# Sometimes Math is Like Pulling Teeth

## The Activities

1. Topic: Counting, Addition, Subtraction: Book: Red Riding Hood’s Math Adventure, by Harcourt. This is an interactive book where the kids get to decide how many cookies to give to various fairytale characters. After each page ask:  How many cookies do you have? How many have you given away? How many total cookies were given away, and are left?
2. Topic: Logic: Logic puzzles from “Thinking Skills age 4-6” by Shapiro. Given 4 pictures of things (like pets or houses), and a few clues, figure out which item the clues refer to.  First use the clues in the book.  Then make it a bit harder by giving clues and asking if the kids have enough info:
3. Topic: Logic, Puzzles: Boat problem. You have one boat that can fit 2 items and a group of items that need to cross the river.  Each boat trip must contain at least one person to drive the boat. If a cow and a carrot are left alone on the riverside with no person to watch, the cow will eat the carrot.  How can you get the following groups across:
1. 2 cows and 2 people
2. 1 person, 2 cows and 1 carrot.  (not possible)
3. 2 people, a cow, and a carrot.
4. 1 person, a carrot, a rabbit, a lion

## How did it go?

We had a Saturday math circle this week, with only 3 kids. My daughter had had a very long day before circle, including having one of her teeth pulled at the dentist.

#### Red Riding Hood’s Math Adventure

Each girl got 12 construction paper cookies.  They were red, pink or blue. Kid #1 and #2 picked pink and red, but then my daughter got extremely upset and threw the blue cookies on the ground.  She kept crying so I had to send her away to David.

Each page has a character which asks for cookies. The girls can give 0, 1, or 2 cookies, and characters’ replies change based on the choice.  I asked each time how many cookies each girl had left and they counted successfully.

Then my exhausted daughter came back and took the blue cookies. She gave the next character 6 cookies. This inspired Kid #2 to give all her remaining cookies. The girls enjoyed telling the ‘bad’ characters like the wolf and troll that they got no cookies.

At one point Kid #1 said my daughter sounded like a baby because she was crying so much. So she started crying again.

After the end of the book, I asked if anyone wanted to try counting all the cookies together.  Kids #1 and #2 wanted to.  First Kid #1 counted and laid out all the cookies.  She got 34.  Then Kid #2 counted the laid out cookies and got 36 (interestingly, she did skip and double count some cookies but ultimately got the right answer).

#### Logic Puzzles

There were several groups of objects, for example, 4 frogs, some green, some brown, some with blue spots, some with purple spots.  I gave a couple clues and the kids had to figure out which one matched all the clues.

The kids had no problem with this at all.  They were able to follow clues like “It has purple” or “It cannot fly” and combine the clues to figure out the right answer.

Next I had my own set of clues for the same pictures, and after each clue I asked the girls if they knew the answer yet.  The only confusion was that Kid #2 thought my clues were *in addition* to the old clues.  After I clarified that we were looking for a different person’s pet she understood.

Finally, I used the same pictures but had the girls ask yes/no questions to figure out the pet.  I assumed they would naturally ask yes/no since I had played lots of Guess Who with my daughter.  However, Kid #2’s first question was: “Which one is your pet?”.  I managed to describe yes/no questions to them and then they were able to solve each problem.

Once Kid #2 asked: “Does it have white?” for a set of picture where there was no white and another kid giggled because she saw this.  Another time a kid asked “Is it looking up?” hoping to distinguish between two frogs, but they were both looking up, so she changed her question to “Is it looking up and its mouth is open?”

#### Boat Problem

All 3 girls were able to immediately solve the 2 cows, 2 people problem.

Next they tried 1 person, 2 cows, and 1 carrot, which is actually impossible.  After trying a bunch of different things they started to claim that it couldn’t be done. So I added in another person, and asked if they could do it now.  Kid #1 was able to solve it.

Next was 1 person, a carrot, a rabbit, and a lion. Kid #2 started this one.  She first took the rabbit across.  Then came back to get the carrot, and then was stuck. Kid #1 also got stuck in the same way. Then she started to lose interest, and I said that it was actually possible.  This brought back her interest.

Finally Kid #3 tried.  She first took the rabbit across.  Then got the lion.  Then she said “I’m scared, I don’t want the lion to eat the rabbit!”.  But I said the rabbit was safe as long as the person is there.  Then I suggested she could take out the lion put the rabbit in the boat.  After she did that, she solved the rest of the problem easily.  Kid #1 saw that it would work and said “She’s solving it, yay!”

Then I asked #1 and #2 if they wanted to solve the problem too.  And they both said no.

#### Graphing

This activity is also from Thinking Skills, age 4-6.  The graphing activity involved counting a number of objects and then coloring a bar chart with the number.  The objects were dolls, balls, and trains.  Everyone wanted to do dolls.  So I randomized who went first and it was Kid #3.  She picked dolls.  Kid #1 immediately said she would not do the activity, and stood to the side pouting. Kid #2 also said she wouldn’t do it. Kid #3 counted the dolls and filled in the chart, but the other girls still refused to participate.

I dismissed the circle, and the girls ran upstairs.  There was more drama when my daughter ran to get her new sparkly shoes and Kid #2 said that she had shoes that were even sparklier than that.  She was sad that Kid #2 said this, so I told her to tell her friend that.  She said “It makes me sad when you say your things are more beautiful than mine”.  Kid #2 looked sad at hearing this but did not want to apologize and went off by herself for a little bit.

# Building a Watermelon

## The Activities

1. Topic: Evens and Odds, Division: Book: Splitting the Herd by Harris. The kids will act out the book with the wooden cows we have.
2. Topic: Combinations: Given a chain of 5 circles, how many different ways can you color in zero circles? 1 circle? 2 circles? 4 circles? For example, OXOOX and XXOOO are two ways to color 2 circles out of 5.
3. Topic: Probability: Kids will roll two dice, compute the sum and fill in a box in a chart.  We’ll end up with a 6×6 grid of all possible sums of two dice.
4. Topic: Sequences: Kids arrange the story cards in order.

## How did it go?

#### Splitting the Herd

This is a really fun book that involves Emma’s 10 cows getting into her neighbor Kirby’s pasture and mixing in with his 10 cows.  The two neighbors split the cows into two groups of 10.  The next night 2 cows run into the neighbor’s pasture, and they split them into two groups of 6, and send 6 back home. The kids saw no problem with this.  Then again two cows run over, and they split the 8 cows.  At this point one kid said “But Kirby only has 4 cows!” and the kids agreed this was unfair. Again 2 cows run over, and now there are 5 cows to split, which can’t be done so Kirby and Emma get married.  I didn’t know how to explain why the cow division ended up wrong, so I talked about how Kirby and Emma should have remembered that there were still some cows in Emma’s field.

#### Circle Coloring Combinations

Given a chain of 5 circles, how many ways can you color in zero circles? 1 circle? 2 circles?

3 of the kids had seen this activity at an earlier circle. One of them remembered she had been able to get 8 different colorings.

This was new to the other 2 kids. I started by coloring in one circle in the chain: XOOOO. I asked Kid #1 if he could make a different chain by coloring in one bead, but he colored in the same bead as me.  So I asked another kid, who found a new way: OOXOO. We continued taking turns until the kids had found 5 different ways to color in one circle.  Then I asked Kid #2 to find another, and after awhile she gave up, and I suggested maybe 5 was all of the ways.

Then I gave each kid a sheet with rows of 5 circles on it, and told them to color in two beads in each chain. One kid got 7 different ways, another found 6. One kid got 5 ways…she had trouble because she felt that reflections were the same, for example: XOXOO and OOXOX.

One kid was stuck so I stood by the kid and tried that each row was a chain and we should color two beads in each. The kid colored one in each row, and sometimes seemed to think the chains should be vertical.  The last kid was more interested in playing with puppets after circle and in telling me her plans to color all the circles in different colors when she got home.

Then I gave the kids a new paper and asked them to color 4 beads in each chain. 3 of the kids got 3 or more different colorings.

#### Probability Charts

By now, we’ve done probability race about 5 or 6 times. We decided the kids might be ready to learn *why* some rolls are more common than others (i.e. 7 is the most likely roll).  I made a chart like this:

 1 2 3 4 5 6 1 2 3 4 5 6

The plan was to write the sum of the two dice in the appropriate box.

The kids all remembered probability race, and were happy to roll dice and count the dots.  I showed them how to fill in the chart, but only one kid seemed to understand. We filled in the results of 12 rolls, and then stopped because the kids got restless.

#### Story Sequences

The kids all loved this activity. The only problem was a bit of restlessness during other people’s turns. Also, some of the kids wanted to tell the other kids how to arrange the cards.  For this circle, we used a bunch of story sequences that we found on the internet and printed out.

• Kid #1 had a boy throwing a ball for a dog.  At first she was intimidated because it had 6 cards, but she started organizing them and corrected herself where she was wrong.
•  Kid #2 got a frog growing up from an egg.  She organized them all correctly, but she had the frog with a tail as the last card.  I told the story as she had arranged it and at the last card I said “then the frog grew a tail”.  All the kids said that sounded good, but then I said I would change something.  Kid #1 immediately swapped the adult and the tail frogs.
• Kid #3 had pictures of building a snowman, and then a melted heap of snowman parts.  She put the melted heap first, and said that that was before the snowman was built.  Kid #4 said she’d arrange it differently: her story was: First there’s a snowman, then all it parts disappear, then it gets a face, then it melts (she was not joking).  Then I let Kid #2 have a turn and she organized them as expected with the melted picture last.
• Kid #4 had one with 3 cards: A man with a watermelon, a man with watermelon in half, man and kids eating watermelon.  Kid #4’s story was: 1. watermelon in half. 2. man with whole watermelon 3. eating:  “A man builds a watermelon, then he cuts it and they eat it.”  Kid #1 reorganized in the expected order.
• Kid #5 had: A: A girl with dog pulling her scarf.  B: Girl waving at dog with scarf. C: Boy chasing a dog with scarf. D: Boy giving scarf to girl.  Kid #5 arranged it as D A B C.  Everyone was tired so I ended circle here.

After circle, Kid #5 wanted to show dad the story cards and tell the story. Also several parents told me about their kids wanting to start math circles and playing pretend math circle at preschool.