Fractional wall
Using the picture of the fraction wall, can you find equivalent fractions?
Problem
Using the image above, how many different ways can you find of writing $\frac{1}{2}$?
Can you find any "rules" for working out equivalent fractions?
You might find it helpful to print off a picture of the fraction wall.
Getting Started
If the purple rod is the whole, what colour rod is one half?
What fraction of the purple rod are each of the other rods?
How many dark green rods, for example, are the same as one half?
If the purple rod is the whole, what colour rod is one third?
Student Solutions
Thanks to the many of you who submitted a solution to this problem. Congratulations to Josie, Dominic and George from St Nicholas CE Junior School, Newbury and also Abigail from Histon Junior School and Charlie from Beckley C of E who all sent in clearly explained solutions. The solution given below was sent in by Cong:
Using the image above, I can find $\frac{1}{2}$ as:
$1$ blue ($\frac{1}{2}$)
$2$ dark greens ($\frac{2}{4}$)
$3$ pinks ($\frac{3}{6}$)
$4$ light greens ($\frac{4}{8}$)
$6$ reds ($\frac{6}{12}$)
$12$ whites ($\frac{12}{24}$)
So I can also say that $$\frac{1}{2}= \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{6}{12} = \frac{12}{24}$$
From the picture, I can find $\frac{1}{3}$ as:
$1$ brown ($\frac{1}{3}$)
$2$ pinks ($\frac{2}{6}$)
$4$ reds ($\frac{4}{12}$)
$8$ whites ($\frac{8}{24}$)
So I can also say that $$\frac{1}{3} = \frac{2}{6} = \frac{4}{12} = \frac{8}{24}$$
Again, using the image of the fraction wall, I can find $\frac{3}{4}$ as:
$3$ dark greens ($\frac{3}{4}$)
$6$ light greens ($\frac{6}{8}$)
$9$ reds ($\frac{9}{12}$)
$18$ whites ($\frac{18}{24}$)
So again I can say that $$\frac{3}{4}= \frac{6}{8} = \frac{9}{12} = \frac{18}{24}$$
The rule for working out equivalent fractions is to multiply the numerator and the denominator with the same whole number.
Teachers' Resources
Fractional Wall
You might find it helpful to print off a picture of the fraction wall.
Why do this problem?
This problem could be used as an introduction to equivalent fractions. It provides a powerful visual representation, helping children develop an understanding of the relationship between different fractions. It gives pupils the opportunity to explore fractions in a non-threatening, open-ended way, encouraging them to develop their own 'rules' for finding equivalent fractions.
Possible approach
Introduce the activity by showing the fraction wall to the class. Ask the children what they can see and invite them to talk about it in pairs, then share their ideas with the rest of the group. You could steer the conversation towards fractions if the children do not naturally bring it up. Ask general questions about the fractions represented by the different bars in the design, taking the purple bar as the 'whole'. Can pupils spot any fractions which are equivalent? Prompts such as "How many quarters is the same as a half?" might encourage children to think about putting the bars together to make fractions such as $\frac{2}{4}$, rather than just thinking about the unit fractions represented by individual bars.
Allow some time for pupils to work in pairs to find equivalent fractions using the fraction wall. A printable version is available here: Word, pdf. Encourage them to write these fractions down and to see what they notice about the numerator and denominator of the equivalent fractions. As a plenary, ask children to share what they have noticed. Has anybody found a 'rule' for finding equivalent fractions without a picture? Why does this rule work?
Key questions
What fraction of the purple bar does each blue bar represent? How do you know?
How many sixths is the same as a third?
Write down the equivalent fractions that you have found. What do you notice?
Possible extension
Once children have completed this activity, they might like to have a go at Fractions Made Faster.
Possible support
Some learners may find it helpful to draw lines on the fraction wall or cut out the different fractions to check that they are identical. Using Cuisenaire rods to represent the fractions (perhaps choosing a rod of length 6 or 8 to represent the whole) would provide a more concrete fraction environment for children to explore.