Developing Mental Strategies for Subtraction

(Curriculum Guidance for Foundation Stage page 76, NNS Section 4 page 14 – 17 & 20 – 21,

NNS Section 5 page 28-41, NNS Section 6 page 36 – 47 , Year 7 Page 92 & 94)
Year / Group Target /

Outcomes

Reception / Must / Count 1 less to find the difference between two numbers. / Most pupils will be able to answer questions such as:
  • There are five cubes in this box. I am taking out two of the cubes. How many cubes are left in the box?
  • There are nine biscuits on this plate. Take three of the biscuits to eat. How many biscuits are left on the plate?
  • There are six toys in a box. I take away three of the toys. How many toys are left in the box?
  • There are 6 cars in the car park. If 2 drive away, how many cars will there be? (When using the cars and garage in small world play).
  • There are 10 sweets in a bag. If I give 3 to my friend, how many sweets do I have left?
  • There are 8 people on the bus and 5 get off. How many passengers are left on the bus?
More able pupils should be able to answer questions such as:
For higher attaining children working on the ‘Could’ target, please see the outcomes for Year 1.
Should / Begin to relate subtraction to ‘taking away’.
Could / Understand subtraction as ‘take away’ and find a ‘difference’ by counting up.
as Year R and Year 1 / Must / Begin to relate subtraction to ‘taking away’. / Most pupils will be able to answer questions such as:
  • I'm giving each of you two number cards [from 0 to 5]. What is the difference between your two numbers?
  • What is 8 take away 4? Show me two numbers that have a difference of 3. Can you think of another pair of numbers with a difference of 3?
  • How many do I count on to get from 3 to 8?
  • 15 ducks are on the pond. 11 of them go away. How many are left?
  • What is the difference between twelve and sixteen?
  • What is left if five is subtracted from twelve?
  • What is thirty-two subtract five?
  • Here are some cubes. Show me how to use them to work out 9 take away 4. How could you record that as a number sentence?
  • Make up a question that uses the words difference between and tell me how to do it.
  • Use number cards 1 to 10. Choose a card and pick up that number of cubes. Can you work out how many more cubes you need to make 10? How did you work it out? Can you use a number track to show that you are right?
  • What is 15 take away 6? How did you work that out? How could you work it out a different way to check? Can you make up another ‘take away’/subtraction question that has the answer 9? How did you work out which numbers to use?
  • What is the difference between 5 and 12? How can you show that using counters? Can you put something on paper to show that? How could you work that out on a number line?
  • Tell me some subtraction questions that have 10p as an answer.
  • Build me two towers that have a difference of four cubes in their heights.
  • Children could be using a variety of mental subtraction strategies such as:
Count back in ones, use known number facts and place value, use patterns of similar calculations.
Higher attaining pupils will also be able to answer questions such as:
For higher attaining children working on the ‘Could’ target, please see the outcomes for Year 2.
Should / Understand subtraction as ‘take away’ and find a ‘difference’ by counting up.
Could / Subtract mentally a single-digit number or a multiple of 10 to or from any two-digitnumber.
Year / Group Target /

Outcomes

as Year 1 and Year 2 / Must / Understand subtraction as ‘take away’ and find a ‘difference’ by counting up. / Most pupils will be able to:
  • Write the answer: 79 – 34, 30 – 15, 63 – 37
  • Write the number which is 11 less than 40.
  • What is 37 – 8? Which number facts will help this time? How much do you need to subtract to go down to the multiple of 10 before 37? How much more do you need to subtract?
  • Show me how you could work out the answer to 47 – 29. What about 72 – 12?
  • Children could be using a variety of mental subtraction strategies such as:
Count back in tens and ones, find a small difference by counting up from the smaller to the larger number, subtract 9
by rounding and adjusting, use known number facts and place value, partition into tens and units and recombine, use
patterns of similar calculations.
Higher attaining pupils will also be able to answer questions such as:
For higher attaining children working on the ‘Could’ target, please see the outcomes for Year 3.
Should / Subtract mentally a single-digit number or a multiple of 10 to or from any two-digitnumber.
Could / Subtract mentally combinations of one-digit and two-digit numbers.
as Year 2 and Year 3 / Must / Subtract mentally a single-digit number or a multiple of 10 to or from any two-digitnumber. / Most pupils will be able to answer questions such as:
  • What is twenty-seven subtract nine?
  • Subtract thirty-two from seventy.
  • The difference between a number and twenty-nine is ten. What could the number be?
  • In a class there are thirty-two children. If there are twenty-three girls, how many boys are there?
  • This table shows the increase in bus fares.

Sohan’s new bus fare is 72p. How much has his bus fare gone up?
Millie says, ‘My bus fare has gone up by 10p’. How much is Millie’s new bus fare?
  • Look at this calculation: 2 – 7 = . Write a digit in each box so that the calculation is correct. How else can you do it? What patterns do you notice?
  • A 95 g orange is placed in some balance scales. There is 35 g in the other pan. How much needs to be added to the 35 g so that the scales balance? How did you work this out?
  • Think of two numbers that have a difference of 9. Write a number sentence to show this. Now find and record some more pairs of numbers with a difference of 9.
  • What is 73 – 7? Explain how you did it. How would you subtract 17 from 73?
  • What is 58 – 30? What is 58 – 29? How did you work these out? Show me on an empty number line.
  • Children could be using a variety of mental subtraction strategies such as:
Count back in tens or ones, find a small difference by counting up from the smaller to the larger number, partition into tens and units and recombine, use knowledge of number facts and place value, subtract mentally a ‘near multiple of 10’, use patterns of similar calculations.
Higher attaining pupils will also be able to answer questions such as:
For higher attaining children working on the ‘Could’ target, please see the outcomes for Year 4.
Should / Subtract mentally combinations of one-digit and two-digit numbers.
Could / Subtract mentally pairs of two-digit whole numbers.

1

Year / Group Target /

Outcomes

as Year 3 and Year 4 / Must / Subtract mentally combinations of one-digit and two-digit numbers. / Most pupils will be able to answer questions such as:
  • How many less than forty-one is seventeen?
  • Subtract one hundred and five from two hundred.
  • Work out 91 – 35 in your head. Tell me how you did it. Did anyone do it a different way? How could we record the method that you used?
  • What number do you need to add to 46 to make 92? How did you work it out? Is there a different way to do it?
  • The difference between a pair of two-digit numbers is 13. What could the pair of numbers be?
  • How would you calculate the answer to 93 – 86? Why would you choose that strategy?
  • Children could be using a variety of mental subtraction strategies such as:
Count back in steps of 1, 10 and 100, count up through the next multiple of 10 or 100, partition into tens and units,
use knowledge of number facts and place value, subtract 9, 19, 29, 11, 21, 31 by rounding and compensating,
subtract the nearest multiple of 10 then adjust, use patterns of similar calculations.
Higher attaining pupils will also be able to answer questions such as:
For higher attaining children working on the ‘Could’ target, please see the outcomes for Year 5.
Should / Subtract mentally pairs of two-digit whole numbers.
Could / Extend mental methods for whole-number calculations, for example to subtract one near-multiple
of 1000 from another (e.g. 6070 – 4097).
as Year 4 and Year 5 / Must / Subtract mentally pairs of two-digit whole numbers. / Most pupils will be able to answer questions such as:
  • What number is two less than nine hundred and one?
  • What is one thousand minus one hundred and ten?
  • What is three thousand subtract ten?
  • What is the difference between one thousand nine hundred and ninety-four and four thousand and three?
  • Which of these subtractions can you do without writing anything down?
  • Why is it possible to solve this one mentally? What clues did you look for? What is the answer to the one that can be solved mentally?
  • How did you find the difference? Talk me through your method. [If the child explains a method of counting backwards, ask:] Is it possible to count up as well? Why will this give the same result? Which is easier?
  • Why is it possible to solve 6007 - 1995 mentally? What clues did you look for? Explain your methods.
  • Suggest a subtraction calculation involving four-digit numbers that you would answer by counting on.
  • Children could be using a variety of mental subtraction strategies such as:
Subtract the nearest multiple of 10, 100 or 1000 and adjust, partition into 100’s, 10’s and units, use known number
facts and place value, subtract the nearest multiple of 10 or 100 then adjust, use patterns of similar calculations.
Higher attaining pupils will also be able to answer questions such as:
For higher attaining children working on the ‘Could’ target, please see the outcomes for Year 6.
Should / Extend mental methods for whole-number calculations, for example to subtract one near-multiple
of 1000 from another (e.g. 6070 – 4097).
Could / Calculate mentally with integers and decimals: U.t - U.t.
Year / Group Target /

Outcomes

as Year 5 and Year 6 / Must / Extend mental methods for whole-number calculations, for example to subtract one near-multiple
of 1000 from another (e.g. 6070 – 4097). / Most pupils will be able to answer questions such as:
  • Subtract one point nine from two point seven.
  • Subtract nought point seven five from six.
  • I buy a magazine which costs one pound forty pence. I pay with a five pound note. How much change should I get?
  • The answer is 12.6. What was the question?
  • Look at these calculations with two-digit decimals. Tell me how you could work them out in your head.
  • Make up a question involving subtraction that has the answer 1.35.
  • Which of these subtractions can you do without writing anything down? Why is it possible to solve this one mentally? What clues did you look for? What is the answer to the one that can be solved mentally?
  • I need a shelf of 1.4 metres in length. I cut the shelf from a plank 5 metres long. How much of the plank is left? Explain the mental calculations that you did to solve this problem.
  • Children could be using a variety of mental addition strategies such as:
Use knowledge of number facts and place value, subtract the nearest multiple of 10, 100 or 1000, then adjust,
partition into hundreds, tens and units.
Higher attaining pupils will also be able to answer questions such as:
  • Calculate ten minus four point three five.
  • Subtract nought point seven five from six.

Should / Calculate mentally with integers and decimals: U.t - U.t.
Could / Consolidate and extend mental methods of calculation to include decimals, fractions and
percentages.