April, 2010 | Maths Blog

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.

Year 6 maths worksheet: How to order decimals

This week I am slightly reorganising the way that pages are being organised. 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. I have decided to start with Year 6 and with ordering decimals. As this is the first full week of the summer term for most schools, it follows as Block A Unit 3 Week 1 in the planning: Counting, partitioning and calculating.

I have added a heading in the Year 6 worksheets called Block and Unit Planning. This page can be found there, as well as in the Year 6 Understanding Number section. A small beginning, but over the weeks this should develop into a useful resource.

How to order decimals (1)

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

Year 4 maths worksheet: Multiplication and addition

Here is another in our series of 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.

Let’s look at 70 + ?? x 4 = 150

The best way to go about this is to go in reverse order; subtract 70 from 150 which leaves 80.

Then work out what number multiplied by 4 makes 80, which is 20.

Therefore the missing number is 20.

It is best to check this by going back to the original question; multiply 20 by 4 = 80 and then add 80 and 70 = 150, making the statement true.

Many children will find these very difficult to work out as they require several steps.

Multiplication with addition_(3)

Year 6 maths worksheet: Rounding to 10 000 (2)

Here we have a re-inforcement page for the recently published page on how to round numbers to the nearest 10 000.

Useful as a homework sheet or consolidation for those who are still unsure about how to do this. Children do not come across larger numbers very often and it can also be used as practice at reading larger numbers out loud.

Practice:_round to the nearest 10 000

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.

Year 4 calculations: Multiplication with words

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. Continue reading “Year 4 calculations: Multiplication with words”

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)

Year 4 maths worksheet: Doubling and halving

It’s always a good idea to think about how we work out answers in our heads and doubling multiples of 5 is a good example of this. Thinking and saying what you do is similar to watching a slow motion movie, in real time everything happens very quickly but by slowing it down each step can be seen in turn.

Let’s look at doubling 65. I know without thinking that double 5 is 10, so I ignore this part and first work out double 60. This is 120. I then add on 10 for the double 5 part, making 130.

A similar process can be used with halving a number such as 130. I take 10 off to make 120 as it is easy to work out half of 120, which is 60. I then add on 5 (which is half of the 10 I took off at the start) making 65.

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.

Double multiples of 5

Year 6 maths worksheet: Rounding to 10 000

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

For example 12 345 rounded to the nearest 10 is 12 350, to the nearest 100 is 12 300, to the nearest 1 000 is 12 000 and to the nearest 10 000 is 10 000. What you round to will depend on the circumstances and how accurate your rounding needs to be.

These pages look at how to round to the nearest 10 000. In this case the two crucial digits to look at are the ten thousand and the thousands digits.

How to round nearest 10 000