What I love about the photo above is that despite the general age of the sets we had in school, the rods looked like new… also, the lovely glimpse of working out on the whiteboard in the top corner… (click to enlarge)
My aims for working with the Cuisenaire Rods were:
- to allow them some hands on work with little recording needed;
- to give them lots of thinking time – time to play with the ideas behind the rods and questions;
- to explore fractions in a different way – I doubt they will have used this equipment before (it always surprises me how, in this computer filled age, the simplest thing like a wooden block can fascinate children in the ways they do);
- to have some interesting discussions about their mathematical thinking. I want to hear their reasoning throughout this task.
My class relished working with these. I gave them a brief introduction to the rods – none of them recalled using them before – and a quick run down of the task (shown in full at the bottom of the full post, click read the rest of this entry to display it), to investigate relationships between the rods when given a statement about them. I emphasised that it was OK not to give an answer as a definite decimal number, but they could leave it as a fraction, or even give their answer as a colour in certain cases. Nevertheless, a few children asked for calculators and I allowed this as I didn’t want to dampen their enthusiasm for finding an answer!
They had around half an hour to explore the task and the rods, during which I took the photos you see dotted around this post and kept a careful ear open for the language and discussions the children were having. They had whiteboards to make jottings on and were told that I wouldn’t be marking them but I wanted them to explain to me how they knew things.
The majority of the 12 were sensibly exploring the relationships and questions associated with the rods. A couple were unsure about how to approach the task – in particular the questions that didn’t have an easily definable answer. One child found it hard to see that with each question the rules were reset. For example, question 1 states that red is equal to one, and in question 2 that association is broken as brown is equal to 10, equivalent to 4 red rods, making red equal two and a half. This child is one who is particularly talented at number work and is adept at working mentally. I expected him to really enjoy and take to this task with minimal effort but it didn’t click with him at all. He wanted to join the rest of the class in their task claiming that he, “didn’t get fractions”. I think his issue was down to a different structure to this lesson than normal and the safety net of a right or wrong answer not being there – he loves being right, and struggles to cope with being wrong.
As far as collaborative work went, the children mostly worked well together, discussing the implications of the criteria set down in the rules and finding relationships within the rods that they could use to guide them to the answer. Some of the questions I have likened to solving a Sudoku puzzle in that you only have a finite knowledge of the whole set of 10 coloured rods and you need to slot the values of the rest in carefully around that knowledge.
One such example of this is question4: “If orange subtract pink is thirty, what is: a) orange plus red? b) orange plus yellow? c) half of orange?”. Above is one child’s working out for this question – they insisted on neatening it up for the second photo… From this, they have worked out:
- Orange subtract pink is dark green;
- Therefore, dark green is worth 30;
- 3 red rods have the same value as dark green (30);
- 1 red rod is worth 10 (30 ÷ 3);
- 5 red rods are the same as orange, so orange is worth 50 (5 x 10);
- Orange plus red is 60 (top picture);
- Yellow is worth 25 (half of orange, so 50 ÷ 2);
- Orange plus yellow is worth 75;
- Brown plus red = orange;
- Dark blue plus white = orange.
Quite a lot of maths for such a short question – the last two not having been asked for, but they wanted to find equivalent lengths.
The great thing is, the quality of the maths here was good. It showed their ability to think in a logical way and discuss their thinking well. The discussions spread further than their pairs, the two tables became one mass talking point in the class, trying to explain to each other how they had worked out their different results. Another positive is that, generally, they agreed on a solution – no matter how they each worked it out.
In conclusion then, this has been a worthwhile experiment. It has given the children a new experience, it has given a new lease of life to dusty Cuisenaire Rods, it has allowed the children to stretch their mathematical thinking and developed their explanation skills. In all, something that ticks many boxes in quite a simple way.
The task in full (taken from the MaST Handbook for Unit 1: Study Block 3: “The Sum and the Parts”)
Use the Cuisenaire Rods to answer the following:
1) If red is one, what is:
- Light green?
2) If brown is 10, what is:
3) If dark green is a hundred, what is:
- Light green?
- Brown plus white?
4) If orange subtract pink is thirty, what is:
- Orange plus red?
- Orange plus yellow?
- Half of orange?
5) If yellow is four, what are the other rods?
6) If red is a third, how many different ways can 1 be made?
7) If dark green is a half, which rods could you use to make one and a quarter?
8) If black is sixty, what is:
- The white rod plus the red rod plus the light green rod?
- The yellow rod plus the pink rod?
9) If dark blue is 243, which rod is:
- And which pairs of two rods are 297?