Year 6 Maths Worksheet: Equivalent fractions

equivalent fractions pg 1

Understanding equivalent fractions is at the heart of understanding how fractions work. Much work needs to be done in earlier years to show that fractions such as 1/2 and 2/4 have the same value. This is usually done by colouring or shading parts of rectangles, circles.

Two fractions which are equal in value we say are equivalent.

2/5 is equivalent to 4/10 which is equivalent to 40/100.

If we start with a fraction and multiply both the numerator (top number) and the denominator (bottom number) by the same number the fraction will remain with the same value. The same is true with division, but not addition or subtraction.

This makes multiplying fractions much easier than adding or subtracting them.

Equivalent fractions (pg 1)

 

Year 4 worksheets: Division with remainders

Division nearly always requires carrying out more than one process, which makes it harder for children to process. A good knowledge of tables is also needed to complete division questions successfully, and this is especially true when there are remainders.

For example: to find the answer to 37 divided by 5: ask how many fives are in 37. This is where the knowledge of tables comes in, as 5 x 7 makes 35.

Then a subtraction take 35 from 37 to leave 2. There is a remainder of 2. (The remainder can never be bigger than the number you are dividing by.)

This remainder can be converted to a fraction. The 2 is the numerator (top number) and the denominator (bottom number) is the number you are dividing by, in this case 5. So the fraction left is 2/5.

This is a much neater finish to the question as the whole number is divided completely, with no messy remainders. Some of the fractions could be cancelled down to their simplest form, although this is not essential at this stage.

Division with fraction remainders (pg 2)

Year 3 Mental Arithmetic Sets 3 and 4

Two sets of mental arithmetic questions suitable for Year 2. These sets of 10 questions cover counting on and back in tens, addition, subtraction and place value.

I have been asked for more in the way of mental arithmetic questions on many occasions and as the weeks go by this should build into a really useful resource. I am also trying to match the questions to the Primary Framework for Mathematics Planning, so this would be especially relevant for the first couple of weeks of the Autumn term.

Year 3_Mental arithmetic (3 and 4)

 

Maths worksheets: Division of money

There are not many questions on this maths worksheet but they are quite tricky and a good knowledge of tables and how to do long division is needed.

Each question has an amount of money to be divided by a 1 or 2-digit number. In all cases the answer wil have a zero in the pounds column.

As well as the long division process there are several key things to remember when doing these, including:

1. putting the pound sign in the answer

2. putting the zero in the pounds column

3. putting in the decimal point.

Money division (1)

Year 1 addition and subtraction

In year 1 there are several key addition and subtraction and skills that have to be learned. Addition is related to counting on which children will still need plenty of practice with. It is also important to realise that addition can be done in any order.

Subtraction is seen as ‘taking away’ or ‘finding a difference’.

We have a number of simple addition and subtraction worksheets in our Calculating section of our year 1 resources. One of my favourites is the Dice: 3 in a row game which is a simple two player game involving adding the totals when rolling two dice. A mixture of strategy and luck will help win this game.

Go to our Addition and Subtraction Year 1 worksheets

Knowing Division Facts: Year 5 maths Worksheet

There is no doubt that most children find division harder than multiplication, yet there is little real reason for this to be so. Most division questions can be turned on their head to be made to look like multiplication. For example:

30 ÷ 5 =??  can be thought as what number times 5 makes 30?

?? ÷ 6 = 7 can be thought of as 6 times 7.

60 ÷ ?? = 10 can be thought of as what number times 10 makes 60?

The key to success with division is to have a really good knowledge of times tables.

This worksheet looks at these types of division question, all with easy numbers and no remainders and is a good assessment sheet to see if division is understood and tables known.

This can be found in our Year 5 Knowing Number Facts category.

Know division facts (1)

Resource of the Week: Magic Square with negative numbers

magic square 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

Year 3 mental arithmetic: Sets 1 and 2

I am embarking on something new this week which will hopefully grow into a really useful resource as time goes by. It is the first in a series of mental arithmetic questions aimed at Year 3.

It consists of two sets of ten questions, followed by an answer sheet. Each set is a full A4 page so that they can be used in several ways. If given orally the teacher/parent only needs to print the answer page as all the questions are included on this and the children can just write the answers or call them out. If the teacher/parent wants the child to read the questions then they can print out the question sheets as well. This could also be shown on a whiteboard.

The first set of questions concentrate on writing whole numbers, counting on and back in tens, addition, subtraction and place value.

Year 3 Mental arithmetic (sets 1and 2)

Short division of decimals (2)

Here is another page of practice on using the short method of division of decimals. With the short method all unnecessary writing down of numbers is avoided. The numbers being divided are just units and tenths which helps with getting the method correct.

One of the best ways to be fluent with this method is to talk it through out loud. Eventually this leads to talking through, ‘in your head’.

If we look at question 1 which is 7.2 divided by 3, the verbal stages are:

a. How many 3s in 7?

b. 2 times 3 is 6 so there is 2 with a remainder of 1.

c. Place the 2 on the answer line, immediately above the 7.

d. Place the decimal point just above the answer line so it can be clearly seen.

e. The remainder 1 is placed just in front of the 2 (usually written smaller).

f. How many 3s in 12?

g. 3 x 4 is 12 so the answer is 4.

h. Place the 4 on the answer line, immediately above the 2 (tenths).

i. Answer 2.4

This page can be found in our Four Rules, Division category.

Division of decimals (2)

Year 3 maths worksheet: Time and calendars

An aspect of learning about time that is often neglected is the use of a calendar. They do need some explanation for children who have not come across them before and they do come in various formats. The month shown on this worksheet starts the week on a Monday, although many start on Sunday. It can seem puzzling to children as to why there are some ‘blank’ days at the start of the first week so it is a good idea to have a calendar showing the whole year available.

This can lead to a great deal of discussion, such as how many days there are in each month, why birthdays fall on a different day of the week each year etc.

Using a calendar (1)