session plan 27 June - circles revisited

M & I aren't able to make it today and they were the only ones who explored circles with us at the beginning of the month so it's a chance to revisit.
What are the opportunities?

• Using a compass
• four colour theorem
• finding the centre of a circle (paper folding)
• circular patterns
• fractal patterns (finding the largest circle that can fit in what's left of a shape)
• marking 6 equally spaced points on the circle and then using to create a star or rose or other

I'll start with an outside activity of trying to get everyone the same distance away from me. Then when we correct we should see a circle.

Importance of the centre of a circle - finding the centre.  Choose 3 points and fold paper to make points touch and make lines in paper to show where the centre is.

Highlight radius as an important measure

Introduce compass (centre - point, radius - width)

Circle activity - different configurations

drawing circles to hit three points

End game - find the right path.  Shoot a shuttle through an asteroid field to get to a home planet (this is the idea that will make me late again!) Likely to be to complicated but worth it to experiment.

great blog  with activities and resources

session evaluation - 20th June

As I was on my own, I decided to go with coordinates.
We had a couple of new explorers and Max was back for a brief visit.  We started with introductions and got people to suggest favourite numbers.  I told everyone mine was seven
 It started well and everyone got into the game that used an A-Z like grid with letters on the x axis and numbers on the y-axis.  To start with some of the kids knew how coordinates worked, others picked it up after one or two turns and some continued to think of letters as the square just above them.  It would be good to do that again or leave as a diy activity.
The next directed activity got kids to visualise a number line.  I stood in a position that I called 7 and showed them 10 and then another position and checked what they thought that was.  After a while I asked them to find other numbers such as 20 or 5.  I got someone to find 0.  When we were all lined up I checked what they

thought would happen to the left of zero. Some of them said minus numbers but not all were ready for that.  I went in between zero and one and got responses of 1 and a half and zero and a half most agreed with zero and a half.
We moved on to a number line game that used two dice and had teams compete to get the counter to move to their end.  Green dice moved the counter in a negative direction and blue in a positive.  They played this well and we carried on until a team won.
I tried to move on to a similar game using an x and y axis to combine the two activities that we had done so far.  It needed more instruction and modelling than I think is good for maths explorers so I brought that to an end and got them to explore whatever they wanted.
It was good to see M and I get on with exploring.  They asked for different activities and really just explored so well. I wish I had got a chance to see I work on the tantrix again.  M designed an impressive golf course and lead the activity really well.  He tried a design with lots of holes to start with and realised that it wouldn't work and so changed it.  He also included sandpits that had other features. H had been practising Hex it seems and is now pretty good.  I tried some strategy

with her but that takes some time with Hex. N and L never have a problem finding something to do and this time created snakes and ladders on a whiteboard.  The new explorers struggled a bit more at this time.  It would be good to develop a few intro activities that all new explorers try to induct them into choosing activities at that time.
The golf game was a good ending but I'm not sure how well the waiting for everyone to play goes.
 We could have two different courses in future.  Or maybe the watching others' moves is good.  I think the waiting was a bit too much though.
A development point is definitely the passport and maybe some kind of map of activities. The territories could be strategy, number sense, shape properties, measure, and the main maths explorer qualities.  Or maybe it should work that you get a stamp having showed enough of all 5 qualities for a territory?

Session ideas - date 11 July - lines and curves part 2 - leading to exploring curves

Kobon triangles (from Don Steward's blog)

I think we could start with a game of some kind that involves lines and intersections possibly. A couple of thoughts were kobon triangles or the line

Line multiplication method

multiplication technique.  Any ideas of ways to turn these into a game of some kind?  Or a different type of challenge like create two multiplications that equal 598.  One to think about.

I would like to look at mystic roses and investigate anything from the number of lines (could also do the handshake problem with this) (might be a good time to get out the number properties list too) shapes found inside and centre intersection or centre shape.


Possibly best to put the curve investigation on hold or save it for a time when it can be the sole focus. I think it would be good to have an activity that students could try themselves during exploration but may be better to save this session for another time.
Next session we could extend the last session by creating circles in circles, ellipses in rectangles and other curves.  It might be a good way to introduce parabolas at least in terms of how a thrown object makes an approximation to a parabola and look at the symmetry of it or get kids to extend certain curves.  exponential curves also?  Link to story ideas such as a number of missiles locked onto each other
updating their trajectory each second.  I've not managed to get that frame by frame breakdown working for the kids before but it might be a good opportunity for that.

Ending game?  Golf again?  That game where you take sticks out of a tube where they are holding up a ball would be a good one.  Does anyone have that (long shot. I know)?  I'll try to check a few charity shops.

Some way of recording what explorers are doing would be good to think about too.  I think we need to create some kind of passport and have stamps that can be qualified with different levels or colours?

Look forward to hearing your ideas.

Session evaluation - 13 June

Got in a little late today but just in time for the explorers.  Nettie and Lily's maths-on-toast pelmanism  cards were the first activity which was a really nice intro.  It was such a simple idea but everyone was well engaged.  It got the idea of different operations, number grouping with simple numbers.

 It was really effective in terms of seeing different representations of the same number.  I wonder if we did enough to get kids to see this or what else we could have done.
Moved back to our area which is much cosier but it might be interesting to start branching out a little to see if we can do things in other parts of the space (especially outside.
Started with the place value investigation.  Given a number of blocks and a tens and units column, what numbers can you make.  Got them to colour code numbers on the hundred square.  This really needed more tens and units columns and for kids to work in smaller groups. They were engaged but so few could take part at a time that it got a bit slow for them.  I think if they had been doing it in pairs they could have all been usefully doing stuff.  I think that they naturally link well into pairs for that session.  Ida and Hana, Lily and Nettie (inseparable) Yunas and Max and possibly Panny and Layla (not sure how well that would work but it's worth pushing for some challenges especially if the challenge can be made to "involve" their toys)
I tried to take this on to digital roots but they had not had enough of a chance to "play" with the first part of the activity and so I found it difficult to get anyone inspired to looking at a new thing.  Added to this is the danger that always comes with getting manipulatives out.  Kids own ideas will take over and they'll start building things or working on their own ideas which is great but means that my plans become difficult to implement.  In this case, Lily engaged with sorting all of the blocks out instead of thinking about the idea or activity being presented.
I decided to cut my losses and took everyone to look at Geoff's curve creations.  This worked brilliantly.  They could all be asked to give an observation about it and moved us smoothly into using rulers.  It also worked really well for a ruler use activity.  They got to think about holding the ruler steady and in the correct place and also to think about measuring evenly spaced points on the axis lines.  Very good preparation for graphs as Geoff pointed out.

The key to making the curves is to match a part close to the origin on one axis with a point far from the axis on the other.  Not every one got this and while making mistakes in that would be really useful if the group were asked about what had gone wrong and how to fix it, I didn't do that with everyone.  Still it would be a great way to reintroduce the topic.

Max winning the golf

Getting explorers to colour in the spaces using two colours went well too.  It introduced Hana to the idea (as she had missed the session).  Max chose to use quite a few colours which worked well for him.  Ida really got into the idea and continued working on the board which was great.
We finished up with angle golf using a clockface for direction and cms for distance.  Yunas struggled with the difference between the two numbers he had to give but getting him to point to the number on the clock and then on the ruler was a good strategy.  We should play this more often and find a way to introduce angles in this way.

Session ideas - 13 June - lines and curves

We focussed on using compasses last week so next session, we can try to use rulers to rule straight lines and get compass use in again.
I plan to prepare materials to introduce the idea of digital roots (possibly would work as a starter with the hundred square.

I am not sure exactly what yet but I would like to move from there towards mystic roses of different sizes.  This can be about working with a ruler and also about how many colours you would need to colour regions separately.

That can lead to curve stitching ideas that can be done on paper and can start by introducing circles again but go on to other curves.  I guess we would need templates but maybe we could get them to design a template if we actually had a board and drawing pins.

Lots of ideas that need to be resourced and framed with in challenges, exploration, games and things that might provide meaning for our explorers including hopefully the really young ones.