Here are some ideas on what multiplication and division facts children are expected to know by the end of Year 4. Children should know and use the following vocabulary:  double, twice, half, halve, whole, divide by, divide into. Children  should have a good working knowledge of all table facts up to 10 × 10. They should also know them 'backwards', eg. know how many eights make 56. Children should know all the squares of number up to 10 × 10 . They should be able to answer a whole range of mental questions such as: What are eight sevens? How many fives are there in 45 ? What is 7 times 8 ? Multiply 5 by 7. What is 9 multiplied by 0 ? What is 24 divided by 6 ? What is 45 shared between five people? What is one third of 24 ? Children should understand that halving is the inverse (opposite) operation to multiplication by 2. They should be able to answer a range of questions on doubling and halving involving decimals used with money (ie. half of £35.60), and simple units such as centimetres. Children should use the words multiple, digit. Children should know the difference between odd and even numbers. Children should be able to carry out tests of divisibility, i.e. see quickly if a number is divisible by another. The most common tests are: Divisible by 100    Number ends in 00            e.g.  300 Divisible by 10     Number ends in 0              e.g.    40 Divisible by 5    Number ends in 0 or 5            e.g.  35,  60 Divisible by 2    Number ends in 0, 2, 4, 6 or 8   e.g.  42, 78, 90 Divisible by 3    Add the digits in the number.     e.g. 57.  Sum of digits If the total is divisible by 3,                    = 5 + 7 = 12. then so is the number.     12 is divisible by 3, therefore so is 57. Divisible by 4    Last two figures (digits) are divisible by 4  e.g. 328 Children should recognise multiples of 10, 100 and 1000 e.g.  5 000 is a multiple of 1 000 500 is a multiple of 100 50 is a multiple of  10 The key concepts are: 1. Multiplying a two or three digit number by 10 or 100. (Remember never say 'add a nought' as this leads to real problems when dealing with decimals later!) 2. Dividing multiples of 1 000 by 10 or 100. 3. Doubling multiples of 5. 4. Halving multiples of 10 up to 200. 5. General multiplication of two digits by one. One of the key things to concentrate on is the method used when working mentally. Occasionally children need to be asked to write down how they did the sums. Generally they find this rather tedious so keep to a minimum. It is usually better to do this aspect orally so that children can learn from each other. Multiplication tables form the basis of so much work from simple sums to cancelling fractions that is very important to practise them often. Tables sheets may be used to encourage children to improve their knowledge and speed up their recall of all tables up to 10 x 10. They may be done as a class or individually at home. In class the children all begin together and put up their hands when they have finished. The teacher calls out their time in minutes and seconds and the children write this down, first on the practice table they have completed and then again in the table on the cover sheet. It is a good idea for the quicker ones to have something else to get on with while they then wait for the slower ones. At home the children begin at a suitable time and, with practice, will be able to time themselves, recording the time in the same way. The aim, of course, is to increase speed whilst retaining or improving accuracy. Fractions Children should be able to identify two fractions which total one whole one. There are two aspects to this: firstly the concept that if the numerator and denominator are the same then the fraction will total one: eg This can be demonstrated by viewing the fraction as a division sum: 4 divided by 4 is 1. Secondly, a knowledge of equivalent fractions is needed when the bottom numbers or denominators are not the same eg and   need to be changed to eighths to add or subtract. At this stage we are keeping to those fractions which children should be familiar with: halves, quarters, eighths, fifths and tenths. Checking answers Techniques for checking calculations need to be developed. It is very easy for children to assume that because a calculation is done on a calculator, it must be correct. Their faith in the electronics is probably justified, but what about their faith in their own abilities? There are several methods that can be used: a) Doing the inverse operations. If a division has just been calculated, do the opposite multiplication to check. eg.  180 ÷ 5 = 36          Check by doing 36 × 5 to see if it comes to 180. b)  Perform an approximate calculation to see if the answer is in the correct range. eg.  88 × 6 = 528         Check: 100 × 5 = 500 e)  Carry out some simple tests such as two even numbers multiplied together always give an even number. Go to Year 4 Know Multiplication and Division Facts