Mental Division Strategies: year 4

Having a browse round the site there seemed to be some areas which are a little short of pages; one of these being the year 4 division pages. So, here is a Year 4 division worksheet which looks at some of the strategies children need to be confident with in order to carry out quick, efficient division calculations.

The worksheet is divided into 4 sections, each with a different purpose. The first set of questions looks at basic concepts, such as dividing by 1 and the fact that, unlike addition the calculation has to be carried out in the order stated e.g. 34 divided by 2 is not the same as 2 divided by 34.

The second set of questions takes a quick look at division facts. Many teachers are now of the opinion that division facts should be learned, just like multiplication facts (tables.) This can be argued with in that if a child knows all the times tables they can quickly use them to work out division problems.

The third set looks at dividing money by 10. Of course this is easily done by moving each digit one place to the right. As it is money there should be 2 digits after the decimal point. e.g. £32 divided by 10 should be £3.20. Watch out for those children who get confused because they have been told to ‘add a nought’ when multiplying by 10. Never a good idea!

The last set is all about dividing by 4. Often this can be done by halving and then halving again.

Mental division strategies

More long division: 3-digits divided by 2-digits

One of the hardest things children try to do in primary school is long division. It is hard because it requires a good knowledge of tables,  the ability to multiply, estimate, use trial and improvement and go through several steps to reach the answer. These steps include:

e.g. 789 divided by 36

First carry out an estimate of the answer. I think 789 divided by 36 is about 20.

a. How many 36s in 78?

b. 2 x 36 is 72.    3 x 36 is 108 which is too many, so it must be 2.

c. Put the 2 in the tens column above the question.

d. Place the 72 below the 78 and subtract.

e. 78 – 72 is 6.

f. ‘Bring down’ the 9 to make 69.

g. How many 36s in 69.

h. By trial and improvement and some rough work multiplying 36 by my estimated numbers I find that 36 x 1 = 36.

i. Put the 1 in the units column above the question.

j. Place the 36 under the 69 and subtract.

k. The remainder (33) must be less than the original number you are dividing by.

Good luck with these, but many year 6 children will find them too tricky! When I was at school I used to like doing pages of these because I had learnt the method ‘off by heart’ and it was just a matter of repeating it.

Division 3 by 2

Year 3 maths worksheet: more mental division

This page has 14 division questions which should be answered mentally. It keeps to the easier times tables, including 2x, 3x, 4x, 5x and 10 x tables. Children who have a good knowledge of times tables should whizz through this in little time. If tables are not known it becomes a much more laborious process.

The early questions are set out in the usual form with the number to be inputted being the answer to the division calculation. The later questions have different parts of the division number sentence missing. An example:

12 divided by ? = 2

Here the relationship between division and multiplication comes into play. if it is known that 6 x 2 = 12 then this is easy.

More mental division practice

Resource of the Week: Division with remainders as fractions

This week we are looking at worksheets where the remainders from division are written as fractions. Children need a good knowledge of tables to work out the division ‘in their heads’ and this is probably best suited to Year 4, aged8/9+ years old.

Children will be used to the concept of a remainder when dividing but this goes one step further, removing the remainder altogether. When writing the answer as a fraction the remainder goes on the top line (numerator) and the bottom number (denominator) is the number you have divided by.

This is a much neater finish to the question as the whole number is divided completely, with no messy remainders. Some of the fractions could be cancelled down to their simplest form, although this is not essential at this stage. There are several similar pages to be found in our Year 4 Calculating category.

Division with fraction remainders (pg 2)

Maths worksheet: Division of money

I have had several requests to produce another division of money worksheet as it seems this is quite hard and children need plenty of practice with it – so here it is. Dividing money by 2-digit numbers requires a very good knowledge of multiplication, tables and subtraction. The long division method can be found in other worksheets in this category but as a reminder the question should be started as follows:

eg £3.64 divided by 26.

1. ask how many 26s go into 3.

The answer is zero, so put the zero in the pounds column of the answer.

3. remember the decimal point.

4. Ask how many 26s go into 36 and continue with the long division method.

Money division (2)



Year 5 maths worksheet: multiplication and division hops

Each of the questions on this page has two sets of coloured arrows above the spaces which need to be filled in. The arrows give the instruction, red for multiplication and yellow for division. There are eight hexagons, one of which has been filled in. The aim is to complete the other seven using the arrows to work out what to put inside each hexagon.

Sounds complicated but it is easier to complete than to explain!

This is good practice for

a. knowing tables

b. knowing division facts

c. knowing that multiplication and division are the inverse of each other.

This page can be found in the Year 5 Know Number Facts category.

Multiplication and division hops

Year 5: Knowing Division Facts (2)

By Year 5 children should have a good knowledge of tables and this division page will show whether tables are known. It is also important to understand the relationship between division and multiplication as some children see the two as completely separate processes.

It is the second page on this knowing division facts as I have had several requests for more on dividing mentally. They can both be found in the Year 5 Maths Worksheets, in the Knowing Number Facts category.

Know division facts (2)

Year 4 worksheets: Division with remainders

Division nearly always requires carrying out more than one process, which makes it harder for children to process. A good knowledge of tables is also needed to complete division questions successfully, and this is especially true when there are remainders.

For example: to find the answer to 37 divided by 5: ask how many fives are in 37. This is where the knowledge of tables comes in, as 5 x 7 makes 35.

Then a subtraction take 35 from 37 to leave 2. There is a remainder of 2. (The remainder can never be bigger than the number you are dividing by.)

This remainder can be converted to a fraction. The 2 is the numerator (top number) and the denominator (bottom number) is the number you are dividing by, in this case 5. So the fraction left is 2/5.

This is a much neater finish to the question as the whole number is divided completely, with no messy remainders. Some of the fractions could be cancelled down to their simplest form, although this is not essential at this stage.

Division with fraction remainders (pg 2)

Maths worksheets: Division of money

There are not many questions on this maths worksheet but they are quite tricky and a good knowledge of tables and how to do long division is needed.

Each question has an amount of money to be divided by a 1 or 2-digit number. In all cases the answer wil have a zero in the pounds column.

As well as the long division process there are several key things to remember when doing these, including:

1. putting the pound sign in the answer

2. putting the zero in the pounds column

3. putting in the decimal point.

Money division (1)

Knowing Division Facts: Year 5 maths Worksheet

There is no doubt that most children find division harder than multiplication, yet there is little real reason for this to be so. Most division questions can be turned on their head to be made to look like multiplication. For example:

30 ÷ 5 =??  can be thought as what number times 5 makes 30?

?? ÷ 6 = 7 can be thought of as 6 times 7.

60 ÷ ?? = 10 can be thought of as what number times 10 makes 60?

The key to success with division is to have a really good knowledge of times tables.

This worksheet looks at these types of division question, all with easy numbers and no remainders and is a good assessment sheet to see if division is understood and tables known.

This can be found in our Year 5 Knowing Number Facts category.

Know division facts (1)