Princess of an Alien World

I led the older circle this week. 4 kids attended.

The Activities

1. Topic: Multiplication: Book: Amanda Bean’s Amazing Dream, by Neuschwander. 2. Topic: Proofs: Prove that after every odd number comes an even number. Then prove that even + even = even.

A visual proof that Even + Even = Even

A visual proof that Even + Even = Even

3. Topic: Permutations: You are astronauts who have landed on an alien planet. The aliens do not like you.  However, if you learn their language their feeling will improve. Each alien word is made of 4 letters: ABEK. Every permutation is a legal word. How many alien words can you find?  You start as an enemy. If you learn 9 words, you become a visitor. If you learn 16 words, you’re a friend. 20 = Lord/Lady. 24 = Prince/Princess.

The clip art chart showing how the aliens feel as you learn more alien words.

The clip art chart showing how the aliens feel as you learn more alien words.

A close-up of some of the alien words we discovered.

A close-up of some of the alien words we discovered.

4. Topic: Tesselations: Make a tesselation pattern out of a square.  A tesselation is a shape that can cover a plain with no gaps.  You can make a tesselation pattern piece out of a square by cutting a shape into one side, and taping it to the opposite side. This also works with diamonds and hexagons.

My daughter's pattern piece, made from a square.

My daughter’s pattern piece, made from a square.

My daughter's completed tesselation.

My daughter’s completed tesselation.

How did it go?

This was another review circle where we repeated activities we have done in the last 2 years.  The kids were very excited to see the alien clip art on the wall, and they all remembered (and enjoyed) making tesselations.

The Amanda Bean Multiplication Book

This book is about Amanda who loves to count. She learns in the book that it is important to learn multiplication facts so she can count faster.  All  6 kids in circle go to different schools. One girl’s school is working on multiplication memorization, so at various times during the book she tried to remember a multiplication fact like 8×4. It turns out the other kids are actually faster at counting 8 four times, so I’m not sure if the message of the book was fully convincing 🙂

Even Number Proofs

I started by asking the kids if 2 is even or odd.  They all shouted “Even!”. 3? “Odd!” 4? “Even!”  I got up to about 12 before one girl said, “It’s a pattern! Even then odd!”. I then asked if they could prove that after every even number comes an odd number. I put 2 equal piles of cubes in front of me and said it was an even number. One of the kids then said, “If you add one more cube it will be odd because you can put it in either pile, because they won’t be equal”.  Another kid joined in, “If you add one more, then it will be even again!”. Next I asked them if you add two even numbers is the result even or odd?  They all said even.  I asked them to prove it.  Again I started with an even number of cubes, divided into two equal piles.  Then I gave them another even number of cubes in two equal piles.  One kid then said the result must be even because you can put the same number of cubes in each of the original number’s piles, and you know you can do it because the number is even. I then asked what about odd + odd? A couple kids immediately said odd, but then everyone thought a bit and said even.  We did a couple examples and saw that looked right. However, the kids got a bit restless before they could explain how to prove it.

Alien Permutations

I showed them the clip art chart of alien words. They were very excited by the different pictures and all wanted to get a high alien title, though one kid pointed out that she doesn’t care about princesses 🙂 They all started randomly looking for permutations. As they found new ones, they got to add it to the chart on the wall.  We got to about 21 numbers before it became pretty hard to find new entries.  At that pointed I asked how many they had found that started with A.  We counted and found 4.  There were 6 that started with K, 6 for E and 5 for B.  One kid then said we must be missing 2 that start with A and 1 that starts with B. They started searching for these missing words, and soon found them all!  This was a significant improvement in search strategies from when we last did this activity. At that time they got stuck around 18 or 19.  The kids were all happy to have reached the highest alien title of Prince/Princess.

Tesselations

The kids all remembered tesselations, and were all very impressed by my sample tesselations.  They jumped right in cutting pieces from two sides of their squares. They had to wait a couple minutes while I taped the pieces to the other sides, one by one, but as soon as their patterns were ready they started tracing.  Several kids stayed late so they could start coloring in their tesselations.  This really is a fun activity.

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