Resource of the Week | Maths Blog

Resource of the Week: Magic Square with negative numbers

With the Year 6 SATs all over and still a half term’s maths to get through there has never been a better time to introduce some investigations and puzzles. One of my favourites topics is the magic square, as it can be incredibly simple or extremely complex. This particular magic square is quite challenging as it involves adding negative and positive numbers, so it is a good check to see if children are confident dealing with negative numbers

The numbers to put into the squares are given on all three magic squares and on the first puzzle there is a clue that each row, column and diagonal adds up to -3.

One of the best strategies to use with these is to work out what the centre number should be and what the total of each row etc should be. it is also a good idea to cut out small squares with the numbers on so that they can be moved around the board with ease.

Please note that there are several different ways of solving these magic squares and just one way is shown on the answer page.

Magic square negative numbers

Resource of the Week: Year 6 converting metric units

Children in Year 6 still need plenty of practice using the metric system, in particular converting larger metric units to smaller ones. Here we are highlighting a page which looks at converting metres to centimetres, kilos to grams and litres to millilitres.

One of the trickier aspects of this is to convert a weight such as 6.09 kg into grams, which of course is 6090 g. watch out for common mistake children make of writing just 609 g.

This is one of several similar pages found in our Year 6 Measuring section of the site.

Year 6 Larger units to smaller units (1)

Year 2 maths worksheets: symmetry

Folding to create symmetrical patterns is a popular past-time in schools. These maths worksheets for year 2 are quite tricky as they ask children to colour the correct spots on the other side of the line of symmetry to make sure that the shape is symmetrical.

Pegboards are a useful aid to this work, as is a mirror, which can be laid along the line, or axis of symmetry to see how the pattern continues.

More can be found in our year 2, Understanding shape section.

symmetry_1

KS2 maths test questions

Don’t forget that we have some excellent ‘booster’ pages for children who will be doing their SATs this summer. Here we have some examples of the type of arithmetic questions that come up. An interesting example is the question which asks to put the digits 7, 3 and 4 into the boxes to make the total of 41.

Sometimes there is more than one way to do this type of question and it is a matter of using ‘trial and improvement’ to solve it.

One good way to tackle it is to look at the units (in this case 1) and see which two digits added together will put a 1 in the units. The only option here is is to add the digits 7 and 4 (which make 11), put these in the units boxes and it is easy from there on.

Thanks to MathSphere for letting us use this worksheet.

Booster maths worksheet 3

Learning the 4 times table

The normal route through learning tables is to start with the twos and tens as these are probably the tables most familiar to children. The next stage is usually to learn the fives, followed by fours. The four times table has a number of characteristics which can be pointed out to help children. Firstly, all the answers are even, so must end in 0, 2, 4, 6 or 8. Secondly it is double the two times tables. Doubling is a very powerful mental arithmetic tool and some cultures incorporate it into all their multiplying.

This is a page most suited to those just starting to learn their four times table as it has a number line to help. Try to use this only when uncertain of the answer. It can be found in our Four Rules section, under Tables. It is expected that children in Year 3 (7/8 years old) should be learning this table and have a good knowledge of it by the end of the year.

4 times table (3)

Written addition methods

Addition of two 3-digit numbers is usually done on paper, using the following standard method.

The method is to add the units first, put the units in the answer, and ‘carry’ the ten into the tens column. Then add the tens and continue in the same way into the hundreds. Whilst all the questions on the free maths worksheet have carrying to both tens and hundreds, this will not always be necessary if the sum of the digits is less than 10.

To see each step in more detail, together with a page of questions and answers, view the pdf below:
Standard written addition of two 3-digit numbers

There are also lots more written addition pages in our Four Rules section.

Learning the 6 times table

Now we come to some of the harder tables, starting with the 6 times table.
There is nothing especially ‘catchy’ to remember about this table, it is pretty much just hard work. It should not be learned until the 2, 3, 4, 5 and 10 times tables have been learned. If this has been achieved, then over half the 6 times table has already been mastered!
Someone with a good knowledge of the three times table can always double the answers to get the six! Also six sixes is thirty six has a nice rhythm to it.

The whole idea of tables is that they are learnt, off by heart. To do this it is essential to say them out loud:

One times six is six
two times six is twelve
three times six is eighteen
four times six is twenty four
five times six is thirty
six times six is thirty six
seven times six is forty two
eight times six is forty eight
nine times six is fifty four
ten times six is sixty

Below are two worksheets for the six times table. A good way to do these is to time them to see how long your child takes.
When you get really good with a table you should be able to say it in under ten seconds (missing out unnecessary words ie one six, six; two sixes, twelve…etc).

6x_table (1)

Percentage worksheet for Year 5

Here is the second of our percentages worksheets for Year 5. It is typical of the English that we manage to write per cent in two different ways. Unlike the Americans who use percent we use two words per cent, apart from when we write percentage when we put it altogether.

Anyway, as to the maths: remember that many percentages can be worked out ‘in your head’ by remembering that 10% of an amount is equivalent to dividing the amount by 10. At this stage we will only be dealing with whole tens so it is probably the best approach. Later more complicated percentages will be found by dividing by 100 and multiplying by the percentage.

To find 20% of £350.

Find 10% of £350, which is £35

If 10% is £35, then 20% will be £35 x 2 = £70.

Percentages (pg 2)

Resource of the week: partitioning large numbers

Our resource of the Week looks at place value with larger numbers, something that many children find tricky.

By year 5 children are expected to be able to read and write some seriously large numbers. A really good understanding of place value is needed to read large numbers successfully. The key to looking at a number and working out how to say it lies in separating the number up into a series of hundreds, tens and units.

Let’s look at 123 456 789

Take the first set of three digits (on the right:789) as a set of hundreds tens and units: that is seven hundred and eighty nine.

Take the second set of three digits (456): that is four hundred and fifty six; but it is four hundred and fifty six thousand.

Take the third set of three digits (123): that is one hundred and twenty three; but it is one hundred and twenty three million.

Put them together to make one hundred and twenty three million our hundred and fifty six thousand and seven hundred and eighty nine.

An abacus is a really good way to look at how to read numbers and is a very powerful mathematical tool – anyone who has been to Hong Kong or China and seen how they calculate with an abacus will be amazed!

Partition up to 5-digit numbers (pg 2)

Year 4 maths worksheet on time

By year 4 children are expected to know that:

1 week = 7 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds

This maths worksheet uses this knowledge to answer some straightforward questions. It also requires a calculator so more detailed information can be found, such as the number of minutes in a week. This, in turn, can lead on to some interesting investigative work, such as finding out how long a year is in minutes, and then how many minutes you have been alive (not forgetting leap years). It is quite an eye opener to realise how many precious minutes have been taken up in queues, traffic jams etc!!

This worksheet can be found in our Year 4 resources, under Measures

Days, hours, minutes and seconds