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Coming soon: Calculators, rounding and decimals

Calculators are very much the theme for next week.

Many people criticise the fact that children use calculators and, indeed, they have huge potential for giving incorrect answers: numbers left in the memory and mishit keys are just two ways of ensuring wrong answers. That is why it is so important that a mental calculation, no matter how brief, always goes on at the same time as the calculator is used, to ensure that the answer is ‘sensible’.

For example, a child might want to know quickly what 3 876 x 3 is. By all means use the calculator, but at the same time, he should be rounding 3 876 to 4 000 and multiplying 4 000 by 3 to make 12 000. This should take only a second or so to do in his head. He then knows that the answer will be just less than 12 000.

This is why the ability to round quickly and sensibly is so important. Hence our worksheet on rounding, found in our Year 5 Counting and Number section.

A calculator will be needed for our Year 6 page as changes have to be made to decimals, using just one step. This is a good practice page for understanding multiplying and dividing decimals by 10, 100 or 1000, as well as some nifty mental arithmetic adding and subtracting. It is the second of our pages for the Year 6 plans for Counting, partitioning and calculating. (Block A Unit 3 Week 2) which most schools wil be following next week.

Also coming soon is another in our series of nifty calculator activities for year 3 children. It is a two player game intended to help with reinforcing the 4 times table.

If it’s something away from the calculator you are looking for then we will also be publisheing a page on Multiplication using words for Year 4.

Resource of the Week: Tests of divisibility

This maths worksheet is another in our set on rules of divisibility. Knowing these rules will really help children in their maths up to the end of High School and beyond.

The rule for dividing by 10 is the easiest of them all:

If the whole number ends in a 0 then the number is divisible by 10.

The rule for 9 is also easy, but it does require a little adding up:

Add up all the digits. If the total of the digits is divisible by 9 then the whole number will be.

Example: 2304

2 + 3 + 0 + 4 = 9

So 2304 is divisible by 9.

Example: 9630

9 + 6 + 3 + 0 = 18

18 is divisible by 9 therefore 9630 is also divisible by 9.

The second part of the worksheet asks which numbers are divisible by both 9 and 10. Probably the best way to do this is to ignore any numbers that do not end in a zero, then add up the digits of the rest and see if they come to a multiple of 9.

If they do, and the last digit is a zero, then they are multiples of both 9 and 10. Easy!!

Divisible by 9 and 10

Coming soon: Year 6 Maths Block Planning worksheet

I have had a lot of requests from teachers asking if resources can be organised in terms of the Block and Unit Planning required by the Primary Framework for Teaching. This seems like a sensible idea and I have decided to start with Year 6 and with ordering decimals. As this will be the first full week of the summer term for most schools, it follows as Block A Unit 3 Week 1 in the planning. Just a small start but each week there should be a new year 6 activity for the Block and Unit plans.

Next week we have a re-inforcement page for the recently published worksheet on how to round numbers to the nearest 10 000. Useful as a homework activity or consolidation for those who are still unsure about how to do this.

I will also be publishing another in our series which looks at the order of calculating with multiplication and addition, suitable for Year 4 upwards. The rule is that multiplication should be worked out before the addition and in most of these questions that is fairly straightforward. However the questions towards the end are quite tricky.

Resource of the Week: Addition of 4-digit numbers

This week’s resource looks at how to add larger numbers using written methods. Addition of two 4-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 and finally the thousands.

A clearer explanation is available on the first page of the worksheets, together with a page of questions, but briefly:

Looking at 5687 + 2546 the steps are:

Step 1: add the units

7 + 6 = 13

Put the 3 in the units below the question.
Then place the one ten below the answer in the tens column.

Step 2: add the tens
8 (tens) + 4 (tens) + 1 (ten) = 13 (tens)
Place the 3 (tens) in the tens column and the 1(hundred) in the hundreds column below the answer.

Step 3: add the hundreds
6 (hundreds) + 5 (hundreds) + 1 (hundred) = 12 (hundreds)
Place the 2 (hundreds) in the hundreds column and the 1(thousand) in the thousands column below the answer.

Note: there may not always be tens, hundreds or thousands to carry.

Step 4: add the thousands
5 (thousands) + 2 (thousands) + 1 (thousand) = 8 (thousands)
Place the 8 (thousands) in the thousands column.
Answer: 8233

Standard addition of 4-digits (pg 1)

Coming soon: Rounding, doubling and multiplication

Rounding larger numbers can be tricky to understand as you get different results depending on what you round to.

Next week’s page look at how to round to the nearest 10 000, probably best suited to Year 6 children with a good understanding of larger numbers. In this case the two crucial digits to look at are the ten thousand and the thousands digits.

It’s always a good idea to think about how we work out answers in our heads and our page on doubling multiples of 5 is a good example of this.
Try to get children to explain how they do these doubling and halving questions.
This page can be found in the year 4 worksheets section.

By year 4 it is expected that children have a pretty good knowledge of their tables, but, of course, they also need to know when multiplication is the correct option. This depends on having a good understanding of the vocabulary involved. Next week we have a worksheet which uses a variety of different terms to multiply, including ‘lots of’ and ‘times’.

Resource of the Week: Pairs that make 20

This week it is a page from our year 2 worksheets which looks at pairs of numbers which make 20. Before doing this children should be confident with, and know by heart, all pairs of numbers which make 10. Once they know these, pairs that make 20 becomes easy; just one of each pair is ten more e.g. 6 and 4: 16 and 4. Being able to work quickly with mental arithmetic is one of the keys to success in school as so much of the maths lesson today is carried out orally and children gain or lose confidence very quickly when answering in front of a whole class.

Know pairs that make 20 (pg 1)

Coming soon: Fractions, handling data and multiples

A real mixed bag of pages coming up next week.

We will post the second page where we look at questions such as:

‘How many sixths make two and a half?’

Children need to know that there are six sixths in one whole one and also need to understand equivalent fractions and that a half is equivalent to three sixths.

An important early stage in Handling Data is to be able to record the results and we will be publishing a simple page where two sets of shapes can be sorted and recorded on the columns.

The outlines of the cylinders and cubes are provided and it is just a matter of counting the number of each shape and recording by colouring the correct number on the columns.

Also coming soon is another in our series of fun games to play, suitable for year 3 children who have got a good grasp of the three times table.

Resource of the Week: Decimals that make 10

Here we have mental arithmetic maths worksheet on decimals, most suitable for Year 5. This page looks at pairs of decimals that make 10. Once again there are several ways of tackling these questions.

One way is to add on from the smaller number, firstly, the tenths to make the next whole number, and then the units to make 10.

eg 10 – 6.7

Count on from 6.7 to 7 which is 0.3

Then count on from 7 to 10 which is 3

Answer 3 + 0.3 = 3.3

Another way is to count on the units first and then the tenths, but beware the answer which counts on 4 from 6 to make 10 and than counts on 0.3 as this will result in an answer which is one too many: a common slip-up.

Another way of doing this is to ignore the decimal and think of the question as 100 – 67. Work it out mentally (which is 33) and then convert back to 3.3.

Decimals with a total of 10

Coming soon: 3D shape, division with remainders and percentages

A real cross section of resources coming up next week. To start with we have a 3D shape page for year 1. The best way to learn about 3D shapes is to handle them but it is also important to recognise drawings of them on paper. Four shapes which children should be familiar with are the cube, cuboid, cylinder and cone.

Next we have another page where the remainders from division are written as fractions. Children need a good knowledge of tables to work out the division ‘in their heads’ and this is probably best suited to Year 4, aged8/9+ years old.

Also next week there is a straightforward introduction to finding 10% off multiples of 10p up to a pound. This is ideal for year 5 children with a good understanding of multiplication and division by 10.

Resource of the Week: Adding decimals mentally

Mental arithmetic is the key to success with calculating. At first glance you might reach for a pencil to do a sum such as 2.5 + 4.7. However, the Primary Framework for Maths suggests that children should be competent in adding two 2-digit numbers in their heads, and there is no reason why, with a little practice this can’t include adding two decimals. The most common approach is almost identical to adding tens and units. Continue reading “Resource of the Week: Adding decimals mentally”