Year 3 maths: Pairs that make 100

shape imageWhen working out how many more to make a number up to 100 it is important not to mix up two different ways of doing it. Let’s take the question:

‘How many more is there from 45 to 100?’

One way of doing this is to add 5 to 45, making 50 and then counting on 50 to make 100. That’s 55 in total.

Another way is to count on in tens from 45 to 95, which is 50, and then add on the extra 5, again making 55.

Watch out for children who get slightly confised, add on from 40 to 100, making 60 and then adding on another 5. This method will always result in ten more than the correct answer.

The ultimate aim of questions like these is to make the answers second nature or even to know them ‘off by heart’.

This page can be found in our Year 3, Calculating section.

Complete number sentences (pg 2)

More year 4 mental arithmetic: subtraction

This is the second page of ‘quite hard’ subtraction questions for year 4, which should be answered using mental arithmetic methods, although many adults would struggle to reach the correct answers: they really are quite hard!

Once again it shows that there are several possible ways to approach each question; the key is to choose a method which is efficient and quick. For example, they can all be done by counting on, but this may well not be the quickest way and it is speed and accuracy that we are looking for.

It is also always a really good idea to check answers by carrying out the inverse operation; in this case an addition of the answer and smallest number should give the largest number.

This, and other similar pages can be found in our Year 4 Calculations category as well as in the Four Rules section.

Quite hard mental arithmetic: subtraction_(2)

What boosts school performance?

We all know that smaller classes, uniforms and primary homework are ways of boosting schools’ performance. Or are they? Not according to a recent report from the Sutton Trust. In fact, reducing class sizes, setting homework during primary school, and introducing school uniforms are among the least effective ways of improving school results.

Looking at class sizes they found that benefits, “are not particularly large or clear, until class size is reduced to under 20 or even below 15”.

Another myth seems to be that hiring more classroom assistants is effective. This is at odds with what most teachers think as 44% said that hiring more teaching assistants was one of their top three priorities. The report says that hiring more teaching assistants  is associated with “very small or no effects on attainment”.

Significant gains in attainment meanwhile come from proven classroom approaches – providing effective feedback on pupil’s performance, encouraging students to think about their own learning strategies, and getting pupils to learn from each other. Implemented correctly, these approaches can increase pupils’ performance by an extra eight or nine months in a school year for a very low cost, according to the guide.

Key findings include:

On effective feedback – “One study even estimates that the impact of rapid feedback on learning is 124 times more cost effective that reducing class sizes.”

On peer tutoring – “Benefits are apparent for both tutor and tutee, though the approach should be used to supplement or enhance normal teaching, rather than replace it.”

On meta-cognitive approaches – “Studies report substantial gains equivalent to moving a class from 50th place in a league table of 100 schools to about 25th.”

On homework – “It is more valuable at secondary school level and much less effective for children of primary school age.”

On teaching assistants – “Most studies have consistently found very small or no effects on attainment.”

On school uniforms – “No robust evidence that introducing a school uniform will improve academic performance.”

On reducing class sizes – “Overall the benefits are not particularly large or clear, until class size is reduced to under 20 or even below 15.”

On one-to-one tuition – “Pupils might improve by about 4 or 5 months during the programme, but costs are high as the support is intensive.”

On ability grouping – “There may be some benefits for higher attaining pupils, but these are largely outweighed by the negative effects on attitudes for middle and lower performing learners.”

The full report can be found at:

The Sutton Trust


Reading, writing and ordering numbers at level 1

To attain maths level 1 children need to be able to recognise the number names up to 20, say them clearly and write them. They will be counting forwards and backwards up to 20, starting at any whole number.

To enable this to happen the numerals need to be displayed clearly on a wall so that they can be frequently referred to. Every opportunity needs to be given to count on and back in practical situations, around the home, in the kitchen, at the supermarket, in the car etc. There are lots of games which involve counting and using dice. Number lines and number tracks are really useful; pointing at each number before it is said whilst counting up and down. Eventually the number track can be visualised in a child’s head, helping with fast mental arithmetic.

To herlp with all of this, I have a good selection of worksheets for counting in:


Year 1

and Year 2 which will help with this process.

Resource of the Week: Year 6 maths challenge

Here is a tricky little puzzle which is aimed at Year 6 or upper juniors (9/11). Ideal for wet breaks!

Using just the digits 1 to 9 complete the number sentences, both across and down, so that they are all correct.

A good knowledge of tables is needed, together with the ability to add and subtract mentally.

The hardest part of this puzzle is getting started and the best approach is to use trial and improvement by picking one row or column which can only have a limited number of possibilities. This might well not be the first row across or column down.

Looking at this particular puzzle the first row is a x b – c = 34. Start by looking at combinations of numbers that when multiplied make more than 34 (but not more than 43 as the maximum to subtract is 9) and then see which number can be subtracted to leave 34.

An important note on this: all calculations are done in the order shown: Bodmas does not apply.

One to nine (1a)

Should maths lessons be quiet?

Should maths lessons be quiet is clearly a tricky one to answer. There should certainly be allowances made for children to discuss the work they are doing, explore ideas, work in small groups on a tricky investigation, but there is a big difference between quietly discussing options and shouting at each other. There are ceertainly times when everyone should be quietly concentrating.

The most recent research also suggests that the acoustics of the room can make it more difficult for children to learn. Researchers have found that 14-16 year olds working in a noisy environment performed at a similar level as 11-13 year olds working in a quiet classroom.

Dr Daniel Connolly of the Institute of Education said the study shows that poor noise levels are not good for learning.

“In a lot of tasks, higher noise levels take the older age group back to the same level as the younger age group. There will always be a certain amount of noise in a school, but if you put students in an acoustically poor room it will amplify that,” he said.

When you went to your child’s classroom was it noisy, even with nobody talking? I remember working in one classroom where the chairs made a horrendous scraping noise every time someone moved. It certainly was disturbing and onlty solved with fitting carpets. Noise from outside can also be disturbing – with some classrooms right next to the school playing fields, or schools under the Heathrow flightpath!

See Independent for more.

Percentages and Fractions

The relationship between percentages and fractions is one that many children fail to grasp, yet it is essentially quite easy. What is harder, is understanding equivalence and that fractions of the same size can be written in different ways.

100% means 100 out of 100. It can written as a fraction 100/100 and is equivalent to one whole one.

50% means 50 out of 100. it can be written as a fraction 50/100. This can be simplified to 5/10 or 1/2.

20% means 20 out of 100. It can be written as a fraction 20/100. This can be simplified to 2/10 or 1/5.

This exercise looks at multiples of 10% and how they can be shown as fractions. All the fractions can be simplified, at least to tenths. By colouring the shapes it should be clear that, for example colouring 3 out of 10 is the same as colouring 3 tenths which is the same as 30 hundredths, or 30 out of 100 or 30%.

This page can be found in our Year 5 Counting and Number category.

Percentage and fractions

0 to 9 cards

I am continuing to add to the useful Resources section of the site. Today I have added a set of 0 to 9 cards. There are actually two sets, using different fonts. It is mainly the number 4 which changes from font to font and many teachers like to use a font which shows the four in the same way that it is written.

These cards can be used in a wide variety of ways. If you don’t want children to call out the answer to a question give them cards so they can hold up the answer. Use then for ‘show me’ activities (eg ‘Show me two less than 5 etc). They are also very useful for generating 2-digit or 3-digit numbers and when numbers need to be moved about to find different solutions to a puzzle.

These types of cards can be found in many places, or you could use playing cards. However, it would be sensible to include a set here.

0 to 9 cards

Written methods of subtraction

During the early years children are not expected to employ written methods to subtract numbers. The aim at this stage is to use mental methods and become really efficient with this. However, the time comes when they must be taught one efficient method of subtraction.

There are three essential skills children should have before embarking on the standard written method:

a. know, off by heart, all addition and subtraction facts to 20

b. be able to subtract multiples of 10 (such as 150 – 60)

c. partition 2-digit and 3-digit numbers into multiples of one hundred, ten and one in different ways (For example partition 83 into 80 and 3 or 70 and 13).

When these skills have been securely grasped it is time to move towards the standard method, which is usually known as decomposition. We have a number of worksheets which explain this method and give practice with it. They can be found in our Four Rules section under subtraction.

Go to our written subtraction worksheets

Multiply by one and ten

We often presume that much of what young children have to do in maths is self evident and easily understood by them. However, often this is not the case, especially if children have missed some time or not had enough practice to consolidate their learning. Here we have a simple exercise to just check that children really know what happens when numbers are multiplied by one and ten.

This page can be found in our Year 2, Know Number Facts section.

Multiplying by 1 and 10