Evaluation - session 5 - place value/number systems

We explored something behind the ideas of using place value as a number scheme and the effect of different place values or similarities and differences.
We started by listing all of the coins or notes that can be used in the UK. Explorers listed as many as they could on paper. I had examples of each of them and so I laid them out in a tabular form with different place values being in rows and the first digits being in columns (1, 2, 5 are the only first digits in current UK money.
I asked why and we looked at how easy or difficult it is to count in those numbers (1, 2, 5 and 10, 20, 50 etc.)  compared to other numbers.
From there we went on to see how the base 10 number square organised these tables and noticed that they were all in columns but non coin/note values were all over the place.
I moved on to getting explorers to create a little book of different place value based number squares.  Explorers went for it in a very exploratory manner. Quite a few parents were on board for this class and helped out. This was really useful and might be a good way to set up a session.  A particular family learning type session where I set up activities, resources and challenges and give some advice about how to let children explore and how to encourage them to go further.

It gave me a chance to work with some of the more reticent explorers which showed me the importance of a part like this in every session.  I would need to think about what I could do with those explorers who have no problem doing whatever comes into their head but don't check how they are doing.

The extension task was quite engaging and even parents seemed intrigued by it. They had to create one for base 12.  Explorer C61 did fantastically (with the help of R98) and managed to complete the table, refusing to give up until she did!

Evaluation Session 4 - Place value/Number systems

Did this session achieve its aims?  I'm not sure how well defined the aims of this session were. Much of the planning is something like a sculpture.  I start preparing activities without fully seeing the kind of experience I hope to create.  This continues into the sessions where I am always hoping for inspiration to help determine the next step.

We started by looking at the numbers that form the sequence of powers of 2.  Some of the explorers new about the game 2048 and so could say something about that and others could work out other interesting things to say about them.  Many others did not contribute.  I wonder what is best in these situations.  A think-pair-share routine might be a good thing to use for these parts.  Or think-pair-group-share. This could be linked with a badge acknowledgement system.  Contribution is not for everyone and it may be that allowing people not to contribute is just what they need.  Exploration must happen outside a comfort zone but by what means should someone get there.  And which part of the comfort zone should they be outside?  All of it?  unlikely but for the most hardened explorer and then that is probably just a different comfort zone.
I digress.
We went on to use the numbers in a slider game something like 2048.  This worked well and I noticed that girls and boys had very different approaches for this game.  Not surprisingly, boys tended to be competitive and girls collaborative. (or maybe that is surprising).
It worked well for all the groups and they managed to achieve at least up to 32 on each table.  The idea here was to get used to doubling these numbers and understanding their value in relation to each other.
We went on to look at exploding dots 2 to 1.  The challenge was set.  What is the maximum number of cubes that you can put in the system so that no cubes are pushed out side of the grid.  Google exploding dots to see how it works if this makes no sense.  There were still issues using this idea butt quite a few made good discoveries (including the set up discovery that any time there was just one cube, it corresponded to the numbers from the game.  That would have made a good challenge question.  What numbers end up with just one cube somewhere in the grid?
from there we looked briefly at the binary calculator and how to calculate to and from binary.  To give explorers a chance to use it, I set up some codes using the ascii grid.  Explorers tried to create some codes and two of them broke my code.
A varied and active session, with games, challenges and questioning
Almost a model maths explorers session.

Place value session 3 - evaluation

What did I expect on going into this session? Some of my concerns were the amount of instructions needed for Explorers to be able to benefit from the tasks. As a group, they aren't the most attentive. I realise that M28, P79and R2D are far more likely to stop and listen attentively. Cat and joy pick things up excellently, as they did today if they're in the mood for it. 007 is on and off. If c61 is there, she's always involved. The littler ones need a more instruction drill, drill type of approach which may mean either that they should be doing less involved tasks or that they are not ready to explore. Our founding principal is that everyone is ready to explore from birth but not all ready to be influenced in this direction.
The games session started with draughts and different forms of chess. There was limited choice but everyone was engaged to a degree. The little ones used the pieces as play things and fought each other. I wanted to influence their actions but I was unable able to.  For me it would have been good to get them using the moves if not strategies. Maybe a knight's move challenge or chess solitaire would have been good.  Suicide chess may have worked also. It was great that the older ones tried all the games even though the rules changed a bit. Should have brought and set up "Go".

The place value session had a healthy dose of chaos added to the mix. We started with finger signed numbers which would be good as a regular feature.
We looked at the sequence of powers of 2 which were well known to those who played 2048.
Moved on to Exploding dots. The task was to find out how many would end up in the 4th 5th and sixth positions. Most had big problems sticking to the method. Gq8 and m28 did it really well. And discovered everything that had been set up to discover. But what next for them?
It was a useful way for the others to try the drill to learn the system. I can make it optional next time with others using  the binary converters. I'll set it as homework.
My aim is a comparable place value system. Ideally we would be able to compare them using our abacuses or something. It would ready them for Base 12.
Next week, converting to and from Binary and Base 5 to Base 10. Set up a spy system using ascii so that they can decode a message.