Category: Maths Resources

Divide 3-digit numbers by 7

Here is another page for practising the short division method. When I was young I was taught the short method before the long method and by repeated practice learned the method, although probably not knowing why it works. Today the long method is usually introduced first as a means of showing exactly how it works, usually with easier numbers. The key to both methods is, of course, a good knowledge of tables, although on this page I have written out the 7 times table to help.

For example: 7)627

‘How many sevens in 62?’

‘7 times 8 is 56, 7 times 9 is 63.’

‘7 goes into 62, 8 times with 6 left over.’

Write the 8 in the answer above the 2.

Write the remainder 6 beside the 7 units, making 67.

‘How many sevens in 67?’

‘9 times 6 is 63.’

‘7 goes into 67, 9 times with 4 left over.’

Write the 9 in the answer in the units and write rem 4 next to it.

Division 3-digit numbers by 7

 

Resource of the Week: half way between

This week I am highlighting a page which, on the face of it this looks quite a simple task, but many children (and adults) find very tricky. The page is on how to work out what half way between two numbers is. Often there is a lot of ‘trial and improvement’ going on in people’s heads as they guess their way towards finding half way.

Two methods make the task fairly straightforward.

For method one a number line is very useful to start with. Put a finger of the left hand on the first (lower) number shown on the number line and a finger of the right hand on the second number. Then move the left hand finger one place to the right and the right hand finger one place to the left. Repeat this until the two fingers meet – that is your half way number.

The second way of finding half way involves two steps:

step 1: add the two numbers.

step 2: halve the answer.

This is the better method as it works for all numbers, not just those shown on the number line.

This page can be found in our Year 3, Counting and Number section

Half way between_(1)

Short multiplication by 6

Here is the latest worksheet which looks at the short multiplication method; this time multiplying 2-digit numbers by 6. It is called the short method because it eliminates the process of putting parts of the answer in two or three columns below, as in the ‘long’ method. The stages are the same as before:

1. writing the question out correctly so that it is in vertical format. it is a good idea to write a small h, t and u above to show the hundreds, tens and units columns.

2. Multiplying the units and carrying any of the tens across, below the answer line.

3. multiplying the tens and putting any hundreds into the answer.

More clarification of this method is shown on the worksheet.

The 6 times table is one of the harder tables to learn, but knowing it off by heart makes this type of multiplication so much easier.

Short multiplication by 6

Useful resources: 0 to 99 number grid

I recently published a number grid (or number square) from 1 to 100 and today I am publishing a similar page, but for numbers from 0 to 99.

Number grids can be used in a wide variety of ways, and many patterns can be found. it shows clearly the pattwern of odd and even numbers as well as the patterns created by multiplying. For example, colour squares green that are multiples of 2; colour squares red that are multiples of 3 and colour squares green which are multiples of 4. Which squarea are coloured more than once? Why? etc.

0-99 number grid

 

Subtraction of decimals

Here we have another page which looks at the written method of subtracting decimals. The key here is to lay the question out in the traditional method, with the smaller number below the larger number and with the decimal points in line.

Sometimes these can be quite tricky; for example with a subtraction such as 8.5 – 6.26 it is important to write down a zero making the 8.5 into 8.50.

Also watch out for children who subtract the top number from the bottom number in an attempt to avoid the ‘decomposition’ process.

Standard subtraction of decimals (1)

Resource of the Week: probability as a fraction

Probability does cause some confusion with children, partly because it can be expressed in several ways and because it is very hard to find events which are absolutely certain to happen, or not happen.

One way of displaying the probability of an event is as a percentage: for example, there is a 50% chance of landing on a head when tossing a coin.

Another way is as a fraction: there is 1/2 chance, or one in two chance of landing on heads.

A third way is as a decimal fraction, where zero means no chance and 1 is certain: there is 0.5 chance of landing on heads. Probability can be displayed along a number line marked from zero to one.

A the end of the page there is a tricky probability line where the events have to be placed in order of likelihood.

This year 6 maths worksheet is the second published which looks at probability as a fraction and then as a decimal fraction. A calculator would be useful to do the conversion and it is suggested that the answer should be displayed to 2 decimal places. A useful homework sheet.

Giving the probability as a fraction_(pg 2)

Year 3 maths worksheet: adding three numbers

Here we have a simple page which looks at adding three multiples of ten to make a variety of whole hundreds. It is quite open ended as there are many possible answers and the page could be repeated several times or used as the starting point for a mini investigation.

The page could be answerred very simply eg 280 + 10 + 10 = 300

but encourage children to make it as tricky as possible to show how good they are at maths;

e.g. 30 + 120 + 150.

This page can be found in our Year 3 Calculations category, together with many others.

Revise addition of three numbers

Standard written method for adding decimals

Here we have a very straightforward page of addition questions with decimals. All the numbers use 2 decimal places, so it is very similar to adding money. I have also kept to adding just two numbers so this page is ideal for children who are getting to grips with the standard method of addition.

The only real cause for problems is the decimal point and it is vital that this is written in the answer in line with the other decimal points. The first 9 questions have already been laid out in the correct way but the last three need to rewritten.

Later children will need to add numbers where the number of digits after the decimal point varies eg. 26.4 + 1.78 and it will help enormously if the are confident with how to set them out.

The speed of answering this type of question depends on how well number bonds (eg 5 + 6) have been learned ‘off by heart’.

Standard method of adding decimals

Useful resources: 1 to 100 number grid

Having a browse round the site I noticed that there is not very much in the Useful Resources section so I thought it was about time I added some! A number grid (often called a number square) from 1-100 is a very useful resource, especially when used for counting and looking for patterns. An obvious use is to help children count up in ones to 100, but it can also be used for more complex counting.

For example, counting in threes and colouring each third number will give an interesting diagonal whilst counting in fives will produce two vertical lines. Do them both on the same grid will show which numbers are divisible by both 3 and 5 e.g. 15 and 30.

Number grids such as this can also be used as an aid for addition and subtraction.

Go to 1-100 number grid

Divide 3-digit numbers by 6

This is a short division page which concentrates just on dividing 3-digit numbers by 6. Short division, as its name suggests is a shortened version of the long division method where subtractions and remainders are done mentally.

The key to answering these is to have a set speech for the process.

For example: 6)457

‘How many sixes in 45?’

‘7 times 6 is 42.’

‘6 goes into 45, 7 times with 3 left over.’

Write the 7 in the answer above the 5.

Write the remainder three beside the 7 units, making 37.

‘How many sixes in 37?’

‘6 times 6 is 36.’

‘6 goes into 37, 6 times with 1 left over.’

Write the 6 in the answer in the units and write rem 1 next to it.

Division: 3-digit numbers by 6