# The Chaos of Sorting

## The Activities

1. Topic: Money: Book: The Coin Counting Book by Williams.
2. Topic: Sorting: Sort the cards 1 – 104 in 15 minutes

My daughter in the middle of the sorting activity.

3. Topic: Sets: Play ‘Set’ with the Attribute Blocks.  Find a set of 3 shapes that for each attribute are the same or all different. The attributes are color, size, shape, and thickness.

This is a set. Thickness: same, Size: same, Shape: different, Color: different.

Not a set. Color: same Thickness: same Shape: different. Size: this is the problem. two are big but one is small.

4. Topic: Numbers and Counting: Make decimal and Egyptian numbers out of the Base Ten Blocks unit blocks. For example, I say make 237, and the kids should grab 2 hundred squares, 3 ten bars and 7 unit cubes.  Or I show a number written in Hieroglyphics and the kids make it out of blocks.

## Preparation

This was an easy circle to prepare.  For the sorting activity we used the cards from the card game Category 5.  We printed out simplified heiroglyphic numbers.

## How did it go?

We had 5 kids at circle this week.

#### Sorting

We’ve done sorting several times before, and it is always fascinating to watch.  Last week we had the 3 parents do this same activity, and the kids watched, hopefully learning some strategies from watching the parents.

I shuffled up the deck of 104 cards, and hand a stack to each kid. Then I say ‘Go!’, and watch what happens.  This time one of the kids started telling the others to sort the cards into a separate pile per decade (i.e. 20s in one pile, 30s in another). This is how the parents solved this problem last week.

At first the kids each sorted into their own separate piles, but eventually 3 of the kids started working together. Then one kid took the #s 1 – 10 to lay out on the floor but didn’t tell anyone else, so the other kids were shouting “Where are the low numbers?” The kids used their decade piles to lay out the 30s, 40s, and 50s, but by then the remaining cards had gotten mixed together.  All the kids then grabbed their own random pile of cards, and progress really slowed down.

They got to 75 before the timer beeped and then they begged to keep going.  At this point 2 kids were holding the last 30 cards, and they were giving them out one by one. One of the other kids started laying out each card approximately where it should go, even if it left a gap. This sped everything up dramatically, and they finished all 104 in 4 extra minutes.

#### Attribute Block Set

At first, the kids didn’t quite understand what they were supposed to do.  As soon as you see a ‘Set’ of three shapes you call out ‘Set!’ and pick them up. We started playing a round, and two of the kids got 5 sets, while the others got 2, 3, and 3. By the end of the round everyone understood, and wanted to play another round. This time it was more even: 5, 3, 3, 3, 3.

#### Big Numbers

First I called out the number ‘782’.  All the kids immediately gathered together 7 hundred squares, 8 ten bars and 2 unit blocks.  Next I showed them the Egyptian number chart, and asked them to make an Egyptian number out of Base Ten Blocks.  All the kids quickly did this, and when I asked them the English name of the number they were able to answer ‘576’. The Egyptian numbers are fun to work with because they are pretty pictures, and it’s a different way of representing numbers.

# The Infamous Easter Goblin

## The Activities

Today we had an Easter-themed Math Circle!

1. Topic: Probability: Book: Probably Pistachio by Murphy
2. Topic: Logic: There’s a beautiful egg hidden behind a door numbered 1 – 36. The kids get 10 guesses to find the egg, or else the Easter Goblin gets it. They can ask yes/no questions like: Is it higher than 10?
3. Topic: Combinations: You have a row of 5 Easter eggs. How many different ways can you color 3 out of 5 eggs. i.e. you could color the first 3, or the first 2 + the last one.
4. Topic: Addition: Draw 3 plastic Easter eggs out of a bag. Each egg contains a one or two digit number. Add the numbers together, and the kid with the highest number wins the round.

## Preparation

For the Easter Goblin activity, I colored a few cute paper Easter eggs that the kids would want to save from the silly Easter Goblin (a clipart female goblin).  We printed out a bunch of sheets with 5 egg-shaped ovals on them for the combinations activity.  For the easter egg addition, I used all the left-over plastic easter egg shells, and filled each with a number on a scrap of paper, instead of candy.

## How did it go?

We had 4 kids this week.

#### Easter Goblin

First the kids got 10 questions to find the hidden egg, hidden behind a door numbered 1 – 36. The first kid asked if it was in a door higher than 14. ‘No.’ The next kid asked if it was in a door less than 5.  ‘No.’  The 3rd kid asked if it was number 9.  ‘No.’ The first two kids immediately groaned and said it was not a good question.  I asked why, and they said it’s because it only crossed off one number.  One kid observed that you should ask something more in the middle. Then the 4th kid asked if it was in door number 7.  The first 2 kids again groaned. 🙂

The kids loooved this game, and kept begging for more rounds, but I moved on to the next activity after 4 rounds.

#### Combinations

We did a variation of this activity with the kids a long time ago, and they were not very good at it. This time they had much better strategies. Kid #1 jumped to the lead quickly finding 6 ways to color 3 out of 5 eggs. Kid #2 was right behind.  One strategy #1 and #2 used was to reverse each novel pattern they found, so they would get two at a time.

Kid #2 then moved to the lead, finding a 7th way. This annoyed Kid #1, who sat on the floor for the rest of the activity, making very little progress, but not bothering anyone. Suddenly Kid #3 found a new pattern and had 9 different ways. Kid #4 was just trying all different things, without worrying if some of the patterns were repeats.

Finally Kid #3 found the 10th and last way. Then we compared the other kids papers to find the ones they had missed.  It turned out that Kid #4 unknowingly actually had all 10 patterns among the 26 rows they had colored.

The numbers in the eggs ranged from 1 – 45, with more 1-10 than others. The kids really enjoyed drawing out eggs and opening them to see the numbers. They could tell right away who had won a round because they’d see someone with a 45 or something, but they were still willing to add their own numbers. I let them use  Base Ten Blocks, and they were all pretty good.

# My Daddy Has Twice As Much Money As That!

## The Activities

2. Topic: Sorting: As a group, sort 103 numbered cards in 15 minutes.
3. Topic: Money: Find all the ways to make 1 cent, 5 cents, 10 cents, and 25 cents.
4. Topic: Puzzles: Towers of Hanoi: Work on 4, 5, 6 disc puzzles.  The object is to move all the discs to the rod at the other end, but you can only move one disc at a time, and cannot put a larger disc on top of a smaller one.

A 4-disc Tower of Hanoi puzzle.Sort 103 numbered cards in 15 minutes. This time the kids only sorted 60 cards.

## Preparation

For the money activity, I had a bag of cleaned up coins of various denominations.

Somewhere online I found super-cheap Towers of Hanoi puzzles (~\$4 each), so I bought 6 so each kid could use their own.

## How did it go?

We had 5 kids at this circle.

#### Sorting

This is really a fascinating activity and I have very interesting video of the kids working on this.  This time I gave the kids a few minutes to strategize before starting, but they didn’t want to talk at all.

3 of the kids spread all their cards out face up on the ground. But Kid #4 and Kid #5 held on to their cards.  They quickly laid out cards 1- 25. But then the first 3 kids got bored while waiting for Kid #4 and #5 to find cards in their hands.  So Kids 1-3 started picking random cards.  This slowed the group down drastically.  The problem is that the kids page throught cards in their hands one at a time, without sorting them at all, so it takes forever.

Kid #3 actually sorted the cards ina pile for 40s, 50s, and 60s, but didn’t pay attention to the other kids, so missed it when they called for 40s.

They ended up sorting 60 cards in 15 minutes, which is worse than the last time they did this.  I asked them why they did worse this week. They had no insights.  Then I asked if there were times when they went faster or slower today.  Kid #4 said they went fast in the 30s and I asked why. She said because there were more of them. I said “are there?” and she said no.  I pointed out that they had going faster in the beginning when cards were on the floor.

#### Money

There was a lot of excitement when I brought out a bag of coins.  Several kids said basically “My daddy has twice as much money as that!”  They all grabbed a big pile of coins and starting stacking, sorting and talking. After a bit of this, I brought out a money chart where I had taped each denomination on a paper and written the name and amount of each.  Several kids said they wanted to make a chart like that.

The kids quickly saw there is only one way to make 1 cent.  They also got 2 ways for 5 right away. 10 cents took a bit longer, and 25 cents was hardest. Several of the kids would drift off into their own world and not suggest any ways to make 25, unless I explicitly asked them.

#### Towers Of Hanoi

The kids were excited to see the Towers again, especially Kid #1 who had begged her parents to buy her a Towers of Hanoi app so she could practice. Kid #1 easily finished 5,6,7,8 discs. I *think* all the moves were legal, but I wasn’t watching too closely.

Kid #2 did 4 and 5 discs easily, but got really frustrated on 6. It didn’t help that Kid #3 kept pointing out that Kid #1 was doing more discs than Kid #2.

Kid #3 – 5 solved 4 discs, and worked hard to get 5.