1. KS3 Mathematics N5 Using Fractions
The aim of this unit is to teach pupils to:
Use fraction notation; recognise and use the equivalence of fractions and decimals.
Material in this unit is linked to the Key Stage 3 Framework supplement of examples pp
N5 Using Fractions

2. N5 Using fractions Contents N5.1 Fractions of shapes
N5.2 Equivalent fractions
N5.3 One number as a fraction of another
N5.4 Fractions and decimals
N5.5 Ordering fractions

3. Quarter or not?
The aim of this activity is to ensure that pupils are able to identify which shapes have one quarter shaded. For shapes drawn in three dimensions pupils will need to imagine the parts of the shape that are not visible in the two dimensional drawing.

4. Quarters
Each quarter can be a different shape as long as each part has the same area. There are infinitely many ways to divide this shape into four equal parts.

5. Dividing shapes into given fractions
The aim of this activity is to divide the shape shown into the given fraction using straight lines.
Give some examples and then ask pupils to come to the board and show their own examples. Challenge pupils to make each part, not only the same size, but also the same shape. Encourage more imaginative divisions.
Links:
S2: Tessellations
S8: Area

6. 1 4 Fractions of shapes Remember, one quarter is written: one thing
divided into 4
four equal parts
Remind pupils of the meaning of fraction notation.

7. Fractions of shapes What fraction of this diagram is shaded?
Briefly discuss how much is shaded.
The diagram is divided into five equal parts called fifths. Two parts are shaded.
We call this fraction two fifths.
How much is unshaded? (3/5)
Three-fifths is the complement to 1 of two fifths.

8. 2 5 Fractions of shapes Two fifths is written as: two parts numerator
out of 5
five parts altogether
denominator
Ask pupils if they can remember the name given to the number at the top of a fraction and the number at the bottom of a fraction.
Reveal these key words on the board.

9. Fractions of shapes activity
Start by selecting a shape.
Activity 1 – Shading in a given fraction
Choose how many parts to divide the shape into.
Ask a volunteer to shade in a given fraction of the shape. Repeat for other examples.
Use different colours to show different fractions.
For example, select the square and divide it into 12 equal parts. Ask a volunteer to shade in 1/4 red, 1/3 yellow and 5/12 blue.
Activity 2 – Finding the fraction shaded
Choose another shape and shade in a random number of parts. Ask pupils to tell you how many parts have been shaded.
This activity can also be used to introduce equivalent fractions.
Extend this activity by hiding the divisions and asking pupils to estimate the fraction shaded.

10. N5.2 Equivalent fractions
Contents
N5 Using fractions
N5.1 Fractions of shapes
N5.2 Equivalent fractions
N5.3 One number as a fraction of another
N5.4 Fractions and decimals
N5.5 Ordering fractions

11. Equivalent fractions Start by showing two bars.
Set one bar to show 1/8s and the other to show 1/4s.
Ask a volunteer to shade in half of the bar showing 1/8s.
How many 1/8s make 1/2? (4)
4/8 is the same as one half.
How many sixths make one half? (3)
3/6 is also the same as one half.
Show this amount on the bar.
Turn on another bar. Set it to show fifths.
Can any number of fifths make a half?
Now set the bar to show sevenths.
What about sevenths?
Establish that to make a fraction the same as a half the bar must be divided into an even number of equal pieces.
Ask pupils to state any other fractions they can think of equal to a half.
Turn on all four bars and ask pupils to show their suggestions on the board.
Repeat the exercise for 2/3. Start by setting two of the bars to thirds and sixths. Ask a volunteer to shade in two thirds of the bar showing thirds and continue as before.
Establish that to show a fraction equal to 2/3 the bar must be divided into a number of parts equal to a multiple of three.
Ask pupils what they notice about the numerator (the top number) for all fractions equal to 2/3.
The numerator is always a multiple of 2 (an even number) and the denominator is always a multiple of 3.
Repeat the exercise for ¾.
Establish that, in this case, the denominator is always a multiple of 4 and the numerator is always a multiple of 3.
Pupils should notice that the numerator and the denominator are multiplied by the same number. Ask a volunteer to justify this using the fraction bars.

12. What does equivalent mean?
Equivalent fractions
What does equivalent mean?
Ask pupils what equivalent means.
Equal to or the same as.
Many words that start with equ- have something to do with things being equal. Can you think of any?
Some examples include equilateral, equation, equidistant.

13. 3 6 18 = = 4 8 24 Equivalent fractions Look at this diagram: ×2 ×3 ×2
Ask pupils what proportion of the diagram is shaded (3/4).
Look what happens if we cut each quarter into two equal parts.
Click to divide.
We now have 1/8s.
Exactly the same amount is shaded, but you can see how we can call this amount 6/8?
What have we done by cutting each quarter into two equal parts?
Explain that we have multiplied the number of shaded sections by two (we had three shaded sections; now we have six) and we have multiplied the number of equal parts by two (we had four; now we have eight).
Click to reveal the arrows showing the numerator and the denominator being multiplied by 2.
We’ve multiplied the numerator by 2 and the denominator by 2.
The numbers have changed but exactly the same proportion of the circle has been shaded. 3/4 and 6/8 are equivalent fractions.
We could divide each of these eights into three equal parts. Look what happens. Click to reveal.
Now, how many equal parts are there altogether? (3 x 8, 24)
How many of those equal parts are shaded? (3 x 6, 18)
So we now have 18 out of 24 parts shaded.
Click to reveal this fraction.
Explain that we have multiplied both the numerator and the denominator by three. The numbers have changed but exactly the same proportion of the circle has been shaded.
What would we multiply the numerator and the denominator of 3/4 by to get 18/24? (6)
You can se that each quarter of our original diagram has been divided into six equal parts.
3/4, 6/8 and 18/24 are equivalent fractions. Can you think of any other fractions that are equal to ¾?
How many different ways could we write ¾? (Infinitely many!) 3 6 18 = = 4 8 24 ×2 ×3

14. 2 6 24 = = 3 9 36 Equivalent fractions Look at this diagram: ×3 ×4 ×3
Explain this set of equivalent fractions as in the previous slide. 2 6 24 = = 3 9 36 ×3 ×4

15. 18 6 3 = = 30 10 5 Equivalent fractions Look at this diagram: ÷3 ÷2 ÷3
Ask pupils what proportion of the diagram is shaded. (18/30)
We could simplify this diagram by removing these horizontal lines.
Click to remove some of the horizontal divisions.
We now have ten equal parts.
Exactly the same amount is shaded, but you can see how we can call this amount 6/10. By removing those horizontal lines we have made every 3/30 into 1/10.
Explain that we have divided the number of shaded sections by 3 (we had 18 shaded sections; now we have 6) and we have divided the number of equal parts by 3 (we had 30; now we have 10).
Click to reveal the arrows showing the numerator and the denominator being divided by 3.
18/30 and 6/10 are equivalent fractions.
Tell pupils that by dividing the numerator and the denominator by the same number, we have simplified the fraction. It is simpler because the numbers are smaller.
Can we simplify this fraction any further?
Yes, 6 and 10 are both even numbers, so we could divide the numerator and the denominator by 2. Remember, if we divide the numerator and the denominator by the same number the numbers that make up the fraction change but the fraction itself has exactly the same value.
Click to show the numerator and the denominator being divided by 2.
6/10 is equivalent to 3/5.
We can see this in the diagram by grouping each 2 tenths into one fifth.
Click to reveal.
Can we simplify 3/5 any further?”
No, 3 and 5 have no common factors, there is no number which divides into both 3 and 5.”
We have expressed the fraction 18/30 in its lowest terms. This is also called cancelling the fraction down.
How could we have cancelled 18/30 to its simplest form in one step?
Establish that we could have divided the numerator and the denominator by 6.
We call 6 the highest common factor of 18 and 30. 18 6 3 = = 30 10 5 ÷3 ÷2

16. Equivalent fractions
Use this activity to generate patterns of equivalent fractions.
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.
Link:
N8 Ratio and Proportion: Scale factors

17. 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.
There is something different about the last fraction, what is it?
Point out that it is top-heavy. The numerator is bigger than the denominator.
This is called an improper fraction.
Ask how we could write this improper fraction as a mixed number. (2 and 2/15)
Fractions which are not shown in their lowest terms can be simplified by cancelling.

18. Drag and drop equivalent fractions
Ask pupils in turn to choose a fraction and justify where it goes by dividing the numerator and the denominator by the same number. For fraction diagrams pupils must state the fraction shaded first.
Continue until all the fractions are in the correct place.
Ask pupils to come up in turns and choose a fraction to drag and drop into the correct place.

19. 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 =

20. 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.

21. Mixed numbers to improper fractions2 7 3
Convert to a mixed number. 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. There are
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 …

22. 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.

23. N5.3 One number as a fraction of another
Contents
N5 Using fractions
N5.1 Fractions of shapes
N5.2 Equivalent fractions
N5.3 One number as a fraction of another
N5.4 Fractions and decimals
N5.5 Ordering fractions

24. Writing one amount as a fraction of another
Sometimes we need to know one amount as a fraction of another.
What fraction of one week is three days?
Monday
Tuesday
Wednesday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Stress that when we write one amount as a fraction of another the numbers have to be in the same units, in this example, days. 3
three days
out of 7
seven days altogether

25. Writing a number as a fraction of another
We can describe one number as a fraction of another.
What fraction of 72 is 45? ÷9 45 72 5
We write = 8
To simplify the fraction ask pupils to tell you the highest common factor of 45 and 72.
Explain that we must divide the numerator and the denominator by 9 to write this fraction in its lowest terms.
Reveal this on the slide. ÷9
We can say 45 is 5/8 of 72.

26. Writing a number as a fraction of another
What fraction of 2.5 metres is 75 centimetres?
First, convert 2.5 metres to 250 centimetres.
÷25 75
250 3
We write = 10
÷25
What should we do before we write 75 cm out of 2.5 m as a fraction?
Establish that we must write both measurements in the same units.
Stress that before writing one amount as a fraction of another, the units must always be the same.
Ask pupils for the highest common factor of 75 and 250 before cancelling.
We can say 75 centimetres is 3/10 of 5 metres.

27. Writing a number as a fraction of another
We can also write a larger number as a fraction of a smaller one.
What fraction of 25 is 35? ÷5 35 25 7
We write = 5
Explain that when we write a larger number as a fraction of a smaller one we expect the answer to be greater than 1 because the numerator is larger than the denominator.
The resulting fraction can be written as an improper (top-heavy) fraction or a mixed number. ÷5
We can say 35 is 7/5 of 25 or 12/5 of 25.

28. Writing one amount as a fraction of another
Ask pupils to tell you what fraction the yellow shape is of the blue one. Ask pupils to cancel their answers as appropriate or convert to mixed numbers.

29. Fractions of distances
Use this tool to ask pupils for fractions of distances given in metres.
For example, set the total distance to 1 metre.
Drag the slider to 40 cm and ask pupils:
What fraction of one metre is 40 cm?
Explain that to write one distance as a fraction of another we must convert them to the same units.

30. Fractions on a clock face
Use this tool to ask pupils for fractions turned through by the minute hand between two given times.
As an extension ask pupil to determine the fraction turned through by the hour hand between two given times.
In the case of the minute hand one full turn represents 60 minutes. Pupils must therefore calculate the number of minutes between the two times given and write this as a fraction out of 60.
In the case of the hour hand one full turn represents 12 hours (or 720 minutes). Pupils must therefore calculate the number of hours between the two times given and write this as a fraction out of 12. Alternatively they can calculate the number of minutes between the two times given and write this as a fraction out of 720.

31. N5.4 Fractions and decimals
Contents
N5 Using fractions
N5.1 Fractions of shapes
N5.2 Equivalent fractions
N5.3 One number as a fraction of another
N5.4 Fractions and decimals
N5.5 Ordering fractions

32. Pelmanism – Fractions and decimals
The aim of this activity is to revise the fraction to decimal equivalents that pupils should already be aware of.
Select pupils to come to the board in turns. They must turn over 2 cards. The object is to match cards showing equivalent fractions and decimals.

33. Comparing decimals and fractions
Start by stating that any terminating decimal can be written as a fraction.
Who can tell me what a terminating decimal is?
Next draw the pupils’ attention to the counting sticks on the board.
The counting sticks can be configured to show 1/50s between 0 and 1/5, 1/25s between 0 and 2/5, 1/20s between 0 and 1/2 and 1/10s between 0 and 1.
Start by selecting 1/10s between 0 and 1. Reveal the first number and the last number on the top counting stick (decimals).
You should know how to convert any number of tenths to a decimal already.
Go through these in random order.
Next, select 1/20s between 0 and 1/2.
The first value on this number line is 0 and the last value is 0.5. What will each step be worth? (0.5 ÷ 10 = 0.05)
Start by using the number line to count on in 0.05s from 0 to 0.5. Reveal the decimals on the line as you go through. Continue counting on in 0.05s. Stop at 2 and then count back to 0.
Next draw the pupils’ attention to the second number line.
This counting stick shows fractions in their lowest terms. Each fraction is equivalent to the decimal in the line directly above it. For example, 0.5 is equivalent to ½.
Click to reveal ½. Continue for other conversions.

34. Converting decimals to fractions
Start by stating that calculators always show answers as decimals.
It is often helpful to be able to write a given decimal as a fraction. To do this we need to re-visit the place value system.
Remember the first digit after the decimal point tells us the number of tenths, the next digit tells us the number of hundredths, the next digit tells us the number of thousandths.
Let’s start by entering the number 0.35 into the place value chart.
As you enter the digits into the chart say,
There are 0 units, 3 tenths and 5 hundredths.
To add together 3/10s and 5/100s we need to write 3/10 as 30/100. This is equivalent to 3/10 because we multiplied both the numerator and the denominator by the same number, 10.
Click to reveal the next stage in the calculation.
30/ /100 is equal to 35/100.
Why can’t we leave the answer as 35/100? We need to cancel this fraction down to its lowest terms. 35 and 100 are both divisible by 5.
Click to reveal the final stage.
0.35 = 7/20.
Go through more examples. Take suggestions from pupils.
Suggest to pupils that they could leave some of these stages out. If the decimal has two digits after the decimal point they can just write this number out of 100 and then cancel if necessary.

35. Using equivalent fractions over 10, 100, or 1000
We can convert some fractions to decimals by converting them to an equivalent fraction over 10, 100 or 1000.
For example,
× 5 13 20 = 65
100
× 5
Point out that this method only works for fractions whose denominator is a factor of 10, 100, or That is if the denominator is 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250 or 500.
If necessary remind pupils about the place value system.
Links:
N1.1 Place value, ordering and rounding
100 65 =
0.65

36. Converting fractions to decimals
Explain that we may be asked to convert a fraction to a decimal without using a calculator.
Converting fractions to terminating decimals
Choose the configuration that supports denominators to 100. If you enter a fraction with a denominator of 2, 4, 5, 10, 20, 25, or 50 then the corresponding equivalent fraction out of 100 (or 10) will be displayed. Relate this to the decimal place value system and ask pupils to convert the fraction to a decimal before revealing the answer.
Extend the activity by choosing the configuration that supports denominators to If you enter a fraction with a denominator that is a factor of 1000, for example, 8, 40 or 125, then the corresponding equivalent fraction out of 10, 100 or 1000 will be displayed. Relate this to the decimal place value system and ask pupils to convert the fraction to a decimal before revealing the answer.
Use the pen tool to show pupils how the equivalent fractions over 10, 100 or 1000 are obtained by multiplying the numerator and the denominator by the same number.
Converting fractions to decimals by dividing
If the numerator of the fraction is not a factor of 1000 then the program will convert the fraction to a decimal by dividing the numerator by the denominator. State that this can also be done using a calculator or short division.
Investigating recurring decimals
Tell pupils that any fraction can be written as either a terminating decimal or a recurring decimal (and that any terminating or recurring decimal can be written as a fraction). You may also like to mention the existence of decimals that are irrational and cannot be expressed as a fraction, for example π or √2.
Investigate the patterns given by various recurring decimals.
For example, demonstrate the decimal equivalent of 1/9, 2/9 and 3/9 and ask pupils to predict the decimal equivalent of 4/9, 5/9, 6/9 etc.
Repeat for other sequences such as: 1/7, 2/7, 3/7 … or 1/11, 2/11, 3/11 …

37. Fractions and division
A fraction can be thought of as the result of dividing one whole number by another.
For example, 30 8 6 8 3 3 4
30 ÷ 8 = = =
We can also write this answer as a decimal:
Draw the pupils’ attention to the symbol that we use for division, ÷. The dots above and below the line in the division sign represent numbers above and below the line in a fraction.
How can we write the improper fraction, 30/8 as a mixed number?
What is 36/8 in it’s lowest terms?
We can leave the answer as 33/4. Sometimes it is useful to write the answer as a decimal. For example, if we need to compare it to another number.
Point out that if we were to calculate 30 ÷ 8 on a calculator, the answer would be shown as 3.75. 3 4
3.75 =

38. Converting fractions to decimals
There are many ways to convert a fraction to a decimal.
The quickest way is to use a calculator.
For example, 5 16
This is a terminating decimal.
= 5 ÷ 16 = 6 11
= 6 ÷ 11
= …
This is a recurring decimal.
Instruct pupils to convert 5/16 to a decimal using their calculators and dividing 5 by 16. Tell pupils that this is a terminating decimal. The number of digits after the decimal point is finite.
Reveal the decimal equivalent of 6/11. Define a recurring decimal as a decimal whose digits repeat infinitely. In this example the digits 54 repeat infinitely. We can write this with dots above the 5 and the 4 to show that these digits recur.
Stress that all fractions written as decimals will be either terminating or recurring.
(If a decimal is not terminating or recurring then it cannot be written as a fractions. These are irrational numbers such as √2 or π).
All recurring and terminating decimals can be written as exact fractions.

39. Recurring decimals = 0.3 . 1 3 = 1 ÷ 3 = 0.33333… = 0.16 . 1 6 = 1 ÷ 6
= …
= 1.18
. . 2 11
= 2 ÷ 11
= … = . 3 7
= 3 ÷ 7
= …
Explain the notation used for recurring decimals.
For … we write a dot above the 3.
For … we write the dot above the 6.
For … we put dots above the 1 and the 8 to show that they both recur.
For … we have a repeating chain of digits. In this case, we write a dot above the first and last digits in the chain, 4 and 1.
When we have a long chain of recurring digits it is usual to round the decimal to a given number of decimal places.
Pupils can investigate these in the main part of the lesson or using the fraction to decimal converter.
We can also write = 0.43 (to 2 decimal places). 3 7

40. Using short division
We can also convert fractions to decimals using short division.
For example, 5 7
= 5 ÷ 7 . 7 1 4 2 8 5 7
. . . 7 5 1 3 2 6 4 5
Talk through the method for converting a fraction to a decimal using short division.
Point out that we can write as many 0s after the decimal point as we need to without changing the value.
We’ll start by dividing 5.00 by 7.
7 doesn’t go into 5, so write a 0 above the 5. We carry the 5 and write the decimal point in the same position above the division line. 50 divided by 7 is 7 and we carry divided by 7 is 1. Let’s add some more 0s so we can carry the remainder 3 and see how the decimal representation of 5/7 continues.
When you arrive at the point where we divide 50 by 7 to get 7 ask if anyone can predict what will happen next. The digits will start repeating. We could continue in this way forever. Once we see that the digits are repeating we can stop.
Pupils may notice the similarity between the decimal equivalent of 5/7 and the decimal equivalent of 3/7 on the previous slide. These can be investigated further by pupils using their calculators or short division.
There are two more ways of converting fractions to decimals: We can use known facts as we did at the beginning of the lesson. We can also write the fraction as an equivalent fraction over 10, 100, 1000 or any power of ten. This only works for fractions that can be written as terminating decimals i.e. fractions whose denominators have a prime factor decomposition containing only 2s and/or 5s. = . 5 7

41. N5 Using fractions Contents N5.1 Fractions of shapes
N5.2 Equivalent fractions
N5.3 One number as a fraction of another
N5.4 Fractions and decimals
N5.5 Ordering fractions

42. Using diagrams to compare fractions
Use the diagram to compare the given fractions. Start by dividing each line into the correct number of equal parts and shading the required fraction.

43. Using decimals to compare fractions
Which is bigger or ? 3 8 7 20
We can compare two fractions by converting them to decimals. 3 8
= 3 ÷ 8 = 7 20
Tell pupils that another way that we can compare two fractions is to write them both as decimals.
Ask pupils to convert the two fractions into decimals using their calculators. Reveal these on the board.
State that we could also use short division to convert the fractions to decimals.
= 7 ÷ 20
= 0.35
> 0.35 so 3 8
> 7 20

44. Using equivalent fractions3 8 5 12
Which is bigger or ?
Another way to compare two fractions is to 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

45. Using a graph to compare fractions
Tell pupils that we can use a graph to compare fractions by plotting the numerator against the denominator and drawing a line from the point to the origin. The steeper the line, the greater the fraction.
Links:
A5: Finding the gradient of a straight line

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

47. Fractions on a number line
Ask volunteers to come to the board and drag the given fraction to the correct position on the number line.

48. Mid-points
Start by revealing all three fractions and ask pupils to explain (using equivalent fractions or otherwise) how we can tell that the fraction in the centre is exactly half-way between the other two.
Reset the activity, reveal two of the fractions on the line and challenge pupils to find the hidden fraction.
Links:
D2: Finding the mean; finding the median.
N1: Ordering decimals.
N2: Ordering Integers

49. Connect three fractions
Divide the class into two teams. Each team selects a team leader to stand at the board and enter the agreed values.
Decide which team will start and ask them to enter a fraction less than 1. The numerator can be between 1 and 9 and the denominator can be between 1 and 10. Members of the team may put up their hands and advise them where to start.
Calculators are not allowed.
A cross corresponding to the chosen fraction will appear on the number line.
It is then the turn of the other team. They, too, must enter a fraction on the number line following the advice of their team members.
The winner is the first team to get three of their crosses together in a row.
Discuss tactics as the game progresses. This will involve converting the fractions to decimals or percentages in order to compare them. Pupils will need to decide how to block their opponent by, for example, placing their crosses between their opponents crosses.