Maths Blog - Free Maths Worksheets, Resources and Reviews

Perpendicular lines

The term perpendicular was usually introduced to children in the upper primary years and indeed into secondary school, but it is now thought that it should be introduced in year 3. At this stage children just need to be able to recognise two lines which are perpendicular to each other and to make it easier all the pairs of lines shown on the worksheet either cross or touch.

Of course, the key to being able to do this is to recognise a right angle and plenty of practice with recognising right angles must be done before going on to using the term perpendicular. When the lines are vertical and horizontal it is quite easy to spot perpendicular lines but other placements make it more difficult to see just by looking and there is no harm in using the corner of a piece of paper to judge whether this is the case.

Perpendicular lines

Year 6 resource of the week: factors

Understanding factors and multiples is something many children fail to grasp. Here we have a page 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!

One point that even brighter children take a while to understand is that you only need to continue to divide up to when the number squared is larger than the original number eg to find the factors of 62 you only need to divide 62 by numbers up to 7 because eight eights are 64. It is a good idea to spend some time explaining and showing the logic of this to children.

This can be found in our Year 6 Understanding Number section.

Factors 1

Roman numeral clock faces (2)

Our Roman numerals clock face worksheet has proved very popular so I thought I would post another similar page, but including quarter to and quarter past the hour times. I have also been asked why the clock face shows IIII for four o’clock rather than IV. In fact most Roman clockfaces do show the four Is and nobody is sure why.

One reason is that when looking at the numerals opposite to each other – all of them are in perfect balance, except for the ‘heavy’ VIII and the ‘light’ IV; optical balance is re-established by printing an also ‘heavy’ IIII.

Another reason which has been given is to do with the old casting process of the numerals; ‘ Since some numerals were cast out of metal, or carved out of wood or bone, you need 20 I’s, 4 V’s, and 4 X’s, even numbers of each, if you use four I’s for “four”. The molds would produce a long centre rod, with 10 I’s, 2 V’s, and 2 X’s on each side.’

A third possibility is that clocks use IIII rather than IV out of respect for the Roman God Jupiter, the king of the Gods, whose name, in Latin, begins IV (the V being the U we now use, the I the J). Very old sun dials seem to use the IIII and early clocks followed suit; it has also been suggested that Wells Cathedral clock, one of the earliest cathedral clocks used the IIII and everyone copied this, and yet another reason is that Louis XIV preferred IIII over IV and ordered all clocks to be made in this way, and it has remained like this ever since.

Finally it has also been suggested that Romans were not great at subtraction so IIII was easier to work out than IV! I have no idea which, if any of these has the best claim to being true but interestingly Big Ben uses the IV convention.

Roman numerals clock 2

Resource of the Week: Year 5 Number Challenge

I really like this challenge, partly because there is no, one right way to answer it and partly because it really makes children think.

There are 10 digits, from zero to nine to be placed in the 10 boxes in such a way that the targets can be matched as closely as possible. The catch is that each number can only be used once!

Now the obvious way to start is to make 98 the largest even number, but immediately that means that you can not have 97 as the largest odd number. By the time you reach the last target, number closest to 30, you have only two digits left and only two choices!

But what counts as the best possible answers? This is as big a challenge, if not bigger. I have had a class try to make a set of rules to try to be as fair as possible, but it involved a great deal of addition and subtraction. One group made a set of rules that went like this:

1. Find the difference between 98 and the answer given.

2. Find the difference between 99 and the answer given.

3. Add the two differences.

This will give your total so far – the larger the total, the worse you have done.

I won’t continue with this as it might spoil the fun!

This page can be found in our Year 5, Using and Understanding Maths category.

The very best 2-digit answer

Subtracting mentally in Year 4

Making the correct choice in deciding how to work out an answer is the key to fast mental arithmetic. Many children are unaware that there are often several ways of working out a calculation and that those who choose the best methods find maths easier and are able to answer questions more quickly and more accurately.

Let’s look at ‘Subtract 38 from 63.

This should be done, ‘in your head’ and will involve several stages, depending on the method used.

First, I could take 30 from 63 to leave 33. Then I could count back 8 from 33 which gives me 25.

Secondly, I could take 40 from 63 leaving 23 and then compensate by adding 2, which gives me 25.

Thirdly, I could take 38 from 68, leaving 30 and then compensate by subtracting 5 (because 63 is 5 less than 68).

There are several other ways very similar to these, but this does show that there is no ‘one right way, when it comes to mental arithmetic.

Quite hard mental arithmetic:_subtraction (1)

Mental division practice

being able to divide mentally is essential and is made much easier by knowing times tables.

Here is a follow up page to one published earlier, giving more practice with simple division. If children have a good knowledge of the 2x, 4x, 5x and 10x tables they should find these quite straightforward. The only potentially tricky ones are where the missing number is in the middle of the number sentence

eg 24 divided by ? = 6

This requires a good understanding of what the number sentence means, but all that is required to answer is a knowledge of ‘what multiplied by 6 makes 24’.

This worksheet can be found in our Year 3 Knowing Number Facts section.

Y3 division practice 2

Add decimals mentally

Here is another page which looks at adding decimals mentally and once again shows the different approach which is usually taken compared to the standard written method.

To illustrate what I mean let’s look at the first question: 5.7 + 2.5. If this was done by the written method the two numbers would be placed in a vertical form:

5.7

2.5

and added starting with the tenths before going on to the units.

When using mental methods it would be quite usual to start with the units, adding the 5 and 2 to make 7, holding this in our memory, then adding the 7 and 5 tenths, making 1.2 before finally adding the 1.2and 7 to make 8.2.

The second set of questions on the page are probably best done by adding on. For example:

0.8 + ?? = 3

I would do this by adding 0.2 to 0.8 to make 1 and then counting on 2 more to make 3. There are , of course, other ways but the important thing is that whatever method is used it needs to be quick and accurate.

Add two decimals (3)

More of this type of question can be found in our Four Rules category.

Pairs of numbers that make 20

Here we have a straightforward maths worksheet on knowing pairs of numbers that add up to twenty. This is suitable for year 1/2 children or those who are already very confident with knowing pairs of numbers that make ten.

If these facts are not known there are several ways of working the answers out, including:

1. Counting on from the smaller number.

2. Counting on from the smaller number up to 10 and then adding another 10. (If smaller number is below 10.)

3. Counting back from 20, which is trickier.

A good follow up to this page is to ask how many different ways you can make 20 by adding just two numbers.

Know pairs that make 20 (pg 2)

Roman numeral clock faces

One of the new targets for maths in year 3 will be to, ‘tell and write the time from an analogue clock, including using Roman numerals from I to XII’. As I haven’t published any time sheets using Roman numerals I thought that now was the perfect opportunity; so here it is!
It is best that children are introduced to the Roman system of numbers before doing this worksheet, although it is interesting to understand that many adults do not look at the numbers around the clock, just the angle of the two hands and indeed many fashion watches fail to have numbers on at all, but we still manage to be able to tell the time.

This page sticks to just whole hours and half hours, although perhaps it should be pointed out that Julius Caesar and his chums would never had read the time in this way!!

Roman numerals: clock faces

Resource of the week: year 1 investigate addition

shape Welcome to a new term and plenty of new maths material coming up over the next few months.

From our current resources here is a nice little investigation for young children which will show how well they can organise their thinking and work in a logical way.

The question is simple: how many different ways can you score 8 when throwing two dice?

It’s always a good idea to sit down with your children when doing this type of activity. In this way you can ask questions which will help them clarify their thoughts. The sheet is designed to be used as a record of results. At first they might just keep rolling the dice and adding up the totals until a total of 8 is achieved. Other children might dive straight in with some answers eg 4 + 4 makes 8.

A good question to ask at the end is “How do you know that you have got all the possibilities?

Free Y1 maths worksheet: Investigate dice