Maths Resources | Maths Blog

Year 3 maths worksheet: more mental division

This page has 14 division questions which should be answered mentally. It keeps to the easier times tables, including 2x, 3x, 4x, 5x and 10 x tables. Children who have a good knowledge of times tables should whizz through this in little time. If tables are not known it becomes a much more laborious process.

The early questions are set out in the usual form with the number to be inputted being the answer to the division calculation. The later questions have different parts of the division number sentence missing. An example:

12 divided by ? = 2

Here the relationship between division and multiplication comes into play. if it is known that 6 x 2 = 12 then this is easy.

More mental division practice

Resource of the Week: Rounding to the nearest million

One of the earliest posts that I made, back in 2007 was about rounding large numbers, up to millions. Many children are fascinated by large numbers and these two pages can help them both with reading and writing large numbers and rounding.

Thanks to mathsphere.co.uk for letting me use these resources, as they are taken from the ‘it’s All Figured Out’ CD.

Larger numbers can be rounded in just the same way as rounding hundreds or thousands; the key is to refer to the digit below the one you want to round.

Eg rounding to a million, look at the hundred thousand digit:

2 345 456 is rounded down to 2 000 000 (two million) to the nearest million because the hundred thousand digit is only 3.

2 987 654 is rounded up to 3 000 000 (three million) to the nearest million because the hundred thousand digit is 9.

There are plenty of good sources in geography, such as population figures, areas of countries etc

Rounding to the nearest million (pg 1)

Rounding to the nearest million (pg 2)

KS2 Maths Paper 2010: Questions 16

Symmetry is a favourite topic for the SAT papers and this is a typical question. Four patterns of shapes are given and if a shape has symmetry mark it with a tick, if not, mark it with a cross. A maximum of 2 marks if all patterns of shapes are marked correctly. Interestingly, although it states that a tick or a cross must be used, other options will gain the marks.

Two marks are also given if:
a. If two correct are ticked and incorrect two are not marked at all.
b. If correct lines of symmetry are drawn and the other two shapes left blank.
c. If other alternative and unambiguous signs are given eg Y and N.

One mark is given if three of the four diagrams are ticked or crossed correctly.

Suggested method:
Children are usually given a small mirror to help with symmetry questions. The mirror can be placed along potential lines of symmetry and look from either side. If it is symmetrical the shape will look like the original.
Without a mirror, it is a little trickier. Probably the best way is to draw a potential line of symmetry on the shape and imagine what it would be like if folded along the line. If one half would fit exactly over the other it is symmetrical.

Question 16 from SATs Paper A 2010

Question 16 answers and suggested method

Multiplying 2 and 3-digit numbers by 10 or 100

Today I have published another multiplying worksheet, suitable for Year 4 children. Of course, multiplying by ten is easy; just move each digit one place to the left and place a zero in the units. Repeat this for multiplying by 100, but avoid the trap of saying ‘add a nought’.

This page has incomplete number sentences. Often the answer is given and the numbers to be multiplied have to be found. This leads to a little more thought and develops the relationship between multiplication and division.

This page can be found in the Year 4 Calculating section of the site.

Multiplying 2 or 3-digit numbers by 10 or 100

Reading and writing Roman numerals

Reading and writing in Roman numerals is quite tricky and if you are thinking of doing addition and subtraction with them it is much easier to convert them, do the sum and then rewrite the answer in Roman letters.
The Roman system is based round 7 letters:
I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1000

Interestingly there is no zero!
Numbers can be written by writing these letters, and then adding them up. So:
XVI is 10 + 5 + 1 = 16.
There are a few rules to follow:
1. It is possible to repeat a letter many times (xxxx = 40) but a general rule is that a letter can only be repeated three times.
2. If a letter is placed after a letter of greater value then add. eg VI = 5 + 1 = 105
3. If a letter is placed before another letter of greater value subtract that amount. eg IV = 5 – 1 = 4
Roman numerals are still used in certain circumstances. You may see them on a clock face, in an index or, probably most often used for the date at the end of a film or TV programme. These two pages of worksheets explore some of the easier aspects of reading and converting Roman numerals.

These worksheets can be found in the Year 6 Understanding Number category.

Reading and writing Roman numerals

KS2 Maths Paper 2010: Questions 14 and 15

Suddenly the questions become harder as questions 14 and 15 require a little more thought before trying to answer them.
With question 14 a knowledge of what happens when a number is multiplied by a half will give a clue that the most obvious answer involves using the only card without a half on (the 2) as the one outside the brackets. This means that the cards inside the bracket must add up to 5 and is just a matter of finding a pair which add up to 5.

This also assumes a knowledge that the addition inside the brackets is carried out before the multuplication.

The second correct answer given on the SATs answer booklet is much harder to work out and it would require a knowledge that ten divided by two and a half is 4 and then finding two cards that add up to 4.

Another alternative approach is to convert the fractions into decimals and this does make the multiplication easier. Interestingly a correct decimal answer is accepted for the full mark.
Question 15 is worth two marks.
If the answer is incorrect but appropriate working out has been shown, then one mark can be given.

An iced cake costs 10p more than a plain cake.

Sarah bought two of each cake.

They cost £1 altogether.

What is the cost of an iced cake?

There are several ways of looking at this. I would halve £1 to get 50p and then work out in my head two prices 10p apart that make 50p: ie 30p and 20p.

But the SAT testers are thinking about written evidence, so another way is to say that if two of each cake cost £1 then one of each cake would cost 50p. As the iced cake is 10p more expensive, take 10p from 50p which is 40p. Divide 40p by 2 is 20p. As the iced cake is 10p more add 10p to 20p which is 30p.
£1 ÷ 2 = 50p; 50p – 10p = 40p; 40p ÷ 2 = 20p; 20p + 10p = 30p
Another working out, using different thought processes might show:
10p x 2 = 20p; £1 – 20p = 80p 80p ÷ 4 = 20p 20p + 10p = 30p
It must be noted here that that many children will do this more as a trial and error process and find an answer without any working out shown.

Questions 14 and 15 from SATs Paper A 2010

Questions 14 and 15 answers and suggested methods

Year 1 addition game

Early years teachers are great at coming up with resources to help with addition, without them just being rows of sums. The teacher writers at urbrainy.com have come up with some excellent resources for year 1, including this great little board game for two people which involves both using a strategy and knowing addition facts. It is best played with one adult and one child, but beware you may lose! You will need 2 dice, 2 sets of 5 different coloured counters or cubes plus a calculator and the games sheet.

Decide who is to go first.Player one goes first and rolls the two dice. Add up the total and place a counter on a square showing that number. If the number has already been covered it becomes the next players go. Then player 2 has their turn. Some numbers, such as 7, come up on the grid several times (as there is a greater chance of throwing a 7 than any other total) so it is important to think about which 7 the counter is placed on.

The winner is the first person to put three counters in a row, across, down or diagonally. Sometimes it is more important to block the opponent than to try to create your own 3 in a row.

This game can be found in our Year 1 Calculating category

Dice: 3 in a row addition game

Completing multiplication number sentences

This maths worksheet is suitable for Year 5 children who have a good knowledge of the times tables and can manipulate numbers ‘in their heads’.

It is surprising the number of different strategies we use to calculate mentally. The same type of question can be processed several different ways, often depending on the numbers being use. If we look at some of the questions on this worksheet it will become clearer as to what I mean, as I try to explain how I go about answering them, although you may well have different (and better) alternatives.

Question 1: ? x 2 = 120

Looking at the question I immediately think that I have to halve 120 to get the answer. I do this by halving 12, which is 6 and multiplying by 10, making 60. This is all done in a split second, and I might be tempted to think I did it in one, but it is important to stop and think of the steps that you go through.

Question 3: ? x 4 = 48

I could have halved and halved, or divided by 4, but, in fact, I learned my 12 times table many years ago and I know, instantly, that 12 x 4 = 48 so the answer of 12 came immediately.

Question 4: 41 x ? = 205

The answer was not immediately obvious. I looked at the unit (1) and the unit in the answer (5) and it struck me that I need to multiply by 5. A quick check that4 x 5 will give me 20 confirmed this.

These are just a few of the ways of working out the answers and it is well worth asking children how they go about finding the answers.

Complete multiplication number sentences (1)

Resource of the Week: Congruent shapes and scalene triangles

Today we look at two mathematical terms which are less commonly known. Firstly, congruent is a word to conjure with! In fact it has a very simple meaning. If two shapes are congruent then they are identical in every way, including size.

Whilst this is very straightforward, unfortunately people who design maths tests papers make this as difficult as possible, as children are expected to be able to spot congruent shapes even when one of a pair has been turned. By far the easiest way to spot two congruent shapes is to cut one out, or trace it and see if it fits exactly over the other – if it does it is congruent. On this worksheet the aim is to find pairs of shapes which are congruent, and as always, the answers are provided! I do recommend the tracing option!

The second term is scalene. Most people are familiar with equilateral triangles and isosceles triangles but the term scalene triangle is the one that is most frequently forgotten. Quite simply, a scalene triangle is one which has no sides the same length and no equal angles.

These two worksheets can be found in the Year 5, Shape and Measures category.

Congruent shapes

Scalene triangles

KS2 Maths Paper 2010 Question 13

This is question 13 from the 2010 SAT Paper A.

It is a nice little question to pick up two valuable marks, especially if near the level 3/4 or 4/5 boundaries, but one again, more than one calculation has to be made to reach the correct answer.

The first thing to do is work out that two of the lighter grey rectangles will total 40 cm. Then subtract 40 cm from 45 cm, leaving 5 cm which is the answer to 13a.

The second part can be worked out in several ways, including:

1. Subtract 5 cm from 20 cm, leaving 15 cm. (Here is the reason for the optional mark if the answer is incorrect as it shows an understanding of the problem.)
2. Work out that 3 of the light grey rectangles will total 60 cm. Subtract 45 cm from 60 cm which gives 15 cm.

One mark is awarded for the correct answer to 13a.
One mark is awarded to the correct answer to 13b.

Question 13 from SATs Paper A 2010

Question 13 answers and suggested method