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Meaning making with manipulatives

September 27, 2019 Leave a comment

This year I have an interesting year 11 class. Most of then are targeted 5 or 6, but only achieved 3 or below in their end of year 10 mocks. They had a poor diet of maths through their KS3 due to staffing issues and long term sicknesses they had some.non maths teachers and also extended periods of time with supply. They did have strong teaching in year 10, and some did in year 9, but they have massive gaps in their core skills and knowledge that I’m discovering and trying to close on the way through. For instance, today they did an assessment which included the question “round 7364 to 3 sf” 50% of them answered 736, and a further 20% had different wrong answers. They lack confidence in their own ability and some of them are turned off by the subject due to it. They are all capable of getting to grade 6 at least, but some of them don’t believe it so I’m working to try build that confidence as well as filling the gaps.

Last week we were looking at probability, venn diagrams had gone well and three diagrams were going very well, until we looked at a question that involved conditional probabilities. Cant remember the exact question, but it was along the lines of their being 8 red things and 3 blue things in a bag, someone takes 2 of them at random without replacement, what is the probability they get 2 the same colour.

They could see the first set of branches, but couldn’t get their heads round the second. I tried explaining it a few ways and nothing was working, so I pulled out the box of multi link cubes that lives in my cupboard and passed some round. They had 8 of one colour and we of another and we looked at what was going on.

This simple use of manipulatives really allowed the students to get their heads round the concept. Normally I think I would have resorted to drawings, because there is, at least in the back of my mind, a feeling that manipulatives are only useful for younger students or those with lower attainment levels. But recently I’ve been trying to build more manipulatives into my practice and many I’ve spoken to have told m how successful they can be with older and higher achieving students.

This use of them not only helped their understanding, but it built their confidence, and after trying a couple of times with the cubes they could answer the questions just aswell without them.

I think I will consider other places manipulatives will be helpful with this class as I move throughout the year, as I think it ca help them with meaning making and understanding, but obviously only where it fits and adds to the learning. I don’t want to b using things for the sake of it where it may detract from the learning taking place.

I’d love to hear any places you use manipulatives and how you use them. If you’d llike to share, please so do in the comments or social media.

Fun with Cusineire

July 18, 2019 Leave a comment

This is the second post in what I hope will become a long series about using manipulatives in lessons.

Last week I posted about how I was going to try and I corporate more manipulatives into my lessons, and that I’ve bought a set of Cusineire Rods for home to play with with my daughter. I’ve not manages to really do much in lessons since, the week has been disrupted by a couple of drop down days and sports day, and the lessons I’ve taught have mainly been around construction and loci, and symmetry and reflection.

I did, however, manage to have a play with some at home. My daughter was interested by the rods, and wanted me to show her some of their uses. First we looked at how they can be used to find number bonds to all different numbers, then we used this to look at adding and subtracting.

She uses Dienes base 10 blocks at school for similar so she started with just the 10 rods and the 1 cubes and showed be how she would use these at school. I then talked to her about how we could use our knowledge of number bonds to do the same thing but using all the rods. This was a fin discussion and allowed be to see some potential benefits to building number fluency with rods over dienes blocks.

She then showed me how she can use manipulatives to divide and to work out a fraction of something. The only fractions she really knew about were 1/2, 1/3, 1/3, 2/4 and 3/4. This led us to a discussion about the nature of fractions and their link to division. She knew that finding a quarter was the same as dividing by 4 and finding a half was dividing by 2 so I asked about finding other unit fractions showing her the notation and she made the link easily.

We then used rods to look at two of the fractions she knew. 1/2 and 2/4. She was surprised to see they always came out the same, and we used rods to investigate this and discussed the nature of equivalent fractions.

She then asked whether you could use the rods to multiply, I thought about it and came up with using them to create arrays:

This was 2 fives. Initially she was counting all the white blocks to get an answer, but after a bit when one of the numbers was one she could count in she started counting in those.

We looked at some where we were multiplying the same number together and I asked her if she noticed anything similar between these shapes and different to the ones we had done before and she picked out that these were squares and the others rectangles. This led to a good discussion as to why this was, linking to the basic properties of squares/rectangles and introducing the terminology square numbers and what that means.

I then looked at these two:

We had done 3 x 4 first then I said to do 4 x 3, she said “it will be the same because it doesn’t matter which way round they are”, so we did it anyway to check and talked about why that was. I tried to incorporate the cords congruent and commutative into the discussion, but I think they went over her head.

At this point her role changed to teacher and we had to teach all these things to her dolls…..

It was fun to play with Cusineire rods like this, and the mathematical discussion they provoked flowed very freely, so I can certainly see that thIs could be very helpful in lessons.

In other manipulative news: I had 20.minutes or so free earlier and spend it looking at Jonny Hall’s (@studymaths) excellent mathsbot website. In particular his virtual manipulatives section. I found what I think to be some good ideas for algebra tiles and double sided counters and think that virtual manipulatives may be a very good way of getting these things into lessons.

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