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

Prime factors 2, 3, 5, (11) - multiplication session 4/3

The key idea here is to start noticing when numbers have prime factors of 2, 3, 5, and possibly 11.

Activities
Guess the prime factors game - I could start this as a game of pelmanism and explorers have to turn over cards with no more than one difference in colour coding - I can ask about what they think the colour coding is.  It would be a good activity to ...
Organise them into a grid (just two of the colours maybe)
100 square sieve - explorers can colour a corner of the numbers in a hundred square to show which
prime factors they have.
breaking numbers down into prime factors - division of numbers or just look into calculator method.
Grid game with attributes - think of attributes such as human, lion, etc as being numbers.
Project - create a system that could be used to show prime factors of numbers
example resource linked to Alchemy with air, water, fire and earth being 2, 3, 5, 11
create a tarot like deck of number cards that people have to guess which number each one is given the clues
Create a set of numbers that explorers must take if they want to work on it.
Discuss if we want different systems.
Need for a system with lots of possible base elements (primes)