Math Circle – Oct. 18, 2014

4 girls this time. After finding their seats around the dining table, we started with a simple warmup. Without instructions, the two 5 year olds (who had done this puzzle last year) and the 6 year old (Jody) all figured out what to do. KC gave up quickly and ran to a different room. This prompted the other kids to get up from their seats as well.

Activity 1

Before the other kids could leave the table, I handed two pictures of cars, trucks, bikes, segways, etc. to each kid and asked how many wheels were there in total. The 6 year old was given a picture of a 12 wheeler (!) and a unicycle. Because the picture of the 12 wheeler only showed 6 wheels on one side, she said there were 6 wheels in total. After some help from her mom, she figured out the answer. Apparently, she already knew multiplications. KC came back to the table at this point and demanded her pictures. CC and Abby then proceeded to argue over who gets to go next. A round of rock-paper-sissors ensued without a clear winner (each kid demanded the other to show her hand first…). This resulted in CC fleeing to the other room, crying. After getting everyone settled back again, I decided to move on to the next game.

Activity 2

Earlier in the week, I made a Tower of Hanoi out of cardboard boxes and popsicle sticks for each kid. Below is what my crude models tried to imitate. Despite the flimsiness of my models, the kids mostly figured out what to do and spent some time working on them. KC and CC already saw these towers a few days earlier and knew what to do. Jody also figured out the puzzle with 4 pieces pretty quickly. On a side note, Tower of Hanoi was featured in the movie Rise of the Planet of the Apes. That ape was able to solve the puzzle pretty fast. I guess once the puzzle is solved, there is no where to go but to either work on speed or increase number of rings. When the kids are older, it would be fun to get them to program some solutions.

Activity 3

After everyone had a reasonable chance at working out the solution for 4 rings, we moved onto the final activity – the money and banana activity I described in the previous post. I put 3 monkeys on the table and asked KC how they can share 3 bananas. KC proudly said one each. Then I asked Abby how they can share 6 bananas and CC how they can share 9 bananas. Both kids got the answer right away (who said kindergarteners can’t understand division?). The 6 year old Jody was probably expecting to divide 12 bananas. Instead, I asked her how the monkeys can share 4 bananas equally. She was stumped for a while and her mom came to the rescue. Meanwhile, CC thought the solution she worked out a few days ago was the best and went to hide in a corner to implement her solution. Abby went to take a peek. A period of chaos followed and, for a while, no one was at the table anymore. At last, the parents corralled the kids back to the table. Jody presented her solution** of allocating one banana to each monkey and dividing the 4th banana equally in 1/3’s. CC presented her solution of dividing each banana by 1/3 and allocating the pieces equally. At that point, the kids were done, collected their stickers as reward and ran off to do face painting.

I passed on two challenge questions to the parents:

1. Two sisters arriving on 5 wheels. How?

2. Two moms and two daughters shared 3 bananas. Each had one banana. How come?

**Today, I asked CC whether or not she remembered Jody’s solution for allocating 4 bananas to 3 monkeys. She said yes and, to my surprise, proceeded to explain why she thinks that is a superior solution to hers – fewer divisions, she said. I thought she wasn’t paying attention during math circle, but apparently she was!

Pre-Math Circle Fun

After a long hiatus, we are gearing up for more regular math circle sessions again. This seems particularly necessary now after attending a school council meeting yesterday where the principal stressed how poorly Ontario students are doing in math.

So today, I asked CC and KC a few questions to get warmed up for math circle sessions that will commence this weekend.

1. Biggest

I made the following two shapes with 6 cubes each and asked the kids which one is bigger without defining what I meant by “bigger. Both kids said B is bigger. When asked why, KC came up with some answer that was incomprehensible to me. CC said B is bigger because it has more blocks, but then fact checked and realized that both shapes have the same number of blocks. Nonetheless, she stuck with her original answer of B.

I then added another shape C. Now both kids said C is the biggest. When asked why, KC back tracked and said they are all very large. CC said something to the effect that C has the largest linear dimension. I then asked that if these shapes represent shapes of bedrooms, which one would they prefer. Both kids said C and justified their choice by saying it is the biggest…

2. Monkeys and Bananas

We had some toy monkeys lying around from Bingo Pongo. So I asked a series of questions about monkeys and bananas using the monkeys as props.

A. if there are two monkeys and two bananas, how do the monkeys share the bananas equally. This both kids got right away. CC took two yellow cubes and gave a cube to each monkey.

B. Three monkeys sharing two bananas equally. CC drew two bananas and a line through each. She allocated 1/2 to each monkey, realized that she had one extra piece left over and allocated that piece to herself. I then explained that the monkeys need to be allocated the entirety of the bananas so she gave her piece to one of the monkeys. KC then joined me to represent the other two monkeys to say “no fair, no fair, the other monkey got a bigger piece”. KC really enjoyed playing this part – younger sister syndrome, probably. CC is then stuck for a while, not knowing what to do. Grandma came over and suggested to CC that she should divide the bananas into smaller pieces. So CC divided each banana into 6 pieces by fluke and found that she was able to allocate equal share to each monkey.

C. Four monkeys sharing three bananas. At this point, the kids were getting antsy. So we practiced dividing a piece of paper into halves and quarters by folding instead.

Free Child Nutrition and Cooking Class

The era of free education is upon us. I am hopeful that in about a dozen years or so when my kids are ready for college, they won’t have to actually go! Thereby saving me tens or hundreds of thousands of dollars. 🙂

To better understand how to start them on that path, I started to take free classes online myself. So far, I am amazed at the quality of the classes and the diversity of interesting topics. The first class I took was called Think101 on EdX taught by people from University of Queensland in Australia (I have actually never heard of this university before I took the class, being generally ignorant of schools outside of North America. Now I know it’s located in eastern Australia, has a gorgeous looking campus, and is one of the top universities in Australia). I was blown away by the quality of the class and the range of guest speakers. Where did they get the budget to produce such an amazing class?! Anyway, thanks to this wonderful experience, I am now hooked on MOOCs and signed up for more classes than I can possibly actually take.

Today, I took a class on Child Nutrition and Cooking from Coursera offered by Stanford Medical School. The topics covered are pretty basic for people who already mostly cook and home, read food packaging labels, do a bit of backyard vegetable gardening and are contentious about what they are feeding their families. I consider myself to be somewhat in that category, but I enjoyed watching several episodes of the video lectures nonetheless for several reasons: 1. I am in awe with the lecturer Dr. Maya Adam who appears to have everything (beauty, talent, beautiful kids, a career that she seems passionate in, and a super organized kitchen). 2. The videos are visually appealing. 3. Dr. Adam does cooking demonstrations of a few things I can try with my kids. Overall, I would recommend this class to anyone who doesn’t cook much at home and to those who do but have some free time to marvel at another mother holding her baby in one arm and cracking an egg with one free hand – all with perfect hair and makeup and a gorgeous kitchen behind her.