Posts Tagged ‘Year 6’

Yesterday, I detailed how I was planning to use Cuisenaire Rods with half of my Year 6s to investigate and consolidate their knowledge of fractions.

That rarest of things, a full Cuisenaire Set!

That rarest of things, a full Cuisenaire Set!

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!

Exploring the rods.

Exploring the rods.

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.

Working out Question 4.

Working out Question 4.

Solving Question 4.

Solving Question 4.

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.

Question 5: If yellow is four, what are the other rods?

Question 5: If yellow is four, what are the other rods?

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.

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On Thursday I followed up Wednesday’s work outside by taking it a step further.

My Year 6 pupils were asked to create mini versions of our large circle using wool and paper plates. I had pre-cut the plates to have a range of evenly distributed and more random slots around the edges. Pupils were then asked to secure the string by sliding it into the slot once, looping it at the back, then sliding it down the same slot.

They were invited to invent their own rules to create a pattern (such as missing every other slot, or missing two slots to go down the third). Finally, they were requested to photograph the resulting patterns, a selection of which, representative of all ability groups, are shown below.

As you can see the potential for discussion about shapes is huge. There are a range of polygons, angles, regular and irregular shapes all visible. Also, with ones that haven’t quite worked, we can look at the reasons why. Interestingly, the plates with evenly distributed slots were far easier for them to use then the irregular patterned ones.

Yes, I could have followed the outdoor work up on paper with pre-drawn circles and dots around the edge as suggested, but I thought that this related to what was done outside, was a little more fun and – important in this world of changing curricula – helped to develop hand-eye coordination skills.

Many boxes were ticked here and all sorts of interesting conversations were had with the children about their predictions for the shapes they would produce and about the ones they created.

Next week, I work with Year 3 children along very similar lines. I haven’t worked with Year 3 for about three years now and so I’m not too sure what to expect as the main differences in outcome – language will clearly be different, especially with it being so early in the school year. As for what else will be different, I’m waiting to find out!

Tomorrow I am trying out two of the three activities we were shown during the first meeting with 11 of my Year 6s – the rest are having a cycle training course, so I have a reduced number. For once this is a helpful thing!

I plan on starting with a secret construction task – starting with a simple house shape made of two colours. This will be the first time they have tried anything like this. I almost feel I’m not going to be pushing them far enough this time around. However, the cycle course is over two days so I will repeat this activity both days, amending the difficulty as needed.

I’ll be listening carefully for the language children will be using – my worry is that the simple shape won’t get much vocabulary out of them. Although clearly an entry level objectivie is needed to begin with – it’s the first time for me too!

To follow up, I’ll be taking them out into our playground where there is a clock face. I’ll be trying out the string shape making activity – passing a ball of string around the people in the circle following a given rule (pass the ball to every 2nd person, for instance) and seeing what internal shape is made when the string is placed on the ground and kept tight. As the clockface has equally spaced dots around the edge, the shapes produced should be regular – my teaching assistant will be the 12th man. However, I only expect to introduce the idea in this way. I plan on moving on to a less evenly spaced, less circular space to investigate irregular patterns. Then, in class, I’ll be following this up with coloured thread on some paper plates with notches cut into the edges. The pupils will be creating their own rule and seeing what shapes are made when moving the string around the plate. For recording purposes, I’ll encourage them to use the school’s digital cameras to take photos of their shapes, which will then make an ideal display.

On Thursday, I’ll be carrying out the other activity – the multilink plan views – with the same Year 6s. This will be more of a challenging thing for them. I’m not sure that visualisation is much of a strong point for them yet. Time will tell!

I have further plans to repeat the string activity with some Year 3 children next week.

I will most certainly update you on what happens.

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