Here we have another page on multiplying decimal fractions by 10 or 100. The method used today is to move each number one place to the left when multiplying by ten and two places to the left when multiplying by 100. The decimal point does not move. I seem to remember moving decimal points around when I was at school but this is certainly not recommended here.

When doing this with money it is worth remembering that two digits should always be written after the decimal point, so that £2.56 x 10 is not £25.6, but £25.60. (This is not an excuse for saying ‘add a nought’.)

Multiply a decimal by 10 and 100 (2)

These are a useful couple of pages for children entering Year 3 next term. Counting on and back will still be important in year 3, using up to three digit numbers. Grouping into tens or fives and using tally charts are both effective ways of counting larger numbers.

Children seldom get a chance to count a larger number of objects – somewhere between 30 and 60. By seeing and counting this many they become more able to estimate larger numbers and be able to give rough approximations rather than wild guesses.

Try similar exercises with heaps of coins, counters etc, dividing them up into fives or tens. A really good idea is to collect change (pennies etc) and guess how much of any one coin there is.

Counting by grouping into tens

Here we have a number of simple tips and practice at adding three 2-digit numbers mentally.

By Year 6 children should have a wide range of techniques at their fingertips for adding mentally.

Some of the tips on this page include:

starting with the largest digit

adding the tens before the units

looking for pairs that make 10

add the nearest whole ten and adjust (eg add 39 by adding 40 and subtracting 1)
How to add three 2-digit numbers

This sequence of calculator games can be found in Year 3 and Year 4 Knowing Number Facts.

7x table calculator game

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.

One to nine (1a)

A similar page to one posted earlier, this again looks at decimal fractions and how to manipulate them. The first set of questions involve changing decimals, using either the multiplication or division keys of the calculator, in just one step.

The second set of questions use the add or subtract keys.

Whilst the calculator is used, nevertheless a good understanding of number and place value is needed to be able to do these quickly and efficiently.

Decimals with a calculator (2)

Here we have a rather nice number investigation for Year 3. Using exactly 5 of the cards, how many ways can 12 be made?

It is probably a good idea to cut out the cards, or make your own, to make it much easier to move the numbers around to make the number sentences.

As with all investigations look out for a  logical, well ordered method, although at the beginning most children will work in a random fashion (as will most adults.) Once it is clear that there are a number of 2-digit subtractions that can be done it is important to show them in some logical way so that it can be seen that all possible combinations have been covered.

Rules can be changed or adapted: one of the first questions which might come up is ‘Can I use the cards twice?’ In the case of adding three single digits the plus sign needs to be used twice, but children can make their own rules for this.

Make 12 investigation

This is our second page on ratio and proportion, an area of maths which is less well covered than the traditional four rules but nevertheless involves key concepts.

An important part of this page is to be able to show the ratios in the simplest form. This process is similar to showing fractions in their simplest form, for example 6:4 can be simplified to 3:2 by dividing each by 2.

Remember, when finding the proportion of something the whole total of all items needs to be worked out. So to find what proportion of the total orders was tea, add up all the orders, which comes to 80. So the proportion of tea is 24/80. This can be simplified to 3/10.

Ratio and proportion (2)

This can be found in our Year 4 resources under Knowing Number Facts.

6x table calculator game

This can be quite a tricky subject for children to fully understand. If there are 6 yellow cubes and four blue cubes we can say that the ratio of yellow to blue is 6 to 4. This can be simplified to 3 to 2.

The proportion is usually written as a fraction of the whole lot, so the proportion of yellow cubes would be 6 out of 10, or when simplified, 3 out of 5. This can be written as a fraction 3/5.

In the same way, the proportion of blue cubes would be 4 out of 10 or 2 out of 5 (2/5).

A good way to check that the proportions are correct is to add the fractions which should make one.

3/5 + 2/5 = 5/5 or 1.

Ratio and proportion (1)