May, 2009 | Maths Blog

Year 4 number worksheet: recognising tests of divisibility for 4 and 5

There are some things which children can learn which can really help them later at High School. Tests of divisibility are a great set of ‘tricks’ to know and will certainly help any child with their maths in the future. This page looks at divisibility by 4 and 5. Being divisible by 5 means that there is no remainder when a number is divided by 5; in other words it divides exactly.

Recognising when a number is divisible by 5 is easy: only whole numbers ending in 5 or 0 are divisible by 5.

Recognising a number which is divisible by 4 is harder: are the last two digits divisible by 4? If so then the number is too. eg 156344 is divisible by 4. (try it with a calculator.)

This worksheet only uses 2-digit numbers which by year 4 children should be able to divide by 4 in their heads. (Halve and halve again: if the answer is a whole number it is divisible by 4).

Divisible by 4 and 5

Understand relationships between addition, subtraction, multiplication and division

Not many questions on this page but an impressive number of maths concepts needed to answer the questions correctly. These include:

Understanding that addition can be done in any order so: 50 + 15 = 15 + 50

Understanding that 45 – 31 is different from 31 – 45

Understanding that addition reverses subtraction, ie addition is the inverse of subtraction

Understanding that division reverses multiplication, ie division is the inverse of multiplication

Understanding that 16 ÷ 8 does not equal 8 ÷ 16

Begin to understand the commutative law (although not the term)

Example of the commutative law: 24 x 12 = 12 x 24

If a child has cracked all these ideas they are well on the way to success.

Understand relationships between addition, subtraction, multiplication and division

Year 2 maths worksheet: finding halves (pg 2)

$y2-fractions-3$ The third in our mini series of fraction maths worksheets. This looks again at halves and finding half of a set of objects, keeping to small, even numbers. The best way to re-inforce this work is to carry out practical activities, dividing groups of objects into two equal groups – make sure you keep to an even starting number. Sweets, marbles, lego bricks etc are ideal for this.

Fractions: finding halves (pg 2)

Mental arithmetic: Subtracting single digits from multiples of 100 and 1000

A pretty straightforward worksheet in two parts. The first part looks at subtraction of a single digit from multiples of 100. The second half looks at subtracting from multiples of 1000. The obvious way to do this is to count back, but when you ask children who are very quick with maths they seem to employ other tactics with little to do with subtraction. For example, one 9 year old boy told me his explanation of 8000 – 6:

‘turn the 800 into 799 and add 4 to make the next whole ten. Answer 7994’

Not the clearest explanation ever, but it seems that he is doing a kind of decomposition in his head – interesting!

Subtract from multiples of 100 or 1000

Coming soon: mental arithmetic on subtraction and division

girlface1small Good luck to all those taking SATs.

We have some great mental arithmetic stuff coming up soon, including worksheets on how to divide by 4 mentally and subtracting single digits from multiples of 100 or 1000. Another interesting post will be on rules of divisibility for the numbers 4 and 5. Also we will be looking at the relationships between addition and subtraction and multiplication and division as well as the second in our series of fractions worksheets for Year 2 children. Plus much more! Watch this space!

Mental arithmetic: Dividing by 4

A nifty way of dividing a number by 4 is to halve the number and then halve again. This method is much easier with even numbers and, of course, whole multiples of 4, but can be used for most 2-digit numbers – just the remainders become tricky. All these questions are multiples of 4 so should be relatively straightforward. Knowing these ‘tricks’ can give children a lot of confidence and can also be a useful way of checking answers which have been calculated on paper, or even on a calculator, to ensure that the answer is sensible.

Divide by 4 mentally

Multiply by 9 mentally (1)

You can multiply most 2-digit numbers by 9 in your head. The most efficient way is to multiply the number by ten and then subtract the number. For example:

45 x 9

First of all multiply 45 by 10 which is 450.

Then subtract 45 from 450 which is 405.

This maths worksheet shows how to do this and then gives some practice questions – but you do have to be pretty good at subtraction to use this method.

Multiply by 9 mentally (1)

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

News: Head teachers to write to parents about SATs.

Head teachers will shortly be writing to all parents of children who would normally be taking the SAT tests next year. The National Association of Head Teachers want to end the tests as they say that they narrow the curriculum and interfere with proper education as teachers are forced to teach to the test.

The Department for Children, Schools and Families has said previously that head teachers have a statutory duty to administer the tests, so would be breaking the law if they did not.

It is not really the tests which are a problem as they only take about three mornings out of the school year, but it is the publishing of the tests, which forces Head Teachers to believe that they need to practice for them, give homework on them, have after school clubs etc so that the school does not ‘fail’.