# Math for Two

## The Activities

1. Topic: Scale. Book: Cut Down To Size At High Noon by Geehan. This is a very silly and entertaining book about hairdressers in the Wild West who cut hair to look like scale models of real things (like stagecoaches or fiddles).

2. Topic: Scale. Give each kid a simple line drawing on graph paper, and ask them to double the drawing.

Some of the drawings we doubled.

My daughter doubles a picture.

3. Topic: Sorting, Teamwork. The two kids tried to sort cards with the numbers 1 – 104 on them. This time I took 5 cards out of the deck before I gave it to them. The previous recod time for this is 13:34.

4. Topic: Partial Ordering, Graphs. Draw a diagram representing the building order for a structure made of blocks. ‘B’ in a box represents the start of the building, and ‘E’ is the end.

To build this structure, you must first put down block 1, then 3, 4, and 2.

Here you can build 6, 7, or 8. After those, you can build 2 or 3.

## How did it go?

This week we ended up having only 2 kids.  The other 3 cancelled in the hours leading up to circle.  It was a nice change having such a small circle, and both kids were pretty focused and engaged throughout.

This week’s lesson plan was based directly on one of the lessons from Math for Three to Seven, by Zvorkin.  I highly recommend that book if you want to start your own circle.

#### Scale Drawing

Kid #2 really enjoyed this one, and was able to double the drawings without any help from me.  My daughter had a harder time on this, especially if the drawing involved diagonal lines.  Her other problem was that she drew a box around the area she wanted to draw on, and then would get upset if her figure didn’t fit in the box.

#### Sorting

The kids saw the sorting cards and were pretty excited to try it again. They thought that it would be harder with only two people.  I made them discuss strategy before they started. Kid #2 suggested they would each hold the cards in their hands and page through the cards to find the next one.  I said I thought that would be pretty slow (that has historically been the worst strategy).  Kid #1 then suggested putting all the cards down on the floor to find the next number.  Then Kid #2 said they could put each card where it belonged, and leave space for the gaps. They both agreed to use that strategy, especially since they knew some cards were missing from the deck this time.

I started the timer, and they started going really fast.  Kid #2 was especially quick, racing back and forth to put her numbers down. Kid #1 sat at the low end of the numbers and paged through hers, laying down all low numbers in order.  Kid #1 was much less willing to move around to put down the high numbers.

As time went on, they started having problems because there was not enough space for some of the number ranges.  Kid #2 spent a lot of time scooting the cards down, and Kid #1 spent a lot of time complaining that there was not space.

Eventually they finished the sort, taking just 12 min and 30 sec, which was a new record for this math circle!  It really helped this time that they stuck to a single strategy the whole time and didn’t get in each others’ way.

#### Partial Ordering Graphs

Both kids enjoyed this activity.  First I showed them a simple structure, and how to make a graph for it.  Then we worked on a more complex one.  After that, the kids started building their own structures and making graphs, or having me draw graphs of their structures.  It was also a fun challenge to take a graph and try to build a structure.  We’ll definitely have to do this again.