Online Circle 4: combinations and Dienes shapes

January 4 2021, 9:00-9:30am. Nia (5), Dil (5) and Gye (5)

I tried to do a fun activity at first, then we repeated the Dienes shapes one from the week before.

Task 1: Socks in the dark

Supplies: Blocks in three different colors and an opaque bag. 

What to do: I told the story that our monster (one with two feet from previous activities) keeps all its socks in a bag in a dark basement. Of course, monsters don't roll them in matching pairs, they just throw them in the bag. It is their task to go and pull out as many socks as they need to have matching socks for the monster. Beware, monsters get VERY angry when they don't have matching socks.
- I showed them a pair of yellow cubes (standing for socks) and a pair of red cubes, then put them in the bag. 
- I asked the kids to pull out socks and figure out the number of socks they have to pull out to guarantee that they have a match for the monster. 
- We did the same for a monster with 4 feet.  

Task 2: Dienes shapes (repeat)

Supplies: Attribute blocks (I call them Dienes block because that's what the book I read called them) 
The set of attribute blocks in the picture below takes an inordinate amount of time to make. It is much faster to print the pdf file and cut it rather than making the shapes themselves. You can also search "attribute blocks" online and buy a set. 

What to do: Explain that each object has four attributes: 
size: large or small
color: red, blue, yellow, or green
shape: triangle, square, circle
with a hole or not (plain or patterned for the ones in the file)

Take an object at random to start and invite the kids to select one that has three common attributes with the first one - it is easier if they name the common attributes. Alternatively, if the child is having trouble, select one with three common attributes and invite the child so say what the two objects have in common. Long chains can be build where one object has three of the same attributes as the previous one. 

How it went

The kids had a lot of fun with the first task. They started pulling two blocks out of the bag – sometimes, they would get a match and of course, sometimes not. I try to get them to tell me why they needed to get 3 socks out to guarantee a match. It didn’t work. I then explained that 3 is the number because, the worst case scenario would be one sock of each color so a third one would definitely match one of the first two.

Then we tried with three pairs of socks and the kids were just pulling two at a time to see if they had a match. At some point, one of them wanted to do the snail (one foot) and they all started clamoring for it. So we put socks in a bag and I asked “how many socks do we need to take out to have a match?” And everyone said “ONE!”. They found it very funny.

For the four-footed monster, the kids again did pull out four socks just to see if they had all four of the same color. Of course, it didn’t happen. They didn’t really try to take out more than 4 socks.

The Dienes shape activity went better than last time. Gye and Nia could give me a shape with three attributes in common with the one I was holding. But Nia was getting quite bored with the activity. I am not sure Dil understood the game. I then showed her two shapes that shared three attributes and asked her to name the three things they had in common and she did it without problem.

This week was more successful. It was fun for me and the kids. It is not hard to find activities but I sometimes, I question how useful math clubs really are. I wanted to raise kids who think of math as games and solving puzzles. And Nia is half of the time bored or not on task. But at dinner that day, dad asked Nia what she did in math club then put 5 pairs of socks in a bag. He then asked how many he has to take out to have a match, Nia answered 6 correctly. When he prompted her to explain, she said that she could pull one of each color and the sixth one would match one of those. So enough self-absorption from my part because that’s the thing with little kids, they do listen even though they look like they are doing something else.

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