# 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.

# Lots of Bunnies (Age 7)

## The Activities

1. Topics: Fibonacci, Sequences: Book: The Number Devil by H. Enzensberger, night 6, which covers Fibonacci numbers.  We explored a number of the properties of Fibonacci numbers (such as that fact that the squares of two consecutive Fibonacci numbers is also a Fibonacci number), and drew “Bunny diagrams” to see how Fibonacci could arise in nature.
2. Topics: Graphs, Coordinates: The kids each did another worksheet from worksheetworks.com.  This time the coordinates included negative values.
3. Topics: Games, Addition: We played Clumsy Thief, which involves finding pairs of numbers that add to \$100.

## How Did It Go?

We had only 3 kids this week.

#### Fibonacci

The kids were able to write out the Fibonacci sequence until about 1000.  The kids varied in how interested they were in the various properties; one kid was “bored”.  One of the kids really understood the bunnies diagram and did quite a few rows.

#### Coordinate Pictures

As usual, the kids enjoyed doing the pictures.  One of them had brought back their homework from a previous week (another coordinate picture) and got a prize.  The negative coordinates confused them for a while, but still the actual difficulty is knowing whether the first coordinate is horizontal or vertical.  By the end they were doing pretty well, and they all finished one picture.

#### Clumsy Thief

Two of the kids liked the game, the other wasn’t so sure; I think this corresponded roughly with how quickly they were able to find the pairs that added up to \$100.

# I Want To Go Last! (Age 7)

## The Activities

1. Topics: Division, Primes: Book: The Number Devil by H. Enzensberger, first half of third chapter.
2. Topics: Primes, Multiplication: Following the chapter from the Number Devil, each kid did a sieve of Eratosthenes up to 70.
3. Topics: Games, Probability: Using percentile dice (two 10-sided dice which together roll a number from 0 to 99), we played this game: going around the circle in turn, each kid picks a number.  I roll the dice, and whoever is closest gets a point (if there’s a tie, each kid gets half a point).  After doing this a few times, we did the same thing except that instead of rolling the dice, we computed how many numbers would make each person win, and they got that many points.  E.g., if the numbers were A: 10, B: 45, and C: 85, then A wins from 0-27 for 28 points, B wins 28-65 (tie on 65) for 37.5, and C wins 65-99 (tie on 65) for 34.5 points.

## How Did It Go?

We had 4 kids this week.

#### The Number Devil

This chapter talks about the connection between multiplication and division, and about prime numbers.  It introduces the sieve of Eratosthenes.  One interesting thing that came up is one of the kids, who knows division already, first said that they hadn’t done division this way before, but then later said that they probably knew this way of doing it because they knew how to do division.

#### Sieve of Eratosthenes

We’ve tried this before, and this time the kids were definitely better.  But some of the kids still made multiple mistakes, particularly when counting by threes.  I tried to explain why it makes sense to cross out every third number, but I’m not sure they fully understand that counting by 3’s gives you multiples of 3.

#### Dice Guessing

The number picks were pretty random for a while; one of the kids guessed lucky numbers, and most of them liked to pick larger numbers.  They did all realize they should pick between 0-99.  After a bit, one kid realized that guessing right next to another guess might be a good idea — but it then backfired on them when the next person did the same thing.  They soon decided that they all wanted to go last — with good guessing, it’s not an advantage to go last, but with the way they were guessing, it definitely was.  I had initially planned to use the dice the whole time, but quickly realized that the variance was too high — one of the kids was winning by a sizable margin despite not having made the best picks.  So I switched to giving points based on number of ways to win (I did all the calculations, it would have been hard for them).  Some of the kids understood this pretty well, but some of them were pretty confused and didn’t know what I was doing.  For one thing, they hadn’t seen notation like 45-58 before, and the idea of writing down all the numbers that would win for them wasn’t obvious.

# Don’t Forget to Count the Feathers! (Age 5)

## The Activities

1. Topics: Graphs, Measurement: Book: The Case of the Missing Zebra Stripes, Chapter 2.
2. Topic: Measurement: I gave each kid some twine and a pair of scissors.  Then I showed them some household objects (varying in size from ~3 inches to ~16 inches), and they had to cut pieces of twine of the right length without measuring, just by looking.
3. Topics: Addition, Games: We played the dice game again, where you roll a twelve-sided die and 5 six-sided dice (some of them 1-3 instead of 1-6) and try to make the number on twelve-sided die using addition and subtraction.
4. Topics: Geometry, Optimization: We had a bunch of “fences” (rectangular blocks) and small wooden animals.  The rules were you could make either rectangular or triangular pastures out of the fences; a 1×1 square could hold two animals, while an equilateral triangle of side 1 could hold one animal.  You could also omit fences between neighboring pastures (so you could make a parallelogram-shaped pasture, for example, which could hold two animals).  Also, you can’t mix animals within the same pasture.  Starting with 1 sheep, I asked what the minimum number of fences it takes to hold that number of animals is.  Then I added another sheep, asked how many fences, etc., until 12 sheep.  Then, I gave them 2 sheep, 2 horses, 2 donkeys, and 1 pig, and asked what the fewest number of fences was.

#### How Did It Go?

We had 4 kids this week.

#### Missing Zebra Stripes

This chapter was about making graphs to measure the heights of giraffes. There was also a part where you were supposed to say which was the longest lizard, or the longest bird. The lizards were curly, so you had to be careful; and I actually missed the fact that one of the birds had crazy tendril-like tail feathers, so we got the wrong answer (this came to light the following week when Corey read chapter 3).

#### Measuring with Twine

The first object (chapstick), the kids all did pretty well. But for the rest of the objects, most of the kids were way too high — often about 50% too long. One of the kids was WAY closer most of the time, and had the closest to the right answer every single time. It also happened that I had to go answer the door during this activity, and almost left behind the object they were supposed to be cutting twine for, but then I noticed that the kid who was doing the best started to reach for it to cheat. So they really wanted to win :).

#### Dice Game

There’s a very clear ordering of the kids for this activity, ranging from instantly getting it every time to having trouble adding up two dice even when given lots of time. And it’s not the same ordering as, say, the twine activity.

#### Building Fences

When I did this with the older kids’ circle, I didn’t introduce triangular areas, but it was a very nice addition and I’ll definitely keep it going forward. The solution to the final problem ended up involving triangles, and one of the kids came up with it without any help (in fact, it was better than the solution I had come up with). There was a lot of interesting experimentation with different arrangements of the fences. It seemed like they were starting to realize that square pens are more efficient than long skinny ones; but I don’t think they fully got the idea yet.

# Double U, not W (Age 5)

## The Activities

1. Topic: Subtraction: Book: Taking Away with Tigers by T. Steffora.
2. Topics: Geometry, Spatial Reasoning:  I went to a different part of the kitchen where the kids couldn’t see what I was doing, and using pattern blocks I made a shape.  Then, I described the shape to the kids and they had to make it just from my description.
3. Topics: Games, Addition: We again played the game where we rolled two dice with varying numbers of sides and then either jumped or clapped a number of times equal to the sum of the numbers on the dice.
4. Topic: Reflections: I gave them a picture I drew with reflected versions of every letter hidden inside, and they had to find all the reflected letters.
5. Topic: Graphs: The kids were given a grid with letters on the rows and numbers on the columns, and a set of coordinates grouped into one or more colors.  They had to find those cells and color them the right color (similar to counted cross-stitch).  You can download the materials here.

## How Did It Go?

We had all five kids this week.

#### Taking Away with Tigers

A very simple introduction to subtraction; very easy for some kids but about right for others.  The most interesting part was probably the tiger facts at the end.  One kid’s review was “I didn’t care about that book.”

#### Describing Patterns

The kids were much better at this than I expected.  They got almost every shape that I described, including “3D” shapes with some pieces standing on edge.  One thing that helped was they all could look at what each other was doing; because I was away from the table, I don’t know whether it was one or two kids figuring it out and the others copying.  But from a few times I came over a little early, it looked like many of them were working independently.  They were able to choose shapes based on just the name (including hexagon and trapezoid), to get the right number of each shape, and to follow complex instructions like “Take two white diamonds and put them so each one is touching both the square and the hexagon”.

#### Dice Jumping

They continue to love this activity.  I had a bunch of different kinds of dice; the kids have mostly caught on that they should choose the die with the most number of sides each time (so they can jump as much as possible).  I had two different kids choose one die each, a third choose jump or clap, and a fourth role the dice, which helped keep everyone involved.  The most number of times we had to jump was 35; counting past 20 is kind of slow for them, so most of them jumped 70+ times.

#### Hidden Letters

The kids enjoyed this quite a bit, and only needed help a couple of times.  They understood the idea of covering half of a reflected letter in order to see the original letter.  One note is that although some letters are part of other letters (e.g., F and E), each letter is present by itself, not as part of another letter.  One tricky case was the reflected U, which they thought was a W.

#### Coordinate Drawings

This is the second time we’ve done this; they were quite a bit better than last time.  All of the kids were able to make progress on their own this time, and several were noticeably faster than last time.  Most of the kids still made a mistake or two.  One interesting thing is that the kids had trouble telling what the pictures actually were; for example, one kid couldn’t tell it was a car until I told them, but then when they showed it to their mom, she knew it was a car right away.