Year 3 mental arithmetic: Sets 45 and 46

As we approach the end of the Spring Term it’s time for another set of mental arithmetic questions. This week it is a mixed bag of calculating, including money.

The first two questions in each set look at adding 4 small numbers. The difficulty in doing this should not be underestimated as it is as much to do with memory as addition skills. This is a much easier question if children can see the numbers, either on the printed page or on a whiteboard.

The next two questions look at addition and subtraction of money. In both cases the pounds stay the same and the pence have to be added or subtracted.

Question 6 can cause difficulties. It asks, ’10 taken from a number is 17. What is the the number?’

Watch out for the child who hears the numbers and just subtracts 10 from 17!

Finally we have some doubling questions. By now children in Year 3 should know the double of small numbers up to ten and be able to work out the double of numbers in the teens. Eventually it is hoped they will know these off by heart.

Year 3 Mental arithmetic (sets 45 and 46)

 

Subtraction of 3-digit numbers

Here is a maths worksheet that concentrates on practising subtraction of 3-digit numbers, using the standard, or efficient, written method.

There are several things to look out for when subtracting, including:

a. where each of the three digits on the bottom line are smaller than the 3 digits above them e.g.

987
654

This is the easiest type of question as there is no ‘borrowing’ or ‘adjusting.

b. Where the units are larger on the bottom line e.g.

456
327

Here an adjustment of ten has to be made from the tens column to the units column to carry out the subtraction.

c. Where the tens are larger on the bottom line e.g.

746
395

here an adjustment from the hundreds to the tens has to be made.

d. Where an adjustment from the tens has to be made, but there are no tens and the adjustment has to be made from the hundreds. e.g.

703

445

This is the hardest and one which many children will make a mistake.

For further details of these go to our Four Rules/Subtraction pages.

Subtraction of 3-digit numbers

Resource of the Week: Simple Maths Games

Whilst most of the mathsblog site is about maths worksheets we do have a small selection of fun maths games for young children.

Listen under the Reception/Year 1 Maths Games there are over 20 simple maths games which younger children children may like to play and which will certanly help with counting, ordering and addition .

Here is one example to help with counting.

Help Ted colour his white balloons. Just by clicking in the balloons the colour will change.

One click will make a balloon go Red.

Two clicks will turn the balloon Blue.

Three clicks will change the colour to Gold.

Don’t forget to press Go when you think the colours are correct!

This is great practice at counting, why not have a go?

More games can be found in our Maths Games section.

[flash http://mathsblog.co.uk/wp-content/uploads/2008/02/colour8balloons1.swf]

Year 3 Mental Arithmetic Worksheets: Sets 43 and 44

This week’s mental arithmetic questions for Year 3 are all about fractions. The first couple of questions are simple, finding halves of multiples of 10. Most children learn the halves of even numbers up to 10 but find it harder to work out half of numbers such as 30 or 50, where this knowledge is not so useful.

The next two questions look at a different aspect of fractions; sharing one whole one into equal parts and naming the parts. Questions 5 and 6 look at finding a quarter of numbers.

Probably the hardest two questions involve counting up in quarters and finding a number half way between two others. Finding the number half way between three and a half and four is quite tricky and children need to have spent some time using number lines and counting in quarters to be successful with this.

Finally a couple of questions which test knowledge of the meaning of a fraction and that the larger the bottom number (denominator) the smaller the fraction will be (if the top number (numerator) is the same).

Year 3 mental arithmetic (sets 43 and 44)

More on equivalent fractions

Equivalent fractions are fractions which look different but have the same value. The easiest example of equivalent fractions is a half and two quarters. If I have half of a fruit cake that is the same as having two quarters of the same cake. (As long as I pick up all the crumbs from cutting it!)

Not all equivalent fractions are that easy to work out, but as a rule it can be said that:

If we multiply the top and bottom numbers in a fraction by the same value we will get an equivalent fraction.

The same can be said of division:

If we divide the top and bottom numbers of a fraction by the same value we will get an equivalent fraction.

Dividing is really useful as it ‘simplifies’ the fraction, often making it easier to read or to picture. For example 10/100 is equivalent to 1/10 as both top and bottom have been divided by 10.

Now, the fraction will only get simpler if we can successfully divide both top and bottom numbers without leaving a remainder! This is the key, and, as so often, a good knowledge of tables helps here.

This worksheet looks at simplifying fractions. As shown above, this is done by dividing the top and bottom of the fraction by the same number. This division process might need to be done more than once. For example: 8/12 can be simplified to 4/6. This in turn can be simplified to 2/3.

Equivalent fractions (pg 3)

Maths Games: Adding game for Year 3 onwards

This Maths game  is a great way to practise addition of small numbers. It is a game for two players and can be a good challenge for adults as well as children.  Each player takes it in turn to place a counter over one of the numbers. When a counter is paced on the board the number is added to a joint total. It is a good idea to write the totals down as you go along, so that totals can be checked, or there might be a dispute! Once a counter has been placed it cannot be picked up.

The aim of the game is to make the total come to exactly 31. The player who does so is the winner.

If a player places a counter to make the total over 31 he/she loses.

This is a game of strategy and  and there are times when the total can not be reached (perhaps if all the ones have been covered).

Make 31

Mental Arithmetic Questions for Year 3

This week’s mental arithmetic questions for year 3 cover just multiplication and division. Year 3 is the start of the learning ‘times tables’, and by the end of the year children should be confident with at least the 2, 5 and 10 times tables as well as developing 3x and 4x.

Some teachers argue that children should also learn the ‘division tables’. These are the equivalent facts for division. For example, the dividing by 5 table would go like this:

5 divided by 5 is 1

10 divided by 5 is 2

15 divided by 5 is 3

20 divided by 5 is 4

25 divided by 5 is 5

30 divided by 5 is 6

35 divided by 5 is 7

40 divided by 5 is 8

45 divided by 5 is 9

50 divided by 5 is 10

Although it must be said that children who really know the ‘times tables’ off by heart can very rapidly work out these facts. Whichever way they do it children should be able to answer a question such as; ’16 divided by 2′ in a second or less.

Year 3 mental arithmetic_(sets 41 and 42)

National Numeracy

Once again the poor performance in maths of many adults rears its head as the charity ‘National Numeracy’ states that almost half of British adults have the maths skills of an 11 year old, or worse. This is a new charity launched today as an organisation to champion the importance of number skills for people of all ages.

Over the last eight years the number of people with the numeracy skills of an eleven year old or worse has increased from 15 million to 17 million (49% of all 16 to 59 year olds.)

The charity also highlights the ‘badge of honour’ that people wear, proudly proclaiming that they are no good at maths, something I have talked about before on several occasions.

Chris Humphries, chairman of National Numeracy and former chief executive of the UK Commission for Employment and Skills, said: “It is simply not acceptable for anyone to say ‘I can’t do maths’.

Lacking maths skills has serious outcomes for people as people with low numeracy skills are twice as likely to be unemployed.

Interestingly, calculators are not blamed,
“Even with calculators they can’t do these problems because they don’t have enough understanding to interpret problems or analyse them,” he said.

Here are questions from the test
1. Screws come in packets of 30. Each bracket needs four screws. What will one packet of screws be enough for?
A: 6 brackets with 3 screws left over;
B: 7 brackets with 2 screws left over;
C: 7 brackets with 3 screws left over;
D: 8 brackets exactly

2. Hasran has planned a new TV cupboard. A TV is 40cm wide and will sit in the middle of a shelf that is 900mm wide. How wide is the gap on each side of the TV?
A: 10cm; B. 25cm; C. 43cm; D. 50cm

3. Match these discounts with the following labels:
1. £300 reduced to £180
2. £240 reduced to 160
3. £350 reduced to £280
Labels:
A. Amazing 1/3 off!
B. Massive 20% off!
C. Slashed by 30%!
D. Reduced by 40p in the £

Go to National Numeracy Charity

Year 4 Maths worksheet: Completing number statements

This Year 4 maths worksheet looks quite straightforward, but many children will find it tricky.

Four numbers are shown as well as four addition and subtraction statements with missing numbers. Just put in the missing numbers from the four shown.

With the addition questions the best way to proceed is to look at the units digit of the answer to the number statement. Then look at the four numbers to see which two added together will match the units digit. Check that the answer is correct by adding in a different order or subtracting one number from the answer, to leave the other number.

For the subtraction statements again it is best to look at the units digit, but remembering that an adjustment from the tens might need to be made to reach the correct numbers.

This page can be found in the Year 4 resources, under Using and Applying Maths.

Complete number statements

Resource of the Week: How to do written multiplication

standard-3-by-1-pg1Some of our most popular resouces are to do with written methods of addition, subtraction, multiplication and division. This is just one of  our worksheets that show how to use the standard or efficient method to multiply a 3-digit number by a single digit. There are other methods equally good, but it is important that children keep to one method that they become confident with. It presumes a good knowledge of tables before starting.

For example: 436 x 7.

First, do an estimate of the answer.
436 x 7 is approximately 400 x 7 which is 2800. The answer will be over 2800.
Then set the sum out in a vertical layout:
436
x 7

Start with the units.
6 x 7 is 42. Put the 2 in the units and carry the 4 tens into the tens column, under the answer line.
Then multiply the tens.
3 (tens)  x 7 is 21(tens). Add the 4 (tens).  to make 25(tens).
Place the 5 in the tens column and carry the 2 (hundreds) into the hundreds column.

Finally the hundreds.
4 (hundreds) x 7 is 28 (hundreds). Add the 2 (hundreds) to make 30 (hundreds).
Place the zero in the hundreds column and the 3 in the thousands column.
The answer is 3052.
A clearer layout of this is available on the worksheet explanation.

Further written multiplication worksheets can be found in the Year 5 and Year 6 Calculations sections.

Standard written multiplication: 3-digits by 1-digit