March, 2011 | Maths Blog

Year 4 Counting and Understanding Number

Our year 4 Counting and Understanding Number section is developing well with over 30 separate worksheets. In year 4 children are expected to develop their recognition of number sequences, and count on and back in steps of equal size.

Four digit numbers are introduced and children are expected to be able to partition, round and order them – there are four pages at present on the site on partitioning into ThHTU. One of the harder concepts for children to understand is negative numbers and it is important to put them within a context or show them on a number line.

If we are thinking of harder concepts, then decimals and fractions won’t be far away. We have some excellent pages on both these topics, including ordering decimals and equivalent fractions.

Why not visit the Year 4 Counting and Understanding Number section of the site?

Ten, nine, eight by Molly Bang

Ten, Nine, Eight by Molly Bang

To celebrate World Book Day, a few words about one of my favourite books for young children to help them with their maths.

Whatever you do, don’t miss this book if you have young children about to enter school. A counting book, in this case counting down from ten toes, nine friends etc as a father and young daughter get ready for bed.

The characters are interesting, an African-American family, and the warm colours of the illustrations really are a delight. Each page has a warm, comforting glow, perfect for a bedtime story.

I know of several children who have memorised the whole book – always a good sign!

Learning the 4 times table

The normal route through learning tables is to start with the twos and tens as these are probably the tables most familiar to children. The next stage is usually to learn the fives, followed by fours. The four times table has a number of characteristics which can be pointed out to help children. Firstly, all the answers are even, so must end in 0, 2, 4, 6 or 8. Secondly it is double the two times tables. Doubling is a very powerful mental arithmetic tool and some cultures incorporate it into all their multiplying.

This is a page most suited to those just starting to learn their four times table as it has a number line to help. Try to use this only when uncertain of the answer. It can be found in our Four Rules section, under Tables. It is expected that children in Year 3 (7/8 years old) should be learning this table and have a good knowledge of it by the end of the year.

4 times table (3)

Year 1 Counting back

One of the most important learning objectives for year 1 is counting objects and beginning to count on and back. This worksheet looks at counting back, using small numbers and should be used after a lot of practical counting back has already been done. Use objects on a tray, taking one off at a time to count down. practice starting at different numbers below ten and counting down to zero. Also don’t forget to use our counting back in ones games.

Count back (1)

Year 3 maths worksheet: Halving

Here is a page for checking understanding of halving. The numbers to halve are all multiples of 10 so it is important that children are confident with halving numbers up to 20 before trying this. By Year 3 children should be knowing these halves off by heart.

The questions with a whole ten answer are very straightforward. The tricky bit is halving a number such as 70. Probably the best approach to begin with is to split the 70 into 60 and 10. Halve the 60 (that’s 30) and halve the 10 (that’s 5) and add the 30 and 5 to make 35.

After a while this will become second nature as the process is mentally ‘internalised’.

This can be found in our Year 3 Calculating category.

Half of multiples of 10

Know addition and subtraction facts in year 5

$add_decimal_fractions_mentally_1$

By year 5 children are expected to know the basic number facts, including tables up to 10. They should also have rapid recall of addition and subtraction facts. We have some excellent pages to help with this, using known facts to rapidly work out answers.
Firstly there are tasks such as ‘making 50’, which include writing all the pairs of even numbers that make 50.

Then there are ‘find the difference’ questions, involving whole tens such as 150 and 80. There should be little or no time spent working this out as a previously learnt fact that 8 and 7 make 15 comes instantly to mind. After all, they have been working on questions such as these for over 2 years.

Similar techniques can be used when finding the difference between two decimals, such as 10 and 8.1. Just think of the difference between 100 and 81 for a clue to the answer.

We also include several calculator multiplication games. The point of these is not to let the calculator do the calculation, but to use it as a check for your own mental calculation. Those with a good mental knowledge will be able to pick the answers they want rather than keying in numbers haphazardly.

Go to our Year 5 Knowing Number Facts category

The Doorbell Rang by Pat Hutchins

Each time the doorbell rings there is less for each child until they are down to only one each.

The Doorbell Rang by Pat Hutchins.
A great writer of children’s picture books, Pat Hutchins has created a wonderfully simple book which helps with the very earliest understanding of sharing. Mum has made 12 scrumptious cookies for her two children – obviously they are going to get lots each. They count them and find that they are going to get six each but then the doorbell rings and friends arrive to share the cookies. Each time the doorbell rings there is less for each child until they are down to only one each. Then the doorbell rings again!!

Written methods of dividing

Today we have a straightforward page of division questions, using the standard method of written division. There are several stages in this process if the correct answer is to be reached.

For example: 74 divided by 3

1. Make a rough estimate of the answer; this can be along the lines of, “It will be over 20 but not as many as 30”.

2. Ask the question, “How many threes in 7?”

There are 2 threes in 7 with a remainder of 1.

3. Place the 2 above the 7 on the answer line and place the one remainder in front of the 4 (making 14).

4. Ask the question, “How many threes in 14?”

There are 4 threes in 14 with 2 remainder.

5. Place the 4 on the answer line.

6. The 2 remainder can be shown as 2/3 on the answer line: making the answer 24 and 2/3.

Remember to set out the last few questions just as the earlier ones have been set out.

Division_2_by_1_p3

Year 3 maths worksheet: Multiples

A multiple is a number produced by multiplying a starting whole number by another whole number. Think of them as the numbers in the multiplication tables.

eg 3 x 4 = 12.

12 is a multiple of both 3 and 4.

The term ‘multiple’ is introduced much earlier than it used to be 30 or 40 years ago and now it is used in Year 3. This page looks at multiples of 2, 3, 5 and 10 with a simple yes or no answer. Those children who know their tables should find this quite easy. If tables are not known it becomes quite hard!

This maths worksheet can be found in our Year 3, Know Number Facts category.

Multiples

Year 6 maths SAT questions

It is about this time of year that schools intensify their year 6 revision for the KS2 SATs. The types of question that come up are fairly predictable and follow a similar layout each year. It is well worthwhile, therefore, to let your children have a practice at the style of questions they are likely to come across on the test.

We have a good selection of SAT questions which can be printed free of charge, including pages on:

writing numbers

making mathematical statements true

completing number sentences

number problems

time problems

symmetry

Why not have a look at our Year 6 ‘Booster’ pages for SATs?