September, 2010 | Maths Blog

Coming soon: factors and division

Understanding factors and multiples is something many children fail to grasp. Next week we have a page for year 6 children on factors and how to find all the factors of a number. The process is fairly straightforward, but can be quite time consuming. A good knowledge of tables and division is also needed. So if children’s knowledge of tables is weak, if they find division difficult and if they have little staying power then it is unlikely that they will enjoy trying to find factors of numbers!

Children generally find division harder than multiplication. This is often because the process involves multiplying to find the answer, especially with pencil and paper methods. Next week, however, we will be publishing a page aimed at rapid answering dividing by 10 questions using mental methods.

Remember, dividing by ten is the inverse of multiplying by ten. To multiply by 10 move each digit one place to the left. To divide by ten move each digit one place to the right.

Dividing by one might seem a bit obvious to us, but it is not always the case for children who don’t yet have a good understanding of division. So for year 3 we will be publishing a page concentrating on dividing by one.

Year 5 Calculator game: Multiples of 8

This is the next in our series of calculation activities to encourage knowledge of tables. It concentrates on multiples of 8 and like the other games we have published the aim is to cover a row of four squares. Some of the answers are quite tricky to find, such as finding what number multiplied by 8 makes 112?

Remember that the calculator can probably be made into a ‘multiply by 8’ machine by pressing: 8 x x = 0, then all you need to type in is the number and = to find out what 8 times the number is.

Multiples of 8 calculator game

Resource of the Week: Year 3 money

We have been building up a good collection of maths worksheets on calculating for Year 3. This is the first of in a series of maths worksheets on money and shopping problems. The worksheet looks at addition of whole tens at the greengrocers, working with multiples of 10p.

These questions should be solved mentally, although children may want to make jottings to help them. Most only need one operation to work out although the later questions involve both addition and subtraction.

Money: shopping with pence (pg 1)

Year 3 maths worksheet: Double multiples of 5

There are a couple of techniques which help with being able to double multiples of 5 quickly ‘in your head’.

Firstly any 2-digit multiple of 5 which is also a multiple of ten (eg 60) is straightforward as only the tens digit needs to be considered.

It is harder to double numbers such as 65. Probably the best way is to double the 60, making 120 and then adding 10 (which is double 5) to make 170. Some children prefer to double the 5 first, but as this always gives us 10 I prefer to do the tens part first, knowing that I have just got to add 10 to the answer.

This is probably most suited to year 3, although many older children will benefit from the practice.

Double multiples of 5

Year 6 maths worksheet: Calculator patterns and recurring decimals

The calculator can prove to be a great tool for those who are fascinated by numbers and these pages give us just one example of this.

It uses simple division sums to produce interesting recurring decimals. For example:

1/9 is 0.111111

2/9 is 0.22222

3/9 is 0.33333

and so on.

It also asks children to use their knowledge of equivalent fractions to see if they can come up with other division questions which also create these patterns. As 1/9 is equivalent to 2/18 then this fraction will also create the same pattern.

A further extension is to ask why this happens and this can be answered by doing the division by written methods where it will soon be noticed that the same remainder keeps recurring, hence the recurring or never ending answer. The numbers can also be continued: 10/9 = 1.111111 etc. Fascinating!!

(A philosophical extra to ask is why doesn’t 9/9 give 0.999999?)

These pages can be found in our Using and Understanding Maths section for Year 6.

Recurring decimals (1)

Coming soon: Doubling, multiples and recurring decimals

The calculator can prove to be a great tool for those who are fascinated by numbers and next week I will be publishing give us just one example of this.

It uses simple division sums to produce interesting recurring decimals. For example:

1/9 is 0.111111

Great for year 6 children who are really developing a good understanding of decimals.

For younger mathematicians there are a couple of techniques which help with being able to double mulitples of 5 quickly ‘in your head’.

Firstly any 2-digit multiple of 5 which is also a multiple of ten (eg 60) is straightforward as only the tens digit needs to be considered. Why not log into our Doubling page on Tuesday to find the second technique?

I will also be publishing the next in our series of calculation activities to encourage knowledge of tables. It concentrates on multiples of 8 and like the other games we have published the aim is to cover a row of four squares. Some of the answers are quite tricky to find, such as finding what number multiplied by 8 makes 112? Suitable for year 5.

Year 4 worksheet: Rapid addition and subtraction

Sometimes it’s useful to have a page that tests how quickly children can respond to a set of questions – and here is one. This Year 4 maths worksheet looks at addition and subtraction of whole tens. There are 30 questions and children who have a good grasp of adding single digits should be able to transfer their skills and answer these quite quickly.

Whilst being aimed at year 4, it could also be used with older children who are unsure of mental methods of addition and subtraction.

Rapid resonse: add and subtract (1)

Raised hands or mini whiteboards?

In the classroom there seem to be two types of child: one type that always has a hand up to answer a question; and the other type that avoids eye contact and doesn’t answer out loud. For teachers, it is much easier for the lesson to flow if she keeps asking those who will answer, so the cycle is repeated.

On BBC later this month Dylan Williams bans hands up in the classroom apart from when asking a question. Instead he asked any of the children. Resistance occurred and the end result was that mini whiteboards were issued on which all pupils wrote their answer.

This is certainly not new – I was using them 10 years ago, and the Victorians used slates! It does raise the issue of participation in the classroom, with a great fear amongst many of giving the wrong answer and being made to look a fool. It also only really works for ‘closed’ questions which can only have one possible short answer. With the introduction of new technology such as ipads how long will it be before all answers are recorded and processed? Some children would love it and some would hate it

Resource of the Week: Multiplication in any order

Here we have a maths worksheet, one of a set from urbrainy.com, which looks at a vital part of understanding the process of multiplication: that it can be done in any order. This is also true of addition, but not of subtraction or division.
This page shows that ‘2 lots of 4’ is the same as ‘4 lots of 2’, therefore 4 x 2 is the same as 2 x 4. It does not matter which way the answer is worked out, it will be 8.
This little piece of knowledge helps children with mental arithmetic and with learning tables. Each table which is learnt gives further knowledge of other tables. Eg If you know 5 x 4 = 20 then you can quickly reverse the number sentence to 4 x 5 = 20.

The URBrainy site has a wealth of material for key Stage 1 and is well worth a visit, especially for teachers.

Multiplication in any order (pg 1)

Mathematical dates

Coming up tomorrow is another of those fascinating dates that mathematicians love. At the sixth second of the seventh minute of the eighth hour of October 2010 the date will be: 06.07.08.09.10 or it can be written as 6.7.8.9.10.

Children also find these dates fun so why not ask when the next interesting pattern can be made from a date. Certainly the 10th October has promise, but so do several others. Can you find them?