# 30 Different Ways to Say “I Love You” (Age 7)

## The Activities

1. Topic: Measurement: Book: Taro Gomi’s Playful Puzzles for Little Hands.  We only did a few puzzles towards the end of the book, most of them involved measurement and were pretty hard!
2. Topics: Geometry, Graphs: I made a set of Valentine’s Day themed arrow direction drawings, downloadable here.  The rules are, using graph paper (ideally with fairly small squares), you start at a vertex and have one of 8 directions and a distance.  I introduced something new this time, which is some of the instructions were in red, which means you moved your pencil but didn’t draw a line.
3. Topics: Counting, Graphs: I gave each kid a box of the kind of candy hearts that have messages like “Be Mine” or “Sweet On You” printed on them.  Each kid sorted their box by heart color, and then we made a combined graph with how many there were of each color.  Then we found as many distinct hearts (message + color) as we could.

## How Did It Go?

We had all five kids this week.  It was a high energy circle, partly because of candy and partly because four of the five kids had just been to Cirque du Soleil.  We spent five minutes at the beginning of circle so each kid who had been to the circus could say their favorite part, and then we got through the rest of circle without any mention of the circus!

#### Taro Gomi

One of the problems asked which of a bunch of hats was the shortest and tallest — we tried to find some kind of trick (e.g., number of stripes), but in the end all we could figure out was the measure.  Similarly, the next page had two different colored poles cut into pieces and asked which pole (when put together) was longest, which seemed really hard as well.

#### Arrow Drawings

The kids did pretty well on these, but there was a pretty big spread in ability.  Most of the kids made a small mistake from time to time, usually either going the wrong distance or not doing a diagonal at 45 degrees.  One kid was noticeably better, going faster and without mistakes.  I was worried the red instructions (pick up your pencil) would be confusing, but they understood it easily.

#### Candy Hearts

I was originally planning to have them sort by message and make a graph that way, but when we opened the boxes, it turned out that the printing quality on the hearts is really bad — probably at least 1/3rd of them have missing or unreadable messages.  Also, it turned out there are a TON of different messages (“Be Happy”, “Nuts 4 U”, …) — we counted 30 different ones — which would have made it hard to make a graph.  So we did color instead.  And then there was another surprise — there were FAR more oranges than anything else — 3 times as many as most of the other colors!  And it was consistent across boxes as well.  Seems like a pretty solid result that I’d expect to hold up across many boxes.  The kids were pretty excited to find all the different messages and laughed every time we found a new one.  The kids were also REALLY excited to eat some of the hearts, but as far as I know they listened to me and didn’t eat any until the end (they got three each).

# 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.

# Corey’s Pretend Party IV (Age 6)

## The Activities

1. Topic: Graphs. Book: The Great Graph Contest by Leedy. In this book, a frog and a salamander compete to see who makes the best graphs. They make Venn Diagrams, Bar Graphs, Pie Charts, and others, covering a variety of subjects. Leedy is a great author, and the kids always love her book. This is no exception.
2. Topic: Voting. Each year around the time of my birthday, I have the kids plan my pretend birthday party. This is the fourth year in a row we have done this activity (twice with the older circle, twice with the younger). This time, I planned to have each kid own one question, and have them collect votes. Then I wanted to make a fancy graph out of each, similar to the graphs in the The Great Graph Contest.
3. Topic: Adding and Subtracting, Word Problems. The kids used Base Ten Blocks to solve problems about my age (36).
1. How old will I be in 36 more years?
2. How many years older am I than you?
3. How much is my age plus yours?
4. Topic: Advanced Birthday Math. My son is extremely good at calculation, so I knew he would cause problems during birthday math. I gave him a much harder problem to work on separately: How old will I be in the year 3022?

## How did it go?

We had four kids this week. The circle was a bit scattered, partly due to me being less organized and partly due to the advanced birthday math not working out.

#### Happy Birthday to Me!

The kids all enjoyed coming up the questions for my party. We came up with:

1. Where should the party be? Pump It Up, Park, Restaurant, Arcade.
2. What treat should we have? Crackers, Oreos, Cupcackes, Tacos.
3. What should be in the gift bag? Bouncy ball, Legos, Light Saber, Balloon.
4. What drink should I server? Water, Apple Juice, Pink Lemonade, Grape Juice

Each kid owned one sheet for voting. Everyone voted on each other’s sheets. The kids made tally marks to record the votes. Two kids remembered that you can cross the fifth tally mark. We had an interesting discussion about why you should cross the fifth one. Some kids said it was because they had seen parents do it that way. I made an example on paper of 15 tallymarks, vs 3 groups of 5 tallymarks. Then one girl said that crossing the fifth meant you could count by fives. We then tried counting the two rows of marks, and found that counting by 5s was much faster.

I had planned to have the kids make graphs out of the votes, but they were getting a bit distracted by the end, and I hadn’t planned it out that well, so I decided to move on to birthday math instead.

#### Birthday Math

First I gave my son his problem (How old will I be in the year 3022?), then started working with the other three. First I asked each kid to count out 36 Base Ten Blocks. All three of them decided to use 10 bars, so they picked out 3 10-bars and 6 units.

Next I asked how old I would be in 36 more years? The kids had lots of silly guesses, like 1000 years old, but finally one girl suggested we should start at 36 and count up 36 more. I suggested counting out 36 more Base Ten Blocks, and then counting them to see how many there were in total.  The three kids eventually did this, though there was some messing around, and also some mistakes in counting (I got answers of 71, 72, and 73).

Meanwhile, my son had decided the advanced problem was too hard. He was trying to subtract 3022 – 2016 in his head, and had come up with 1008, which I said was close but not correct. This frustrated him, so he crumpled up the paper and threw his pencil. He then rejoined us at the table for a bit until he got too wild and had to sit on the couch for the rest of circle.

Next we each collected 36 blocks again. I asked, how old was I when each of you was born? No one knew how to figure this out. Some people said my age was negative, some people said I was 1000.  I suggested we could go back in time by taking away one block at a time. They enjoyed watching me take one block away saying: Now you’re 4, now 3, now 2, now 1, now 0. Then we counted how many blocks were left and found I was 31 years old when this student was born.

My final question what is your age plus my age? By this time, the kids were quite restless, some were saying it was too boring. But we persevered and figured it out, and we even added all 4 of our ages together. Everyone thought it was funny to think about being 53 years old (the sum of our ages).

# Shrinking Ears (Age 6)

## The Activities

1. Topic: Size. Book: The Biggest Fish by Keenan. This is a simple book about a town that has a contest to see who can catch the biggest fish. The kids loved the drawing of a fish as big as a school bus.

2. Topic: Measurement, Graphs, Differences. We used ribbon to measure the kids’ wrists, ear, hand, foot and height. We compared the measurements to last year’s.

3. Topic: Estimation, Graphs, Counting. We guessed how many steps it would take to get from the kitchen to different parts of the house. Then we counted it out and compared the answer to our guesses.

•  First each kid made a guess and counted it out, to different destinations.
• Next, we each made a guess for a farther away destination (the front door), and then counted it to see who was closest. Each kid computed how far off their guess was.
• Finally, we counted how many baby steps it would take to get to that destination.

## How did it go?

This is the one year anniversary of the younger kids circle.  It was also the first circle in 4 weeks, due to Christmas vacations.  The kids had lots of energy, and were excited to see each other after so long.

#### Body Measurement

The kids were all really excited to find out who had the biggest feet/wrist/ ear.  It was a bit chaotic during the measurment phase. Another parent helped, but there was still lots of noise and excitement. Eventually everyone got their new ribbons glued down to their sheets.

As usual, there was a fair amount of measurement error. One girl’s ear appeared to have shrunk since last year 🙂

The kids were especially excited to see who was the tallest. My son won that competition by being one centimeter taller than the next kid. Interestingly, the smallest kid in circle grew the most — seven centimeters since last year. No one else grew more than five centimeters.

The kids had trouble answering, “Which measurement of yours changed the most in the last year?” They all wanted to answer whichever was their biggest measurement, even if it hadn’t changed much.

#### House Measurement

The kids all enjoyed guessing how far it would be to their target. Some of the kids were very strategic when taking their steps, taking smaller and smaller steps at the end, if necessary.

We all guessed how far it would be to the front door. The guesses were 19, 29, 30, 31, and 44. It took us 21 steps to get there.  Each kid then computed how far off their guess was, using our chart.

We had just a few minutes left in circle, and the kids were all joking about taking tiny baby steps, so I decided we would try it out. I picked a kid who had pretty regular baby steps, and then we all counted together as she walked to the front door. It took 115 steps, which was an excitingly big number to the kids.

# 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.

# One Corillion (Age 7)

## The Activities

1. Topic: Place Values, Big Numbers. Book: The Number Devil by Enzensberger. Pages 40 – 46.
2. Topic: Place Values. The kids wrote down a big number like 92,103.  Then they rewrote the number like: 3 * 1 + 0 * 10 + 1 * 100 + 2 * 1000 + 9 * 10000.
3. Topic: Big Numbers. I printed out Wikipedia’s page about the names of large numbers, and read them to the kids.  Then each kid picked a large number like 1 octillion, and wrote out all the zeros.  Finally, each kid got to pick an unnamed number like 10^405, and name it.
4. Topic: Coordinate Graphing. The kids each got a graphing worksheet from worksheetworks.com.  These sheets listed a bunch of points like (2,3), and when complete, there would be a picture.

## How did it go?

We had all five kids this week.  It was a slightly wild circle, but went pretty well except for my daughter getting upset when she made mistakes on the coordinate graphing. (She insisted on doing it in marker, but then would cry if she got any point wrong!).

#### The Number Devil

The kids really do enjoy this book.  They like how mean the number devil is to Robert.  We had several interesting side conversations inspired by the book about the big numbers, and infinity.

#### Place Values

I thought this would be easy for the kids, because the Number Devil had done exactly this exercise, but it turned out be hard for several of them.  One kid got it right away.  Two more got it with minimal help, and the other two needed more help.

#### Big Numbers

The kids loved hearing the crazy names of huge numbers, like 10^57 = Octodecillion.  Then we each picked a big number and wrote it out on paper.  One kid picked Centillion which is 10^303.  I’m not sure he actually wrote 303 zeros, but he definitely had a lot.  Finally, we each got to name a large number.

I named 10^204 a Corillion.

10^150 = Cupcake

10 ^ googol*googol*googol = Pendrillion

10 ^ centillion = peppermint

10 ^ octillion = horsie

#### Cartesian Picture Graphing

I had printouts for three different sets of points that would draw pictures. These were single-quadrant pictures (so no negative numbers).  At first the kids needed lots of help, but soon they started to catch on and make progress. There was a bit of drama whenever someone would make a mistake, but most kids handled it pretty well.

My daughter was pretty upset whenever she made a mistake, but she didn’t have to leave the room.  After circle, she kept working on her picture, at first crying, and then finally laughing once she got efficient at graphing points.

…then happy!!

# Which Dice Did I Roll? (Age 7)

## The Activities

1. Topic: Numbers: Book: The Number Devil by H. Enzensberger, Chapter 2.
2. Topics: Probability, Graphs: We revisited the activity from last week where we made two big charts, one for the sum of two six-sided dice, the other for a twelve-sided die.  This time, I wrote a computer program to simulate dice rolling, and ran it until the winning number came up 50 times.  I ran it twice each for 1d12, 2d6, and 3d4 (left to right below), and then copied each result into a chart.  Then, I showed the kids each chart and asked them how they thought I had made each of the charts.  We had only done 1d12 and 2d6 before, so including 3d4 was kind of cheating.
3. Topic: Spatial Reasoning: We continued the activity from last week where one kid made a shape using pattern blocks and then described it to the other kids.  This time I varied whether the kids worked individual, in one big group, or 2 small groups to follow the instructions.
 Original shape Copied shape

## How Did It Go?

We had all five kids this week.

#### The Number Devil

We read most of the 2nd chapter, which talked about zero and how Roman numerals are unwieldy because they don’t have place values. We stopped and talked at a number of places, the kids were pretty involved.

#### Probability Charts

At first the kids didn’t want to volunteer many opinions. I had them vote on each one, for a while only one or two kids voted each time. After a while, they had grouped into two piles: (1d12, 1d12, 3d4) and (2d6, 2d6, 3d4). They decided 3d4 didn’t fit, and moved it to the other pile. So they got everything as right as possible. Then I told them that I had actually rolled 3d4 for 2 of them, and pointed out how 2 was missing on those charts and how 3 and 12 were so low. They thought it was cheating :).

#### Describing Shapes

We did 3 different patterns this time, the kids are getting increasingly ambitious in their patterns. The pictures above show one of the results. The top part was described as a flower; you can see that the petals are pointed in the wrong orientation. Also, the relationship between the three trapezoids wasn’t described. The final pattern was quite a bit more complicated, and I needed to help or they would have been way off (due to under specification of directions). They do well when the shapes are totally symmetric, because they can guess what it should look like.