Thu 27 Aug - Cuisenaire rods

The focus of today was a tool for learning maths.  It appears that it is quite a common tool but very under used.  Actually Cuisenaire rods are really useful and perfect for this number programme.  They should have been used in all sessions.  Or perhaps a whole programme on activities with them.
There was a good range of activities in the session.  We started by looking at number art and talked a little about pixellated images.  We created badges for those who didn't have them yet.
Cuisenaire rods were introduced and I initially got them to figure out which numbers they were, which they all did easily.
We moved on to the colouring by numbers activity (with the numbers expressed by cuisenaire rod size.  It worked well to get explorers to think more about the sizes.  In most cases they used the rods to check the size of the space.  I got around to speak to a few about other ways they could find out which size it would be but not all.  I imagine that it would be a natural enough transition to finding and using the grid to detect sizes.  Anyway they were asked to finish off at home and so there they would have to use other methods.
The hidden numbers stayed hidden quite well.  They were found eventually and I think that those who found them enjoyed the discovery and hopefully it whet their appetite for more exploration (but just a hope).
We had time to look at the investigation.  I sold it much better in the second session.  I explained that we had to build walls.  The restriction was that in a wall, each layer had to be unique.  we looked at the examples for 1, 2 and 3 and then I tasked them to look at other widths.  In the first group they worked well on the activity but no one bought into it.  They found a few rows but I no one really thought about how high it could be or if they had exhausted all the possible rows etc.  I should have emphasised this by focussing on the number of rows for 4 or somehow made a game that made it worth doing. Maybe come up with a reason why the walls needed distinct rows.
In the second session, I introduced the activity more successfully but still had little buy in until I got Joe to predict the number of rows for 4.
Me: How many rows will there be in the 4th wall?
Joe: 5 (little commitment)
Me: Why?
Joe: One more than in the third.
Me: How many in the first row?
Joe: 1
Me: and the second?
Joe: 2
Me: and the third?
Joe: 4...  Oh it's multiplication
Me so how many in the 4th?
Joe: There will be 8.
Me:  Ok. Try to find them all

He was invested in it after that and found 7 rows.  Jaz worked well on it also but did her work more neatly so didn't get so far with the investigative part.  I wanted them to work in teams but that didn't happen.  They all did their own things.
Here are some of the issues with this investigation or at least the running of it in this session.

General chaos of a session

1) Getting kids to stop playing.  ideally all the session would be play but in order to up the challenge I need to stop the play and have a way to do that so that kids know what's coming.  I have delayed on the organisation of features of this the whole project.  I've started making some progress in terms of forms and support for the organisation but not much actually in session with routines or anything like that.  This will need to become a priority.  I feel like that episode with Joe was a bit of a breakthrough and the idea of challenge level could be a way to deal with this.
2) Understanding the different levels of challenge.  To begin with, it will be understood as a task.  One I've asked them to do.  Finding the way to get them to see it as a challenge is the key to these sessions.  It is an individual thing to a degree but also the impact I'm looking to have and what I should be tracking.  An explorer's ability to find the challenge in a task.
3)Generalising any patterns found.  This is of the real goal but I can't say I'm very clear about how or if this is something that they have any experience of or anything I can link it to.  Finding a general pattern for something that they would understand would be great and needs to be dealt with.

We ended up building a tower with rods.  The first group got on with it quite well as a trio.  The second group struggled with the idea of working together but really got on well with it in the end and produced a very high tower once they worked as a team.

I didn't get around to bringing up the project which was a shame but Ndg and C20 did some great work on it.  More evaluation of that to follow.

I'll have to review the whole summer programme at some point.

Tue 25 Aug Evaluation

A relaxed session and I think I need to remember to relax things from time to time and leave kids doing the exploring.

The number art was a good start and got them not only thinking about how numbers are written but practical things to do with how to put the pieces together, how to create a curve on a hexagonal or square grid or what colours can go next to each other.
We spent a good deal of the session doing this and I wonder if we needed so much time for it, but it was beneficial.  I think the best part of the activity was getting them to change things about the one I had done.  That produced some real exploration and discovery.  We found that the 7 became harder to see.



The next game was an intro to bridging to 10.  It worked well except for T throwing a strop mid way and inexplicably.  Other than that it was fun, got them solving problems around what they would need to add to get to the next 10.  To make it faster, I should give them 3 dice to throw.  I will try starting with that version in the next session.

Mon 24 Aug - Evaluation

I really didn't think anyone would come as it was raining so hard.  It was a pleasure to see T come along as he is such an enthusiastic explorer.  It was only him which didn't dampen his spirits much.  I ad-libbed a few activities for him and went on to the tower activity.
There are a number of differences that I need to work on between groups and 1 to 1.  Conversations can't just be prompted as a clear check of understanding as it is less authentic. He is aware that he isn't teaching me anything whereas sharing answers in a group would be different.  I can use concept questions but without an audience, they need to be well tuned to get an answer that is worth the child taking time to think about.

I will prepare some inquiry prompts for T for tomorrow's session.

Otherwise, a mix of today's session and possibly some number properties or developing the bridging through tens game/challenge.

Monday 24 Aug - equality and difference

This session will more or less use the challenge list from a few sessions back.
I would like to use the King's and Prince's tower activity and see if I can get a few extension questions that they can engage with.  Or a scale to show what the next step is when the first bit is mastered.  We can start with under 20 blocks and increase them, stop using blocks and discuss patterns that they've noticed or look for patterns to discuss.  They should then think how many possible differences there could be in the towers and if there are any impossible differences.  What else could be done? 3 towers perhaps.
Plenty of ways to take this.

The dots/difference activity as a starting activity could work.

It could be good to do the cuisenaire rods challenge then into odd one out and then the towers puzzle.

That way it would probably be better to do Hi Lo to start.

End with the Nim colours game but look to release reliance on the chips by getting them to work out the number of chips left (using wbs if needed). Don't allow counting except at one place in the round.  Consider adding special chips that could have another function (such as being wild or being able to double or add 2 or something else)

I would like to do a bit on properties of numbers also.  This would just be square, triangle, hexagonal, and prime (possibly cubed, rectangle and cuboid.  Add pyramidal also if needed)

I can start with image of a digit using chips and see if they can create something similar.
Plenty to go with depending on who turns up.

Scales and number balance is there too but may be better on Tuesday.

Thu 20 Aug - difference - evaluation

I really need to make sure that I write plans down.  Even very quickly.  Review previous and write a blog for the next plan.  It's a discipline thing I guess.

I did not like the first session and I think that our explorers also did not feel up to doing much of what we did.  M and I were as solid as always.  Well they all were so perhaps it was just me.  I think I went to numbers too quickly.  Block work worked except for those who fashioned small hammers for their toys and proceeded to chop at the chair.

Two things:  A different puzzle.  I should have left the sum difference puzzle as self access (and done some self access).  Kakuro would have been good or something like that.  Arithmagons need to come once that puzzle has been mastered.  Self access from now.

The art starter needed more of an injection process.  I needed suggestions to broaden thinking and I'm not sure how I could have gone about that.

The dots game was good.  Especially as it engaged N & L who are getting more difficult to reach.  They laid their results out really well.  I will have to give everyone the chance to do look at that again.

Second thing (finally) I need to sell activities.  The king and prince
tower worked for that.  I needed that for the wooden blocks which I just gave up on after M had his revalation.  I didn't have any where to go with it from there.  Perhaps a waste of development time but who knows.

Project discussion was a good start and end game (needs a name) also went well.  Maybe needs speeding up and numberising.  Explorers could keep track of counters that they are interested in.

The second session was much more laid back and the activities worked better.  Down and out was really good.  Kakuro went well but I would have liked to find a way to deal with it using blocks.  A good intro would be to get them thinking about combinations that make 7 from 2 or 3 etc.  I suppose that's what the first activity did though.

Key take aways: story or hook for each activity (at least one)

Wed 19 Aug - Adding - place value

Only one today besides Sav and Yunas.  I'm not sure what happened to M&M but they didn't attend.  I started them off with making large letters on the floor with masking tape.  We used the circles in

the basketball court and used the three circles.  There were a few challenges in creating numbers that are larger than you. The main one is drawing them the correct way.  The often started creating it the wrong way even if they never write it incorectly.  It gets you to think clearly about what you're doing.
We then went in and tried the number splits to 30 activity.  This required double digit addition skills that only Tay had so we went through the column method for doing addition.  I didn't really want to get in to it except to see how far they could take it.  Sav more or less got it in the end.  From there we moved to Dicey operations.  This worked well especially the target to provide a goal and focus.  We managed a couple of rounds.

Our last activity involved throwing the juggling batons to make certain numbers from 1 to 20 .  I added the possibility to count or deduct from the number by adding or taking away the number of spins.  Sav was the most vocal about what should happen and she made good decisions.

Tue 18th Aug - Odd even - Evaluation

Today's session had a good focus and lots of engagement.  We focused on odd and even and I felt that they really got a chance to review their experience with the concept.  It was done with two activities.  The first was finding dominoes.  That made the activity more fun but of course took more time.  As our metaphor for learning is exploring it was a perfect way to do it.

I liked today's activities because they were all about arousing curiosity and discussing things and we had loads of discussion.  Kids were able to see things in lots of ways which is just what I felt was needed for this project.

To begin with running to find particular dominoes to place in the grid got them thinking about the words and ideas and ways of communicating usefully about odd and even numbers.

What happened - Students arrived and I introduced them to the grid and got them to explain some of the words and the parts of the table (columns and pairs as the word came out for the rows). I don't think that everyone got the sense of the columns and rows as opposed treating the spaces as meaning what ever card they are close to.  Getting the idea of common traits is a tricky thing to model or present.  There was a lot of this idea in the session today and it would be difficult to find a more important basic idea in maths (basically sets).

Explorers went out and looked for any domino to bring to the grid.  Tay was the only one who hadn't hidden any dominoes and he was the one who was most excited by it and found the most dominoes.  I think some of the others just found ones that they had hidden themselves.

It was a little harder to get them to find a specific types of dominoes.  We had columns that dealt with odd totals and even totals and then rows that dealt with the parity of each side of the domino.  We had plenty of discussion about where things should go and MSJ and C20 (our new code names worked pretty well) never fully internalised the significance of the columns and rows so needed to be asked about it each time.

We moved on to using numicon to explore odd and even.  I got them to put them in order.  Numicon manipulatives are naturally attractive and invite kids to play and try things themselves.  And as these were laid out already, they all just got on with it and played.  

The task I had in mind was easy to engage them with.  I started with ordering and then sorting in their own way.  The sorting into two groups was a little harder for them. The concept of two groups with common elements didn't make sense but the little ones managed to sort them in terms of big and small ones.  Tay then came up with odd and even as a way to split them and they had no difficulty.  I left them to come up with a way to see the difference for themselves.  They did see the extra bit as making it odd.  I asked questions about combining odd and even ones and asked if they would make odd or even.  This took a little work but we got there. I then asked about combining all of the numbers.  Ndg used Gauss' trick to tell that the answer was 55 (sum of 1 to 10).  He showed how it would work using the numicon pieces to make number bonds to 11.  The little ones put it into a long shape and showed that it had an extra bit.  I tried a few other questions like taking a random tile and seeing if they thought it was odd or even and getting them to prove it.  I also tried putting them all together.

We finished off with split 3 ways and started the grid to record the scores.  All except C20 got on well with this.  He was a bit distracted by playing with blocks and had to be persuaded. So I think he only played me.

I think the only think I would do differently about this session is add more structure to the splitting the tiles into two groups.  I could capitalise on the table we had used and get them to write on (or dictate) a heading for each group.

Explorer badges

Joshua

Lilly

Nettie

Ilora

Max

Elam

Ida 

Ruben

Joe

Luca

Hana

Olivia

Emy

Jazmin

canaan

??

Nettie

Capucine

Céleste 

Tue 18th - Brixton session - odd and even

We'll continue with the number bonds and split 3 ways.  Following additions to today:

Record scores of first game of split 3 ways between each person and get them to write their name on the score chart (which will be a table allowing two games).  We can ask what they want to do with results.


The starting game can look at numicon representations of numbers.  I might get out the Venn Diagram (where is that?) circles.  We can look at what numbers they represent, get explorers to group them.

Hopefully they will at some point group them as odd and even whether using the words or not.  I can then get them to put them in order, and find number bonds to different numbers.  Get them to see if they notice anything about the numbers they need to put together.
It might be good to have two groups working on those and one group working with groups and adding to 20.  I would have to think carefully about them changing around and getting a chance to do each activity.

The investigation would also be good.  Finding how many ways numbers can be split.  We could look at it in terms of the shapes but also just as numbers such as would happen in Kakuro.

I would like to see if I could demonstrate Kakuro with blocks and get them to explore some possibilities.

Same ending game but I will get them to put them in piles of ten and record the number there at the start.  We can update as we go through asking others what has changed.

A domino game would be really good where they go around the park finding dominoes with particular traits

Resources needed
A3 of the add to 20 sheet
two way table for competition
Domino property cards

Mon 17 Aug - Brixton Project session 1 evaluation

The first Brixton session.   The space is really good and we made use of most of it.  I think the starting space needed more thought, chairs and tables etc.  Possibly start with warm up activities that are in different places and are just puzzles using trial and error.  and then call everyone together for the first group activity.

The code names worked well.  It would be good to get them using the code names also.  I'll prepare shields for each of them and hopefully can award them personalised certificates at the end.  I should get a kind of spy/explorer theme.

The number bonds activity was just the kind of thing I want to happen more.  I introduced the concept with the number line.  Explorers talked about it a bit and were all interested in showing what they could do.  I got a few examples and then split them up into random groups to do different tasks linked to number bonds and linking numbers up to make different totals.  All the explorers noticed that the number bonds went 'backwards' and those on the hundred square saw other patterns linked to the hundred square arrangements.

We moved on to splitting 3 ways.  I got Nd9 to start things off witha few of them outside.  We all moved out side and the two of us did a demonstration.  I tried with a few others and then got them all playing each other.  I should have got them moving around a bit more and maybe recorded results of different games.  I might produce a sheet for that tomorrow to remind them of the games and get them to see how to record scores or use a table.

I moved on to the 3 way sheet a bit too quickly.  I should have mixed the games by getting a few people to use the sheets against others still using blocks.  Some really got on well with the sheet though.  It's a good format.  I just need to add the shapes I think.

The game at the end was a good end to the session.  We got some observations.  I noticed Nd9 playing really well.  He was checking for best moves and counting whenever he could.  Some were just taking part as they didn't quite understand it yet but every one wanted to win certain colours and got involved.  I'l have to add special chips to it in future or change the win ratio for colours in future sessions.

We'll stay looking at this tomorrow but work on the competition, investigation and Kakuro.  I'll start with some odd and even work using numicon possibly