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)

Resource of the Week: subtraction across the thousands boundary

find-a-difference-by-counting-up-pg-1

This Year 4 maths worksheet can reveal a great deal about how children deal with numbers. It looks at finding differences crossing the thousands boundary.

Let’s look at 3005 – 8 which is easier to do mentally than on paper.

There are several ways that this can be done.

1. Count down, one at a time, 8 from 3005, saying each number as you go. Fingers may be held up on each count down until 8 is reached.

3004, (1), 3003 (2), 3002 (3), 3001 (4), 3000 (5), 2999 (6), 2998 (7), 2997 (8)

2. A different way is to take the 8 from 3000,  then add 5.

3000 – 8 = 2992

2992 + 5 = 2997

3. A third way is to take 5 off the 8 leaving 3.

Then take 3 off 3000 = 2997

It is well worth talking to children about how they do this kind of question and what strategies they employ. Much will depend on their knowledge of number.

If this question ia attempted using the standard written method for subtraction there are many children who will get confused with the adjustments that have to be made (crossing out tens and borrowing etc).

Find a difference by counting up (pg 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

Resource of the week: change from ten pence

Using coins is a vital part of understanding number as it provides concrete examples of numbers in action. It is a really good idea to have a set of coins that can be counted out and swapped e.g. 5 one pence coins exchanged for a 5p piece etc. Why not set up a little shop at home and take turns buying and selling items? There is an amazing amount of maths involved in this, from learning how to write numbers to counting on and back and finding two or three lots of a number. If a shop is not available why not try this page?

Thanks to urbrainy.com for this money worksheet, suitable for year 1 children.

The worksheet asks for the change needed after spending various amounts. The easiest way to work out change is to start with the amount spent and count on up to 10. Eventually it is expected that children will know, off by heart’ the answers. In other words they will know, without counting that if you spend 6p you will have 4p change.

Change from 10p

Year 3 Mental Arithmetic: sets 51 and 52

This week’s year 3 mental arithmetic questions concentrate on addition, with a couple of ‘less than’ questions. Children should be getting more familiar with the various techniques they can use to answer questions ‘in their heads’.

For example:

a. it helps to look for pairs of numbers that make 10 such as 5 and 5 or 6 and 4. These pairs all need to be learnt off by heart.

b. when adding pairs of multiples of ten, use knowledge of adding single digits. If the answer to 6 + 7 is known off by heart it makes it easy to add 60 and 70.

c. when adding pounds and pence make sure the answer is using the correct units e.g. £2.70 + 20p = £2.90. (Not £2.90p)

d. when adding three or four numbers to remember that addition can be done in any order and it is often best to start with the largest number.

Year 3 mental arithmetic (sets 51 and 52)

 

Resource of the Week: Year 6 Prime Factors

The term ‘prime factor’ is one which would make many adults shudder as they try to think back to their school days. In fact, it is a term that children would probably not met until secondary school, but is now firmly incorporated into the primary curriculum.

Here we have a maths worksheet for year 6 on how to find prime factors. Before attempting this page it is necessary for children to have a good understanding of what factors are and what prime numbers are.

One of the easiest ways of finding prime factors is to use a diagram, rather like a tree diagram with the numbers at the bottom all being the prime factors. Frequently the same number is found more than once. For example the prime factors of 36 are 3, 3, 2 and 2.

Starting with the number itself, find two numbers which multiply together to make that number. For example 36 can be made by multiplying 18 by 2. 18 and 2 are both factors of 36. Repeat this process until only prime numbers are left.

A good way of checking if all the factors have been found is to multiply them and the original number should result. e.g. 3 x 3 x 2 x 2 = 36

This page is found in our Year 6 calculating section .

Go to prime factors page

More long division: 3-digits divided by 2-digits

One of the hardest things children try to do in primary school is long division. It 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.

Good luck with these, but many year 6 children will find them too tricky! When I was at school I used to like doing pages of these because I had learnt the method ‘off by heart’ and it was just a matter of repeating it.

Division 3 by 2

Year 3 mental arithmetic: sets 49 and 50

We begin the summer term’s mental arithmetic papers for year 3 with a reasonably easy set of questions. The first two questions look at writing numbers in figures. e.g. ‘write in figures: four hundred and nine. ‘ Most children should be able to do this but watch out for those who are unsure about place value and write 4009.

The next two questions are about finding numbers half way between two other numbers. These are not as easy as they look. There are also questions on ‘more than’ and ‘less than’ as well as a couple of rounding to the nearest whole one hundred.

These mental arithmetic pages can be used in a variety of ways. The questions can be read out without children seeing them or the sheet can be printed out for answers to be written down. If reading them they will need to be repeated at least once and time given for the answers to be worked out. It is much harder to retain information than to have it written.

Year 3 mental arithmetic (sets 49 and 50)

Key Stage 2 Maths SAT practice: graphs (4)

This worksheet is another in our series on the types of questions that come up on the SAT papers. It is another on graphs, but quite a lot harder. The first part of the worksheet looks at a line graph showing temperatures in a kitchen over a 12 hour period.A key difference between this and other graphs is that every point on the line has a value even between the hours marked.

As well as reading times from the graph it also asks the question, ‘At what time do you think the central heating was switched on?’ This involves interpreting the question and assuming that switching on the central heating would lead to a rise in temperature. Given that it would take a little while for the radiators to warm up it would seem that 0500  would be a good answer. Times either side of this could also be given as correct.

The second part of the worksheet looks at a pictogram, where each symbol represents 20 houses. Again, this is a common type of question that children should have met many times before and should not cause any problems.

Graphs (4)