Free Worksheets Maths: four rules

Maths worksheet: Moving towards a standard method of division

This is the second division worksheet which looks at the intermediate stage between mental methods of division and a standard method. I am not a great fan of this method but it is used in many schools.

The first thing to do, as always is to make an estimate of the answer so that any silly slip ups in the calculation may immediately come to light. The second stage is to find a multiple of ten that can be taken away – in all these examples and questions this multiple is 10 itself. Then we move towards the more traditional method of asking ‘how many…. in….’.

If you are just moving towards doing division, perhaps in Year 3/4 it is certainly a method which can be used.

Division 2 by 1 digit (p2)

Standard written subtraction with zeros.

Here is another maths worksheet which looks at the standard method of subtraction, often called decomposition. Once again the numbers are small, and many children will be able to work the answers out ‘in their heads’. However, it provides good practice with the method, whilst not having to worry too much about the size of the numbers involved.

All these subtraction questions have a zero in the number which is being taken from. This can sometimes cause children a few problems: watch out for the mistake of saying ‘0 – 8 is 8’.

Once these have been mastered it is only a short step to being able to successfully complete any subtraction sum.

Standard subtraction with zeros

Multiplying decimals 1

The standard short method of multiplication can be used when multiplying a decimal by a single digit. Children need plenty of practice with this before moving on to working with decimals.

The key to success with these is to place the answer in the correct columns and the best bet is to put the decimal point in first. Think of the decimal point as a fixed point, therefore the point in the answer should be immediately above the point in the question. Apart from that, these should prove to be straightforward.

This maths worksheet shows the method and then gives 12 questions to practice.

Multiplying decimals (pg 1)

Mental arithmetic: subtracting from 100

Here is a maths worksheet on using mental arithmetic to subtract from 100. This is probably the type of calculation we do more than any other, especially when working out change from £1.00. There are several processes or ways to do these.

Let’s look at an example: 100 – 47.

One way is to add on 3 to make 50 then 50 to make 100: add the 50 and the 3 to make 53.

Another way is to add 50 to make 97 then count on 3 to make 100.

Watch out for the very common error that children make which is adding 3 to the 7 and adding 60 to the 40 and coming up with the answer 64!

Subtract from 100 (pg 1)

Multiplying by whole tens pg 1

This method for multiplying by whole tens follows the ‘short multiplication’ method for multiplying 2-digits by 1-digit, but is also the first step in ‘long multiplication’. Children should be very familiar with short multiplication of 2-digits by 1-digit before moving on to this work.

It also assumes a good knowledge of place value and that, by moving a digit one place to the left the number will be multiplied by 10. Therefore by multiplying by 7 and placing each digit of the answer one place to the left, the result is to multiply by 70 (Don’t forget the zero in the units).

This maths worksheet shows the method and sets out 12 questions.

Multiply by whole tens (pg 1)

Standard method of short multiplication pg 2

Here is another maths worksheet to practice the standard method known as short multiplication. All these sums have already been set out in the correct way but it is important to remember to keep the units in the units, tens in the tens column etc. This will become even more important when decimals are introduced later.

Always work in the same order, starting by multiplying the units, carrying any tens on into the tens column and then multiplying the tens. Perhaps the key to success with these is knowing the times tables up to 10 times 10. If each multiplication has to be worked out the whole task becomes laborious.

Standard method of short multiplication pg 2

Maths worksheet: Standard short multiplication 1

This is the standard written method known as ‘short multiplication’. It leads on from the earlier worksheets on ‘Moving towards a standard method’.

Before starting this type of sum a good knowledge of times tables is needed.

The stages are as follows:

Step 1: write the sum out correctly

The question may be put in a different layout eg 38 x 7 =

Make sure it is laid out with the units under each other as shown on the example.

Step 2: multiply the units

Multiply 8 by 7 which 56 or 5 tens and 6 units.

Put the 6 in the answer in the units and place the 5 (tens) in the tens column, under the answer line. Continue reading “Maths worksheet: Standard short multiplication 1”

Times Table practice: 2, 3, 5 and 10 times tables

This is the second in a continuing series of times table practice for the 2, 3, 5 and 10 times tables.

Any child who knows their tables off by heart is at a huge advantage over those who don’t know them. Many maths problems and techniques, such as long multiplication and division, rely on knowing tables, so it is really worth the effort to learn them. Watch how the grid is filled in as it gives good clues as to what has been learned (which takes no time at all to answer) and what has been ‘worked out’ (which might take a while). Say the table out loud many times – there are songs and recordings that will help.

2,3,5 and 10 times table p2

Maths worksheet: Standard written multiplication 3-digits by 1 digit

This worksheet uses the standard or efficient method recommended by the Primary Framework for Maths to multiply a 3-digit number by a single digit. There are other methods equally good, but it is important that children keep to one method that they become confident with. It presumes a good knowledge of tables before starting.

For example: 436 x 7.

First, do an estimate of the answer.
436 x 7 is approximately 400 x 7 which is 2800. The answer will be over 2800.
Then set the sum out in a vertical layout:
436
x 7

Start with the units.
6 x 7 is 42. Put the 2 in the units and carry the 4 tens into the tens column, under the answer line.
Then multiply the tens.
3 (tens) x 7 is 21(tens). Add the 4 (tens). to make 25(tens).
Place the 5 in the tens column and carry the 2 (hundreds) into the hundreds column.

Finally the hundreds.
4 (hundreds) x 7 is 28 (hundreds). Add the 2 (hundreds) to make 30 (hundreds).
Place the zero in the hundreds column and the 3 in the thousands column.
The answer is 3052.
A clearer layout of this is available on the worksheet explanation.

Further written multiplication worksheets can be found in the Year 5 and Year 6 Calculations sections.

Standard written multiplication: 3-digits by 1-digit

Maths worksheet: Dividing a 2-digit number by a single digit.

When parents come to help their children with maths it is often division which is the most problematic area. Frequently it is the parents who claim they do not understand the ‘modern methods’ used in school today. The final efficient, or standard method of division is much the same method as it has always been: it is the stages that are used to reach this standard method which cause most confusion. These stages, or steps are aimed at providing children with an understanding of the whole process, although I believe that sometimes they can lead to more confusion.

Here we have one of these steps towards an efficient method.

77 ÷ 4

4)77

– 40 (10 × 4)

1137

– 36 ( 9 × 4)

0111

Next, take away a tens multiple of the divisor (4). 10 x 4 = 40.

Subtract 40 from the 77 leaves 37.

Then ask, ‘How many 4s in 37?’

9 x 4 is 36 so it is 9 with a remainder of 1.

Add the 10 and the 9 which makes 19.

Answer: 19 remainder 1.

All these questions have a single tens multiple of the divisor. Of course, this will not always be the case as questions become harder.

Division: 2 digit by 1 digit (pg 1)