July 30th - number bonds, split three ways, long addition - evaluation

This was the first time of doing two sessions in one morning and it proved to be very doable though needs more preparation.  Turning up late did not help things.

The first activity was split 3 ways as a game.  We've played it as add to 100 before now but I wanted to try something more visual and tactile and that could include the younger ones or anyone.  I don't think I got the type of engagement I need for a beginning activity in the first session but they are used to doing this just with a paper grid so I should have started with that for them and just tried getting the grid activity going with the younger ones.  I'm still not sure how I could engage them with it though.  Perhaps doing it with a song where they perform the actions in rhythm.  It would be worth working on that again.  I can't be sure how they understand a game like that.  None of them seemed to get the meaning of having a certain number of blocks to start with or that the blocks needed to be shared in some way.  I would not be able to deal with that part of things but it would be a great responsibility for another facilitator, or me if they took on the main activity.  Blocks or any other manipulative are always very distracting if you have an agenda that younger or disengaged kids have not bought into. Care should be taken.
The investigation aspect worked well with the first group.  They produced long lists and of course didn't need the blocks.  Where kids did need the blocks, they had a lot more difficulty with the concept or idea of the investigation.  B struggled with the idea of different sets of numbers.  He seemed to like all the numbers to be the same and was stumped by the issue that there is only one set
of numbers for which this worked.  He tried to add more columns so that he could get multiple 2s to get to 9.  I wasn't sure how to deal with this other than to try to refocus back to the designed activity.  What else could I have done? There is only so much time and shared language to be able to get into explorers' own ideas about a task.  Maybe I could have got him to talk about the best way to split the numbers etc.  Or perhaps got him to fill in the missing number if I put two of the numbers in the column.  I tried it by putting in one number and that worked ok.  Anyway he seemed to have the concept but not really get into the idea of investigating combinations.  This was a bit similar to M who I heard tried some of these things at home and just wasn't interested in enumerating different results.
We took the ability to split 10 and 9 into 3 and looked tried to apply it to the game Dicey Operations.  I envisaged us getting through a few games and being able to talk about how to improve results or get closer to 1000.  Maybe it would have been better to set up a target with results within 100, 200, 300, 400 etc. of 1000 and get them to place their name, avatar or icon  in the place where their score would be.  They could then talk about strategies to get better.  This would make the goal more visual and provide more compelling reasons for kids to try to improve scores.
I managed to get on to our coloured matching nim type game at the end of the second session (as I was able to go over).  I just did an example game.  They will need a few more goes to get it properly I suspect.  Probably should have just started with Nim and left this game until later. Live and learn.

Thursday 30th July - Number bonds and related

Pre task - explore own ability to subitise


Starting Game - adding to 20, 50 etc.
Try as a board game with battleship like set up. explorers split amount of counters into 3 sections and check who has won
Extend by using written sheet and collecting scores to make Leaderboard

Check ability to subitise using different cards like those shown on the right.  See if we can get them to discuss anything they found out or help or coach each other.  See how they think someone might test this skill with a group.

Number Bonds to nine and ten
Using the split 3 way board, how many different ways are there to split 9 into different numbers.  Are there more ways of splitting 10?  How does it change if you can use zero?
How many different ways can you find?  How could you list them?  What is the best arrangement of 9 counters to make it easiest to subitise?  It would be good to carousel this activity but I don't know if that will work.  Need to be ready to organise this in some way.

Dice game - Dicey Operations
Add up to 100 or 1000.  We can use this game by Nrich.  Model this as a competition with two people or anyone else who volunteers.  Throw a dice and put the result in one of the boxes.  Do this 8 more times and get three 3 digit numbers and see what they add up to.  Get explorers to suggest techniques for getting closer to the right number.




Hidato and Beehive Hidato - Consecutive numbers - finding the path
Start this by getting them to take it in turns to place a number.  If we can't go, take back a few steps and try again.  What is the difference in this challenge between the square and hexagonal grids?

Kakuro
This is also a game involving number bonds that explorers can try
I can create a scaffolded example starting with one line etc.

Adding odd and even
What are odd and even numbers?  What happens when you add odd and even numbers?  Can you predict if the answer will be odd or even?

Finding consecutive sums - 
Introduce project to find consecutive sums of different numbers. Tick them off on the sheet.

End game - Coloured matching nim game.  What could be done to help with this game. Elicit too many to subitise.  Try estimating.  How many needed to win different colours.  Add up scores and say first to 50 wins

Organisation - I would like to create a way of tracking progress, ideas or interest.  It could be a small sheet with the activities on them and smiley faces.  It could also be a laminated sheet that people stick stars on or something.  I need to make sure that I record some feedback.
Also getting them to think of next steps for some of their activities would be good.
Th passport idea would be great for these sessions too.
Take home tasks could be linked to the activities in the session and there can be a card to take home with challenges or games and some thing to come back and tell us.

Unfortunately it's 9 tonight and still a few things to get ready for the activities. Much of it may need to wait but it would be great to make some progress with at least one.

Summer session scheme

We are set for two classes each Thursday morning.  There is likely to be different in content as the first class will contain initiates and the second generally those who have not been to the sessions before.

The list of topics that I would like to make available in the later session are:

• Number bonds, negative numbers, place value, dice
• Equality, difference, <, >, unknown values, balancing quantities (inequalities mean easier balancing), consecutive numbers,
• multiplication understanding, Area, primes, factors etc.
• shape properties (number of sides, types of angle, tessalatability, 
• number properties (Square, prime, triangle, consecutive sums
• project-based exhibition at West Norwood Feast Sept 6th - real-projects.org for an overview
• art work representing numbers and relationships between numbers perhaps
• creation of a board, dice or counters game that involves different concepts in maths

write up projects to start week 2

notable omissions are probability and data.  Probability would be important in a game creation so should be squeezed in somewhere

Session Evaluation - 11 July - lines and intersections

The plan for this session was to look at lines and intersections and triangles or other shapes that might be formed.  There was also the plan to do some free exploration but there is rarely time for that. Once passports or whatever tracking mechanism is set up, hopefully that will be easier.
I got a bit caught at the start.  I wasn't sure what starting game to try.  I had in mind trying something with lines and multiplication but didn't have clear enough an idea of how to start it (this is some progress I guess as I would previously have dived in and winged it).  I guess I read the group to a degree and saw that some seemed a bit tired.
We rejigged our nim like game again.  This time we used different colours and set that up to 5 could be taken but only from one colour.  This allowed us to have many winners.  It would be great to keep track of scores.  We could have a standard 100 chips with a set number of the different colours (say 35 yellow, 30 white, 20 blue and 15 red).  It worked really well and gave us a chance to talk about odd and even numbers and look at the arrangements of different numbers of counters.  It also makes us pay attention to each move and update possibilities. For this session, that happened mainly due to my running commentary but it's clear that one or two of them are doing that for themselves.  It would be really good to have groups in pairs so that they could talk through their decisions.  It can be necessary to keep some of them focussed on counting and checking but as we play it more regularly, I'm sure that won't be a problem.
I moved on to look at Kobon triangles after that though not explicitly.  I presented the idea of a line and elicited responses (Ida mentioned diagonal).  I then asked what would happen when I drew another line.  Mel said it would be like a times sign.  I drew the line like that.  I checked if they knew what we called the meeting point and when no one did, I told them it was an intersection but not to worry about the word.  I asked about the next line and I think that most of them thought I would draw it through the intersection that was already there.  I drew it to make a triangle.  I then drew another line to make more triangles.  I asked them how many triangles they could get from four lines and gave out rulers and paper.  They started drawing lines and in a few cases using the rulers but sometimes without.  I noticed that the two working with Geoff got on very well as did Max and Ida who worked independently but with
help from their mum.  I don't think there was enough input from the rest to really know what they needed to do for the activity in terms of how many times to try, how to start an attempt or how to think about different possibilities.  Also, I didn't bring in any review of the task which should have been central to this.  Each line could have been reviewed and we could have had a section in the presentation where we talked about how well a line was placed.

Another thing that I thought about today's session is that it would be good to get more of the younger ones doing what Panny does.  She is so creative with the different games and constantly questioning and trying and setting her own challenges.  She occasionally joins in with us which could be thought about more.  It would be a good path for Elam and Layla if she joins us again.  I could have a box for them and set one or two challenges that they could work on if inspired by them.  And I could try to think of ways to get them involved with one or two things that we are doing.
I moved a few of them on to mystic roses but again this was a missed opportunity because I did not sell the activity at all but passed it on as an extension of the last and just asked them to count the lines.  It would have worked as an introduction to the concept I guess and maybe they will have ideas about what could be done with them next time.
We ended this week with an assortment of games.  Ilora taught the new girls how to play Hex.  Lilly and Nettie have become really good at Hex too. I need to bring more Hex boards and pens with me and have different sized ones.  It would be worth thinking about different ways of playing with hexagonal grids to include perhaps more players or something.  Ida and Hana played Dao which Hana picked up quickly.  Some leaderboards for the different games would be a really good idea.  Each player could have laminated lines for their stats on a game that they arrange on each board.  A two-way table with results of games played each week would also be a nice addition.  I'm not sure where they would fit in space terms but shouldn't be too big an issue.  The impact on the social nature of the group is the real issue to monitor in terms of introducing competition.  Some are far more competitive than others.  It would also be good to have some kind of creativity review each week.  Reviews in general need development.
Another issue to watch is that kids naturally end up running and playing tag of some kind.  It is likely to happen once the sessions finishes but could be a problem for the hotel.  It maybe a need to work on a finishing routine or may not be much that could/should be done.
Handed out the homework activity.  That probably deserves its own
review but for now gratefully received.
Lots to develop for our sessions starting end of July.

4th July - digital roots - evaluation

There was a lot to learn from this session.  We started with a clapping game.  This needs to be developed to include notation of some kind and to be an activity of its own.  I think that it could be to figure out the notation or to remember a sequence or to put a few sequences together in different ways.  Or we could have notes or fractions (or a mix) that can be picked up and ordered to create a new sound.  Maybe bars or rods to represent the length of a note.
Anyway this activity worked mainly because Yunas was not afraid to have a go and get it wrong.  It was a bit too risky for the others.  They warmed up a bit and N was great with the 9 times table.
We explored some patterns for the 9 times table using a 100 square, by writing them in a list, and by finding the digital roots of each multiple of 9.
From here on, H and I were focussed on working out tables and roots and creating root patterns.  N and L floated in and out and became aware of the concept but I don't know if they've mastered it.  L is very quick to come up with

N working diligently on 9x table

digital roots for 2 digit numbers.  Also I think they work best when they can distract themselves.  They focus at times when they get into an activity.  Sometimes I wonder if they would get into more with more focus  or if it is best to leave them to explore what comes up naturally. I should try a complete modelling session next week and get them all to follow steps to see how much of a difference it makes.  This could work with kobon triangles and mystic roses.  Or try the multiplication technique that uses lines.

These activities took us up to the end and to finish up we played a new game using a hundred board, dice and counters.  Explorers throw the dice and choose the score from 1, 2 or 3 of of their dice and move their player.  If they land on a number that isn't in the 7 or 11 times table times, they move back.  These activities worked well
and provided an example of a session where we could work on times tables without too much pressure.

27th June - evaluation

This was one of my favourite sessions.  We had done a similar session a few weeks ago and so tried similar activities.  Also I felt good today.  Sometimes you are just in the mood for dealing with people however adorable they are.  Really useful mood for a teacher.
We started off with a four-in-a-row coordinates game as a reminder of last week.  It was a good start and engaged all of them.  Two teams taking it in turns to place a coordinate and write it down.  L & N won the game but all got into strategic playing and blocking.  And were all clear on coordinates.

We went outside with them for a bit.  I had everyone standing around me.  I said I wanted all of the explorers to stand the same distance away from me as H.  They all then stood near H.  I said they should now spread out but stay the same distance from me.  They tried this and then I used a builders tape to check the distance of them all.  I swung round and corrected those whose lengths weren't right.
The key to this activity is for explorers to realise that the important aspect of a circle is the centre and the radius (didn't use the word)  I asked for the things that make a circle and they came up with the ideas quickly (measure immediately, centre took a little longer).

We then went inside and tried using a pair of compasses.  One of them had a compass and had used it but most had not.  They all got on well but mostly tried to hold too much of the compasses.  We went round and showed them how to hold the end and draw lightly.
They really got into just using the compasses so it was difficult to get there attention and look at different arrangements of circles.  I don't know if it was necessary to do that bit.
Maybe it would have been better to just look at different patterns and then discuss how they were made.  As it was, we looked at the language but didn't get on to the discussion.  Most kids had enough of their own ideas that they wanted to explore.  H had ago at doing a curve stitching pattern for a while but is still a bit shy to ask for help.  She has a really good go at everything though.
She got on well with constructing an perpendicular bisector.  The difficulty is choosing activities that have some meaning for children.  Games and patterns work well.  A goal like winning or building patterns with colours has a lot of meaning as it can be seen, experienced and often looks pretty.  What would be great is to find a way for them to communicate the meaning that it has for them.  It comes out in the discussions a little bit.
Still want to work on the passport idea.  Perhaps launch it after summer.  There should be pages for different countries/topics and in each one record examples of 3 activities from that topic and how the five values have been met.  Just need to figure out how broad the topics will be.
Another tracking measure could be activity led and create players, solvers and leaders of activities.  Maybe create badges for them.
Two more Saturday sessions to go.