revisiting key concepts and applying them in
different contexts.
Lesson Plans
As a hub, we have collated a variety of lesson plans that show
how mixed year classes are taught in different ways. These
highlight how mixed year classes use additional support,
organise groups and structure their teaching time. All these
lesson structures have their own strengths and as a teacher it
is important to find a structure that works for your class.
© Trinity Academy Halifax 2016
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Linking of objectives
Within the overviews, the objectives are either in normal font
or in bold. The objectives that are in normal font are the lower
year group out of the two covered. The objectives in bold are
the higher year group out of the two covered. Where
objectives link they are placed together. If objectives do not
link they are separate and therefore require discrete teaching
within year groups.
Year 4/5
Mixed age planning
Teaching through topics
Objectives split across topics
Most mathematical concepts lend themselves perfectly to
subjects outside of maths lessons. It is important that teachers
ensure these links are in place so children deepen their
understanding and apply maths across the curriculum.
Within different year groups, topics have been broken down
and split across different topics so children can apply key skills
in different ways.
Here are some examples:
 Statistics- using graphs in Science, collecting data in
Computing, comparing statistics over time in History,
drawing graphs to collect weather data in Geography.
 Roman Numerals- taught through the topic of Romans
within History
 Geometry (shape and symmetry)- using shapes within
tessellations when looking at Islamic art (R.E), using
shapes within art (Kandinsky), symmetry within art
 Measurement- reading scales (science, design
technology),
 Co-ordinates- using co-ordinates with maps in
Geography.
 Written methods of the four operations- finding the time
difference between years in History, adding or finding
the difference of populations in Geography, calculating
and changing recipes in food technology.
 Direction- Programming in ICT
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Money is one of the topics that is split between other topics. It
is used within addition and subtraction and also fractions. In
Year 1 and 2 it is important that the coins are taught discretely
however the rest of the objectives can be tied in with other
number topics.
Other measurement topics are also covered when using the
four operations so the children can apply their skills.
In Year 5 and 6, ratio has been split across a variety of topics
including shape and fractions. It is important that these
objectives are covered within these other topics as ratio has
been removed as a discrete topic.
Times tables
Times tables have been placed within multiplication and
division however it is important these are covered over the
year to help children learn them.
Year 4/5
Everyone Can Succeed
More Information
As a Maths Hub we believe that all students can succeed
in mathematics. We don’t believe that there are
individuals who can do maths and those that can’t. A
positive teacher mindset and strong subject knowledge
are key to student success in mathematics.
If you would like more information on ‘Teaching for
Mastery’ you can contact the White Rose Maths Hub at
[email protected]
Acknowledgements
The White Rose Maths Hub would like to thank the
following people for their contributions, and time in the
collation of this document:
Cat Beaumont
Matt Curtis
James Clegg
Becky Gascoigne
Sarah Gent
Sally Smith
Sarah Ward
© Trinity Academy Halifax 2016
[email protected]
We are offering courses on:
 Bar Modelling
 Teaching for Mastery
 Subject specialism intensive courses – become a
Maths expert.
Our monthly newsletter also contains the latest initiatives
we are involved with. We are looking to improve maths
across our area and on a wider scale by working with
other Maths Hubs across the country.
Year 4 / 5
Term by Term Objectives
Year 4/5 Overview
Week 2
Summer
Week 3
Week 4
Place Value
Spring
Autumn
Week 1
Week 5
Week 6
Addition and
Subtraction
Fractions
Time
Statistics
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Week 7
Week 8
Week 9
Week 10
Multiplication and
Division
Decimals and Percentages
Angles
Area
Shape and
Symmetry
Week 11
Week 12
Perimeter
Measurement
Position
and
Direction
Year 4 / 5
Term by Term Objectives
Year
Week 1
4 and 5
Week 2
Term
Week 3
Autumn
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
Week 11
Week 12
Place Value
Addition and Subtraction
Multiplication and Division
Perimeter
Count in multiples of 6, 7, 9. 25 and 1000.
Add and subtract numbers mentally with
increasingly large numbers.
Recall and use multiplication and division facts for multiplication tables up to
12 x 12.
Use place value, known and derived facts to multiply and divide mentally,
including: multiplying by 0 and 1; dividing by 1; multiplying together three
numbers.
Multiply and divide numbers mentally drawing upon known facts.
Multiply and divide whole numbers by 10, 100 and 1000.
Convert between different
units of measure eg
kilometre to metre.
Convert between different
units of metric measure (for
example, km and m; cm and
m; cm and mm)
Find 1000 more or less than a given number.
Count forwards or backwards in steps of powers of 10 for any given
number up to 1000000.
Count backwards through zero to include negative numbers.
Interpret negative numbers in context, count forwards and backwards
with positive and negative whole numbers including through zero.
Recognise the place value of each digit in a four digit number
Order and compare numbers beyond 1000.
Identify, represent and estimate numbers using different
representations.
Read, write, order and compare numbers to at least 1000000 and
determine the value of each digit.
Round any number to the nearest 10, 100 or 1000.
Round any number up to 1000000 to the nearest 10, 100, 1000, 10000
and 100000
Solve number and practical problems that involve all of the above and
with increasingly large positive numbers.
Solve number problems and practical problems that involve all of the
above.
Read Roman numerals to 100 (I to C) and know that over time, the
numeral system changed to include the concept of zero and place value.
Read Roman numerals to 1000 (M) and recognise years written in
Roman numerals.
Know and use the vocabulary of prime numbers, prime factors and
composite (non-prime) numbers.
Establish whether a number up to 100 is prime and recall prime
numbers up to 19
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Add and subtract numbers with up to 4
digits using the formal written methods of
columnar addition and subtraction where
appropriate.
Add and subtract whole numbers with
more than 4 digits, including using formal
written methods (columnar addition and
subtraction)
Estimate and use inverse operations to
check answers to a calculation.
Use rounding to check answers to
calculations and determine, in the context
of a problem, levels of accuracy.
Solve addition and subtraction two step
problems in contexts, deciding which
operations and methods to use and why.
Solve addition and subtraction multi-step
problems in contexts deciding which
operations and methods to use and why.
Recognise and use factor pairs and commutativity in mental calculations.
Identify multiples and factors, including finding all factor pairs of a number,
and common factors of two numbers.
Multiply two digit and three digit numbers by a one digit number using
formal written layout.
Multiply numbers up to 4 digits by a one or two digit number using a formal
written method, including long multiplication for 2 digit numbers.
Divide numbers up to 4 digits by a one digit number using the formal
written method of short division and interpret remainders appropriately
for the context.
Recognise and use square numbers and cube numbers and the notation for
squared (2) and cubed (3)
Solve problems involving multiplying and adding, including using the
distributive law to multiply two digit numbers by one digit, integer scaling
problems and harder correspondence problems such as n objects are
connected to m objects.
Solve problems involving multiplication and division including using their
knowledge of factors and multiples, squares and cubes.
Solve problems involving addition and subtraction, multiplication and
division and a combination of these, including understanding the use of the
equals sign.
Measure and calculate the
perimeter of a rectilinear
figure (including squares) in
cm and m
Measure and calculate the
perimeter of composite
rectilinear shapes in cm and
m.
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Find the next two numbers
6, 12, 18, 24,
7, 14, 21, 28, 35,
9, 18, 27, 36
25, 50, 75,
5000, 6000, 7000
Place Value
What is the same and what is
different about these two number
sequences?
6, 12, 18, 24, 30…..
45, 36, 27, 18, 9……
35
Convince me that the number 14
will be in this sequence if it is
continued.
49, 42, 35, 28 …….
175

Fill in the missing numbers:
14
28
100
Count in multiples of 6, 7, 9. 25
and 1000


200
Hassan counts on in 25’s from 250.
Circle the numbers he will say.
990, 125, 300, 440, 575, 700

Mr Hamm has three disco lights. The
first light shines for 3 seconds then is
off for 3 seconds. The second light
shines for 4 seconds then is off for four
seconds. The third light shines for 5
seconds then is off for 5 seconds. All
the lights have just come on. When is
the first time all the lights will be off?
When is the next time all the lights will
come on at the same time?
Here is a hundred square.
Always, Sometimes, Never
Hayley is counting in 25’s and
1000’s. She says:
- Multiples of 1000 are also
multiples of 25.
- Multiples of 25 are therefore
multiples of 1000.
Are these statements always,
sometimes or never true?
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Problem Solving



Reasoning
Some numbers have been shaded in blue,
and some in pink. Can you notice the
pattern? Why are some numbers maroon?
Work out the patterns on the parts of the
hundred squares below. Could there be
more than one pattern?
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency
Reasoning
 Find the value of
3891 +
= 4891
Place Value


4591
2392
8901
1892

Complete the table.
1000
more

Starting
number
3467
1000
1000
H
T
665
What do you notice?
Why does this happen?
O


1000 more than my number is 100
less than 4560. What is my number?
Fill in the boxes by finding the
patterns.
3210
1210
3110
6010

Add one thousand to 2554
Add ten hundreds to 2554
Find 1000 more than the number in
the place value grid.
Th
Phil says that he can make the
number that is 1000 less than 3512
using the number cards 1, 2, 3 and 4.
Do you agree?
Explain your answer.
1000
less
2219

Henry says ‘When I add 1000 to 4325
I only have to change 1 digit.’
Is he correct?
Which digit does he need to change?
Find 1000 more and less than the
following numbers.
Find 1000 more or less than a
given number.
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
Problem Solving
Using number cards 0-9 can you
make the answers to the questions
below:
1000 less than 999 + 80
1000 more than 7 x 6
1000 less than 9500 – 135

Lucy thinks of a number.
She says ‘The number 1000 more
than my number has the digits 1,2,3
and 4.
The number 1000 less uses the digits
1, 3 and 4’
What number is Lucy thinking of?
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Reasoning

Finish the sequence:
1000, 2000, 3000, ____, _____
350, 340, ____, _____, _____
11800, 11900, _____, _______
Problem Solving
Can you spot the mistake in the
sequence?
18,700
18,800
18,900
Place Value
Jack has made a number on a place
value grid.
TTh
Count forwards or
backwards in steps of
powers of 10 for any given
number up to 1000000.
Th
H
T

O
Count forwards in 100s from these
starting numbers.
What are the third and fifth numbers
you say?
345
Jack adds 5 thousands to his
number.
What number has he got now?

12,742

Spot the error:
289636, 299636, 300636, 301636,
302636
7,621
32
352,600
What are the next three number
sentences in the sequence?
345000-1000= 344000
344000-1000= 343000
343000-1000= 342000
Could you use the same numbers to
write different number sentences?
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Here is a number line.
A
19,100
Correct the mistake and explain your
working.


2000
3000
B
What is the value of A?
B is 10 less than A.
What is the value of B?

Jenny counts forward and backwards
in 10s from 317.
Which numbers could Jenny count as
she does this?
427
997
507
1,666
3,210
5,627
-23
7
-3
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Find the missing numbers in the
sequences:
Place Value
5, 4, 3, 2, 1, 0, _, -2, _
8, 6, 4, 2, 0, _, -4, _,
10, 6, 2, -2, _, -10, __

What temperature is 10 degrees below
3 degrees Celsius?

Use the number line to complete the
questions.
Count backwards through
zero to include negative
numbers.
Reasoning

Anna is counting down from 11 in fives.
Does she say -11? Explain your
reasoning.

Harris is finding the missing numbers in
this sequence.
What is 7 less than 3?
What is the difference between -5 and
4?

Fred is a police officer.
He is chasing a suspect on
Floor 5 of an office block.
The suspect jumps into the
lift and presses -1.
Fred has to run down the
stairs, how many flight must
he run down?

Draw the new temperature
on the thermometer after
each temperature change:
_, _, 5, _, _, -5
He writes down:
15, 10, 5, 0, -0, -5
What is 4 more than -2?
Problem Solving
Explain the mistake Harris has made.

Sam counted down in 3’s until he
reached -18. He started at 21. What
was the tenth number he said?
-In the morning it is 4 degrees, it
drops 8 degrees.
-In the afternoon it is 12 degrees
Celsius, overnight it drops by 14
degrees.
-It is 1 degree, it drops by 11
degrees.
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Year 4 / 5
Term by Term Objectives
All students
Place Value
National Curriculum
Statement
Fluency

Find the missing numbers in the
sequences
5, 4, 3, 2, 1, 0, _, -2, _
8, 6, 4, 2, 0, _, -4, _,

Charlie recorded the temperature at
7am each morning in a table.
Day Temp
Mon
-1
Tues
2
Wed
0
Thurs
-3
Fri
-4
Sat
-2
Sun
1
Which was the warmest/coldest
day?
What was the difference between
the warmest and coldest day?
Order the temperatures from coldest
to warmest.
Interpret negative
numbers in context, count
forwards and backwards
with positive and negative
whole numbers including
through zero.

Katie says
Three hours ago it was -2°c
It is now 5°c warmer.
What was the temperature earlier in the
day?
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Reasoning

Anna is counting down from 11 in
fives.
Does she say -11?
Explain your reasoning.

Harris is finding the missing numbers
in this sequence.
Problem Solving

Fred is a police
officer. He is chasing
a suspect on Floor 5
of an office block.
The suspect jumps
into the lift and
presses -1. Fred has
to run down the
stairs, how many flights must he run
down?

Use the picture below to answer the
following questions.
What number should be where the
light shines from the lighthouse?
How far is it down from the (head of
the) seagull to the (mouth of the)
yellow fish?
There's a little brown sea-horse to
the right of the lighthouse support.
How far from the surface is it?
_, _, 5, _, -5
He writes down:
15, 10, 5, 0, -0, -5
Explain the mistake Harris has made.

Sam counted down in 3s until he
reached -18.
He started at 21.
What was the tenth number he said?
Year 4 / 5
Term by Term Objectives
All students
Place Value
National Curriculum
Statement
Recognise the place value of each
digit in a four digit number
(thousands, hundreds, tens and
ones)
Fluency

Find the value of
in each
statement.
= 3000+ 500+ 40
2000 +
+ 2 = 2702
+ 40 + 5 = 3045

Write the value of the underlined
digit.
3462, 5124, 7024, 4720

1423 is made up of _ thousands, _
hundreds, _ tens and _ ones.

What number has been made in the
place value chart?
Reasoning

Show the value of 5 in each of these
numbers.
5462, 345, 652, 7523
Explain how you know.

Claire thinks of a 4 digit number. The
digits add up to 12. The difference
between the first and fourth digit is
5. What could Claire’s number be?

Create 5 four digit numbers where
the tens number is 2 and the digits
add up to 9. Order them from
smallest to largest.

Use the clues to find the missing
digits.

Jeff says
The thousands and tens digit multiply
together to make 24. The hundreds and
tens digit have a digit total of 9. The ones
digit is double the thousands digit. The
whole number has a digit total of 18.

Hafsa says
Who has the biggest number?
Explain why
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Problem Solving
There are 4 number cards, A, B, C
and D. They each have a four digit
number on. Using the clues below,
work out which card has which
number.
3421, 1435, 3431, 1243
A has a digit total of 10.
B and C have the same thousands digit.
In C and D the tens and hundreds digits
add up to 7.
D has the largest digit total.
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Write these numbers in order from
smallest to largest.
1423
1324
1432
Place Value

Order and compare numbers
beyond 1000.

If you wrote these numbers in order
from largest to smallest which
number would be fourth.
5331
1335
1533
5313
5133
3513


Lola has ordered five 4 digit
numbers. The smallest number is
3450, the largest number is 3650. All
the other numbers have digit totals
of 20. What could the other three
numbers be?
3

You have 2 sets of 0-9 digit cards.
You can use each card once. Arrange
the digits so they are as close to the
target numbers as possible.
Put one number in each box so that
the list of numbers is ordered largest
to smallest.
1
10s
1
1
1
1s
1

3
2
2
1
1
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I am thinking of a number. It is
greater than 1500 but smaller than
2000. The digits add up to 13. The
difference between the largest and
smallest digit is 5. What could the
number be? Order them from
smallest to largest.
Explain how you ordered them.
Using four counters in the place
value grid below make as many 4
digit numbers as possible. Put them
in ascending order.
100s

1342
Here are 4 digit cards. Arrange them
to make as many 4 digit numbers as
you can and order your numbers
from largest to smallest.
1000s
Problem Solving
2341
4 0 5

Reasoning
5
5
3
7
9
0
1
5
True or False: You must look at the
highest place value column first
when ordering any numbers.
1.
2.
3.
4.
5.
Largest odd number
Largest even number
Largest multiple of 3
Smallest multiple of 5
Number closest to 5000.
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Reasoning
What number is represented below?

Place 2500 on the number lines
below.
0
Place Value
I add 7 hundreds and 4 tens to it.
What is the new number?
2000

2000

This ten frame represents 1000
when it is full.

10000
Amelia says ‘The number in the place
value grid is the largest number you
can make with 8 counters.’
Do you agree?
Prove your answer.
1000
What number is represented in the ten
frame?
100
10
1
4000
Show 1600 on the number line.
0
Using 3 counters and the place value
grid below, how many 4 digit
numbers can you make?
1000
Has the place on the number line
changed? Why?
Identify, represent and estimate
numbers using different
representations.
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
5000
0

Problem Solving
100
10
1
Dan was making a 4 digit number
using place value counters. He
dropped two of his counters on the
floor.
These are the counters he had left.
What number could he have made?

If the arrow on the number line
represents 1788, what could the
start and end numbers be?
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Reasoning
Complete the missing values.

Place Value
Read, write, order and
compare numbers to at
least 1000000 and
determine the value of
each digit.
Say 358923 aloud.
Can you write this number in words?

Is she correct?
Convince me.

Give the value of 3 and 6 in each
number. One has been done for you.
Number
3,462
Place value
of 3
3000 or
three
thousands

Order the following numbers in
ascending order:
362354, 362000, 362453, 359999, 363010
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Using the digits 0-9 make the largest
number possible and the smallest
possible.
How do you know these are the
largest and smallest numbers?

Harriet has made five numbers, using
the digits 1, 2, 3 and 4.
She has changed each number into a
letter and has written three clues to
help people work out her numbers.
Year 5 are writing numbers as words
and vice versa.
Can you explain the mistakes that
have been made and correct them?
‘Number 1 is the largest. Number 4’s
digits add up to 12. Number 3 is the
smallest number.’
6,500 - Sixty five thousand
3,303 – Three thousand, three
hundred and thirty
5,800,400- Fifty eight thousand, four
hundred
Place Value
of 6
60 or 6
tens
43,726
69, 314
306,222

Using the digits 0-9 I can make
any number up to 1,000,000
It has __ hundred thousands.
It has __ ten thousands.
It has __ hundreds.
It is made of 580000 and ____
together.

Hannah says
Problem Solving

1.
2.
3.
4.
5.
Simon says he can order the
following numbers by only looking at
the first three digits.

125161, 128324, 126743, 125382, 127942
Is he correct?
Explain your answer.
aabdc
acdbc
dcaba
cdadc
bdaab
How many different ways can you
write the number 27,730?
For example: 27 thousands and 730
ones
Year 4 / 5
Term by Term Objectives
All Students
National Curriculum
Statement
Fluency

Reasoning

Complete the tables.
Nearest
10
Nearest
100
Nearest
1000
667
1274

Place Value
2495
Lowest
possible
whole
number
4500
Round any number to
the nearest 10, 100 or
1000.
________
________

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Caroline thinks that the largest whole
number that rounds to 400 is 449.
Is she correct?
Explain why.
Problem Solving

Make all the three digit numbers that
you can using the three digits. Round
them to the nearest 100. Can each of
the numbers round to the same
multiple of 100? Can all of the
numbers round to a different multiple
of 100?
Henry says
‘747 to the nearest 10
is 740.’
Rounded
number
5000 to
the
nearest
1000
300 to the
nearest
100
___ to the
nearest 10
Highest
possible
whole
number
5499
Do you agree with Henry?
Explain why.

A number rounded to the nearest 10 is
550.
What is the smallest possible number
it could be?

When a number is rounded to the
nearest 100 it is 200. When the same
number is rounded to the nearest 10 it
is 250. What could the number be?
________
74
The school kitchen wants to order
enough jacket potatoes for lunch.
Potatoes come in sacks of 100.
How many sacks do they need for 766
children?
Roll three dice.

Using the number cards 0-9, can you
make numbers that fit the following
rules?
1. When rounded to the nearest 10, I
round to 20.
2. When rounded to the nearest 10, I
round to 10.
3. When rounded to the nearest
1000, I round to 1000.
4. When rounded to the nearest 100,
I round to 7200.

Two different 2 digit numbers both
round to 40 when rounded to the
nearest ten.
The sum of the two numbers is 79
What could the 2 number be?
What are all the possibilities?
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Round the following numbers to the
nearest
a) 10 b)100 c)1,000
4,821
Place Value
Round any number up to
1000000 to the nearest 10,
100, 1000, 10000 and
100000


In 2015, there were 697,852 births
in England and Wales.
What is this rounded to the nearest
1,000?
Nearest 10,000?
Nearest 100,000?
Write five numbers that can be
rounded to the following numbers
when rounded to the nearest 100.
300
7,000
55,600
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
A number rounded to the nearest
1,000 is 54,000.
What is the largest possible number
this could be?
Problem Solving


Round the number 259,996 to the
nearest 1,000.
Round it to the nearest 10,000.
What do you notice about the
answers?
Can you think of 3 more numbers
where the same thing would
happen?
True or False?
All numbers with a five in the tens
column will round up when rounded
to the nearest 100 and 1,000.
Nathan thinks of a number.
He says
My number rounded to the
nearest 10 is 1,150, rounded to the
nearest 100 is 1,200 and rounded
to the nearest 1,000 is 1,000
2,781
69,243

Reasoning
What could Nathan’s number be?

Roll five dice; make as many 5 digit
numbers as you can from them.
Round each number to the nearest
10, 100, 1,000 and 10,000.
From your numbers, how many
round to the same 10, 100, 1000 or
10,000?
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Can you place the numbers in the diagram
below?
Place Value
Between 700
and 1200
Solve number and
practical problems that
involve all of the above
and with increasingly
large positive numbers.
Reasoning
Not between
700 and 1200
Digits
add up
to an
even
number
Digits
add up
to an
odd
number
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
Problem Solving
Three numbers are marked on a  Sasha is playing a game to win prizes.
number line.
Each blue counter is worth 6 points.
Each green counter is worth 7 points.
She wins the following counters.
The difference between A and B is
28
The difference between A and C is
19
D is 10 less than C
Which of these prizes can Sasha get?
What is the value of D?
854
2402
690
3564
793
1198
6428
3421
999
Can you mark D on the number
line?
Jack has 2 more blue counters and one more
green counter than Sasha.
He uses his points on 2 prizes.
Which 2 prizes does he choose?
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency
Place Value

Solve number problems and
practical problems that
involve all of the above.
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
There are three different
numbers.
They are all four-digit odd
numbers.
The digits of each number add up
to 14.
None of the numbers can be
divided by 5.
These numbers read the same
forwards and backwards.
Can you guess the numbers using
these clues?
Jim is thinking of a number.
It is less than 150.
The digits add up to 9.
The first two digits added
together are half of the third
digit.
What could Jim’s number be?
Reasoning


Write two 6-digit numbers.
Add the numbers together and round
the answer to the nearest 100,000.
Now round the original numbers and
add them together.
Do you get the same answer?
Try it again with different numbers.
What do you find?
Here are two number cards.
When rounded to the nearest 100, A
rounds to become B.
A’s digit total is one tenth of B.
What could A and B be?
Problem Solving

Five cars are in a race.
Their number plates are:
1733
5824
6465
9762
7525
The car with the highest number
finished last.
When the digits in the number plates
of the cars that came first and second
are added, they give the same total.
The cars that came in third and fourth
both have an odd number as the last
digit.
The cars that came in second and third
both bear numbers that are multiples
of five.
Use these clues to work out how the
racing cars placed in the race.
Year 4 / 5
Term by Term Objectives
All Students
National Curriculum Statement
Fluency

Reasoning
Match the Arabic numeral to
the correct Roman numeral.
Fill in any missing numbers to
complete the table.

Place Value

Read Roman numerals to 100 (I to
C) and know that over time, the
numeral system changed to
include the concept of zero and
place value.
Bobby says
Convert the Roman numeral
into Arabic numerals.
XVII

XXIV
XIX
Order the numbers in
ascending order.
X
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Look at the multiples of 10 in
Roman Numerals.
Is there a pattern?
What do you notice?
In the 10 times table, all the
numbers have a zero.
Therefore, in Roman
numerals all multiples of 10
have an X

V
8
Is he correct? Prove it.

Problem Solving
What is today’s short date in
Roman numerals?
How do you know?


Treasure huntComplete the trail by adding
the Roman Numerals together
as you go.

If you know 1 – 100 in Roman
numerals.
Can you guess the numbers up
to 1000?
Order these answers from greatest
to smallest
XXII + XXXV =
XXXI + LIV =
LXIII + XXVI =
LV + XXII =
LXXI + XXXVIII=
LXV + XXXII =
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Translate these Roman Numerals:
1. MD
3. CXVI
Place Value

Read Roman numerals to
1000 (M) and recognise
years written in Roman
numerals.

Reasoning

2. MCD
4. DCLX
Write the numbers in Roman
Numerals:
1. 35
4. 283
2. 100
5. 570
3. 99
Count in hundreds and fill in the
pattern:

Write the year of your birth in
Roman Numerals.
Write the current year in Roman
Numerals.
Find the difference between the
years.
Write the difference in Roman
Numerals.

Draw a time line and place these
dates on it.
Can you find an important event
that happened in each of these
years?
C, CC, __, __, D, __, __, __, _, _
Explain what each letter means and
write the translation below each
letter.

Arrange the numbers in size order:
XXXV, XL, XXX, LX, LV, L, XLV, LXV
Complete these calculations:
1. CD + DC=
2. VI + IV=
3. CX + XC
Explain how you ordered the
numbers.

Complete the calculations. Show
how you translated the roman
numerals and added them.
1. XI + IX=
2. XL + LX=
3. CM + MC=

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Problem Solving
Explain why the Romans wrote CM
for the number 900.
MLXVI
MCMLXIX
MDCLXVI
MCMIII
MDCV
MMXIV
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

What is special about these
numbers?
7
Prime Numbers

Know and use the
vocabulary of prime
numbers, prime factors
and composite (nonprime) numbers.

17
37
47

Explain why 1 isn’t a prime number.

Katie says,
Problem Solving

All prime numbers have
to be odd.
Put these numbers into 2 groups.
Label the groups.
11
10
21
31
Do you agree? Convince me.
9
13
47
35
Her friend, Abdul, says,
How many square numbers can you
make by either adding two prime
numbers together or by subtracting
one prime number from another
e.g.
11
-
Prime
numbers
7
=
4
Square
number
That means 9, 27 and 45
are prime numbers.
Find the missing prime factors.
12
2
Explain Abdul’s mistake and correct it.
3
18
2
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Reasoning
3

Always, sometimes, never
When you add 2 prime numbers
together the answer will be even.

Investigate how many prime
numbers are between 2 consecutive
multiples of 10. Include 0 and 10.
Is there a pattern?
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Reasoning
Fill in the missing prime numbers
2
3
7

Fill in the missing numbers so that the
calculation creates a prime number.
13

On a set of flashcards, write a
different number on each. Ask a
partner to do the same.
Shuffle them and take half each.
Take turns to turn them over. Say
either ‘prime’ or ‘not prime’ when a
number is turned over. Whoever
ends with the most cards, wins.

Prime factors are the prime numbers
that multiply together to make a
number e.g.
11
19 –
19
Problem Solving
7
=
5
Is this the only option?
Prime Numbers
Andy says,

Establish whether a
number up to 100 is prime
and recall prime numbers
up to 19

Find all the prime numbers between
60 and 80.
I subtracted an odd
number to find a
prime number.
What is the 16th prime number?
12
Is this possible? How many ways could
he have done this?
Explain your answer.

What number am I?
I am a prime number. I am a 2 digit
number.
Both my digits are the same.
Explain why there is only one option.
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2
3
3
Is it possible to make every number
by multiplying prime numbers
together?
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Work out this missing numbers:
Reasoning

Rachel has £10
She spends £6.49 at the shop.
Would you use columnar subtraction
to work out the answer?
Explain why.

True or False?
Are these number sentences true or
false?
8.7 + 0.4 = 8.11
6.1 – 0.9 = 5.2
Addition and Subtraction
- 92 = 145
740 +
= 1,039
= 580 – 401

Add and subtract numbers
mentally with increasingly
large numbers.
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Peter bought boxes of crisps when
they were on offer. After 12 weeks,
his family had eaten 513 packets and
there were 714 left.
Problem Solving

If 2,541 is the answer, what’s the
question?
- Can you create three addition
calculations?
- Can you create three subtraction
calculations?
- Did you use a strategy?

Using 0-9 dice roll 3 at the same time
to create a number.
Your partner needs to do the same.
Who can add them together
correctly first?
Who can subtract the smallest from
the largest correctly first?
Use a calculator to check.

Kangchenjunga is the third highest
mountain in the world at 28,169 feet
above sea level.
Lhotse is the fourth highest at 27,960
feet above sea level.
Find the difference in heights
mentally.
Give your reasons.
How many did he buy?


Children follow a series of
instructions to find a mystery
number.
Eg
Start with 100
Add 5,000
Take away 400
Add 20
Subtract 750
What number have you got?
Which of the following questions are
easy and which ones are hard?
213,323 - 10 =
512,893 + 300 =
819,354 - 200 =
319,954 + 100 =
Explain why you think the hard
questions are hard.
Year 4 / 5
Term by Term Objectives
All Students
National Curriculum
Addition and Subtraction
Statement
Fluency

Complete the calculations below using
the column method.
354 276=
1425 + 2031=
3864 – 2153 =
2416 – 1732=

Fill in the missing numbers:
432 +
= 770
50 + 199 +
Add and subtract numbers with
up to 4 digits using the formal
written methods of columnar
addition and subtraction where
appropriate.
Problem Solving
Find the mistake and then make a
correction to find the correct
answer.
2451
+562_
8071
- 555 = 8
782
-435
353
5
What is the largest possible number
that will go in the rectangular box?
What is the smallest? Convince me.
Choose whether to solve these
questions mentally or using written
methods.

Desani adds three numbers
together that total 7170
Complete the part whole models.
A game to play for two people.
The aim of the game is to get a
number as close to 5000 as
possible. Each child rolls a 1-6
die and chooses where to put
the number on their grid or the
other players. Once they have
filled their grids then they add
up their totals to see who has
won.
+
?
?
?
?
?
?
?
?

A chocolate factory usually
produce 1568 caramel bars on a
Saturday but on a Sunday
production decreases and they
make 325 fewer bars. How
many bars are produced at the
weekend in total?

All of the digits below are either
a 3 or a 9. Can you work out
each digit?
540 + 460
298 + 342
999 + 999
They all have 4 digits.
They are all multiples of 5
What could the numbers be?
Prove it.
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
= 450
54 + 46
34 + 69 + 26
566 + 931



- 75 = 94

Reasoning
7338=???? + ????
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Calculate 1,434 + 2,517 using place
value counters.
The first number has been
partitioned for you.
Th
Addition and Subtraction
Reasoning
H
T

There are mistakes in the following
calculations.
2451
+562_
8071
O
Problem Solving

Find the missing numbers in these
calculations.

My answer is 5,398
What’s the question?
Create 3 addition calculations.
Create 3 subtraction questions.
Did you use a strategy?
Explain it.
782
-435
353
1000
Explain the mistake and then make a
correction to find the correct
answer.
Add and subtract whole
numbers with more than 4
digits, including using formal
written methods (columnar
addition and subtraction)
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Can you solve 4,023 – 2,918 using
place value counters?
Make the bigger number and take
the smaller number away.



Here is an addition sentence with
whole numbers and digits missing.
+ 3,475 = 6,
Julie has 1,578 stamps.
Heidi has 2,456 stamps.
How many stamps do they have
altogether?
Show how you can check your
answer using the inverse.
Adam earns £37,566 pounds a year.
Sarah earns £22,819 a year.
How much do they earn altogether?
They have to pay £7,887 income tax
per year.
How much are they left with after
this is taken off?
24
What numbers could go in the
boxes?
How many different answers are
there?
Convince me.

A five digit number and a four digit
number have a difference of 4,365
Give me three possible pairs of
numbers.
Year 4 / 5
Term by Term Objectives
All Students
National Curriculum
Statement
Fluency
Addition and Subtraction


Julie has 578 stamps.
Heidi has 456 stamps.
How many stamps do they have
altogether?
Show how you can check your answer
using the inverse.
Reasoning

Jenny estimates the answer to
3568 + 509 ≈ 4000. Do you agree?
Explain your answer.

Always, sometimes, never.
The difference between two odd
numbers is odd.
Estimate the answers to these number
sentences. Show your working.

3243 + 4428
7821- 2941
Estimate and use inverse
operations to check answers to a
calculation.

Check the answers to the following
calculations using the inverse. Show all
your working.
762 + 345 = 1107
2456- 734 = 1822

Harry thinks of a number.
He multiplies it by 3, adds 7 and
then divides it by 2.
How could he get back to his
original number?

If Harry starts with the number
3, write out all the calculations
he will do to get back to his
original number.

With a friend, discuss before
working each out which will be
greater or smaller than the
other.
Why do you think this?
What key facts did you use?
Hazel fills in this bar model
2821
2178
She makes the following
calculations from it.
2821 – 2178 = 757
2821 – 757 = 2178
2178 + 757 = 2821
757 + 2178 = 2821
Is she correct?
Explain why.
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Problem Solving
3567 – 567
3677 – 344
4738 + 36
4738 + 18 + 18
2139 – 85 + 27
2151 – 86 + 30
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency
Addition and Subtraction

Reasoning
A car showroom reduces the price of
a car from £18,750 to £14,999.
By how much was the price of the
car reduced?
Circle the most sensible answer
£3,249

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
53.3 – 52.75=
£4,001

A games console costs £245
Mike pays for this in 5 equal
payments.
To the nearest ten pounds, how
much does he pay per payment?
A coach holds 78 people.
960 fans are going to a gig on the
coaches.
How many coaches are needed to
transport the fans?

True or false.
4,999-1,999 = 5,000-2,000
Explain how you know using a
written method.

There are 1,231 people on an
aeroplane.
378 people have not ordered an
inflight meal.
How many people have ordered the
inflight meal?
Give your answer to the nearest
hundred.
11.48 – 10. 86=

Always, sometimes, never
When you add up four even
numbers, the answer is divisible by
four.

Martin is measuring his room for a
new carpet.
It has a width of 2.3m and a length
of 5.1m.
He rounds his measurements to the
nearest metre.
Will he have the right amount of
carpet?
Explain your reasoning.
£3,751
Use rounding to check
answers to calculations and
determine, in the context of
a problem, levels of
accuracy.
Which of these number sentences
have an answer that is between 0.6
and 0.7?
Problem Solving
The inflight meal costs £1.99 per
person.
The cabin crew have collected £1100
pounds so far.
How much more money do they
need to collect?
Round your answer to the nearest
pound.
Year 4 / 5
Term by Term Objectives
All Students
National Curriculum
Statement
Fluency

There are 2452 people at a theme
park. 538 are children, how many
are adults?
Addition and Subtraction
Sarah draws a diagram to help.
Place a (√) next to the correct diagram
Solve addition and subtraction
two step problems in contexts,
deciding which operations and
methods to use and why.
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• Archie and Sophie are both working
out the answer to the following
question:
Problem Solving

A supermarket has 1284 loaves of
bread at the start of the day.
During the day, 857 loaves are sold
and a further 589 loaves are
delivered.
How many loaves of bread are
there at the end of the day?

John is having a garden party.
He will need to make 4,250
sandwiches in total.
He makes 1,500 tuna, 750 cheese,
1,350 ham and 920 egg.
He decides to make the rest
cucumber.
How many cucumber sandwiches
will there be?

These three chicks lay some eggs.
350 + 278 + 250
They have both used different
strategies.
Adults
2452
538
2452
Adults
538
538
2452
Reasoning
Archie’s method
350+ 278+ 250
350+ 278= 628
628 + 250= 878
Sophie’s method
350+278+250
350+250= 600
600+ 278= 878
Answer = 878
Answer= 878
Adults
Use the correct diagram to help you
solve the problem.
Which do you prefer?
Explain why.

Use the method you preferred to solve
320+ 458 + 180
Alice is trying to complete a sticker
book.
It needs 350 stickers overall.
She has 134 in the book and a
further 74 ready to stick in.
How many more stickers will she
need?
Beth lays twice as many as Kelsey.
Caroline lays 4 more than Beth.
They lay 44 eggs in total.
How many eggs does Caroline lay?
Year 4 / 5
Term by Term Objectives
All students
Addition and Subtraction
National Curriculum
Statement
Solve addition and
subtraction multi-step
problems in contexts
deciding which operations
and methods to use and
why.
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Fluency
Reasoning

When Claire opened her book, she
saw two numbered pages.
The sum of these two pages was
317.
What would the next page number
be?

122 +



On Monday Peter got paid £114 for a
day’s work.
On Tuesday Peter got paid £27 more
than he did on Monday.
On Wednesday Peter got paid £17
less than he did on Monday.
How much did Peter get for the
three days’ work?
How many calculations do you need
to complete to find the answer?
Does it matter what order you
complete the calculations in?

Write a word problem which could
be solved by using this calculation.
+ 57 = 327
Beth and Mabel share £410
between them.
Beth received £100 more than
Mabel. How much did Mabel
receive?
Adam is twice as old as Barry.
Charlie is 3 years younger than
Barry.
The sum of all their ages is 53.
How old is Barry?
352 + 445 – 179 = 618

At the start of the day, a milkman
has 250 bottles of milk.
He collects another 160 bottles from
the dairy and delivers 375 during the
day.
How many does he have left?
Sam calculates the answer.
375 – 250 = 125
125 + 160 = 285
Explain the mistake that Sam has
made.
Problem Solving

Lucy, Katie, Amy, Laura, Sarah and
Maggie are all shooters in different
netball teams.
Between them one Saturday they
scored a total of 33 goals.
Each girl scored a different number
of goals and each girl scored at least
one goal.
Lucy was the top scorer and scored
three more than Katie.
Amy scored one less than Laura but
their total was the same as Lucy’s
and Katie’s scores added together.
Maggie beat Sarah’s scoring level but
their scores together equalled the
number of goals Laura had scored on
her own.
Use these clues to work out how
many goals each girl scored.
Year 4 / 5
Term by Term Objectives
All Students
National Curriculum
Multiplication and Division
Statement
Fluency

Find the answers:
4 x 12 =
5x9=
7x8=
8 x 11 =

Fill in the gaps:
4 x __ = 12
8 x __ = 64
32 = 4 x __
6 = 24 ÷ __

Leila has 6 bags with 5 apples in
each.
How many apples does she have
altogether?
Reasoning

Complete these calculations:
7 x 8=
7 x 4 x 2=
5x6=
5 x 3 x 2=
12 x 4 = 12 x 2 x 2=
Which calculations have the same
answer? Can you explain why?

Problem Solving

x

I am thinking of 2 secret numbers
where the sum of the numbers is 16
and the product is 48. What are my
secret numbers? Can you make up 2
secret numbers and tell somebody
what the sum and product are?

Here is part of a multiplication
square.
True or False
6x8=6x4x2
6x8=6x4+4
How many multiplication and
division sentences can you write that Can you write the number 24 as a
product of three numbers?
have the number 72 in them?

= 24

Explain your reasoning.
Recall multiplication and
division facts of multiplication
tables up to 12 x 12.
Find three possible values
for
and .
Which pair of numbers could go in
the boxes?
x
= 48
Shade in any other squares that have
the same answer as the shaded
square.
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Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency
Multiplication and Division

Fill in the missing numbers:
x 1 = 13
12 x 0 =
3 x 2 x = 18

Sally has 0 boxes of 12 eggs.
How many eggs does she have?
Use place value, known and
derived facts to multiply and
divide mentally, including:
multiplying by 0 and 1; dividing by
1; multiplying together three
numbers.
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Holly has 1 box of 12 eggs.
How many eggs does she have?
Write these two questions as
multiplication sentences.
Reasoning

Always, sometimes, never
Problem Solving

Write the number 30 as the product
of 3 numbers.
Can you do it in different ways?

Try to reach the target number
below by multiplying three of the
numbers together. Cross out any
numbers you don’t use.
An even number that is divisible by 3
is also divisible by 6.

Harvey has written a number
sentence.
13 x 0 = 0
He says
Target number: 144
I can change one number in
my number sentence to
make a brand new
multiplication.
1


Five children share some cherries.
Each child gets 6 cherries.
There are 3 cherries left over.
How many cherries were in the bag
to begin with?
Is he correct?
Which number should he change?
Explain your reasoning.
5
3
0
6
Use the numbers 1-8 to fill the
circles.
8
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency
Multiplication and Division



Multiply and divide numbers
mentally drawing upon
known facts.
© Trinity Academy Halifax 2016
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
8 x 6 = 48.
Use this to help you find the
answers to the number
sentences:
48 ÷ 6 =
6 x 80 =
Reasoning

How can you use 10 x 7 to help you
find the 9th multiple of 7?

Find the answer:
2 x 11 =
4 x 11 =
2 x 12 =
4 x 12 =
2 x 13 =
4 x 13 =
Write down five multiplication
and division facts that use the
number 48.
If I know 8 x 36 = 288, I also
know 8 x 12 x 3 = 288 and 8 x 6 x
6 = 288.
If you know 9 x 24 = 216, what
else do you know?
Problem Solving

If 8 x 24 = 192, how many other pairs of
numbers can you write that have the
product of 192?

Here is part of a multiplication grid.
What is the connection between
the results for the two times table
and the four times table?
If 2 x 144= 288, what is 4 times
144?

40 cupcakes cost £3.60
How much do 20 cupcakes cost?
How much do 80 cupcakes cost?
How much do 10 cupcakes cost?

To multiply a number by 25 you
multiply by 100 and then divide by
4.
Use this strategy to solve.
84 x 25
28 x 25
5.6 x 25
10 times a number is 4350, what is
9 times the same number?
Explain your working.
Shade in any other squares that have the
same answer as the shaded square.

Multiply by 2 and 3 using the direction of
the arrows to complete the grid.
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Reasoning

Solve:
Multiplication and Division
345 x 10 =
345 x 100 =

Multiply and divide whole
numbers by 10, 100 and
1000.
© Trinity Academy Halifax 2016
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
Fill the gaps:
3,790 x
= 379,000
3,790 ÷
= 379
Claire says;
‘When you multiply a number by 10
you just add a nought and when you
multiply by 100 you add two noughts.’
Do you agree?
Explain your answer.
Problem Solving

Harry has £20
He wants to save 10 times
this amount.
How much more does he
need to save?

40
67,000
2,000

David has £35,700 in his bank.
He divides the amount by 100 and takes
that much money out of the bank.
Using the money he has taken out he
spends £268 on furniture for his new
house.
How much money does David have left
from the money he took out?
Show your working.

Sally multiplies a number by 100
Her answer has three digits.
The hundreds and ones digit are the same.
The sum of the digits is 10
What number could Sally have started
with?
Are there any others?
6 x 7 = 42
How can you use this fact to solve the
following calculations?
4,200 70 =
0.6 x 0.7 =
5,890
Can you write three different questions
that could make these numbers by
multiplying and dividing by 10, 100 or
1,000?
Apples weigh about 160g each.
How many apples would you expect
to get in a 2kg bag?
Explain your reasoning.
× 1,000 = 497,200

Here are the answers to the questions.
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency
Multiplication and Division

Recognise and use factor pairs
and commutatively in mental
calculations.
Use 16 cubes.
How many different arrays can you
make?
Think about making towers of cubes that
are equal in height.
Can you write a multiplication sentence
to describe the towers?
The numbers in your multiplication
sentences are the factors of 16!

7x5=

Find the missing numbers
12 x 6 = 6 x ___
2 x 3 x 5 = __ x 5
2 x 7 x 5 = __ x 5

=5x
13 x 12 can be solved by using factor
pairs, eg 13 x 3 x 4 or 13 x 2 x 6.
What factor pair could you use to
solve 17 x 8?
© Trinity Academy Halifax 2016
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Reasoning

Fill in the missing numbers
25 x 3 = = x
x

Use factor pairs to solve 15 x 8.
Is there more than one way you can
do it?

Multiply a number by itself and then
make one factor one more and the
other one less.
What do you notice?
Does this always happen?
Eg 4 x 4 = 16
6 x 6= 36
5 x 3 = 15
7 x 5= 35
Try out more examples to prove your
thinking.
Problem Solving

Place <, >, or = in these number
sentences to make them correct:
50 x 4
4 x 50
4 x 50
40 x 5
200 x 5
3 x 300

The school has a singing group of
more than 12 singers but less than
32.
They sing together in different ways.
Sometimes they sing in pairs and
sometimes in groups of 3, 4 or 6.
Whatever size groups they are in, no
one is left out and everyone is
singing.
How many singers are there in the
school choir?
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency
Multiplication and Division

Calculate the first 5 multiples of the
following numbers.
4

Identify multiples and
factors, including finding all
factor pairs of a number,
and common factors of two
numbers.
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Reasoning
8
3

7
Find all the factors of 20.

Find a common factor of 36 and 12.

Polly is planting potatoes in her
garden.
She has 24 potatoes to plant and
she will arrange them in a
rectangular array.
List all the different ways that Polly
can plant her potatoes.

Rob and James are talking about
multiples and factors.
Rob says ‘0 is a multiple of every
whole number.’
James says ‘0 is a factor of every
whole number.’
Who is correct?

Do you agree?
Explain your reasoning.
True or False
The bigger the number, the more
factors it has.
Sally is thinking of a number. She
says
My number is a multiple of 3. It is
also 3 less than a multiple of 4.
Find three different numbers that
could be Sally’s number.
Tom says;
Factors come in pairs, so
all numbers have an even
number of factors.

Problem Solving

Clare’s age is a multiple of 7 and 3
less than a multiple of 8.
How old is Clare?

To find the factors of a number, you
have to find all the pairs of numbers
that multiply together to give that
number.
Factors of 12 = 1, 2, 3, 4, 6, 12
If we leave the number we started
with (12) and add all the other
factors together we get 16.
12 is called an abundant number
because it is less than the sum of its
factors.
How many abundant numbers can
you find?
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency
Multiplication and Division


Penny says a two digit number
multiplied by a one digit
number will always give a two
digit answer.
Is she correct?
Justify your answer.

Find the mistake that has been
made in the calculation below.
Explain and correct it.
Add up the columns and
exchange counters where
needed to find the answer.
Multiply two digit and three digit
numbers by a one digit number
using formal written layout.
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Use counters to solve 126 x
4
Draw 4 rows and make 126
in each of them.
Reasoning
X

Sahil has 45 packets of
sweets.
Each packet has 6 sweets in
it.
How many sweets does he
have altogether?

x 4 = 140
What could the numbers in the multiplication
be?
Every digit is different.
x
3

Miss Wood orders some new whiteboard pens
for Year 3 and 4.
There are 160 children in Year 3 and 4.
If she orders 6 boxes of 27 pens, will she have
enough?
Show your calculation.

In one month, Charlie read 814 pages in his
books.
His mum read 4 times as much as Charlie which
was 184 pages more than Charlie’s dad.
How many pages did they read altogether?
Use a bar model to help.
What digit goes in the missing
box? Convince me.
3

47
8
3256
Problem Solving
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency
Multiplication and Division



Multiply numbers up to 4
digits by a one or two digit
number using a formal
written method, including
long multiplication for 2
digit numbers.

Solve the calculation:
Calculate:
5612 x 4
654 x 34
Reasoning

Problem Solving
Spot the mistake and make a
correction.
527
x 42
10540
2018
12648

Using the digits 1, 2, 3 and 4 in any order in
the bottom row of the number pyramid,
how many different totals can
you make?
What is the smallest/ largest total?

Find the missing digits:
5

Mo Farah runs 135 miles a week.
How far does he run each year?
Laura thinks that a 4 should be
placed in the empty box. Do you
agree?
4
There are 18 rows of 16 stickers
on a sheet.
How many stickers on 1 sheet?
How many stickers on 10 sheets?
×
1
7
7
5
3
x
2
3
0
2
1
1

0
9
What goes in the missing box?
12
14
2 ÷ 6 = 212
2

3
0
6
4
7
2
7
7
Start with 0; choose a path through the
maze. Which path has the highest/ lowest
total? You can go up, down, left or right.
S
+6
x5
x2
-4
+7
X8
+9
x7
x6
x5
+3
x4
+9
E
4 ÷ 7 = 212
Prove your answer.
© Trinity Academy Halifax 2016
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Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency
Multiplication and Division

Calculate
Reasoning

68 ÷ 4 =
1248 ÷ 3 =
Problem Solving

The answer to the division has no
remainders.
Find the missing numbers.
Correct the errors in the calculation
below.
Explain the error.
266 ÷ 5 = 73.1

Andrew says that the answer to 166
divided by 4 can be written as ’46
remainder 2’ or as ’46.5’.
Do you agree?
Explain your reasoning.
I am thinking of a number.
When it is divided by 9, the
remainder is 3.
When it is divided by 2, the
remainder is 1.
When it is divided by 5, the
remainder is 4.
What is my number?

When 59 is divided by 5, the
remainder is 4
When 59 is divided by 4, the
remainder is 3
When 59 is divided by 3, the
remainder is 2
When 59 is divided by 2, the
remainder is 1
What number goes in the box?
323 x
1 = 13243
Prove it.

Find the missing numbers:

x 5 = 475
Divide numbers up to 4
digits by a one digit number
using the formal written
method of short division
and interpret remainders
appropriately for the
context.
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3x

= 726
194 pupils are going on a school trip.
One adult is needed for every 9
pupils.
How many adults are needed?

Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency
Multiplication and Division


Recognise and use square
numbers and cube numbers
and the notation for squared
(2) and
cubed (3)
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Work out:
62=
33=
4 squared =
8 cubed =
Reasoning

Julian thinks that 4 is 16.
Do you agree?
Convince me.

Always, Sometimes, Never.
2
A square number has an even
number of factors.
Fill in the missing answers from the
grid below:

Problem Solving

Last year my age was a square
number.
Next year it will be a cube number.
How old am I?
How long must I wait until my age is
both a square number and a cube?

How many square numbers can you
make by adding prime numbers
together?
True or False
Here’s one to get you started.
Square and Cubed numbers are
always positive.


Which is bigger?
32
2+2=4
23
Show your working.
Jack thinks that the numbers both
equal 6.
Explain to Jack what he has done
wrong.
Can you arrange the numbers 1 to 17
in a row so that each adjacent pair
adds up to a square number?
3 6 10
3+6=9
6 + 10 = 16
Use number cards 1 – 17 to help you
solve the problem.
Can you arrange them in more than
one way? If not, can you explain
why?
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency
Multiplication and Division

Solve problems involving
multiplying and adding, including
using the distributive law to
multiply two digit numbers by
one digit, integer scaling
problems and harder
correspondence problems such as
n objects are connected to m
objects.
© Trinity Academy Halifax 2016
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

Harry buys 6 chocolate bars, one
chocolate bar costs 54p. How much
does Harry spend?
a) Write a number sentence to
represent the problem.
b) Solve the problem.
Dan is using a number machine.
Every number he puts in is
multiplied by the same number.
He puts 4 numbers in and the
numbers that come out are 21, 49,
84 and 140.
What could the machine be
multiplying by?
Laura is making a sequence using
shapes. She uses 3 circles, 4
pentagons and 5 rectangles. If she
uses the same pattern to make a
longer sequence, how many
pentagons will she use in a
sequence with 72 shapes
altogether?
Reasoning

Miss Smith estimates;
Problem Solving

399 x 60 = 240000
How many different
ice cream sundaes
can be created from
5 different flavours of
ice cream, 3 different
toppings and 4
different sauces?
Is this a good estimate?
Explain why.

In a box there are red and yellow
cubes.
For every 5 red cubes there are 3
yellow cubes.
Hannah says;
If I have more than 10
red cubes, I will
definitely have more
than 10 yellow cubes.
Do you agree? Convince me.
An ice cream sundae is made from
one scoop of ice cream, one
topping and one sauce.

Jenny needs to buy 20 cupcakes for
a party.
A shop has two offers on cupcakes.
5 cupcakes
for 40p
4 cupcakes
for 30p
Which offer is better?
How much money will Jenny spend
altogether?
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency
Multiplication and Division

Order the digits to make a three
digit number that is divisible by 3
and when you remove the final digit
it is divisible by 2.
1
2


Here is a multiplication pyramid.
Each number is made by multiplying
the two numbers below.
54
3
Using the digits 1 – 4, order the
digits to make a four digit number
that is divisible by 4 and when you
remove the final digit it is divisible
by 3 and if you remove the third
digit it is divisible by 2.
Do the same with five digits,
starting with a five digit number
that is divisible by 5.
Solve problems involving
multiplication and division
including using their
knowledge of factors and
multiples, squares and
cubes.
© Trinity Academy Halifax 2016
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Reasoning
6
8
9
2 3 3
2 1 3 1
Use this to complete this
multiplication pyramid.
48
Here are three number cards.
A
B
C
A + B + C = square number
A + B = square number
B + C = square number
A + C = 5 less and 6 more than
square numbers
What are the values of A, B and C?
4
2
2
Problem Solving

Six children are taking part in a
lottery game at school.
They have lotto balls with the
numbers 1-50 on them.
They have decided to split the balls
between them using the rules below.
Child A will have all the factors of 36.
Child B will have all the prime
numbers.
Child C will have all the multiples of
5.
Child D will have all the square
numbers.
Child E will have all the factors of 50.
Child F will have all the multiples of
3.
Are there any balls that need to be
shared between two or more
children?
Which child gets the most?
Which child gets the least?
Are any balls left over?
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency
Multiplication and Division


Solve problems involving
addition and subtraction,
multiplication and division
and a combination of these,
including understanding the
use of the equals sign.
© Trinity Academy Halifax 2016
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
I have 84 marbles.
I keep 19 for myself and share the
rest between 5 of my friends.
How many marbles will each friend
get?
There are 7 tubes of tennis balls
each with 6 balls in and a box of 31
balls.
How many balls are there
altogether?
Reasoning


I read 25 pages of a book each day
for 5 days and 78 pages over the
weekend.
How many pages do I read over the
week?

I have 47 trading cards.
I buy 7 new cards each week.
How many cards will I have in 8
weeks’ time?

A cinema has 4 screens each with 60
seats.
There are 195 people in the cinema.
How many empty seats are there?

Problem Solving
Complete the number sentences
using the same number in both
boxes.
24 +
=
x4
24 ÷
=
-2
Using the number cards 1 – 9 and the
four operations how many ways can
you make 100?
You must use each of the number
cards once but can you use the four
operations as many times as you
like.
Use four operations in the number
sentences below to balance each
side of the equals sign.
21
21
21
3 = 12
3 = 12
3 = 12
6
5
2
What’s the same and what’s
different about each of the number
sentences?

Sally bought five tickets to watch a
game of football with her friends.
The tickets were numbered in order.
When the numbers are added
together, they total 110.
What were the ticket numbers?

Can you fill in the missing digits using
the clues below?
x
6
The four digits being multiplied by 6
are consecutive numbers but not in
the right order.
The first and the final digit of the
answer are the same number.
The 2nd and 3rd digit of the answer
add up to the 1st digit of the answer.
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Complete the statements:
100cm = _____m
1km = ______m
1500ml = ______l
3.5kg = ________g
Perimeter

Convert between different
units of measure e.g
kilometre to metre.

The answer is 475 metres.
What could the question be?

Hamid says ‘To convert kilometres to
metres, add three zero’s on to the
end of the number.’
E.g 2km=2000m
Use the word and number cards to
complete the statements.
multiply
divide
10
100

A plank of wood is 4.6m long.
Two lengths are cut from the wood.
350cm
2 m
How much wood is left?

Laura is 2.72m tall.
She is 59cm taller than her sister.
How tall is her sister?
Give your answer in centimetres.

Put these amounts in order starting
with the largest.
1000
Are these statements true or false?
1000m = 1km
1000cm = 1m
1000ml = 1l
1000g = 1kg
1000mg = 1g
Problem Solving
Do you agree with Hamid?
Explain why.
To change from cm to mm _____ by __
To change from kg to g _____ by ____
To change from ml to l _____ by ____

© Trinity Academy Halifax 2016
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Reasoning

James and Sita do a sponsored walk
for charity.
They walk 1.2km altogether.
James walks double the amount that
Sita walks.
How far does Sita walk?
Half of 5 litres
Quarter of 8 litres
700 ml
They each raise 75p for every 100m
they walk.
How much money do they each
make?
Explain your thinking.
James ________
Sita _________
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Use <, > or = to complete the
statements below
750g
500ml
Reasoning

0.8kg
Perimeter
Convert between
different units of metric
measure (for example, km
and m; cm and m; cm and
mm; g and kg; l and ml)


A plank of wood is 5.8m long.
5.8m
Two lengths are cut from the wood.
175cm
A 5p coin has a thickness of 1.6mm
2cm – 5mm
True or false?
1000m = 1km
1000cm = 1m
1000ml = 1l
1000g = 1kg
3 m
How much wood is left?
Jake makes a tower of 5p coins
worth 90p.
What is the height of the coins in
cm?


Cola is sold in bottles and cans.
Laura buys 3500g of potatoes and
Yasmin buys 5 cans and 3 bottles.
She sells the cola in 100ml glasses.
1500g of carrots.
She sells all the cola.
How many glasses does she sell?
Bryan is 2.68m tall.
He is 99cm taller than his sister.
How tall is his sister?
Give your answer in centimetres.
She pays with a £20 note.
How much change does she get?
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
Half a litre

17mm
Adam makes 2.5 litres of lemonade
for a charity event. He pours it into
650ml glasses to sell.
He thinks he can sell 7 glasses.
Is he correct?
Prove it.
Problem Solving
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Find the perimeter of the rectangle.
Reasoning

8cm
Problem Solving
The perimeter of a square is 16cm.
How long is each side?

What is
the length
of the
rectangle?
3cm

80m
Perimeter
30m
Measure and calculate the
perimeter of a rectilinear
figure (including squares)
in cm and m
8
m
0
Which of these lengths
could be the perimeter
of the shape?
Draw and find the perimeter of the
shapes in centimetres.

The width of a rectangle is 2 metres
less than the length.
The perimeter of the rectangle is
between 20m and 30m.
Find the missing lengths on the shape
and calculate the perimeter.
4cm
What could the dimensions of the
rectangle be?
40mm
3cm
5cm
20mm
© Trinity Academy Halifax 2016
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
48cm 36cm 80cm 120cm 66cm
3
m
0

Here is a rectilinear shape. All the
sides are the same length and are a
whole number of centimetres.
The perimeter of the rectangle is
33m.
80mm
Draw all the rectangles that fit these
rules.
Use 1cm=1m.
Year 4 / 5
Term by Term Objectives
All students
National Curriculum
Statement
Fluency

Reasoning
Find the perimeter of the following
shapes.

4cm
The length labelled ‘x’ is a multiple
of 1.8
What could ‘y’ be?
Explain to a partner why you have
chosen these measurements.
16m
7cm
4.5m
10cm
x
Perimeter
12m
Problem Solving

Investigate the different ways you
can make composite rectilinear
shapes with a perimeter of 54cm.

Amy and Ayesha are making a
collage of their favourite football
team.
They want to make a border for the
canvas.
Here is the canvas.
0.4m
8cm
y
9m
Measure and calculate the
perimeter of composite
rectilinear shapes in cm
and m.
2.5m
8m
0.6m
0.6m
Here is a square inside another
square.
0.5m
x
1.5m
0.3m
0.3m
12cm
3
16cm
8 cm
19cm
© Trinity Academy Halifax 2016
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
The perimeter of the inner square is
16cm.
The outer square’s perimeter is four
times the size of the inner square.
What is the length of one sides of
the outer square?
How do you know?
What do you notice?
0.6m
They have a roll of blue ribbon that is
245cm long and a roll of red ribbon
that is 2.7m long.
How much ribbon will they have left
over?