subtraction | Maths Blog

Year 4 quite hard mental subtraction

Many children are unaware that there are often several ways of working out a calculation and that those who choose the best methods find maths easier and are able to answer questions more quickly and more accurately.

Let’s look at ‘Subtract 38 from 63.

This should be done, ‘in your head’ and will involve several stages, depending on the method used.

First, I could take 30 from 63 to leave 33. Then I could count back 8 from 33 which gives me 25.

Secondly, I could take 40 from 63 leaving 23 and then compensate by adding 2, which gives me 25.

Thirdly, I could take 38 from 68, leaving 30 and then compensate by subtracting 5 (because 63 is 5 less than 68).

There are several other ways very similar to these, but this does show that there is no ‘one right way, when it comes to mental arithmetic.

Quite hard mental arithmetic:_subtraction (1)

Written subtraction of 3-digits (2)

Written subtraction is one of those areas of maths that children frequently get wrong, mainly because they do not fully understand the method. This page looks at 3-digit subtraction and all the questions need ‘decomposition’ in order to get them correct. The last three questions should be laid out in the same way as the questions above.

Watch out for when there is a zero on the top line; for example when faced with question one:

zero subtract six is not six.

Rather, say ‘zero take way six cannot be done so I need to borrow 10 from the tens column.’ (I don’t really like this phrase because zero take away six can be done: the answer is negative six, but this takes us into a completely different method of subtraction which I will discuss one day when it’s been raining all day!)

It is always a good idea to check the answer by adding the answer line to the line above, which, in turn should give you the number at the top of the question.

This page can be found in our Four Rules section, under subtraction.

Standard subtraction of_3_digits_(2)

Year 1 maths worksheet: early subtraction

It is sometimes difficult to find subtraction worksheets that are basic enough for very young children. This page looks at subtracting one or two from 1-digit numbers. There is no number line to help, so it is very much a mental arithmetic exercise. Most children will approach it by counting back one or two, possibly using their fingers to start with.

Don’t forget to colour in the smiley (hopefully) faces at the bottom to show how many were correct.

Early subtraction

Year 4 maths worksheet: More addition and subtraction

Here is a second page of questions on adding and subtracting multiples of 10, which year 4 children should be able to take on and answer rapidly.

It is always fascinating to ask children how they work things out in their heads. Let’s look at 330 + 90. I would do this by adding 100 to make 430 and then subtracting 10 to make 420. It could also be done by adding 33 and 9 to make 42 and adjusting to take account of the hundreds; and there are other ways. Any way which reaches a correct answer is OK, but we are really looking for methods which are very fast and if children are not using them they should be shown.

Rapid response: Add and subtract (2)

Year 4 worksheet: Rapid addition and subtraction

Sometimes it’s useful to have a page that tests how quickly children can respond to a set of questions – and here is one. This Year 4 maths worksheet looks at addition and subtraction of whole tens. There are 30 questions and children who have a good grasp of adding single digits should be able to transfer their skills and answer these quite quickly.

Whilst being aimed at year 4, it could also be used with older children who are unsure of mental methods of addition and subtraction.

Rapid resonse: add and subtract (1)

Resource of the week: Subtraction crossing thousands

Today we revisit a page that shows maths can be much easier than it at first appears. There are many occasions when a 4-digit subtraction can be done ‘in your head’. These questions, suitable for Year 5, are examples of this. They all involve numbers which are just over and just under a whole thousand.

For example: 3003 – 2994

Probably the easiest way to do this mentally is to count on 7 from 2993 to make 3000 and then count on, or add, the extra 4, making 11.

This is much easier than doing the question on paper, with lots of ‘borrowing’ and carrying, crossing out etc!

Count up crossing thousands

Resource of the Week: Year 4 Find a difference

Sometimes a simple question can reveal a great deal about how children deal with numbers. This maths worksheet on finding differences is full of such questions.

Let’s look at 3005 – 8 which is easier to do mentally than on paper.

There are several ways that this can be done.

1. Count down, one at a time, 8 from 3005, saying each number as you go. Fingers may be held up on each count down until 8 is reached.

3004, (1), 3003 (2), 3002 (3), 3001 (4), 3000 (5), 2999 (6), 2998 (7), 2997 (8)

2. A different way is to take the 8 from 3000, then add 5.

3000 – 8 = 2992

2992 + 5 = 2997

3. A third way is to take 5 off the 8 leaving 3.

Then take 3 off 3000 = 2997

It is well worth talking to children about how they do this kind of question and what strategies they employ. Much will depend on their knowledge of number.

Find a difference by counting up (pg 1)

Subtract a single digit from a multiple of 100

A nice little revision exercise to check that children are confident with counting across the hundreds boundary and also have quick mental arithmetic strategies.

These questions are all subtracting a single digit from a multiple of 100. Some children will do them by counting back, others will employ different strategies such as subtracting 10 and adjusting. Generally, we are looking for quick and accurate methods.

The last three questions ask children to write down the method they usedm, which can reveal a lot.

This page can be found in our Year 4, Calculating section.

Subtract single digit (2)

Maths Worksheet: Use the Subtraction Sign (Year 1)

This worksheet can be used as a check to see how well your child has learned their subtraction facts. There are several ways that this page could be tackled, depending on the confidence and knowledge of the child. Some children may want to use the number line to count back, others might prefer to use their fingers. What we are really hoping for, however, is that some of these facts have been committed to memory: the calculation does not have to be worked out by counting back, rather the fact is already known. Those children who know their number facts will complete this page much more quickly than those who don’t.

Use the subtraction sign (pg2)

Written subtraction with zeros

One of the hardest ideas to get across to children is when they are carrying out a subtraction which requires adjusting across two columns. This only happens when there is a zero involved.

For example:

703

286 –

3 – 6 does not give a positive answer so an adjustment to the top number needs to be made. A ten can not be borrowed as there are none.

The procedure then is to borrow from the hundreds, move to the tens and then move again to the units. Often children will borrow from the hundreds, ignore the zero in the tens and move straight to the units. They cross out the 7 and make it 6 and make the 3 into 13.

This does not work as it has been 100 borrowed, not 10. Extra steps need to be taken by making the tens column 10 and then taking one ten, making this 9, and adjusting to the units.

Some children will see a quicker way ie of making the 70 one less (69) and adjusting to the units.

More explanation is available on the worksheet.

Standard subtraction with zeros in the tens (pg 1)