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

Maths game for reception: Make 5

An often overlooked part of our site is the maths games category for Reception/Year 1. Here we have a number of simple maths games including this, the first in our addition and subtraction series, where children are given a number and have to state what is needed to make it up to 5. Ideal for a quick few minutes adding on practice. A simple print out is available after 5 questions, which is useful to show what has been done.

You can go to Reception/Year 1 maths games to play all our games.

Dora Dino has 5 eggs somewhere. She can only see some of them, so can you help her work out how many are needed to make 5.

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Two more years of maths

It might sound like their worst nightmare for many teenagers, but Michael Grove has just announced that students who do not achieve a good GCSE pass in maths will be forced into continuing to study the subject until they do, or at least until they are 18. A good GCSE pass is considered to be Grade C and last summer 45% of 16 year olds failed to reach this standard. Also the CBI have stated that more than one third of businesses are unhappy at the level of numeracy shown by college leavers.

Following a review by Alison Wolf the government intends to bring in this change from 2015, so it will directly effect those children who at present are in the Upper Primary stage. Could the thought of an extra two years studying maths prove to be an incentive to study harder now? Possibly, but children’s long term planning has generally always been poor and I am not sure I would like to be the teacher taking the maths for the extra two years!

Year 4 Counting and Number

Year 4 is where you can really see children take off with their maths knowledge and understanding. They can deal with larger numbers, and show their understanding by partitioning, including numbers in the thousands. Place value is crucial to this understanding as is being able to multiply and divide by 10 and 100.

Fractions also play a much more important role, with much time spent on equivalent fractions (the key to all understanding of fractions) which can then lead on to addition, subtraction of fractions in later years.

Why not visit our Year 4 Counting and Number worksheets. There are over 30 in total, covering place value, partitioning, fractions, decimal fractions and negative numbers.

Go to Year 4 Counting and Number worksheets

Number Ladders: 0 to 10

Our ‘Useful resources’ for maths category has been rather neglected so I thought I would try and build up these resources over the coming weeks. Something which early years teachers find very useful are Number Ladders from zero to ten. Here are two number ladders, one featuring butterflies and one cars.

They can be used in a variety of ways for helping with counting on and back, simple addition and subtraction. It is a good idea to cut them out and laminate them, or use sticky back paper to make sure that they last a long time.

0 to10_number ladders: butterflies

0 to10_number ladders_cars