You need 2 strips of plain paper per pair. It is important that these strips are identical in length.
Why do some children find visualising fractions difficult?
I found that some of my students were having difficulty visualising equivalent fractions. We often use fraction walls for this concept; however I found they were still having difficulty comparing them. I used this activity as part of my assessment for learning in order to guide my future teaching.
What could I learn about the children if I listened to them talking as they discuss equivalent? Do they recognise its relationship with equal?
What I did:
Initially I asked each pair (could do individually) to fold one piece of paper to show me a half. Some children folded it width ways. We discussed the different ways you could do this. I then explained for the purposes of this activity we were going to fold the paper in half lengthways. (Always a good idea to have some spare strips in case children do fold it width ways)
I then asked them to divide the second strip into thirds. This was more difficult for some of the children. I asked a few how they did this. Some will want to use a ruler to measure and this is fine as long as they have come up with the idea themselves. I also asked why they had divided the strip into three pieces in order to get the students thinking about the meaning of a third.
Would it be better to look at halves and quarters first to gain clearer picture of children’s prior knowledge of equivalence. Then use second strip to investigate thirds/sixths?
I then moved on to get them to compare the two strips. Is one third bigger or smaller than one half? Can they explain or show you how they know? This is where you can encourage some excellent mathematical talk. Some children looked at the bottom numbers and compared these: ‘three is bigger than two so thirds must be bigger’. The strips were a great way to address this misconception as they can see halves are bigger than thirds so clearly.
Is there a way of making the language of numerator and denominator more accessible for younger children?
You can continue to move this activity on by discussing and folding into quarters and sixths and asking similar comparison questions. You can also investigate patterns with equivalent fractions by discussing what happens to the numerator and denominator.
This activity gave me a real insight into what the children understood about fractions and equivalent fractions. The visual aspect to the activity really helps those students who haven’t grasped the written format of fractions. ‘I can see what the fractions look like and put them together to check which is bigger’
I found there were a few light bulb moments. For example when a child finally grasped how sixths related to thirds. ‘There are two sixths in every third’. This was especially important as so often I have found that children have a certain level of understanding that allows them to answer questions but do not have a proper grasp of the whole concept.
How could I extend this for another year group or higher attaining children?