AFRICAN INSTITUTE FOR MATHEMATICAL SCIENCES SCHOOLS ENRICHMENT CENTRE TEACHER NETWORK FRACTION WALL
This wall is 1 unit wide.
What fractions does it show?
Explain how it shows that two quarters are equivalent to one half
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Write down all the equivalent fractions you can see to each of the following fractions:
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1. three quarters !
2. five sixths
!
!
3. seven twelfths
!
!"
!
4. six twentyfourths !"
Can you find any rules for finding equivalent fractions?
Can you find any rules for checking whether two fractions are equivalent?
SOLUTION
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!
In the diagram, two quarters (shown in dark green) are the same width as one half (in blue) showing ! = !
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1. three quarters ! = ! = !" = !"
2. five sixths
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!
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!"
!
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= !" = !"
3. seven twelfths
= !"
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!
4. six twentyfourths !" = !" = !
To find an equivalent fraction you multiply the top and bottom of the fraction by the same number, or divide
the top and bottom of the fraction by the same number.
To check whether two fractions are equivalent multiply the numerator of one with the denominator of the
other (cross multiply). If the two products are the same then the fractions are equivalent.
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!
For example !" = ! because 6×8=3×16=48.
NOTES FOR TEACHERS
Why do this activity? This visual representation of fractions is very powerful. The main aim of the activity is for learners to find
equivalent fractions using the image, but then to deduce a "rule" (or more than one) for finding equivalent
fractions without a picture.
Intended learning outcomes
Grades 4 and 5
Describe and compare common fractions in diagram form. Recognize and use equivalent forms of common
fractions.
Possible approach
This is a lesson where mini whiteboards or showboards will be very useful.
They can be made by laminating a sheet of A4 paper that is plain on one
side and has squares on the other. Each learner will need a showboard, a
whiteboard marker pen and a small piece of cloth to clean the board. The
teacher asks everyone to write an answer on their showboard and then, at a
signal from the teacher, everyone must raise their showboard at the same
time so that the teacher can see what they have written. In this way the
teacher can quickly assess what the children do and do not understand and who are succeeding and who
need more support and help.
You might like to make a large photocopy of the fraction wall (A4 or A3 size) to demonstrate and then
display it on the classroom wall so that learners can refer to it.
Each learner might draw and colour a fraction wall for themselves on squared paper making the wall 24
squares wide or alternatively they could have their own copy of the fraction wall picture and paste it in their
book.
Don’t tell the learners that this will be a lesson on fractions but show them the picture and ask the learners
what they see in the diagram. They may spontaneously talk about fractions. If not ask some of the key
questions such as “What do you notice about the lengths of the different bits in the picture?” How many
pink bits are there?”, “How many of the brown bits match the purple bit?” and “If the purple bit is one unit
then what fraction is a brown bit?”.
Then tell the class “This wall is 1 unit wide”. And ask “What fractions does it show?”
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!
Then ask the learners to explain how the picture shows that two quarters are equivalent to one half ! = ! .
Ask several learners to explain this and then explain it for them to reinforce the idea.
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Then ask them to write on their showboards and hold up fractions equivalent to !. Write all their answers on
the chalkboard including incorrect answers. If this list does not include all three equivalent fractions that can
be seen on the board, ask the learners if they can find another one and write it on their showboard. Then ask
them to hold their showboards up when you say ‘NOW’. Then ask if all the answers on the chalkboard are
correct and if not why not. Orchestrate a discussion where the learners try to explain which are correct
answers and which are incorrect and to give reasons why. Do NOT name the learners who supplied the
wrong answers. When you are satisfied that the learners know and understand which fractions are equivalent
!
to ! move on to the other fractions and discuss them in the same way.
2 Ask the learners if they can find rules for finding equivalent fractions and for checking whether two
fractions are equivalent. Give the learners time to talk in pairs or small groups about this and then
orchestrate a class discussion asking the learners to explain their rules.
Finally summarize what the class has learnt giving the explanations that you think are needed.
Key Questions
What do you notice about the lengths of the different bits in the picture?
How many pink bits are there?
How many of the brown bits match the purple bit?
If the purple bit is one unit then what fraction is a brown bit?
How many of the bits of this colour match how many bits of that colour?
Possible extension
Ask learners to make up some questions of their own relating to the fraction wall and to provide their
answers. You might ask them to compare fractions and say whether one is bigger or smaller than another.
Possible support
You can make a photocopy of the picture given, on page 4 (preferably on card) and cut it out.
If you have it available the class can make their own fraction wall with multilink cubes.
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