Points, lines and shapes 1 evaluation

Perpendicular!

The Brixton sessions have a very different character to Tulse hill. We are in our own room so no one can see what we do and we can use the space much more as we like.
My plan for floor space has on occasion led to other ideas for activities much like today's block and roll idea.

It was very much a workshop style session today.  We had some nice elements such as the parallel/perpendicular call which should be a feature.  One explorer called out regularly and others started getting into it at the end.

Finding parallel and perpendicular examples in the room was ok but would have been much better in the playground.

The triangle investigation was not as thorough as I had thought it might be but I misjudged the time it took.  We didn't get many doubles ( I think two explorers did a different 7).  But it would be good to mock up a few straws on 7, 8, and 9 and see if they can get more than one triangle by moving them around.

We talked a bit about the history of right angles and historic ways of creating them.  I hoped to get on to creating a grid on the floor using parallel and perpendicular lines but didn't get a chance to do that.  Instead we played block and roll using paper.  This was quite a good way to do it though as it was a better place to introduce the game.  They can practise online and we can try to create the grid next week.

We didn't get to use rulers but we started to see the use of set squares and we can use set squares that we make ourselves.

Games focused session evaluation

One of the challenges I face in this and perhaps all of the sessions I facilitate is to figure out my role in the growth process. Both of the sessions this week gave me an opportunity to reflect on this aspect. These are some of the roles I picked out.

Challenger
Ideally I would like my main role to be to set challenges that take care of themselves. An Explorer gets a vision and embarks on the mission. This was most evident in the straw challenge where the initial challenge was set and then they went off and tried different things to achieve the tallest tower possible.

Setting the challenge with the rubik's snakes to create a square worked well in this regard.  On Saturday E and J discussed ideas about why it could or might not be possible

Ideas board

Our twin explorers are fantastic and so advanced for their age.  And so different. Chatting about ideas with Will was very cool.  None of them were very mathematical but they were linked to the activities at least initially.  But it gave me a chance to see more about his way of thinking and I assume it gave him more of a chance to be heard and find out something that was relevant to the moment.

Encouragement
this is mainly in the planning of the process of the session.  I am trying to gamify the workshop to the extent that explorers try a range of activities and review what they have done.  I am attempting to do that by a levelling up scheme where comments are reviewed and both reviewing and having well reviewed comments gets explorers points that lead to levelling up.  Still in progress.

Authority
We had problems this week with a couple of explorers going a bit wild before I got there.  It is fairly clear that it is getting close to the time when I'll have to move this session on to another venue as there we are quite limited there and it's clear that it is becoming a strained relationship but that's another point.



This is a strange role and one I'm exploring as I need to be able to influence some of their decisions about exploration but many of them clearly would not accept if it went against a decision that they have already made.  This is a good thing up to a point and I need to make sure that I distinguish that line.

To Provide examples
We started by playing split 3 ways on paper.  This was not a problem for many of the children but some needed help getting some numbers to start playing with.  Once they had the idea that I could help them to get numbers to play with, those that needed this were comfortable asking for this help and would then get on with playing the rest of the game.  I gave examples some times as a demonstration with blocks, sometimes working out the answers and sometimes just checking

Games Focus
I think that focussing on games development is a really useful way for me to see these sessions.  I don't need it to be the explicit focus for explorers, just to be there as a way of framing my planning of the session.  It will be useful to see how it works for this term.

Multiplication session 5/4 - Evaluation

This was a key session in the course and really the pinnacle of the programme. The idea of multiplication being a relationship between numbers is a difficult one to see and so not easy to explore. 

I wanted to make an activity that forced them to think in terms of multiplying numbers and that also might lead to the project idea of representing primes as parts and composite numbers as completed products.  

To encourage this idea, I tried a few things:

We looked at characteristics of different multiples and how tables of multiples are symmetrical.  We looked at other tables that linked characteristics and asked about why the central diagonal didn't have symmetrical doubles.

We explored the patterns made by times tables in a 100 square.

I restricted the numbers to only the "friendly" primes.  We explored the numbers created using 2, 3, 5, and 11 only.  I called these the friendly primes because they have easily discoverable patterns in a 100 square.

I recommended the playing the app Alchemy that involves mixing base elements (Air, fire, water, earth) to make all kinds of compounds.

We started the session in Brixton using cards that had prime factors in the form of coloured dots on the back.  I used this as a way to remind everyone about the colours introduced last week and to get questions and observations.  The first two observations were about the card with 3 red dots (8 as it is 2x2x2) and three green dots (27 - 3x3x3) on first encounter, everyone assumed that they should be 6 and 9 respectively.  I half explained half left them to figure it out.  It would have been good to have some strategies for that.  Even if I had just explained the homework rule that they can only use the numbers from the dots and the times button.  That may have still caused them to think 2 x 3 instead of 2x2x2.
I don't think it was a big problem anyway.  E and N went on to get the concept very well as did the rest of them I think.  One or two didn't really get past the times tables on 100 square that we did last week but reinforcement of that is a good thing.  I think the way C20 understood it afterwards was one of the best moments as he often does not get our activities or draw his focus away from whatever it was on but today he did a lot of the prime map and also asked questions about what he was doing and checked with me regularly.
An activity that was very helpful for setting this one up was to create number system using the 100 square.  We added blocks corresponding to the colours for that number.  I started off with this one just letting them do what they wanted but had to work more strictly to get a good outcome.  I took the board away and asked if they thought they could find some cards and  then build a tower with the correct colours and number of blocks.  They all got on well with that.  transferring it to the paper copy was a little more difficult.
I tried a 2048 style game at the end but I haven't thought the rules through sufficiently yet so I'll try that another day.  One thing is that I should leave out the miss a go part as too many goes were missed and that made the game too slow.

Session 4/3 evaluation

 It came to me about an hour before the session and proved to be a really useful resource for working with a hundred square. I could see it being used for all kinds of number square investigations.
The basis for this week's exploration was understanding how the multiples of certain primes are distributed over the hundred square.  As has become a feature of this programme, I wonder how much meaning explorers are able to fix onto maths like this. Nevertheless, we are committed to providing experiences that allow children to explore ideas in as many ways as possible.
We started with colour coded cards and wanted to see if our explorers could break the code.  Those who were there succeeded in saying lots of things about the possible links with colours and numbers.  Many noticed times tables and combined times tables.
We discussed prime numbers and what I called friendly primes. From that we worked on colouring a 100 square using the same code.  This is a way to start explorers seeing the patterns.  I should have started with 11 with this one though as many of them got the idea from the 2 times table that they all just go down.  and without any more thought proceeded to colour the numbers in, in columns (rather than the diagonal line of squares.
This was on top of the templates that revealed the answers if help was needed.
This session was also an opportunity to get to know some of the boys a bit more.  One of them had been asked to try colouring in the 2 times table.  He just said that he didn't want to do it.  His mum checked in with him and told me that he didn't know his two times table.  This was a bit of a revelation (as he is very able mathematically) but now I think back, I have excused playing up as boredom rather than inability.  This will be an important aspect of the sessions to master.  When to offer support. I imagine it will be whenever someone doesn't want to do an activity.  It works very differently with others of course.

 We had quite a good game to finish up.  We started with all the colour code cards colour down.  I threw the 2, 3, 5 and 11 cards up and asked explorers to find cards that had the same colours as those that had landed colour up.  It was a bit of a dash with explorers turning up every card that they could. rather than figuring it out from the numbers.  Little by little I suppose.

 I don't take in homework in maths explorers sessions but this week, one of our explorers had really looked at the missing multiples game on Nrich.  She went through lots of levels and really figured out how it worked.  I should find a way to get more homework in or talked about or recognised.  Hopefully with the project this time round.  I've set homework to find all the numbers under 100 that are built using friendly primes.  I must remember to send out a reminder.

multiplication session 5/4

The penultimate session.

Look at multiplying with lattice method.

bring in the idea of characteristics being transferred to the product and thus new factors (e.g. something with a factor of 3 multiplied by a multiple of 5 will definitely have 15 as a factor - why?)

Unit endings always the same with etc.

introduce the idea of a symbol that is a digit.  I can do this with a simple multiplication and then a slightly more complicated one.  I could also produce part of a hundred square (or a whole hundred square with shapes rather than digits.
This may be quite a jump for the littler ones of course.  They will need some more consolidatory work on multiplication and what it actually is.

This idea of cycling cards might be worth thinking about.  If it could be done wiht multiplication and the analogy (or an analogy) it would help give a lot of examples of what I had in mind for the project.
If I could get the coded timestables into a more hands on activity that shows up the letters for what they are (they could put numbers on top of the appropriate symbol and then of course add the same number to all the other symbols of that kind.
If the numbers were cut out like the lattice numbers it would reinforce the tens units and that system.

Brixton - Session 1

Based on the experience of the Tulse Hill sessions and the fact that two (or 3 as I later discovered) explorers from the first session booked I decided to start with the second of the two session that I ran in Tulse Hill.
There were two benefits to that.  First, it was a much more engaging session and clearer aims and things to take away.  There was room to think quite deeply about some of the things that the activity threw up but also the chance to just work on times tables and practice.
I had not prepared enough for young people who were not to be able to do one of the times tables.  I don't know what stopped them as it was possible to copy from the card sorting activity.  As always, I forget how little meaning any of these things have for some of the children.  This is one of the issues that needs figuring out.  Explorers are encouraged to come up with ideas and observations.  I don't it is a problem if they are not able to check their observations though.
Anyway, the card hunt was a popular activity.  Explorers laid out the found cards and started to find ways to work with them.  The discussion in this period is a real asset to the session and it would be good to find a way to make more of this by, for example, recording one or two quotes each day.  May be a small group activity where they tell me what.
Linking the times tables to the unit circles was not a straight forward start even the second time round.  It is a strange concept and I can only imagine what someone would think if they didn't have the firmest grip on timestables, each as a kind of entity themselves.
I didn't get on to the numberline multiple hopscotch or lattice method.  I think they would be good towards the end of the course as a way of reintroducing the ideas we looked at in the beginning.

Multiplication session 3/2

Multiplication grid poker
Multiplication table jigsaw
Cuisenaire rod challenge
Times table charts area based
Properties table game - must find
Coded multiplications activity
Challenge using unit circles grid with cells corresponding to various numbers based on intersection of particular tables
Project start and discussion