# Tricky Towers (Age 6)

## The Activities

1. Topic: Time: Book:  At The Same Moment, Around The World by C. Perrin.  After we read the book, I asked the kids for different places they had visited and we figured out what time it was there.  Also I asked why sleeping was more difficult after a long trip.
2. Topic: Probability:  We did probability charts with two six-sided dice.  Each kid had a chart, and repeatedly rolled the dice and filled in a box (from bottom to top) for that number.  Once one of the numbers gets to the top (5 rolls) that number “wins”.  Most of the kids did 2-3 charts, and then we checked to see what numbers had won most often.
3. Topic: Puzzles: Each kid got a Tower of Hanoi set, and they tried to solve as many discs as they could.

## How Did It Go?

We had four kids this week.  The kids were all very engaged the whole time.

#### At The Same Moment

The kids got the idea of the book and liked naming the places they had been.  All of them have been on very long trips so the idea of time zones and figuring out the time in another place was pretty natural for them.  They were also quite familiar with jet lag, particularly the ones who had gone halfway around the world.

#### Probability Charts

This is always a popular activity and this week was no exception.  One of the kids immediately asked why there was a 13 and 14.  The kids went at wildly different speeds — in the 20 minutes we did this activity, one kid finished 4 and another finished only 1.  The kids are pretty good at adding up the dice now, but some still need to think a bit for the bigger numbers.  At one point, one kid noted that someone else’s chart looked like a pyramid (which is exactly what it looks like “in expectation”).  As expected, we had lots of charts with 6, 7, and 8 winning; I asked them why and they didn’t have a good answer.  One kid noticed that a different kid had two winning charts with “8”, so I asked whether it mattered who rolled the dice.  The kid said “I don’t know” and then “I don’t think so?”

#### Tower of Hanoi

The kids really made a lot of progress during circle.  Two of them started with 5, solved 6 without too much trouble; one of them finished 7 by the end of circle while the other almost did.  Another kid started with 4, and after getting the hang of it solved up to 6.  The final kid had a lot of trouble with 4, so I helped them with 3, then 4, and they were able to solve 5 by the end of circle.  They all worked hard solving the problems and were clearly getting the idea of moving piles in order to clear up the discs they needed to move.

# Trick or Treat Math (Age 6)

## The Activities

1. Topic: Counting. Book: How Many Donkeys? An Arabic Counting Tale, by MacDonald. In this simple book a man can’t figure out if he has 9 or 10 donkeys because he keeps forgetting to count the donkey he is riding. The kids caught on quickly and laughed whenever he got it wrong.
2. Topic: Maps, Spatial Reasoning, Logic: Fill in a map of a treat-or-treating neighborhood based on the following clues. Here is the clipart we used: halloweencharacters.
1. Directly to the West of your house is the Witch’s house.
2. The Zombie house is 2 houses West of the Witch’s house.
3. Olaf’s house is across the street from the Zombie’s house.
4. Elsa’s house is directly South of the Witch’s house.
5. The pumpkin house is directly East of your house.
6. The Spider house is on the very West end of the South side of the street.
7. The Butterfly is scared of the Spider. The Butterfly’s house is on the same side of the street as the Spider’s, but as far away as possible.
8. The Goblin is between the Zombie and the Witch.
9. The skeleton is directly across the street from the Spider.
10. Next to Elsa’s house is a Graveyard that takes up two houses.
11. The Ladybug’s house is right next to the Butterfly’s.
12. The Fairy can fly right across the street to the Ladybug’s house.
13. The Wizard’s house is East of the Fairy’s.
14. Anna’s house is next to Elsa’s house.

The completed puzzle

3. Topic: Estimation, Subtraction. Guess how much candy is in a container. Then put the same candy in a shallower container and guess again. Then count the candy and figure out whose guesses were the closest.

The Candy

4. Topic: Logic. Tape a Halloween character to each kid’s head. Then the kids ask each other yes/no questions to figure out who they are. The hardest part of the game is not telling your friends what is written on their heads.

## How did it go?

I wore my witch costume during circle, and I organized it so the kids would get to ‘trick or treat’ after completing each activity from my bucket of small prizes and candy.

#### Halloween Logic

Each clue was pretty easy for kids, especially after they understood what phrases like “directly West” means. The hardest clue was: “The Spider house is on the very West end of the South side of the street.” Two of the kids figured it out on their own. The other two needed some help from their friends to understand the “south side of the street”.

#### Candy Estimation

The kids were very excited to see so much candy, especially when I told them that the person who guesses closest would get to trick or treat twice after the activity. Interestingly, the guesses did not get closer after I spread out the candy. Most second guesses were at least as wrong as the first guess. I guessed after the candy was spread out (and I got within 2 of the correct number).

After everyone wrote down their guesses I asked the kids to count the candy. They immediately began discussing counting strategies. They eventually decided to sort the candy by type and then count each type. However, they soon realized that some types had too many pieces to be easily counted, and they didn’t know how to add the results anyway. So they switched to counting each piece of candy as it was thrown back into the tub. Two kids both wanted to throw in candy and everyone ended up missing a bunch of pieces when the two throwers could not coordinate. They came up with 67 pieces, but I counted it again and found 72 pieces.

#### Halloween Twenty Questions

The kids loved seeing costumes taped to their friends’ heads, especially when one boy got ‘Princess Leia’. I told them at the start that it is very important not to tell your friends what is written on their heads, and the kids did pretty well at this. However, some kids asked questions like “Am I a zombie?” because they saw “Zombie” on their friend’s head. The hardest to get turned out to be superman. The kid knew he was a strong hero who wears red and blue, and has an S, and has a cape, but couldn’t think of superman.  Everyone else figured theirs out eventually (with some hints from me about what questions to ask). Everyone really enjoyed this activity. At the end, we had five minutes left so one of the kids moms played and had to figure out she was a pumpkin. The kids loved hearing her questions and shouting out answers. “Can you eat me?” “Yes, but it’s yucky and too chewy!”

# Impossible Flips (Age 6)

## The Activities

1. Topic: Puzzles:  Book: Taro Gomi’s Playful Puzzles for Little Hands.  Still haven’t quite finished, this time it was mostly mazes.
2. Topics: Number Line, Number Recognition.  We revisited higher/lower number guessing again, mostly from 1-100.  As usual, the theme of the game was a bear who wants to steal our picnic food.  But the bear print-out was missing so kids took turns standing next to the wall and using their finger as the bear.  I did a few numbers, and then each kid took turns thinking of their own number.  At the end, we had a discussion about what makes a good or bad guess, and then I did one from 1-1000.
3. Topics: Combinatorics, Geometry:  Using wooden pattern blocks, find as many ways as possible to make a 2×2 diamond.
4.  Topic: Logic:  We did the Seven Flipped activity from youcubed.org.  Starting with 7 shapes face-down (we used Scrabble tiles), you could flip 3 tiles at a time.  The goal is to flip all the tiles face up.  After they solved that, I switched to 7 tiles, flip 4 at a time (which is impossible) and then 5 tiles flip 2 (also impossible), and we discussed why it might be impossible.

## How Did It Go?

We had all five kids this week.

#### Number Guessing

There is a very wide range of abilities in this game.  By the end, three of the kids completely understood how the game worked, and during the discussion two of them worked together to figure out that they should guess half-way in between each time.  One of the other kids usually made proper guesses, but the final kid frequently made guesses outside of the current range (even when they were just reminded of what the current range was).  I also made a couple “illegal” guesses when I was playing, but was called out on it.  1-1000 is still pretty challenging even for the kids that get it.

#### Diamond Variants

The kids weren’t as in to this activity as I expected.  A couple of them went off task pretty quickly, building whatever they felt like.  One kid tried hard to use the skinny white diamonds, which doesn’t work.  Another kid was trying but kept building diamonds that were 3 units on the side.  One kid tried for a while to use squares, without success, but then eventually figured out a key insight for building different diamonds, which is that you can swap two adjacent triangles for a diamond, or vice-versa.  So that kid generated more than half of the variants we found.

#### Seven Flipped

The kids each had their own set of tiles.  There was lots of cheating, but it didn’t matter because I would just ask them to show me again.  At first the kids decided it wasn’t possible, but after a few minutes one of the kids figured it out.  Another kid watched them demonstrate, and then the two of them taught the other three.  Then I switched to 7/4.  There were lots and lots of claims of having done it, but it’s impossible :).  After a while, I asked them to try 5/2 instead.  A couple of the kids started to get the idea that it was impossible.  I myself made a bunch of moves on this problem with the kids watching, and we kept track of how many were face up.  With a hint the kids noticed is was only 0, 2, and 4.  I made a set of maybe 11 tiles with 6 flipped up, and then showed them all the possible moves (2 down -> 2 up, 2 up -> 2 down, and 1 up, 1 down -> 1 down, 1 up), and they saw that it could only be +2, -2, or 0.  One or two of the kids might have understood this proof that 5/2 is impossible.

# Taking a Finger Walk (Age 6)

## The Activities

1. Topic: Puzzles: Book: Taro Gomi’s Playful Puzzles for Little Hands.  We’re most of the way through now, probably one circle left of puzzles.
2. Topic: Logic: I printed sheets with 6 uncolored flowers on one side, and 9 on the other.  There were two puzzles: For 6 flowers, “There are more red flowers than purple, and more yellow flowers than red.  For 9 flowers, “There are more red flowers than purple, more blue than red, and the same number of blue and yellow.”
3. Topic: Spatial Reasoning:  Corey and I built a number of models out of Legos.  The kids each picked a model and had to copy it exactly.  They could pick it up and look at it from any angle.  Each kid copied several models.
4. Topic: Attributes, Games:  We played a couple rounds of Set with just the solid cards.

## How Did It Go?

We had four kids this week.  One kid had been gone for a couple months, but now everyone is back from summer trips.  This circle went well, the kids were all interested in all the activities.

#### Playful Puzzles

We spent quite a bit of time on a puzzle with two kids at either end of a very windy path, with the question “Where will they meet?”  We measured by placing coins from either end.  They also enjoyed a page where you were supposed to “take a walk” with your finger by tracing a path and following various instructions along the way (e.g., “Take a rest here” or “Go around this corner really fast”).  Every kid did it once.

#### Flower Logic

The kids figured out the answers pretty quickly.  Interestingly, different kids figured out the second one from the first.

#### Lego Models

Different kids definitely had different skill levels on this one.  One kid breezed through a whole bunch, while others took quite a bit longer.  The trickiest ones were the dinosaur, because it was irregular and a bit complicated internally, and an offset colored square because it was tricky to get the right pattern of blocks on the bottom row (the kid working on it initially had the colors going the inverse rotation).

#### Set

We’ve played before with this circle, which the kids remembered, but not all kids remembered the rules.  Our son has played a lot, so after he got a few I said he had to let other kids get sets.  I was happy because all the other kids got at least one set on their own.

# Birthday Treasure Hunt (Age 6)

## The Activities

1. Topic: Multiplication. Book: Too Many Kangaroo Things To Do, by Murphy. This book is about friends planning a surprise party for Kangaroo, using multiplication along the way. The kids all enjoyed the book, taking turns computing the simple multiplication (1×1 up to 4×4). One kid proudly predicted that the animals must be planning a surprise party.
2. Topic: Various, Story Problems. I made a grid of hexes that were hidden at first. The goal was to find the hex with a diamond printed on it. Each turn the kids got to move their piece to uncover a new hex and then solve a different type of math problem for each picture type. Here are the hex pictures you need, and the full list of problems is below. We worked as one team, and I asked each kid to try each problem. If someone solved it faster than the others, then they were supposed to whisper the answer in my ear instead of shout it out. As soon as the jewel was uncovered, all 4 kids got to pick a prize from our treasure box.
1.  Firefly – square numbers:
1. First square bigger than 0.
2. First square bigger than 5.
3. First square bigger than 10.
4. First square bigger than 20.
5. First square bigger than 30.
6. First square bigger than 40.
7. First square bigger than 50.
8. First square bigger than 60.
9. First square bigger than 70.
2. Unicorn – fractions:
1. Divide a circle in half, then split each piece into 3 pieces.  How many pieces do you have?
2. Divide a circle in half, then split each piece in half, then split each piece in half. How many pieces do you have?
3. Divide a circle in four pieces. Then split each piece in 3 pieces. How many pieces do you have?
4. Divide a circle in half. Then split each piece into 3. Then split each piece into 2. How many pieces do you have?
3.  Dragon – money:
1. A diamond ring costs \$100. How many rings can Hans buy with \$125?
2. Diamond earrings cost \$20. How many earrings can Olaf buy with \$207?
3. A diamond necklace costs \$11. How many necklaces can Marshmallow buy with \$110?
4. Elsa bought 20 diamond rings that each cost \$10. How much money did Elsa spend?
5. Sven bought 4 bracelets that each cost \$32, and 3 rings that each cost \$14. How much money did Sven spend?
6. Anna spent \$60 on 5 necklaces. How much did each necklace cost?
7. Hans spent \$39 on 3 bracelets. How much did each bracelet cost?
4. Troll – story problems:
1. A troll had 12 muffins. He ate some of them. Now he has 7 muffins. How many did he eat?
2. There are 20 muffins. Some trolls came. Each troll ate 4 muffins. How many trolls are there?
3. 4 trolls brought muffins to a party. Each brought the same amount. There are 24 muffins at the party. How many did each troll bring?
5. Witch square – codes: Figure out what the coded word is by subtracting the given number from each letter. For example, DBU -1 = CAT
1. -1:  DBU
2. -2: DTQQO
3. -1: QPJTPO
4. -2: JCV
5. -1: TQFMM
6. Maze – patterns:
1.  1 5 9 13 __   __
2.  1 2 2 3 3 3 4  __  __  __  __
3. 91 82 73 64 __   __   __
4. 11 22 33 __  __  __  __
5. 1 1 2 3 5 8 __  __  __
6. 1 2 4 8 __  __

## How did it go?

We had four kids today and they were all very motivated by wanting to earn a prize in honor of my son’s upcoming birthday. We played the game with 37 hexes, and the kids got unlucky and didn’t find the jewel until they had uncovered 30 hexes. Toward the end I started letting them move 2, 3, or 4 hexes without solving the problems, just to make sure we found the jewel.

All four kids worked hard on the game questions. My son is quite far ahead of his age in calculation and story problems but he did a really good job not telling the other kids the answers. The other kids stayed involved though, and we made sure to work out each answer as a group, using Base Ten blocks or counting on our fingers if necessary. One kid got bored after 30 minutes but didn’t distract the others. Another kid especially enjoyed problems the required counting by 4, 20, or 11. At first he didn’t think he could count by 11s, but quickly he saw the pattern and took the lead.

The fourth kid is the least comfortable with the number line but he got really excited by square numbers and solved all three square problems before anyone else (smallest square above 0, smallest square above 5,  smallest square above 10). We used Base Ten Blocks to do this. I showed the kids how 9 is a square number because you can make a square out of 9 unit cubes, and he then spent some time making other squares out of unit cubes. He also solved this pattern: 1, 2, 2, 3, 3, 3, 4, _, _, _, _ first.

Everyone enjoyed decoding the witch’s code and trying to sound out the trickier words…pasta? pesto? poh-aye-son? Ooohhhh: poison!

The unicorn fraction problems turned out to be tricky. All the kids could follow the instruction: draw a circle and divide it in half. But “Now divide each piece into three pieces” was tricky. Only my son figured out how to divide each half into three equal pieces. The other kids ended up drawing straight lines and getting three very uneven pieces. Most kids also forgot to divide *each* half, so they would get ‘4’ as the answer instead of 6.

We finally uncovered the jewel, and celebrated. Then everyone picked a prize and ran around outside to get rid of their pent up energy. A very successful circle!

# A Pride of Fish? (Age 6)

## The Activities

1. Topic: Comparisons: Book: Too Tall Tina by D. Merritt.
2. Topic: Measurement: I gave each kid a 12″ ruler and asked them to look around the first floor for something 3″ long.  Then I asked 6″, 11″, and 1″.
3. Topic: Verbal Discussions: I asked the kids a bunch of questions about what you call groups of things: cows (herd); sheep, birds (flock); wolves (pack); flowers (bouquet, bunch, garden); fish (school); geese (gaggle); cats (?); ants (colony); bees (hive, swarm); lions (pride); people (crowd); whales (pod); witches (coven); rabbits (warren); thieves, robbers, musicians (band); soccer players (team); dancers (troupe, company); soldiers (troop, army, legion); girl/boy scouts (troop); kittens, puppies (litter); math students (circle); cards (deck, pack); grapes, bananas (bunch); books (shelf, stack, library); wheat (field); hay (bale); knives (rack); ships (fleet); stars (galaxy, cluster, universe); planets (solar system); sailors (crew); actors (cast).
4. Topics: Logic, Numbers: I did an activity from  Math Logic & Word Problems, Gr. 1-2, Guess Benny’s Number and Guess Jenny’s Number.  Each had a series of clues that narrowed down to a single number.  We used a 100 Number Board to keep track of which numbers were eliminated.The first puzzle was
1. The number has two digits.
2. Both digits are greater than or equal to 5.
3. The tens digit is greater than the ones digit.
4. The sum of the digits is 12.

The second puzzle was

1. The number has two digits.
2. Both digits are less than 8.
3. The ones digit is greater than the tens digit.
4. The sum of the digits is 10.
5. The number is even.
5. Topics: Counting, Games:  Using the 100 board again, we played the following game.  Each turn, a kid rolled a six-sided die.  They could then advance that number of spaces up to 10 times (so if they rolled a 5, they could advance 0, 5, 10, …, 45, 50).  The goal was to get to 100.  The first time they started at 0, but the second time I had them start at 1 since it’s more interesting.

## How Did It Go?

We had three kids this week.

#### Too Tall Tina

Not much math in this book, but loosely ties into the next activity.

#### Finding Objects

Some of the kids needed some help measuring at first.  One of the kids spent a lot of time measuring different parts of their mom’s body.  They were pretty excited when they found matching things.

#### Groups

The kids weren’t able to think of many of them — e.g., for cows, they only knew herd once I told them.  One of the few that they did get was bees, where our son got both “hive” and “swarm” right away — which is pretty funny, because he’s rather afraid of bees.  They also got band of musicians, circle of math students, pack and deck of cards, and solar system of planets.  One kid guessed “pride” for fish, and then when we got to lions realized that it actually went with lions.  For stars, with some help one of the kids thought of pictures in the sky, but couldn’t remember the word constellation.

#### Guess Jenny’s Number

This activity was kind of hard for them.  First, they weren’t that familiar with the concept of ones and tens digit.  Second, it’s pretty tricky that you need to cover all the squares that DON’T match.  They kept trying, though, and with some help, they were able to do it.  One neat thing is you get some nice patterns along the way.  Our 8-year-old daughter worked on one of them after circle, and it wasn’t trivial for her either.

#### Skip Counting

This was a good exercise for skip counting — the game made it a bit more interesting, but mostly it was about practicing skip counting.  Switching to starting at 1 made for a much more interesting game — the first time, two players finished in 3 rolls.  One of the kids realized that once you were on 96, if you rolled a 3, you should stay on 96 because there are more ways to win, which is the most interesting part of this activity.

# Star Wars Battles and Bent Legs

## The Activities

1. Topics: Addition, Graphs, Time:  Book: Get Up and Go! by S. Murphy.
2. Topics: Logic, Venn Diagrams:  First, we did our standard Venn diagrams activity using fairy tale characters.  The two problems we did were “Animals” and “Magic”; and “Scary Things” and “Girls”.  Then I shuffled up the cards and flipped over sets of 4 (later 6) cards, and the kids had to come up with as many different ways to group the cards into two groups, with explanations.

Just Animals vs. Not Just Animals

3. Topics: Simulation, Charts: I introduced “Star Wars battles”.  The idea is that you have two characters, each with a certain amount of Attack and Health.  Each simultaneously deals damage to the other, and when you get to zero health you are knocked out.  The battles end in a tie if both are simultaneously knocked out.  They also can have armor, which reduces the damage received by one each time.  I designed 6 characters (we happened to have figures for all of them): Kylo Ren (4 attack, 4 health), Rey (2 attack, 8 health), BB-8 (1 attack, 12 health), Flame Trooper (6 attack, 1 health), Finn (6 attack, 6 health), and Phasma (1 attack, 9 health, 1 armor).  We used glass beads to keep track of health, and the kids took turns setting up and running the battles.  We started with the first 4 characters and played all pairs; I kept track of the results on a chart (see picture).  Then we added Finn, did all the pairs with him; and then Phasma.  Then we figured out the win-tie-loss records for each character and compared them.  Finally, I asked them whether they could make a character that tied with Finn.

## How Did It Go?

We only had two kids this week; as usual things were easier with such a small group.

#### Get Up And Go!

A straight-forward book about getting ready in the morning, adding up the time for each individual activity in order to get the total time to get ready.  I gave each of the kids a worksheet to take home and fill out for their own routine.

#### Venn Diagrams

It’s been a while since we did Venn diagrams, one of the kids remembered them pretty well but the other was rusty.  The fairy tale Venn diagrams is always fun because the kids have to decide what’s an animal, what’s magical, what’s scary, etc.  This time, the gingerbread man wasn’t magical, for Pinocchio: Child: “Is this magical?” Me: “It’s a living puppet.”  Child: “Ok, no.  Wait, yes?”, ogres and trolls are animals.

Grouping the cards is also fun.  I stumped them once by grouping a cat, bear, and wolf together vs. a dragon, goose, and frog.  They often went for very small bits of color when grouping cards.  My favorite was “bent legs”, when “legs” would have accomplished the same split.

#### Star Wars Battles

Our son has been doing something similar outside of circle on his own, so naturally he loved it.  The other kid also liked it quite a bit.  It took a bit of time for the other kid to catch on, but by the end both kids could run the battles smoothly using the glass beads.  With the stats I picked, it’s pretty interesting because it’s quite non-transitive: Finn has the best record (4 Wins, 1 Tie) while the Flame Trooper has the worst (2 Ties, 3 Losses), yet Finn and the Flame Trooper tie.  For the final question about tying Finn, our son was able to figure out that he would tie with a character with 1 attack and 36 health, because 6 * 6 = 36 damage from Finn.  Pretty nice!

Reading the chart was somewhat tricky, so only one of the kids followed the second part about calculating the records for each character and comparing them.