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Year 3 mental artihmetic: sets 59 and 60

As we move towards the end of the year 3 term the mental arithmetic questions become slightly harder. These two pages of addition and subtraction questions include some quite tricky problems. The first few questions are quite straightforward with adding or subtracting multiples of 100 from 3-digit numbers, although there are many children who are not at all comfortable with larger numbers. This can often be shown by asking them to count on in whole hundreds from a given number such as 34.

The last four questions look at subtraction either side of a multiple of 100. For example, at first glance 603 subtract 598 looks as if it should be done using paper and pencil methods, but it is quite easy to do by counting on.

Count on 2 from 598 to make 600. Then count on another 3 to make 603 which gives an answer of 5. No harm in using fingers to do this sort of question, especially if the question is given orally and the numbers cannot be seen.

Year 3 mental arithmetic_(sets 59 and 60)

Counting on in steps of 10p, crossing the hundreds.

I recently published a page on counting on in steps of 10p which was quite straightforward, but this one is much trickier. This time the counting on crosses the hundreds boundary and in the case of money this also crosses the decimal point.

The first set of questions just looks at 2-digit numbers which cross the hundreds boundary;

For example: 96p + 10p = 106p.

Questions 7 to 10 are much harder as they show the money as pounds rather than pence.

For example: £6.94 + 10p = £7.04.

There is quite a lot to remember here, including putting the pence as .04.

Some children will find this difficult and may well use their fingers to count on in single digits. Others will not convert to pounds properly; often answers such as this are seen:

£6.94 + 10p = £6.104

which shows a lack of understanding of the decimal system.

Count on in 10p crossing hundreds

Maths board game: Four Stars

I shall be publishing some fantastic strategy games over the next few weeks which can really help children develop their logical thinking and predicting what will happen. This is a great little game that does not need a lot of equipment and only takes a short time to play, but can get quite addictive. It’s a good idea to test out if going first or second leads to any advantage, and if so how this can be maximised. I will leave it up to you to decide!

Equipment:
Two sets of four counters.
A playing board
Rules:

This is a game for two people.
Each player has four counters.
The aim of the game is to get the four counters in a straight line.

The player going first places a counter on one of the circles.

Then the second player places one of his/her counters on a circle. This continues until all the counters have been placed.

If neither player has got 4 counters in a straight line then the first player slides a counter along a line to a circle that is not already covered.

The other player then slides a counter to an adjacent circle. Counters can only move along one line into an empty space. They cannot jump over counters.

If a player cannot move a counter she/he misses a go.

This is best played at a fast pace and a time limit set for winning.

On the first page you will find a board which can be printed out onto card. It is a good idea to cut out and either laminate or ‘sticky back’ this board.

Four star

Resource of the Week: Long division

If there is one thing which really proves to be tricky for primary school children it is long division. In fact there have been calls for it to be abandoned with the calculator taking over. However, if children do grasp the method they can get great satisfaction from working their way carefully through the method to reach a correct answer.

Long division is hard because it requires a good knowledge of tables, the ability to multiply, estimate, use trial and improvement and go through several steps to reach the answer. These steps include:

e.g. 789 divided by 36

First carry out an estimate of the answer. I think 789 divided by 36 is about 20.

a. How many 36s in 78?

b. 2 x 36 is 72. 3 x 36 is 108 which is too many, so it must be 2.

c. Put the 2 in the tens column above the question.

d. Place the 72 below the 78 and subtract.

e. 78 – 72 is 6.

f. ‘Bring down’ the 9 to make 69.

g. How many 36s in 69.

h. By trial and improvement and some rough work multiplying 36 by my estimated numbers I find that 36 x 1 = 36.

i. Put the 1 in the units column above the question.

j. Place the 36 under the 69 and subtract.

k. The remainder (33) must be less than the original number you are dividing by.

I would suggest that only those children who have really mastered the basics of times tables and written methods for addition, subtraction and multiplication try these.

Division 3 by 2

Year 3 Mental Arithmetic: Sets 57 and 58

We will soon be coming to the end of our sets of mental arithmetic questions for year 3, with just three more sets after these. Today the emphasis is on addition skills as well as a little subtraction.

The questions include:

adding a single digit to a 3-digit number in the context of money: e.g. £352 plus £4

adding a 2-digit number to a 3-digit multiple of 100: e.g. £400 + £88

adding a 2-digit multiple of 10 to a 2-digit number: e.g. to add 34

subtracting a single digit from a multiple of 100: e.g. 600 subtract 4

These are all important steps in becoming confident with working with numbers ‘in your head’ and they should be practiced as often as possible.

Year 3 mental arithmetic (sets 57 and 58)

Resource of the Week: decimal fractions

$decimal-fractions-hundredths-y5$

Some children have difficulty realising that the same numbers can be written in different ways, especially when dealing with decimals and decimal fractions. This page is a good test of understanding, probably most suited for year 5 children (/10 yrs old).

0.23 can be read as 23 hundredths or 2 tenths and 3 hundredths. As a fraction it would be written as 23/100.

With a number such as four and three hundredths it is important to keep the zero in the tenths so that it is written as 4.03.

Watch out for a common mistake on a question such as thirteen hundredths when children write 0.013; the one digit has been placed in the hundredths column when it should be in the tenths with the 3 digit in the hundredths.

Decimal fractions: hundredths (pg 1)

Maths worksheet: ordering amounts of money

Children in the Early Years get plenty of opportunity to handle coins and work on ordering small amounts of money. Yet, when children get older and the numbers get larger this is a concept which is often not practised in school. So here we have a maths worksheet which looks specifically at ordering 2-digit amounts of money written in pence.

There are four amounts in each row and it is best to take a step by step approach; first of all finding the smallest number, writing it in the answer column and then crossing it out on the top row. Crossing out is important as it can easily be seen that that number has been eliminated. Then proceed to the next number and so on.

Order money

Year 3 mental arithmetic: sets 55 and 56

Two more sets of ten questions which add to the great collection now available for year 3 children. This week there are some tricky questions which must be listened to carefully if the correct answer is to be worked out.

For example: ‘8 added to a number is 37. What is the number?’

The danger here is to add 8 to 37 rather than subtract it!

other questions cover doubling numbers in the teens. This is quite hard for year 3 children but it is hoped that they learn the answers to these off by heart as soon as possible. The rest of the set are mainly concerned with the addition of multiples of 100.

Year 3_mental arithmetic:_(sets 55 and 56)

Counting on in steps of 10p

This page looks at the way money and coins can be used with helping to count on in tens. The questions become progressively more difficult and this would be most suitable for year 3 children as well as year 2 children who are confident with counting in tens.

The first three questions look at adding 10p to a multiple of 10p and should be very straightforward. The second set look at adding 10p to any 2-digit number, which again should not prove too tricky.

The third set are more tricky as they require adding 10p to money represented in pounds,using the decimal point. Watch out for children who add a ‘p’ at the end so that both the pound and pence sign are showing. This, of course, is not necessary and is strictly incorr3ct – just the pound sign is sufficient.

The last set of questions looks at counting on in steps of 10p, but at this stage the counting does not go over the next 100 or next pound. This will be the next step.

Counting on in steps of 10p (1)

Year 3 mental arithmetic: sets 53 and 54

I continue on with the weekly sets of mental arithmetic for Year 3. This week the questions concentrate on addition and subtraction, including adding three numbers ‘in your head’. Both the first two questions are designed so that pairs that make 10 can be spotted e.g. 11 + 8 + 9, where the easiest way to do this is to firstly add the 11 and 9 to make 20.

Children need to listen carefully to the questions to make sure that they carry out the right calculation. For example;

‘What must I add to 14 to make 25?’

Some children will here add, 14 and 25 and immediately add 14 and 25 to make 39, when they should, of course, subtract.

In a similar ay, the question:

‘How many more than 4 is 23?’

will be interpreted by some as adding 4 to 23 rather than counting on from 4 to 23.

Year 3 mental arithmetic sets 53 and 54