Laminated cards with a 6 small circles laid out in a triangle shape.
I was teaching a Year 4 class that had several children who had very low confidence levels in maths and seemed particularly reluctant to take risks when doing their work or answering questions, regardless of their ability. I wanted a resource that would encourage them to 'have a go' without fear of getting ‘answers’ wrong, so I developed the idea of target triangles.
What I did:
I started the activity by showing the children a simple example for the target number of 15 on the whiteboard, with some numbers filled in. I explained that the idea was to make each side of the triangle total the target number they were given and that they could not use a number more than once.
I worked through the example intentionally making errors and talking through my thinking and clearly modeling trial and error techniques. I then showed a second example for the target number of 15 without any numbers and asked them to work with their partner to have a go at this one but not to use the triangle previously shown.
The children struggled and were generally using random guess work at first, putting numbers in without any thought for the combinations of numbers. But, you could see that as they progressed there was more of an element of reasoning behind their ideas. We came back together as a class to discuss some of these strategies, address misconceptions and also present solutions. I could see the children's confidence grow as they moved from guesswork to using strategies.
What evidence would I look for when assessing the children’s confidence levels? Could I use observation as a valid assessment?
Once the children had become confident in how the activity worked I put up a selection of two-digit target numbers on the whiteboard and asked them to have a go at making some of them on the triangle with their partner. For my selection of target numbers, I used a random number generator on my interactive whiteboard. I was then able to say to the children that I did not know the answers either.
I emphasised the point that there may be some target numbers that have more than one answer and others where there may be no answer. The children continued the activity well and were all willing to have a go at working out the answer and generally were very successful. They were enthusiastic to begin a new number after completing their first one or began to try to explain why it could not be done.
For lower attaining children, it was possible to keep the target number smaller, at the level of their addition skills, but continue the activity in the same way to keep them motivated and able to access it.
How could I extend and challenge my more able learners?
Now the children know the activity, I have been able to repeat it as a starter and children continue to be enthusiastic at having a go to find any given target number.
The fact that the cards were laminated and used with whiteboard pens which could easily be rubbed off meant that the children felt that there was less fear of having a go and realising that it didn't matter if a mistake was made. The children really enjoyed the activity and seemed to relish in the idea that I did not know the answer and they could show me how to do it. The fact that they achieved a successful answer by 'having a go' has had some impact on this culture in the classroom.
I was pleased that there were other benefits of the activity beyond my original expectations including quicker mental addition and subtraction of two-digit numbers, cooperative working with a partner and excellent discussion which involved building up vocabulary, oral explanation and reasoning skills. Children very quickly developed strategies to inform their trial and error methods and would often reason their thinking, for example 'if I put this number here, then this one would have to be greater' or 'what other way can we make this number?'.
It was great to see Shinelle having a go and reasoning clearly with her partner and Sara’s excitement when she came to tell me her solution.
I wonder how my lower attaining children will cope with this activity. How could I give them support to ensure they access it?
I think the fact that children have willingly chosen to do the activity at other times in the classroom is a measure of its success.
Are there other ways to use these target triangles?