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What Makes A Good Resource - Always, Sometimes, Never

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Created on 08 September 2009 by ncetm_administrator
Updated on 03 September 2010 by ncetm_administrator

Always, Sometimes, Never

Resource description:
A set of 15 cards containing statements on them. The idea is for the students to work in pairs and discuss which ones are “Always True”, “Sometimes True” or “Never True”. Some are likely to be placed quite easily and other I deliberately wrote to be provocative and promote discussion.

Teacher comment:
I was starting with a new Year 7 class on some calculation work. I really wanted to find out what their understanding of multiplication and division was like. I’m also aware of the new programme of study and Functional Skills and so am working this term on allowing my students opportunities to develop their reasoning and analysing alongside developing understanding of content.

What I did:
I handed out the cards and they worked with their neighbour. I said that the point of the activity wasn’t for them to put all of the cards in the ‘right place’ but was to help them understand what a good mathematical explanation might ‘look like’. I said that I really wanted each person in the pair to be able to explain to each other and to me why they had placed each card where they had. It didn’t matter if they didn’t place all of the cards.

There was a little bit of diffidence in starting and then a fair bit of ‘Sir, is this right?’ (which I ignored or deflected as much as possible). However, they soon settled, became engaged and started deciding whether the cards were always, sometimes or never true.

I stood back and listened to some of the conversations that were taking place. The 10 ÷ 3 = 4 card caused a lot of discussion and really polarised opinion. We didn't really get to a shared answer on that one (although everyone in the group could justify why they thought it was or wasn't possible). The '5 can't be divided by 10' card gave some literacy problems (some wanted to put it in the always pile even though their reasoning was that '5 can always be divided by 10'. I guess there's a double negative?) I'm thinking about changing the wording to '5 can be divided by 10' but I quite enjoyed the discussion that was provoked by the wording and by them trying to interpret what was meant.

I stopped them after about 25 minutes and invited a couple of pairs to talk about which card they had found most difficult to place and how they eventually decided. I remember being pleased at the time that many students had been suitably confused by some of the discussion (suitably confused is, I think, where they've had the boundaries of their understanding pushed a little).

Reflection:
Looking back I guess that there are two things about this activity that I really liked. The first is that I didn’t have to do any ‘telling’. Of course I set the task up, but I didn’t have to tell them what to think or how to ‘do’ anything. A colleague the other day drew a distinction between teaching multiplication and teaching how to multiply. I think that this activity sits firmly in the former.

I also like the lack of a ‘right answer’. So often in maths it feels that the students are trying to guess what’s in my head, to get it right. Here I was able to listen to them thinking aloud and developing their own understanding by challenging themselves and their peers.

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22 January 2013 10:58
I do like this sort of activity - you can find more in "We Can Work It Out" (from the Association of Teachers of Mathematics) and some Tarquin materials (e.g. "We Can Work It Out").

I've got two or three simple sets I'm happy to share, built on multiplication tables and for Y6/Y7. True / False statements like 6x6=38, and assertions such as "All square numbers are even" or "If you double a number twice you multiply it by 4"
15 July 2011 15:33
I've used this too - I like the '10 divided by 3 = 4' card - caused a lot of conversation amongst teachers and pupils
Thanks
14 July 2011 21:31
wonderful resource, thank you!