Mathematics Medium Term Plan
Year 4
Reasoning strategiesThe strategies embedded in the activities are easily adaptable and can be integrated into your classroom routines. They have been gathered
from a range of sources including real lessons, past questions, children’s work and other classroom practice.
Strategies include:
Spot the mistake / Which is correct?
True or false?
What comes next?
Do, then explain
Make up an example / Write more statements / Create a question / Another and another
Possible answers / Other possibilities
What do you notice?
Continue the pattern
Missing numbers / Missing symbols / Missing information/Connected calculations
Working backwards / Use the inverse / Undoing / Unpicking
Hard and easy questions
What else do you know? / Use a fact
Fact families
Convince me / Prove it / Generalising / Explain thinking
Make an estimate / Size of an answer
Always, sometimes, never
Making links / Application
Can you find?
What’s the same, what’s different?
Odd one out
Complete the pattern / Continue the pattern
Another and another
Ordering
Testing conditions
The answer is…
Visualising
Autumn
Spring
Number and Place Value
Summer
The Big Ideas
Imagining the position of numbers on a horizontal number line helps us to order them: the number to the right on a number line is the larger number. So 5 is greater
than 4, as 5 is to the right of 4. But –4 is greater than –5 as –4 is to the right of –5.
Rounding numbers in context may mean rounding up or down. Buying packets of ten cakes, we might round up to the nearest ten to make sure everyone gets a cake.
Estimating the number of chairs in a room for a large number of people we might round down to estimate the number of chairs to make sure there are enough.
We can think of place value in additive terms: 456 is 400 + 50 + 6, or in multiplicative terms: one hundred is ten times as large as ten.
count in multiples of 6, 7, 9, 25 and 1000
count from zero in multiples of 6 and 9 A1/C1
Mastery
Gemma counts on in 25s from 50.
Circle the numbers that she will say:
990 550 125 755 150
count from zero in multiples of 7 and 11 A2/C2
Mastery with greater depth
Here is a sequence of numbers:
20, 30, 40, 50
What will the nineteenth number in the sequence be?
What will the hundredth number in the sequence be?
count from zero in multiples of 6, 7, 9, 11, 12, 25
and 1000 A3/C3
Reasoning
Spot the mistake:
950, 975,1000,1250
What is wrong with this sequence of numbers?
True or False?
324 is a multiple of 9?
find 1000 more or less than a given number
add and subtract a 4 digit number and hundreds
mentally using jottings to support me A1
find 100 more or less than a given number A2
add and subtract a 4 digit number and hundreds
mentally, finding 100 or 1000 more or less than a
given number A3
Mastery
Mastery with greater depth
Reasoning
What comes next?
6706+ 1000= 7706
7706 + 1000 = 8706
8706 + 1000 = 9706
……
count backwards through zero to include negative numbers
Mastery
Mastery with greater depth
recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
count backwards through zero to include negative
numbers A3
Reasoning
partition and recognise the value of each digit in 4 digit
numbers up to 10 000 A1
Mastery
Write the missing numbers in the boxes
partition and recognise the value of each digit in 4
digit numbers up to 10 000 A2
read and write numbers to 10 000 in numerals and
words A2/E2
Mastery with greater depth
The sea level is usually taken as zero.
Look at the picture of the lighthouse.
If the red fish is at –5 m (5 metres below sea level):
Where is the yellow fish?
Where is the green fish?
Reasoning
Do, then explain
Show the value of the digit 4 in these numbers?
3041
4321
5497
Explain how you know.
Make up an example Create four digit numbers
where the digit sum is four and the tens digit is one.
Eg 1210, 2110, 3010
What is the largest/smallest number?
What temperature is 20 degrees lower than 6 degrees Celsius?
order and compare numbers beyond 1000
order 4 digit numbers A1
begin to understand the place value of decimals to
one decimal place A3
begin to compare and order numbers beyond 1000 A2
compare and order numbers up to 10 000 A3
compare numbers with the same decimal places up
to 2 decimal places A3
Mastery
Kiz has these numbers:
1330 1303 1033 1003 1030
He writes them in order from smallest to largest.
What is the fourth number he writes?
Using these 4 digits:
Mastery with greater depth
5000 years ago Egyptians carved number symbols on
their tombs:
Reasoning
Do, then explain
5035 5053 5350 5530 5503
If you wrote these numbers in order starting with the
largest, which number would be third?
Explain how you ordered the numbers.
1730
What is the smallest number you can make?
What is the largest number you can make?
What is the value of these Egyptian numbers?
identify, represent and estimate numbers using different representations
identify, represent and estimate numbers using
identify, represent and estimate numbers using
different representations A1
different representations A2
Mastery
Mastery with greater depth
round any number to the nearest 10, 100 or 1000
round any number to the nearest 10 A1
Mastery
round any number to the nearest 10 or 100 A2
Mastery with greater depth
Reasoning
round any number to the nearest 10, 100 or 1000 A3
Reasoning
Possible answers
A number rounded to the nearest ten is 540. What is the
smallest possible number it could be?
What do you notice?
Round 296 to the nearest 10. Round it to the nearest 100. What
do you notice? Can you suggest other numbers like this?
solve number and practical problems that involve all of the above and with increasingly large positive numbers
solve number and practical problems that involve all of
the skills in this unit with increasingly large numbers
solve number and practical problems that involve
all of the skills in this unit with increasingly
solve number and practical problems that involve all of
the skills in this unit with increasingly large numbers
A1/A2/A3
large numbers A1/A2/A3
A1/A2/A3
work out how to solve problems with one or two steps
A3
Mastery
Match 4600 to numbers with the same value.
Mastery with greater depth
How many different ways can you write 5510?
Pupils should suggest answers such as:
• 551 tens
• 55 hundreds and 1 ten
• 5 thousands and 510 ones
Reasoning
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 1-10 (I - X) A1
read Roman numerals 1-50 (I - L) A2
read Roman numerals to 100 (I - C) A3
read Roman numerals 1-12 (1-XII) E
understand how the number system has changed over
time A3
Mastery
Mastery with greater depth
Reasoning
Mathematics Medium Term Plan
Autumn
Year 4
Spring
Addition and subtraction:
Summer
The Big Ideas
It helps to round numbers before carrying out a calculation to get a sense of the size of the answer. For example, 4786 – 2135 is close to 5000 – 2000, so the answer will
be around 3000. Looking at the numbers in a calculation and their relationship to each other can help make calculating easier. For example, 3012 – 2996. Noticing that
the numbers are close to each other might mean this is more easily calculated by thinking about subtraction as difference.
Mental calculations
Reasoning
True or false?
Are these number sentences true or false?6.7 + 0.4 =
6.11
8.1 – 0.9 = 7.2
Give your reasons.
Hard and easy questions
Which questions are easy / hard?
13323 - 70 =
12893 + 300 =
19354 - 500 =
19954 + 100 =
Explain why you think the hard questions are hard?
add and subtract numbers with up to 4 digits using the
add and subtract numbers with up to 2 digits using the
formal written methods of columnar addition and
subtraction where appropriate C1
Mastery
Fill in t6
+33he empty boxes to make the equations correct.
formal written methods of columnar addition and subtraction where appropriate
add and subtract numbers with up to 3 digits using
add and subtract numbers with up to 4 digits
the formal written methods of columnar addition
using the formal written methods of columnar
and subtraction where appropriate C2
addition and subtraction where appropriate C3
Mastery with greater depth
Reasoning
Complete this diagram so that the three numbers in
Convince me
each row and column add up to 140.
- 666 = 8 5
What is the largest possible number that will go
in the rectangular box?
What is the smallest?
Convince me
Now create your own diagram with a total of 250.
Decide on a mental or written strategy for each of these
calculations and perform them with fluency.
• 64 + 36
• 640 + 360
• 64 + 79 + 36
• 378 + 562
• 876 + 921
• 999 + 999
• 1447 + 2362
• 1999 + 874
Ali and Sarah calculate 420 + 221 + 280 using different
strategies.
Write three calculations where you would use mental
calculation strategies and three where you apply a
column method.
Explain the decision you made for each calculation.
Write >, = or < in each of the circles to make the
number sentence correct.
Pupils should reason about the numbers and
relationships, rather than calculate.
Which do you prefer?
Explain your reasoning.
Now calculate 370 + 242 + 130 using your preferred
strategy.
estimate and use inverse operations to check answers to a calculation
estimate and check the result of a calculation
A1/A2/A3
estimate and use inverse operations to check answers to
estimate and check the result of a calculation
A1/A2/A3
estimate and use inverse operations to check
estimate and check the result of a calculation
A1/A2/A3
estimate and use inverse operations to check
a calculation C1/C2/C3
answers to a calculation C1/C2/C3
answers to a calculation C1/C2/C3
Mastery
Write down the four relationships you can see in the bar
model.
Mastery with greater depth
Identify the missing numbers in these bar models.
They are not drawn to scale.
Reasoning
Making an estimate
Which of these number sentences have the
answer that is between 550 and 600
1174 - 611
3330 – 2779
9326 - 8777
Always, sometimes, never
Is it always sometimes or never true that the
difference between two odd numbers is odd.
Select your own numbers to make this bar model
correct.
Fill in the missing numbers.
Fill in the missing digits
What do you notice about the calculations below?
Can you find easy ways to calculate?
Find the missing numbers.
What do you notice?
solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why
explain how I add and subtract two-digit numbers in my explain how I solve problems, using diagrams and
solve addition and subtraction two-step
head A1
symbols to help me A2
problems in contexts, deciding which operations
solve addition and subtraction two-step problems in
solve addition and subtraction two-step problems in and methods to use and why C1/C2/C3
contexts, deciding which operations and methods to use contexts, deciding which operations and methods to
and why C1/C2/C3
use and why C1/C2/C3
Mastery
Mastery with greater depth
Reasoning
Mathematics Medium Term Plan
Autumn
Year 4
Spring
Multiplication and division:
Summer
The Big Ideas
It is important for children not just to be able to chant their multiplication tables but to understand what the facts in them mean, to be able to use these facts to figure
out others and to use them in problems.
It is also important for children to be able to link facts within the tables (e.g. 5× is half of 10×).
They understand what multiplication means and see division as both grouping and sharing, and to see division as the inverse of multiplication.
The distributive law can be used to partition numbers in different ways to create equivalent calculations. For example, 4 × 27 = 4 × (25 + 2) = (4 × 25) + (4 × 2) = 108.
Looking for equivalent calculations can make calculating easier. For example, 98 × 5 is equivalent to 98 × 10 ÷ 2 or to (100 × 5) – (2 × 5). The array model can help show
equivalences.
recall multiplication and division facts for multiplication tables up to 12 × 12
recall and use multiplication and division for the 6 and 9 recall and use multiplication and division for the 7
recall and use multiplication and division facts
times tables A1/C1
and 11 times tables A2/C2
up to 12x12 A3/C3
Mastery
Mastery with greater depth
Reasoning
Use your knowledge of multiplication tables to complete
True or false?
Missing numbers
these calculations.
• 7×6=7×3×2
• 7×6=7×3+3
72 x
Explain your reasoning.
Which pairs of numbers could be written in the
Can you write the number 30 as the product of 3
boxes?
numbers?
Can you do it in different ways?
Which calculations have the same answer? Can you
explain why?
By the end of the year pupils should be fluent with all table
facts up to 12 × 12 and also be able to apply these to
calculate unknown facts, such as 12 × 13.
What do you notice about the following calculations? Can
you use one calculation to work out the answer to other
calculations?
2×3=
6×7=
9×8=
2 × 30 =
6 × 70 =
9 × 80 =
Place one of these symbols in the circle to make the
number sentence correct:
>, < or =.
Explain your reasoning.
Making links Eggs are bought in boxes of 12. I
need 140 eggs; how many boxes will I need to
buy?
2 × 300 = 6 × 700 =
20 × 3 = 60 × 7 =
200 × 3 = 600 × 7 =
9 × 800 =
90 × 8 =
900 × 8 =
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
use place value, known and derived facts to multiply and
use place value, known and derived facts to multiply
derive facts linked to the multiplication tables
divide mentally, including multiplying by 0 and 1 C1
and divide mentally, including dividing by 1 C2
that Know (e.g. If Know that 4x6=24, I also
know that 24÷6=4 and 240÷6=40) A3/B3
Mastery
Three children calculated 7 × 6 in different ways.
Identify each strategy and complete the calculations.
Mastery with greater depth
Multiply a number by itself and then make one factor
one more and the other one less. What happens to the
product?
E.g.
4 × 4 = 16
6 × 6 = 36
5 × 3 = 15
7 × 5 = 35
What do you notice? Will this always happen?
use place value, known and derived facts to
multiply and divide mentally, including
multiplying together three numbers (e.g. know
and can use the associative law 2 x (3 x 4) = (2
x 3) x 4 & know 2 x 6 x 5 = 10 x 6 C3
Reasoning
Use a fact
63 ÷ 9 = 7
Use this fact to work out
126 ÷ 9 =
252 ÷ 7 =
Now find the answer to 6 × 9 in three different ways.
recognise and use factor pairs and commutativity in mental calculations
identify factor pairs A1
recognise and use factor pairs in mental calculation
for x and ÷ A2 B2
Mastery
Mastery with greater depth
Reasoning
Making links
How can you use factor pairs to solve this
calculation?
13 x 12
(13 x 3 x 4, 13 x 3 x 2 x 2, 13 x 2 x 6)
Always, sometimes, never?
Is it always, sometimes or never true that an even
number that is divisible by 3 is also divisible by 6.
Is it always, sometimes or never true that the
sum of four even numbers is divisible by 4.
multiply two-digit and three-digit numbers by a one-digit number using formal written layout
multiply two-digit numbers by a one-digit number C1 multiply two-digit numbers by a one-digit number
using formal written layout C2
Mastery
Mastery with greater depth
multiply two-digit and three-digit numbers by a onedigit number using formal written layout C3
Reasoning
Prove It
What goes in the missing box?
6 x 4 = 512
Prove it.
How close can you get?
X 7
Using the digits 3, 4 and 6 in the calculation above
how close can you get to 4500? What is the largest
product? What is the smallest product?
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 multiplying and adding,
including using the distributive law to multiply twodigit numbers by one-digit (e.g. distributive law 39
x 7 = 30 x 7 + 9 x 7 )C1/C2/C3
Mastery
Tom ate 9 grapes at the picnic. Sam ate 3 times as
many grapes as Tom.
How many grapes did they eat altogether?
The bar model is a useful scaffold to develop fluency in
this type of question
solve problems involving multiplying and adding,
including using the distributive law to multiply twodigit numbers by one-digit (e.g. distributive law 39
x 7 = 30 x 7 + 9 x 7 )C1/C2/C3
Mastery with greater depth
Sally has 9 times as many football cards as Sam.
Together they have 150 cards.
How many more cards does Sally have than Sam?
The bar model is a useful scaffold to develop fluency in
this type of question.
solve problems involving multiplying and adding,
including using the distributive law to multiply twodigit numbers by one-digit (e.g. distributive law 39
x 7 = 30 x 7 + 9 x 7 )C1/C2/C3
solve integer scaling problems & harder
correspondence problems such as n objects are
connected to m objects C3
Reasoning
[Algebra]
Connected Calculations
Put the numbers 7.2, 8, 0.9 in the boxes to make the
number sentences correct.
=
x
=
÷
Estimate and use inverse operations to check the answers to a calculation
Reasoning
Use the inverse
Use the inverse to check if the following calculations
are correct:
23 x 4 = 92
117 ÷ 9 = 14
Size of an answer
Will the answer to the following calculations be
greater or less than 300
152 x 2=
78 x 3 =
87 x 3 =
4 x 74 =
Mathematics Medium Term Plan
Autumn
Year 4
Spring
Fractions
Summer
The Big Ideas
Fractions arise from solving problems, where the answer lies between two whole numbers.
Fractions express a relationship between a whole and equal parts of a whole. Children should recognise this and speak in full sentences when answering a question
involving fractions. For example, in response to the question What fraction of the chocolate bar is shaded? the pupil might say Two sevenths of the whole chocolate bar is
shaded.
Equivalency in relation to fractions is important. Fractions that look very different in their symbolic notation can mean the same thing.
recognise and show, using diagrams, families of common equivalent fractions
recognise and show, using diagrams, families of
use the number line to connect fractions, numbers
common equivalent fractions (using factors and
and measures with numbers up to 10 D2
multiples to help me) D1
use the number line to connect fractions, numbers
and measures with numbers less than one D1
understand that fractions and decimals are a way of
expressing proportions D1/D2/D3
understand that fractions and decimals are a way of
expressing proportions D1/D2/D3
Mastery
Draw diagrams to show two fractions that are equivalent
to 2/8
Mastery with greater depth
How many ways can you express 2/8 as a fraction?
.
use the number line to connect fractions, numbers
and measures with numbers beyond 10 D3
understand that fractions and decimals are a way of
expressing proportions D1/D2/D3
Reasoning
Odd one out.
Which is the odd one out in each of these trio
s¾
9/12 4/6
9/12
10/15 2/3
Why?
What do you notice?
Find 4/6 of 24
Find 2/3 of 24
What do you notice?
Can you write any other similar statements?
count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten
recognise that hundredths are made by dividing an
recognise that hundredths are made by dividing
recognise that hundredths are made by dividing an
object by a hundred D1
tenths by 10 D2
object by a hundred and dividing tenths by 10 D3
count up and down in hundredths D1
count forwards and backwards using simple fractions
and decimal fractions D1
Mastery
Mastery with greater depth
Reasoning
Spot the mistake
sixty tenths, seventy tenths, eighty tenths, ninety tenths,
twenty tenths
… and correct it.
What comes next?
83/100, 82/100, 81/100, ….., ….., …..
31/100, 41/100, 51/100, ….., …..,
What do you notice?
1/10 of 100 = 10
1/100 of 100 = 1
2/10 of 100 = 20
2/100 of 100 = 2
How can you use this to work out 6/10 of 200?
6/100 of 200?
True or false?
1/20 of a metre= 20cm
4/100 of 2 metres = 40cm
solve problems involving increasingly harder fractions
is a whole number
solve problems involving increasingly harder fractions
to calculate quantities, and fractions to divide
quantities, including non-unit fractions where the
answer is a whole number D1/D2/D3
Mastery
Put these fractions on the number line:
to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer
solve problems involving increasingly harder fractions
to calculate quantities, and fractions to divide
quantities, including non-unit fractions where the
answer is a whole number D1/D2/D3
solve problems involving increasingly harder fractions
to calculate quantities, and fractions to divide
quantities, including non-unit fractions where the
answer is a whole number D1/D2/D3
Mastery with greater depth
Insert the symbol >, < or = to make each statement
correct.
Reasoning
Make up three similar statements using >, < or =.
8 girls share 6 bars of chocolate equally.
12 boys share 9 bars of chocolate equally.
Who gets more chocolate to eat, each boy or each girl?
How do you know?
Draw a diagram to explain your reasoning.
Find:
• 1/10 of 10
• 1/10 of 20
• 1/10 of 30
• 1/10 of 40
• 1/10 of 50
What do you notice?
What’s the same? What’s different?
Children should be able to express the ideas that:
• They are all divided into 4 equal parts.
• Each part represents a quarter of the whole.
• Each of the parts in the triangle are the same
shape and area (congruent).
• The shapes in the square are different but each
has the same area (not congruent).
• The bananas represent fractions of quantities.
If the picture represents 2/12 of a rectangle, draw a
picture of the whole rectangle.
Can you draw it in two different ways?
8 girls share 6 bars of chocolate equally.
12 boys share 9 bars of chocolate equally.
Clare says each girl got more to eat as there were fewer
of them.
Rob says each boy got more to eat as they had more
chocolate to share.
Explain why Clare and Rob are both wrong.
Captain Conjecture says,
'To find a tenth of a number I divide by 10 and to find a
fifth of a number I divide by 5.'
Do you agree?
Explain your reasoning.
Two paper strips are ripped. Identify which original
paper strip is longer.
Explain your answer.
If the picture represents 1/3 of a shape, draw the whole
shape.
add and subtract fractions with the same denominator
add and subtract several fractions with the same
add and subtract two fractions with the same
denominator (answers less than 1) D1
denominator, even if the answer is more than one D2
Mastery
Mastery with greater depth
True or false?
Peter wrote down two fractions. He subtracted the
smaller fraction from the larger and got 1/8 as the
answer.
Write down two fractions that Peter could have
subtracted.
Can you find another pair?
add and subtract several fractions with the same
denominator, even if the answer is more than one D3
Reasoning
What do you notice?
5/5 – 1/5 = 4/5
4/5 – 1/5 = 3/5
Continue the pattern
Explain your reasoning.
Can you make up a similar pattern for addition?
The answer is 3/5, what is the question?
What do you notice?
11/100 + 89/100 = 1
12/100 + 88/100 = 1
13/100 + 87/100 = 1
Continue the pattern for the next five number
sentences
A soup recipe uses 3 4 as many onions as carrots. Jo is
making the soup and has 8 carrots.
How many onions does Jo use?
A soup recipe uses 3/4 as many onions as carrots.
Complete the table below.
Explain how you worked out the number of onions. Did
you use the same method
each time?
Recognise decimal equivalents of ½, ¼, ¾
Reasoning
Ordering
Put these numbers in the correct order, starting with
the smallest.
¼
0.75
5/10
Explain your thinking
recognise and write decimal equivalents of any number of tenths or hundredths
recognise and write decimal equivalents of any
number of tenths or hundredths D2
Mastery
Mastery with greater depth
Match each fraction to its decimal equivalent.
Using these cards can you make a number between 4·1
and 4·61?
Reasoning
Complete the pattern by filling in the blank cells in this
table:
1
10
10
100
0.1
Circle the equivalent fraction to 0·25
2
10
20
100
3
10
40
100
0.3
Round to the nearest whole number.
What is the smallest number you can make using all four
cards?
Another and another
Write a decimal numbers (to one decimal place) which
lies between a half and three quarters?
… and another, … and another,
What is the largest number you can make using all
four cards?
A soup recipe uses 3 4 as many onions as carrots. Jo is
making the soup and has 8 carrots.
How many onions does Jo use?
A soup recipe uses 3/4 as many onions as carrots.
Complete the table below.
Explain how you worked out the number of onions. Did
you use the same method each time?
find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths;
round decimals with one decimal place to the nearest whole number
round decimals with one decimal place to the nearest
find the effect of dividing a one- or two-digit
whole number D2
number by 10 and 100, identifying units, tenths and
hundredths D3
begin to understand the place value of decimals to
one decimal place E3
Mastery
Mastery with greater depth
Reasoning
Do, then explain
Circle each decimal which when rounded to the nearest
whole number is 5.
5.3 5.7 5.2 5.8
Explain your reasoning
Top tips
Explain how to round numbers to one decimal place?
Also see rounding in place value
Undoing
I divide a number by 100 and the answer is 0.3. What
number did I start with?
Another and another
Write down a number with one decimal place which
when multiplied by 10 gives an answer between 120
and 130.
... and another, … and another,
Compare and order fractions
Reasoning
Give an example of a fraction that is more than a half
but less than a whole.
Now another example that no one else will think of.
Explain how you know the fraction is more than a half
but less than a whole. (draw an image)
compare numbers with the same number of decimal places up to two decimal places
compare and order decimal amounts and quantities
(with one decimal place)D1
compare and order decimal amounts and quantities
(where all numbers have two decimal places) D2
compare and order decimal amounts and quantities
(with the same number of decimal places) D3
Mastery
Mastery with greater depth
Reasoning
Missing symbol
Put the correct symbol < or > in each box
3.03
3.33
0.37
0.32
What needs to be added to 3.23 to give 3.53?
What needs to be added to 3.16 to give 3.2?
solve simple measure and money problems involving fractions and decimals to two decimal places
solve simple measure and money problems D1
solve simple measure and money problems involving
fractions and decimals to one decimal place D2
Mastery
Mastery with greater depth
solve simple measure and money problems involving
fractions and decimals to two decimal places D3
Reasoning
Mathematics Medium Term Plan
Autumn
Year 4
Spring
Measurement
Summer
The Big Idea
The smaller the unit, the greater the number of units needed to measure (that is, there is an inverse relationship between size of unit and measure).
convert between different units of measure [for example, kilometre to metre; hour to minute]
convert between different measures (e.g. kilometre
to metre; hour to minute) E2/E3
Mastery
Mastery with greater depth
Complete the missing measures so that each line of
In total Sam and Tom together cycle a distance of 120
three gives a total distance of 2 km.
km. Sam cycles twice the distance that Tom cycles. How
far does Sam cycle?
measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres
measure and calculate the perimeter of a rectilinear
figure (including squares) in centimetres E1
convert between different measures (e.g. kilometre
to metre; hour to minute) E2/E3
Reasoning
The answer is ….
225 metres
What is the question?
measure & calculate the perimeter of a rectilinear
figure (including squares) in centimetres & metres &
can begin to record this in algebra (e.g. 2(a + b) where
a & b are the dimensions in the same unit E3
Mastery
The shape below is made from two rectangles.
Identify the perimeter of each of the two rectangles.
How many 1 cm squares would fit into the smaller
rectangle?
How many more squares fit into the larger rectangle?
Mastery with greater depth
The rectangular tiles here are three times as long as they
are wide.
What is the perimeter of the centre square?
Reasoning
[Algebra]
Undoing
If the longer length of a rectangle is 13cm and the
perimeter is 36cm, what is the length of the shorter
side?
Explain how you got your answer.
Testing conditions
If the width of a rectangle is 3 metres less than the
length and the perimeter is between 20 and 30 metres,
what could the dimensions of the rectangle lobe?
Convince me.
find the area of rectilinear shapes by counting squares
find the area of rectilinear shapes by counting
squares E2/E3
Mastery
Mastery with greater depth
find the area of rectilinear shapes by counting
squares E2/E3
Reasoning
Always, sometimes, never
If you double the area of a rectangle, you double the
perimeter.
See also Geometry Properties of Shape
estimate, compare and calculate different measures,
estimate and calculate different measures including
money in pounds and pence E1/E2
compare different measures including money in
pounds and pence E1
Mastery
Complete the missing measures so that each line of
three gives a total distance of 2 km.
including money in pounds and pence
estimate and calculate different measures including
money in pounds and pence E1/E2
Mastery with greater depth
In total Sam and Tom together cycle a distance of 120
km. Sam cycles twice the distance that Tom cycles. How
far does Sam cycle?
estimate, calculate and compare different measures
including money in pounds and pence E3
Reasoning
Top Tips
Put these amounts in order starting with the largest.
Half of three litres
Quarter of two litres
300 ml
Explain your thinking
Position the symbols
Place the correct symbols between the measurements >
or <
£23.61 2326p
2623p
Explain your thinking
An empty box weighs 0·5 kg. Ivy puts 10 toy bricks
inside it and the box now weighs 2 kg.
How much does each brick weigh?
How much does the car weigh in grams?
How much does the doll weigh in grams?
Write more statements
One battery weighs the same as 60 paperclips;
One pencil sharpener weighs the same as 20 paperclips.
Write down some more things you know.
How many pencil sharpeners weigh the same as a
battery?
Which would you rather have, 3 × 50p coins or 7 × 20p
coins?
Explain your reasoning.
Sid and Sam share some money. Sid gets twice as much
as Sam. Tick the coins which Sid might take.
Possibilities
Adult tickets cost £8 and Children’s tickets cost £4. How
many adult and children’s tickets could I buy for £100
exactly?
Can you find more than one way of doing this?
Put these amounts in order starting with the largest.
Half of 3 litres
Quarter of 2 litres
Is there more than one way of sharing the coins?
Fill in the missing boxes so that the amounts are in order
from smallest to greatest.
300 ml
Explain your thinking.
read, write and convert time between analogue and digital 12- and 24-hour clocks
read and write time in both analogue and digital 12
read and write time in both analogue and digital 12
and 24 hour clocks E1
and 24 hour clocks (using Roman numerals from I to
convert time between analogue and digital 12 and 24
XII) E2/E3
hour clocks E1/E3
Mastery
Mastery with greater depth
convert time between analogue and digital 12 and 24
hour clocks E1/E3
read and write time in both analogue and digital 12
and 24 hour clocks (using Roman numerals from I to
XII) E2/E3
Reasoning
Explain thinking
The time is 10:35 am.
Jack says that the time is closer to 11:00am than to
10:00am.
Is Jack right? Explain why.
What do you notice?
What do you notice?
1:00pm = 13:00
2:00pm = 14:00
Continue the pattern
solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days
solve problems involving converting from hours to
solve problems involving converting from hours to
solve problems involving converting from hours to
minutes; minutes to seconds E1
minutes; minutes to seconds; years to months E2
minutes; minutes to seconds; years to months; weeks
to days E3
Mastery
Mastery with greater depth
Reasoning
Undoing
Imran’s swimming lesson lasts 50 mins and it takes 15
mins to change and get ready for the lesson. What time
does Imran need to arrive if his lesson finishes at
6.15pm?
Working backwards
Put these times of the day in order, starting with the
earliest time.
A: Quarter to four in the afternoon
B: 07:56
C: six minutes to nine in the evening
D: 14:36
Mathematics Medium Term Plan
Autumn
Year 4
Spring
Properties of shapes:
Summer
The Big Ideas
During this year, pupils increase the range of 2-D and 3-D shapes that they are familiar with. They know the correct names for these shapes, but, more importantly, they
are able to say why certain shapes are what they are by referring to their properties, including lengths of sides, size of angles and number of lines of symmetry.
The naming of shapes sometimes focuses on angle properties (e.g. a rectangle is right-angled), and sometimes on properties of sides (e.g. an equilateral triangle is an
equal sided triangle).
Shapes can belong to more than one classification. For example, a square is a rectangle, a parallelogram, a rhombus and a quadrilateral.
compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
know and can identify isosceles, equilateral and scalene
triangles B1
compare & classify geometric shapes, including
triangles, based on their properties and sizes B1
record my sorting and classifying in appropriate tables
and charts B1/B2/B3
use ICT to help me solve problems B1/B2/B3
compare lengths and angles in order to identify if
shapes are regular or irregular B1/B2
record my sorting and classifying in appropriate
tables and charts B1/B2/B3
use ICT to help me solve problems B1/B2/B3
Mastery
Below are five quadrilaterals: a rectangle, a rhombus, a
square, a parallelogram and an unnamed quadrilateral.
Write the names of each of the quadrilaterals.
Draw lines from each shape to match the properties
described in the boxes below.
Mastery with greater depth
Captain Conjecture says that a rectangle is a regular
shape because it has four right angles.
Do you agree? Explain your reasoning.
Captain Conjecture says that a quadrilateral can
sometimes
only have three right angles.
compare & classify geometric shapes, including
quadrilaterals, based on their properties and sizes
B2
record my sorting and classifying in appropriate
tables and charts B1/B2/B3
use ICT to help me solve problems B1/B2/B3
know and can identify; isosceles, equilateral and
scalene triangles and the quadrilaterals;
parallelogram, rhombus and trapezium B3
compare lengths and angles in order to identify if
shapes are regular or irregular B1/B2
know and can identify the quadrilaterals;
parallelogram, rhombus and trapezium B2
Reasoning
Visualising
Imagine a square cut along the diagonal to make
two triangles. Describe the triangles.
Join the triangles on different sides to make new
shapes. Describe them. (you could sketch them)
Are any of the shapes symmetrical? Convince me.
Do you agree? Explain your reasoning.
Always, sometimes, never
Is it always, sometimes or never true that the two
diagonals of a rectangle meet at right angles.
Other possibilities
Can you show or draw a polygon that fits both of
these criteria?
What do you look for?
”Has exactly two equal sides.”
”Has exactly two parallel sides.”
identify acute and obtuse angles and compare and order angles up to two right angles by size
use a protractor to measure angles B1
identify obtuse angles B2
identify acute angles B1
Mastery
Mastery with greater depth
identify acute and obtuse angles B3
compare and order angles up to two right
angles by size B3
Reasoning
Convince me
Ayub says that he can draw a right angled triangle
which has another angle which is obtuse.
Is he right?
Explain why.
identify lines of symmetry in 2-D shapes presented in different orientations
identify lines of symmetry in 2-D shapes
presented in different orientations B3
recognise line symmetry in a variety of
diagrams, including where the line of symmetry
does not dissect the reflected shape B3
Mastery
Draw some 2-D shapes that have:
• no lines of symmetry
• 1 line of symmetry
• 2 lines of symmetry.
Mastery with greater depth
Tom says, ‘In each of these shapes the red line is a
line of symmetry.’
Do you agree?
Explain your reasoning.
Reasoning
What’s the same, what’s different?
What is the same and what is different about the
diagonals of these 2-D shapes?
complete a simple symmetric figure with respect to a specific line of symmetry
solve problems involving symmetry and coordinates in
the first quadrant B1/B2/B3
Mastery
solve problems involving symmetry and coordinates
in the first quadrant B1/B2/B3
solve problems involving symmetry and
coordinates in the first quadrant B1/B2/B3
complete a simple symmetric figure with respect to
a specific line of symmetry with different
orientations of lines of symmetry B2/B3
complete a simple symmetric figure with
respect to a specific line of symmetry with
Mastery with greater depth
different orientations of lines of symmetry
B2/B3
Reasoning
Other possibilities
Can you draw a non-right angled triangle with a
line of symmetry?
Are there other possibilities.
Mathematics Medium Term Plan
Autumn
Year 4
Spring
Position and direction
describe positions on a 2-D grid as coordinates in the first quadrant
describe positions on a 2-D grid as coordinates in the
draw a pair of axes in one quadrant, with equal
first quadrant B1
scales and integer labels B2
Mastery
Mastery with greater depth
Summer
Reasoning
Working backwards
Here are the co-ordinates of corners of a
rectangle which has width of 5.
(7, 3) and (27, 3)
What are the other two co-ordinates?
describe movements between positions as translations of a given unit to the left/right and up/down
describe movements between positions as translations
of a given unit to the left/right and up/down B1
Mastery
Mastery with greater depth
Reasoning
plot specified points and draw sides to complete a given polygon.
plot specified points and draw sides to complete a given
read, write and use pairs of coordinates (2,5)
polygon B1
including using coordinate-plotting ICT tools B2
Mastery
Mastery with greater depth
Reasoning
Mathematics Medium Term Plan
Autumn
Year 4
Spring
Statistics
Summer
The Big Ideas
In mathematics the focus is on numerical data. These can be discrete or continuous. Discrete data are counted and have fixed values, for example the number of
children who chose red as their favourite colour (this has to be a whole number and cannot be anything in between). Continuous data are measured, for example at
what time did each child finish the race? (Theoretically this could be any time: 67·3 seconds, 67·33 seconds or 67·333 seconds, depending on the degree of accuracy
that is applied.) Continuous data are best represented with a line graph where every point on the line has a potential value.
interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs.
present discrete and continuous data using appropriate
present discrete and continuous data using
present discrete and continuous data using
graphical methods E1
appropriate graphical methods, including bar charts appropriate graphical methods, including bar
interpret discrete and continuous data using
E
charts and time graphs E3
appropriate graphical methods E1
interpret discrete and continuous data using
interpret discrete and continuous data using
appropriate graphical methods, including bar charts appropriate graphical methods, including bar
E2
charts and time graphs E3
use an increasing range of scales in my
representations E3
Mastery
Check that children can answer questions about data
presented in different ways:
Are they able to make connections when looking at the
same data presented differently?
Can they answer questions about the data using inference
and deduction or only direct retrieval?
Are they able to present data in different ways?
Do they label axes correctly?
Do they understand the scale and do they use an
appropriate scale when presenting data?
Mastery with greater depth
Children hypothesise beyond the data that are
presented, asking and answering questions such as
‘What would happen if..?’
These two graphs represent the same data.
What’s the same? What’s different?
Make up a story that fits the graph.
Reasoning
True or false? (Looking at a graph showing how
the class sunflower is growing over time) “Our
sunflower grew the fastest in July”.
Is this true or false?
Convince me.
Make up your own ‘true/false’ statement about
the graph.
What’s the same, what’s different?
Pupils identify similarities and differences
between different representations and explain
them to each other
Which graph is better?
Explain your reasoning.
solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs
solve comparison, sum and difference problems using
solve comparison, sum and difference problems
solve comparison, sum and difference problems
information presented in bar charts, pictograms and
using information presented in bar charts,
using information presented in bar charts,
tables E1
pictograms, tables and other graphs E2/E3
pictograms, tables and other graphs E2/E3
Mastery
Mastery with greater depth
Reasoning
Here is a table of the average temperature for each month of Here is a table of the average temperature for each
Create a questions Pupils ask (and answer)
last year:
month of last year:
questions about different statistical
representations using key vocabulary relevant to
the objectives.
(see above)
Answer the questions below and explain your reasoning:
On average what was the hottest month of the year?
In which months was the average temperature below
10°C?
In which months would you choose to go outside without
your coat on?
Choose another way to represent the data.
Write the word ‘true’, ‘false’ or ‘unknown’ next to each
statement, giving an explanation for each response.
I would need to wear my coat outside in January.
The hottest day of the year was in August.
A temperature of –2 was recorded in January.
Choose two other ways to represent the data.