Category: Maths Resources

KS2 Maths SAT question 22 from 2010 Paper A

Question 22a and 22b look at interpreting pie charts.

For 22a  An acceptable answer is within the range of 13/100 to 1/5 inclusive.
This range includes the fractions 1/6 and 1/7.
Decimals can be accepted within the range 0.13 to 0.2 inclusive.
Percentages can be accepted within the range 13% to 20% inclusive.
One mark for this question.
Suggested method:
This can be thought of as a visual question. Split the circle in half by continuing the vertical line down (between Books and DVDs.).  From this it can be seen that DVDs are just about 1/3 of the half, so will be about 1/6 of the whole circle. Because it is only an estimate there is a fair range to be within.

For 22b Answers in the range of 500 to 800 inclusive.
One mark for this question.

Suggested method:
Again this can be done by comparing the size of the two. Book sales are about 3 times that of CDs. So if 200 CDs were sold then about 600 books were sold.

Question 22 from Maths Paper A 2010

Question 22 answers and suggested methods.

Year 4 maths worksheet: multiplying by 5

By the end of year 4 children should be developing a wide range of strategies for working answers out ‘in their heads’. To be successful they do need plenty of practice with these strategies. One such technique is to be able to efficiently multiply 2-digit numbers by 5. Sometimes the best way to do this is to take the tens digit and multiply by 5 then do the same with the units. On other occasions it is easier to multiply the whole number by ten and then halve the answer; or, if the number is even, halve the number and multiply by ten.

This worksheet looks more closely at this .it is not always the best option, but it is ceertainly one that children should be confident with using.

Multiply by 5

Year 3 maths worksheet: 4x table

This is a useful page for children who are beginning to get to grips with learning the 4x table. The questions are in pairs, with the same answer. This can reinforce the idea that multiplication can be done in any order; so 3 x 4 is the same as 4 x 3. There is only one question where this does not apply, and that is where 16 is the answer, which of course is the square of 4, or 4 x 4 . Another answer needs to be placed in the second number sentence, such as 2 x 8.

A good test of how well children know the 4x table will be the speed at which these worksheets are answered.

Thanks to urbrainy.com for letting me publish this resource and I can highly recommend their maths resources, which you can view on a free trial at www.urbrainy.com

Missing numbers 4x table

 

Key Stage 2 SAT questions

We roll on with the next two questions taken from the Paper A 2010 SATs. These two questions involve fractions and perimeter.

20.  5/8                                      One mark for this question.

Unambiguous indications will also be accepted as correct eg a tick next to 5/8.

Suggested method:

The standard recommended way to do this question might be to convert them all so that they all have the same common denominator. In this case it would be quite time consuming and a little further investigative work might prove to be easier.

Firstly the answer has to be greater than a half. For a fraction to be more than a half the top number (numerator) has to be more than half of the bottom number (denominator). Looking at each fraction in turn this counts out 2/5, 1/3 and 3/6 so a faint line can be put through these. That just leaves 7/8 and 5/8.

Now, 3/4 is equivalent to 6/8 (multiply numerator and denominator by 2) so the answer has to be 5/8.

21. 18 cm
2 marks for a correct answer.

If the answer is not correct a mark can be awarded for working out that shows an understanding of the process. (eg 50 ÷ 2 = 25. 25 – 7 = ‘wrong answer’.)

Suggested method:
The perimeter of a shape is made up of the length (twice) and the width (twice). Probably the easiest way to do this question is to divide 50 cm by 2. This will give the total of the length and the width.

50 cm ÷ 2 = 25 cm.
The width is 7 cm so the length must be 25 cm – 7 cm = 18 cm

Another way could be:
to double the width: 7cm x 2 = 14 cm.
Take 14 cm from 50 cm = 36 cm
Divide 36 cm by 2 = 18 cm.

Questions 20 and 21 Maths Paper A 2010

Questions 20 and 21 answers and suggested method

 

Bonfire night maths worksheet: percentages

Thanks to urbrainy.com for letting me publish this page. There are more bonfire night pages on their site, which you can trial free of charge at urbrainy.com

It’s always nice to have something topical to use as part of the maths curriculum. Here we have a page on percentages, linked to the theme of bonfire night, or fireworks.

Four different kinds of fireworks are on sale, with 20% off. The questions involve working out how much the boxes cost and how much in the way of savings can be made.

Finding 20% is relatively straightforward if done in two parts:

first find 10% by dividing by 2

find 20% by doubling the answer.

You can find this page in my Year 6, Understanding Number section.

Thanks to urbrainy.com for letting me publish this page. There are more bonfire night pages on their site, which you can trial free of charge at urbrainy.com

Bonfire night percentages

Year 3 mental arithmetic

It is easy to miss this growing set of resources for year 3, tucked away in the Know Number Facts category of the year 3 section. If you are working with year 3 children this is a very useful set of mental arithmetic questions.

So far there have been 24 sets of questions published and further sets will be published for each of the next two terms. They consists of two sets of ten questions, followed by an answer sheet. Each set is a full A4 page so that they can be used in several ways. If given orally the teacher/parent only needs to print the answer page as all the questions are included on this and the children can just write the answers or call them out. If the teacher/parent wants the child to read the questions then they can print out the question sheets as well. This could also be shown on a whiteboard for a whole class to work on at the same time.

The first set of questions concentrate on writing whole numbers, counting on and back in tens, addition, subtraction and place value.

Year 3 Mental arithmetic (sets 1and 2)

Question 19 from SATS Paper A 2010

Dotty paper and right angles are a favourite with the SAT paper writers, but they never make it quite straightforward, as the right angle to be found or drawn is never along horizontal or vertical lines.

There are just two possible answers to this. Either answer will gain one mark.
Slight inaccuracies in drawing are allowed. This means within a radius of 2mm of the correct point.

Some children will instantly see where the right angle will be, but there are several ways to make it easier.
One way is simply to turn the paper so that the line AB is running horizontally in front of you. This makes it easier to perceive a right angle.
Another approach is to use a right angle, such as the corner of a piece of paper and slide one edge of the paper along the line AB, with the corner at A and then mark where the other edge crosses a dot.
Don’t forget that a ruler must be used.
Why not visit ks2-maths-sats.co.uk for free SATs papers and a great SAT revision programme?

Question 19 from SATS Paper A 2010

Question 19 answer and suggested methods

Maths for Halloween

More Halloween worksheets can be found on the urbrainy.com site – well worth a visit.

Nobody seems to be sure about the origins of Halloween but celebrations in the UK seem to be on the increase, perhaps following its popularity in the USA. We do know that it is always on the eve of All Saints Day and that pumpkins, apple bobbing, dressing up and demanding sweets seem to be important modern features.

So why not try a maths worksheet on Halloween? With less emphasis on the government’s planning more schools are developing themes for their maths. This page is suitable for older children who have a grasp of multiplication. A number is put through the two pots, firstly multiplying by 3 and then adding 9. The second set of questions show the resulting number and have to be worked backwards to find the number that is inputted.

Finally there are some missing digit questions. All very spooky!

This page can be found in my Year 5 calculating category.

Halloween

More Halloween worksheets can be found on the urbrainy.com site – well worth a visit.

Year 6 maths worksheet: Adding fractions

One of the big stumbling blocks in maths is working with fractions, especially addition, subtraction, multiplication and division. The problem is caused by a lack of understanding of what a fraction actually means and how they can be manipulated to make the task easier. (Equivalent fractions being the key.)

A common fault when adding fractions is for a child to simply add the two top numbers and then add the two bottom numbers. This will always lead to a wrong answer and it is important to stress to children that to add two fractions the bottom numbers (denominators) must be the same. The reason for this can easily be shown by cutting a shape in to different sized parts and then asking how much two of the parts could be.

This particular worksheet takes all the stress out of the problem as the denominators are already the same for each addition question. Where an answer can be simplified a further answer is expected.

Adding fractions

Maths SAT Paper A 2010: Questions 17 and 18

Question 17 of the Maths SAT Paper A 2010 asks for three different numbers that add up to 40. Each number is less than 20 and each number is even.Surprisingly there are only four possible answers:
18 + 16 + 6
18 + 14 + 8
18 + 12 + 10
16 + 14 + 10
One mark given for any of these. The numbers can be given in any order.
Suggested method:
There are two key points here: firstly each even number is below 20 and secondly all the numbers are different.
I approached this by thinking what was the first even number below 20, which of course is 18. I took 18 from 40, leaving 22. I then thought of two even numbers that made 22. (20 and 18 had already gone) so 16 and 6 would be fine.

Question 18 is all about negative numbers and counting back in steps of 125.

Subtracting 125 from 50 is tricky and best done making notes rather than trying to write a standard subtraction method out. The best way is to subtract 50 taking the number to zero. Work out that 75 more needs to be subtracted, making -75.
Subtracting another 125 is easier now that both numbers are negative. Mentally adding 75 and 125 will give 200 so the same process with negative numbers will give -200.
Children find negative numbers quite tricky and this is a question which many will get wrong.

Questions 17 and 18 from SATs Paper A 2010

Questions 17 and 18 answers and suggested methods.