1. Mathematics
Fractions Re-cap1

2. Equivalent fractions spider diagram
Tell pupils that all the fractions on the board are equivalent to the one in the centre. Ask them to use proportional reasoning to work out the hidden numerators and denominators.
Stress that every fraction on the board is exactly the same fraction written in a different way. Establish that there are infinitely many ways to write the same fraction.
When all of the equivalent fractions have been revealed, ask pupils how we could convert between any two given fractions on the board by multiplying and/or dividing the numerator and the denominator by the same number.
Ask pupils to give examples of other fractions that are equivalent to those on the board.

3. Cancelling fractions to their lowest terms
A fraction is said to be expressed in its lowest terms if the numerator and the denominator have no common factors.
Which of these fractions are expressed in their lowest terms? 7 5 2 14 16 20 27 3 13 15 21 14 35 32 15 8 7 5
Ask pupils what we mean when we say a fraction has no common factors.
Establish that there is no number other than 1 that divides into both the numerator and the denominator.
For each fraction ask pupils whether or not they think this fraction has been shown in its lowest terms, before revealing the answer.
If pupils do not think that the fraction has been shown in its lowest terms, ask them for a number which will divide into both the numerator and the denominator.
Explain that when cancelling it is always best to divide both the numerator and the denominator by the highest number that divides into both, that is, the highest common factor. However, if you do not cancel by the highest common factor the first time round, you can always cancel again.
Go through the cancellation of each fraction asking what we are dividing by each time.
Establish that the last fraction is an improper fraction and ask pupils how we could write this as a mixed number (2 2/15).
Fractions which are not shown in their lowest terms can be simplified by cancelling.

4. Mixed numbers and improper fractions
When the numerator of a fraction is larger than the denominator it is called an improper fraction.
For example, 15 4
is an improper fraction.
We can write improper fractions as mixed numbers. 15 4
Talk through the diagrammatic representation of 15/4. Every four quarters are grouped into one whole, and there are three quarters left over.
can be shown as 15 4 3 4 =

5. Improper fraction to mixed numbers37 8
Convert to a mixed number. 37 8 = 8 + 5 5 8 1 + = = 4 5 8
Explain that to convert an improper fraction to a mixed number we can divide the numerator by the denominator to find the value of the whole number part. Any remainder is written as a fraction.
Relate fractions to division. 37/8 means 37 ÷ 8.
Talk through the division of 37 by 8. Discuss the meaning of the remainder in this context. We are dividing by 8 and so the 5 represents 5/8.
This number is the remainder. 37 8 = 4 5 8 4 5
37 ÷ 8 =
4 remainder 5
This is the number of times 8 divides into 37.

6. Mixed numbers to improper fractions2 7 3
Convert to an improper fraction. 2 7 3 = 2 7 1 + = 7 + 2 = 23 7
We can explain this conversion by asking for the number of 1/7 in 3 whole ones.
Explain that to convert a mixed number to an improper fraction in one step we multiply the whole number part by the denominator of the fractional part and add the numerator of the fractional part (refer to the example). This gives us the numerator of the improper fraction. The denominator of the improper fraction is the same as the fractional part of the mixed number.
Explain that there are 21 sevenths in three wholes. Two more sevenths makes 23 sevenths altogether.
… and add this number …
To do this in one step, 3 3 2 2 23
… to get the numerator. = 7 7 7
Multiply these numbers together …

7. Find the missing number
In this activity equivalent fractions, mixed numbers and improper fraction are generated.
Ask pupils to find the value of the missing number, explaining their reasoning.

8. Finding a fraction of an amount2 3
of £18?
What is
We can see this in a diagram:
Stress that 2/3 means 2 lots of 1/3.
1/3 of £18 is £6 so, 2/3 of £18 is 2 x £6.
Click to reveal £12.
Explain that we divide by 3 to find 1/3 and then multiply by 2 to find 2/3. 2 3
of £18
= £18 ÷ 3 × 2
= £12

9. Finding a fraction of an amount1 2 5
What is of 3.5m?
To find of an amount we need to add 1 times the amount to two fifths of the amount. 2 5 1 2 5
of 3.5 m =
1 × 3.5 m =
3.5 m
and
1.4 m
Discuss the meaning of 12/5 of an amount.
Go through the example on the board.
An alternative would be to convert 12/5 to an improper fraction, 7/5. We could then divide by 5 to get 0.7 m and then multiply by 7 to get the answer 4.9m
Ask pupils if they can give you an equivalent decimal calculation (1.4 x 3.5 m) or an equivalent percentage calculation. (140% of 3.5 m).
so,
of 3.5 m = 2 5 1
3.5 m m =
4.9 m
We could also multiply by 7 5

10. MathsBlox
Divide the class into two teams – red and blue – and nominate a spokesperson for each team.
The spokesperson from the first team chooses a number on the grid. A question appears when the number is selected and everyone on that team must try to work out the answer. They may use jottings if they wish. Select a member of the team at random to give you their answer (if they pass the hexagon is coloured in the opposing team’s colour.
Click on the ‘show answer’ button. If it is correct, colour the hexagon in the team colour if it is incorrect the hexagon is coloured in the opposing team colour. Spend a few moments discussing mental strategies to answer the question.
Play then passes to the other team.
The winning team is the first team to connect a line of hexagons either from top to bottom or from left to right.

11. Using equivalent fractions3 8 5 12
Which is bigger or ?
To compare two fractions convert them to equivalent fractions.
First we need to find the lowest common multiple of 8 and 12.
The lowest common multiple of 8 and 12 is
24.
Now, write and as equivalent fractions over 24. 3 8 5 12
Tell pupils that another way to compare two fractions is to convert them into equivalent fractions with a common denominator.
Talk through the example on the board.
Tell pupils that the quickest way to find the lowest common multiple of two numbers is to choose the larger number and to go through multiples of this number until we find a multiple which is also a multiple of the smaller number. This method also works for a group of numbers. ×3 ×2 3 8 = 24 9 5 12 = 24 10 3 8 5 12
<
and
so, ×3 ×2

12. Ordering fractions
Ask pupils to order the fractions on the board using an appropriate method.