Maths Resources | Maths Blog

Resource of the week: division as sharing

Our resource of the week this week looks at early understanding of division. Division is usually the hardest of the four rules for children to learn, but in the early stages it is quite straightforward. Children often come across division for the first time when sharing, usually between two. The key concept,of course, is that the sharing is done equally. So, for example, 6 sweets shared between 2 children implies that the sharing is equal and they both receive the same number.

By far the best way to practice sharing is to use practical apparatus or use real life situations: e.g. share the strawberries equally between two, share or deal the cards equally etc. Usually this is done on a ‘one for you and one for me’ type process until there are none left. This maths worksheet replicates a practical situation, with the ultimate aim that children begin to remember the answers, which, of course are the inverse of multiplication.

Be careful when sharing that it is not always done into two, as some children begin to think that to share something it can always be divided by 2 and no other number.

Division as sharing (pg 1)

Count back in threes

Counting is one of those activities that it is all to easy to assume that children can do. In fact there are many children in Primary Schools who are very shaky in their knowledge of numbers and counting in ones, forwards or backwards. Yet one of the targets for Year 1 is for children to count on and back in twos and threes. This page is a help towards achieving this as it looks at counting back from a 2-digit number in threes. Starting at 43 count back 1, 2, 3 and reach 40; colour the square and count back a further three and so on. When the end of the line has been reached get children to read the numbers which have been coloured, both forwards and backwards. predictions could also be made as to which number comes next.

A blank sheet has been provided at the end of these pages so that different starting numbers can be used, or children asked to fill in the numbers themselves.

This page can be found in our Year 1 Counting category.

Count down in threes

Resource of the Week: Maths SAT questions

For anyone in Year 6 the Maths SAT tests will be coming up before too long! Don’t forget that we have a whole section of past questions and answers, including great explanations of the best ways to approach each question. Invaluable help to achieve those higher levels!

This week I am highlighting are two questions from the Maths SAT Paper 2011 Paper B. The first involves equivalent fractions and the second angles and shape.

The answer to Question 8. 3/4
One mark awarded for a correct answer.
Equivalent fractions accepted as is 0.75.
Suggested method:
This question is another reading a number line problem and if children can count in quarters it is an easy mark. Firstly, it has to be recognised that the number line is showing quarters (1/2 is equivalent to 2/4 and 1 is equivalent to 4/4) making the missing number 3/4.

The answer to Question 9. A and D.
One mark awarded for a correct answer.
The letters can be given in either order. Both need to be given with no incorrect angles added.
Suggested method:
Answering this question correctly depends on 3 things:
Firstly, a recognition of the conventions for labelling angles, using the arc.
Secondly, a knowledge that an obtuse angle is larger than 90 degrees but less than 180 degrees.
If either of these are unknown it becomes purely a guessing game. (Some children do think that the angle depends on the length of the lines rather than a measure of turn.)

Thirdly, if these are known, then the obtuse angles still need to be recognised. One way to do this is to slide a right angle (eg a corner of a piece of paper) into the angle to see whether it is smaller or larger.

Why not visit ks2-maths-sats.co.uk for free SATs papers and a great SAT revision programme?

Questions 8 and 9 from SAT Paper B 2011

Questions 8 and 9 answers and suggested method 2011 Paper B

Year 5 maths worksheet: solve single step word problems

This page contains a set of ten problems written in words. They look quite long, but they can all be worked out using a single step, using one of the operations: addition, subtraction, multiplication and division. Because they only require one step they are easier than questions which involve two or steps, but each calculation is quite tricky, with several needing a good knowledge of written methods to be able to do them.

It is important that all working out is shown for several reasons, including to show that a calculator was not used and to be able to spot where errors occur. Wrong answers are an excellent step towards new learning!

It is also interesting to see how children approach the questions. One or two questions in particular may cause problems. Question 6, involves subtracting of decimals and can be laid out in the standard format but could also be answered by adding on: e.g.

27.89 + 0.11 = 28

28 + 72 = 100

100 + 200 = 300

answer = 0.11 + 72 + 200 = 272.11

Solve single step word problems

More adding three 2-digit numbers mentally

I have had a number of requests for more on adding three 2-digit numbers mentally, so, here is another page. There are a number of different techniques which can be used when adding these and it certainly would not be the best way to proceed to just add them in the order they appear. Looking for pairs that make 30, doubling of teens, adjusting by 1 or 2 are just some of the skills needed to answer these quickly and accurately.

Also, don’t forget that correct answers are better than fast incorrect answers, so it is always a good idea to check by adding them in a different order.

Add 3 2-digit numbers practice (2)

This page can be found in the year 5 Calculating category, but many more addition pages can also be found in the four rules section.

Year 3 maths: adding with 2013

Knowing how much I like anything mathematical to do with dates, those kind people at urbrainy.com have let me publish a nifty little investigation to introduce the new year of 2013.

It is a simple idea; how many different addition questions can you find by just using the four digits, 2013.

At first it would be a good idea to look at adding two single digit numbers. Then there are the possibilities of adding a 2-digit number to a single digit; then adding two 2-digit numbers, and so on.

This is good practice at addition as well as encouraging logical thinking and presenting results in a well ordered, methodical way.

There are plenty of extension ideas with this investigation. For example the digits could be used twice, or the numbers could be multiplied rather than added, or even a mixture of the two

e.g. 2 x 0 + 1 = or 2 x 1 + 0 =

Subtraction could also be used, which might well lead on to negative numbers.

This page can be found in the year 3, Using and Understanding Maths category.

Addition using 2013

Resource of the Week: Christmas maths activities

It’s getting very close to Christmas now and with many activities going on in school why not try a little Christmas maths as well?

This page is quite an open ended challenge as all the possible combinations of presents need to be found. There are four items with prices; a set of beads for £2, a box of chocolates for £3, a bag for £5 and a bottle of perfume for £7.

The task is to find as many different combinations of presents that can be bought for up to £10. The key here is that the whole £10 does not have to be spent.

So 3 sets of beads and a box of chocolates is one possibility, costing £9 in total.

As usual, look for well a well organised logical approach.

This page can be found in the year 4 Using and Applying Maths category.

Christmas presents

12.12.12 an interesting date

Those of you who have followed the site for some time will know that I enjoy the quirky dates which come up from time to time, and we have a really good one next week; on 12th December 2012 the date can be written as 12.12.12. On the 12th second of the 12th minute of the 12th hour it can be written as 12.12.12.12.12.12!!

It will be quite some time before this type of recurring number pattern happens again; in fact not until 2101, when I don’t think I will be around to enjoy it!!

of course there are the usual doom mongers suggesting that the world will end as we all get sucked into a black hole, but I think it is a great chance to do a little maths and I was delighted to see that urbrainy.com have published a superb couple of worksheets which they have allowed me to publish.

The first takes a look at the digits 121212 and how many different 3-digit addition sums can be made from them. This type of activity really encourages thinking in a logical, well ordered way and it also brings some issues up, in particular whether the order of addition makes any difference as is 111 + 222 the same as 222 + 111. This is suitable for children around year 4 and can be found in the Year 4 Using and Applying Maths category.

The second set of worksheets looks at using three twelves and the four operations and raises all kinds of interesting mathematical questions. Suitable for Year 6 who have been introduced to BODMAS or as an introduction to it.

Adding with 121212

Calculating with 12 12 12

Year 4 maths worksheet: suggesting suitable units to measure

By year 4 it is important that children have a good understanding of the units used to measure and what kind of unit would be sensible to estimate or measure length, mass or capacity.

They should be able to respond to questions such as;

‘About how heavy is a tennis ball?’

‘Would you expect a bungalow to be 2 metres, 6 metres or 60 metres tall?’

They should also be able to suggest things that could be measured in:

millimetres, centimetres, metres or kilometres

kilograms or grams

litres or millilitres.

This page takes a look at some common objects and what would be the most sensible estimate of them. it can be found in our Year 4 Measuring category.

Sensible units

Resource of the week: scalene triangles

This week we take another look at types of triangle. A lot of work is done on triangles in Primary Schools and by year 5 and 6 most children are familiar with the properties of right angled triangles, equilateral triangles and isosceles triangles. An equilateral triangle has all three sides equal and all three angles equal; an isosceles triangle has two equal sides and two equal angles. However, fewer children know about the scalene triangle. A scalene triangle is one which has no sides the same length and no equal angles. Right angled triangles could also be scalene if all the sides are different lengths.

Thanks to MathSphere Ltd for this worksheet: and there are many more similar pages, both on their site and part of the ‘It’s All Figured Out’ CD.

This page can be found on the blog in the Year 5 section under Shape.

Go to our year 5 shape resources