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Subtraction one exchange - Foundation, Core and Higher
These are differentiated worksheets for year 4 covering subtraction with one exchange
They are well differentiated, and answers are attached for easy check.
One exchange Foundation, Core , higher
Each sheet comes with well explained answers.
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Addition, Decimals Fractions Reasoning
These are reasoning activities with well differentiated tasks.
with answer sheets
Reasoning with addition - two worksheets
decimals up to two places - Foundation
Tenths as decimals - Foundation, Core and Higher.
Tenths on a place value chart - Foundation , Core and Higher
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Decimals Reasoning
These are year 4 reasoning activities.
Decimals - divide whole number by 10
Tenths as decimals - Foundation, Core and Higher
Tenths on a place value chart - Foundation, Core and Higher.
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Addition
In these worksheets, children revisit the use of the column method for addition and learn to apply this method to numbers with more than four digits.
As a support in this step the place value counters, and place value charts will be extremely helpful.
These representations are particularly useful when performing calculations that require an exchange.
Ask, “Will you need to make an exchange?”
“Which columns will be affected if you do need exchange?”
" How do you know?"
Watch for:
Children may not line up the numbers in the columns correctly.
Adding 4-digit numbers with one exchange Higher with reasoning sheet
The numbers can be made using place value counters in a place value chart, alongside the formal written method.
When discussing where to start an addition, it is important to use language such as begin from the “smallest value column” rather than the “ones column” to avoid any misconceptions when decimals are introduced later in the year.
After each column is added, ask,
“Do you have enough ones/ tens/hundreds to make an exchange?”
Extra reasoning sheet attached.
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Adding and Subtracting Mental strategies
Add and subtract numbers mentally with increasingly large numbers.
In this worksheet, children recap and build on their learning from
previous years to mentally calculate sums and differences using
partitioning.
They use their knowledge of number bonds and place
value to add and subtract multiples of powers of 10.
If they know that 3 + 4 = 7, then 3 thousand + 4 thousand = 7 thousand
and 3,000 + 4,000 = 7,000.
Children need to be fluent in their knowledge of number
bonds to support the mental strategies.
How does knowing that 6 + 3 = 9 help you to work out 60,000 + 30,000?
“How can the numbers be partitioned to help add/subtract them?”
"Are any of the numbers multiples of powers of 10? "
“How does this help you to add/subtract them?”
Adding two numbers with no exchange with extra reasoning sheet.
In this worksheet, children add 3- or 4-digit numbers with no exchanges, using concrete resources as well as the formal written method.
The numbers being added together may have a different number
of digits, so children need to take care to line up the digits correctly.
Even though there will be no exchanging, the children
should be encouraged to begin adding from the ones column.
With extra reasoning activity sheet
Add numbers with up to four digits using the formal written methods of columnar addition.
Solve addition two-step problems in contexts, deciding which operations and methods to use and why.
Adding and Subtracting Mental strategies Higher
Add and subtract numbers mentally with increasingly large numbers.
In this worksheet, children recap and build on their learning from
previous years to mentally calculate sums and differences using
partitioning.
Children explore strategies such as compensation and
adjustment to mentally calculate the answer to questions
such as 73,352 + 999 or 16,352 − 999.
Children need to be fluent in their knowledge of number
bonds to support the mental strategies.
"Are any of the numbers multiples of powers of 10? "
“How does this help you to add/subtract them?”
"What number is 999 close to?
“How does that help you to add/subtract 999 from another number?”
Adding and Subtracting Mental strategies Foundation
Add and subtract numbers mentally with increasingly large numbers.
In this worksheet, children recap and build on their learning from
previous years to mentally calculate sums and differences using
partitioning.
They use their knowledge of number bonds and place
value to add and subtract multiples of powers of 10.
If they know that 3 + 4 = 7, then 3 thousand + 4 thousand = 7 thousand
and 3,000 + 4,000 = 7,000.
Children need to be fluent in their knowledge of number
bonds to support the mental strategies.
How does knowing that 6 + 3 = 9 help you to work out 60,000 + 30,000?
“How can the numbers be partitioned to help add/subtract them?”
"Are any of the numbers multiples of powers of 10? "
“How does this help you to add/subtract them?”
Efficient Subtraction Core
The purpose of this worksheet is to encourage
children to make choices about which method is most appropriate
for a given calculation. Children can often become reliant on
formal written methods, so it is important to explicitly highlight
where mental strategies or less formal jottings can be more
efficient.
Children explore the concept of constant difference, where
adding or subtracting the same amount to/from both numbers
in a subtraction means that the difference remains the same,
for example 3,835 – 2,999 = 3,835 – 3,000 or 700 – 293 = 699 – 292.
This can help make potentially tricky subtractions with multiple
exchanges much simpler, sometimes even becoming calculations
that can be performed mentally.
Number lines can be used to support understanding of this concept.
Rounding to check answers Higher
Round any number up to 1,000,000 to the nearest 10, 100, 1,000,
10,000 and 100,000
Add and subtract numbers mentally with increasingly large numbers
Use rounding to check answers to calculations and determine, in the
context of a problem, levels of accuracy.
Children should be familiar with the word “approximate”, and
the degree of accuracy to which to round is a useful point for
discussion.
Generally, rounding to the nearest 100 for 3-digit numbers,
the nearest 1,000 for 4-digit numbers.
Ask,
“What place value column should we look at to round the
number to the nearest 10/100/1,000/10,000/100,000
“How could you use your estimates to check your answers?”
" Is the actual answer going to be greater or less than your
estimate? Why?”
One worksheet with answers attached.
Inverse operation to check answers Foundation
In this worksheet, children explore the inverse relationship
between addition and subtraction.
Addition and subtraction are inverse operations and addition is commutative and subtraction is not.
Bar models and part-whole models are useful representations
to help establish families of facts that can be found from one
calculation.
Children use inverse operations to check the accuracy
of their calculations, rather than simply redoing the same
calculation and potentially repeating the same error.
Ask:
What are the parts?
What is the whole?
Given one fact, what other facts can you write?
What does “inverse” mean?
What is the inverse of add/subtract
Inverse operations to check answers Core
In this worksheet, children explore the inverse relationship
between addition and subtraction.
Addition and subtraction are inverse operations and addition is commutative and subtraction is not.
Bar models and part-whole models are useful representations
to help establish families of facts that can be found from one
calculation.
Children use inverse operations to check the accuracy
of their calculations, rather than simply redoing the same
calculation and potentially repeating the same error.
Ask:
What are the parts?
What is the whole?
Given one fact, what other facts can you write?
What does “inverse” mean?
What is the inverse of add/subtract
Rounding Numbers within 1,000,000
Children round any number up to 1,000,000 to any power of 10 up to 100,000.
You may wish to practise counting in 100,000s first, and then
practise rounding to the nearest 100,000 before looking at mixed questions.
Ask,
“Which multiples of 100,000 does the number lie between?”
" How can you represent the rounding of this number on a number line?"
“Which division on the number line is the number closer to?”
" What is the number rounded to the nearest 100,000?"
Estimation and Inverse operation to check answers Higher reasoning
Estimate and use inverse operations to check answers to a calculation.
Problem solving and reasoning questions for higher ability students with answers attached for easy check.
Estimations can be used alongside inverse operations as an
alternative checking strategy.
Children use inverse operations to check the accuracy
of their calculations, rather than simply redoing the same
calculation and potentially repeating the same error.
Estimations can be used alongside inverse operations as an
alternative checking strategy
Efficient subtraction Higher
The purpose of this worksheet is to encourage
children to make choices about which method is most appropriate
for a given calculation.
Children can often become reliant on
formal written methods, so it is important to explicitly highlight
where mental strategies or less formal jottings can be more
efficient.
Children explore the concept of constant difference, where
adding or subtracting the same amount to/from both numbers
in a subtraction means that the difference remains the same,
for example 3,835 – 2,999 = 3,835 – 3,000 or 700 – 293 = 699 – 292.
This can help make potentially tricky subtractions with multiple
exchanges much simpler, sometimes even becoming calculations
that can be performed mentally.
Bundle
Adding two 4-digit numbers with extra reasoning sheets
Children add two 4-digit
numbers with one exchange in any column.
The numbers can be made using place value counters in a place value chart, alongside the formal written method.
When discussing where to start an addition, it
is important to use language such as begin from the “smallest
value column” rather than the “ones column” to avoid any
misconceptions when decimals are introduced later in the year.
After each column is added, ask,
“Do you have enough ones/ tens/hundreds to make an exchange?"
This question will be an important one in this worksheet , as the children do not know which column will be the one where an exchange is needed.
Extra reasoning activity sheets
Rounding to check the answers Core
In this worksheet, children practise rounding in order to estimate
the answers to both additions and subtractions.
They also review mental strategies for estimating answers
Round any number up to 1,000,000 to the nearest 10, 100, 1,000,
10,000 and 100,000
Add and subtract numbers mentally with increasingly large numbers
Use rounding to check answers to calculations and determine, in the
context of a problem, levels of accuracy
Bundle
Multiples of 3
These are three differentiated worksheets.
Recall multiplication and division facts for multiplication tables up to 12 × 12.
Recognise and use factor pairs and commutativity in mental calculations.
Watch for:
Children may think that any number with 3 ones is a multiple of 3.
An early mistake when counting in 3s will affect all subsequent multiples.
Children may always begin counting from 3 to find a larger multiple of 3, when they could use the multiples they already know to find the new information.
In the higher ability worksheet ( with three faces), children explore how to recognise if a number is a multiple of 3 by finding its digit sum: if the sum of the digits of a number is a multiple of 3, then the number itself is also a multiple of 3.
Challenge by asking :
How do you find the digit sum of a number?
How can you tell if a number is a multiple of 3?
Are the multiples of 3 odd or even?
In the foundation worksheet (one face), children explore the link between counting in 3s and the
3 times-table to understand multiples of 3 in a range of contexts.
They use number tracks and hundred squares to represent multiples of 3.
Ask:
What is the next multiple of 3?
What is the multiple of 3 before?
How many 3s are there in?