# 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).

# Robots, Planes, and Pie (Age 8)

## The Activities

1. Topics: Puzzles, Arithmetic: Book: Edgar Allan Poe’s Pie: Math Puzzlers in Classic Poems by J. Patrick Lewis.  We read 5 or 6 of the poems and they solved the math puzzle.  For some of the poems, I found the original version and read it to them first.
2. Topics: Logic, Hard Problems: You have available an unlimited number of airplanes.  Each airplane can hold 12 units of fuel, and the airplanes can refuel each other in midair.  Each unit of fuel lets an airplane go 1000 miles.  Airplanes can only land at the starting line — if they run out of fuel anywhere else they crash.  I asked the kids to try to get as far from the starting line as possible without having any planes crash.  I created a powerpoint with planes and distance track as a visual aid — the planes show the fuel units and the kids could fill in the units in pencil as they simulated their solution.
3. Topics: Counting, Factors: We did the Robot Stepper activity from youcubed.org.  I made a square grid of the numbers from 1-100 for the kids to fill in, and gave each kid a different starting number and number of steps.  After each kid had done several different charts, we looked at them as a group to see what kind of patterns we could find.

## How Did It Go?

We had all five kids this week.

#### Edgar Allan Poe’s Pie

The kids liked the puzzles and did a pretty good job listening and trying to solve them.  However, they weren’t very interested in hearing the original poems, some of them said they were boring or “Why are we doing this?”  I was surprised because I thought they might like the change of pace.

#### Long-Range Airplanes

As is often the case on this kind of problem, a couple of the kids tried hard and the rest were distracted most of the time.  They all liked the planes — one kid was even grabbing other kids’ planes :(.  One of the kids made quite a bit of progress.  I gave the kids a way to get to 7 using 2 planes (they both move 4 spaces, one plane gives 2 fuel and returns home, other plane has enough to get to 7 and then back home); the one kid quickly figured out you can get to 8 using 2 planes, and kept improving until they got a plane to distance 12 and back (using 5 or 6 planes, can’t remember).  Framing the problem as “How far can you get?” rather than “Can you get to X?” was good, I think, because it took the pressure off.

#### Robot Stepper

Everyone was into making the charts.  One kid made a couple mistakes, decided to X out the mistakes, and then decided to go ahead and X out every skipped square.  All the kids noticed patterns as they were coloring, and often stopped actually counting and just used the pattern instead.  The best insight on this problem was one kid was able to explain why stepping by 9 created a backwards diagonal (going down adds 10, going to the left subtracts 1).  Unfortunately the kids weren’t super interested at the end when we laid out all the diagrams and analyzed them, but maybe it’s just because circle was almost over at that point.

# 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!”

# 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.

# Unifix Estimating (Age 6)

## The Activities

1. Topic: Estimating. Book: Betcha! by Murphy. Two friends walk around town estimating the number of people, cars, and jelly beans they see.
2. Topic: Estimating, Counting. Predict how many Unifix cubes can fit in a small bowl. How many Unifix cubes tall are you? How many Unifix cubes tall am I?
3. Topic: Logic. A little boy rides the elevator alone to and from his 15th floor apartment. Whenever he goes down, he goes all the way down to floor one. Whenever he goes up, he takes the elevator up to the 7th floor, then the stairs up to the 15th. Why?
4. Topic: Geometry. How many rectangles are in various pictures? How many triangles?
5. Topic: Spatial Reasoning.  Cover a checkerboard with rectangular tiles that are two squares long. Are some boards impossible to cover? Why?

## How did it go?

This week we had four kids, after a couple weeks with just two kids per circle. The kids were all interested in the activity and stayed on task really well.

#### Unifix Estimating

First we each guessed how many cubes would fit in a cup. Then each kid tried to get as many as possible inside.

The guesses ranged from four to eight. At first everyone fit 9 in their cup (with the lid sealed). But I managed to fit 11 in.  After a lot of trying my son managed to squish in 12 cubes, much to his excitement.

12 cubes!!

Next we guessed how many cubes tall each kid was. We estimated by hold a stick of 10 cubes up to the kid’s body. A taller kid then decided to estimate his height by adding a few to the other kid’s height. The guesses were around 59 – 64 cubes. It was quite challenging to stick together that many unifix cubes, but the kids all stuck with it, and ended up with ~68 cubes per kid. We then guessed that I must be 100 cubes tall. I laid on the floor while kids made a very long unifix pole, and when we counted, it was 90 cubes long

#### The Boy in the Elevator

I got this story from Math from Age Three to Seven by Zvonkin. A little boy rides the elevator alone. When he goes down from the 15th floor, he goes all the way to the bottom. But when he goes up, he only goes to the 7th floor then walks up the stairs the rest of the way. Why?

The first suggestions were that maybe he wants exercise. Or maybe he doesn’t like the other buttons. At that suggestion, I drew them the buttons to see what they looked like:

I taped them up to the wall. No one had much to say about this, but then I asked one kid what would happen if her little brother pressed the buttons? She said he may be too short. Then another kid suggested maybe the boy was too short to reach the 15, and could only reach up to the 7. And on the way down, he can reach the 1 button easily.

#### Counting Shapes

In this activity, I showed the kids pictures of shapes I had drawn and we tried to find all triangles or rectangles in the picture.

At first the kids only see four rectangles in a picture like this. But after some looking, they noticed the big rectangle around the outside edge. Then later they noticed the long thin rectanble highlighted in green, and lastly the squareish rectangle in black. All the kids enjoyed this activity.

#### Tiling Checkerboards

I gave the kids a bunch of tiles that each would cover two squares on a checkerboard. Then I gave them increasingly interesting checkerboards to try to cover.

First they got a 4×4 checkboard which everyone easily covered.

Next was a 5×5 board:

Notice that one square is uncovered. The kids spent several minutes trying to rearrange the tiles to cover the last square. Eventually I suggested that maybe it’s impossible? If so, can you explain why? One kid suggested the tile is the wrong shape. Or maybe you should be allowed to let the square hang off the edge of the checkerboard?

Eventually, my son counted the squares on the board (5 on top, 5 down the side => 25 squares) and he said: “it’s impossible! 25 is odd, and the tiles can only cover an even number”. We checked it out with the other kids and eventually they were convinced.

My son said it should be possible because there’s an even number. But no one could do it. A couple kids suggested they would need to put the squares diagonally. I asked about the color of the remaining squares? We noticed it was always two white squares left. I asked if one tile can ever cover two white squares? The kids tried it and said no, but were not fully convinced.

The final board

This was the last board. Everyone immediately said it was impossible. One kid pointed out it would be possible if you could overlap the pieces, but no one had a clear explanation of how they were sure it was impossible otherwise.

# How Much For The Whaleshark? (Age 6)

## The Activities

1. Topic: Money: Book: Follow the Money! by L. Leedy.
2. Topics: Money, Addition, Subtraction: I ran a “store” where the kids could (pretend) buy various small toys.  Each round, I gave each kid 4 or 5 “dollars” (play money), and then they chose something to buy and payed me for it.  Some things cost more than \$5, so if they wanted to buy them they had to buy something cheap so they’d have enough next round.  We did three rounds, then reset.  The second run through, I paid them using \$5 bills so they had to make change.  The third run through, I had them keep track on a “ledger” in addition to paying me with physical play money.
3. Topics: Counting, Sorting: We repeated the activity where the kids sorted dominoes according to the sum of the spots.  I gave them 6 dominoes to start, and gave them 3 more at a time when they finished.  I went up to dominoes with 9 spots on each side.  One of the kids has learned his times tables, so he sorted by product instead.  After we used up all the dominoes, I had the kids sort the entire set (by sum).

## How Did It Go?

We had all five kids this week.

This book didn’t have a ton of math, but it did show making change a number of times.  It also introduced the various dominations and was a nice introduction to the next activity.

#### Play Store

The kids got the hang of buying things quickly.  However, they weren’t very good at making change — I think several of the kids didn’t ever quite understand what it meant.  Also, some of them can’t do subtraction, so they also couldn’t do it directly.  That is, if you have a 5 dollar bill and need to pay \$3, either you can make change into ones and pay 3 of them, or you can subtract 3 and get back 2.  Some of the kids didn’t understand either; some understood the change method, and some understood both.  The ledger was also a challenge for many of them, both because they didn’t know subtraction and they didn’t understand how it related to paying for things.  A few got it, but at best the others understood the mechanics but not the meaning.  So we can definitely explore more both the ideas of making change and keeping track of quantities using a running tally.

After we finished the money activity, I had each kid make up a story about a simple math problem.  For example, I would write “3 + 2” and they would say “There were 3 birds sitting on a branch, and then 2 more came, so there were 5 birds”.  Some of the kids closely followed earlier stories, but we got several different types of stories by the end.

#### Sorting Dominoes

The kids were pretty good at this.  All of them were able to finish on their own, with only a few mistakes here and there.  They even handled the 9 spot dominoes pretty well.  For the group sorting, it took them a while to get organized, but once they had at least one domino in each position they made faster progress.  Not everyone participated the whole time but they all contributed.

# Sorting Extravaganza! (Age 6)

## The Activities

1. Topic: Numbers. Book: Missing Math: A Number Mystery, by Leedy. This is a fun, but simple book about all the numbers disappearing. It illustrates various places we depend on numbers, like calendars and phone numbers. In the book, one character can’t remember how old she is because the numbers have disappeared. One kid from circle said she would remember how old she is, even if there are no numbers.
2. Topic: Counting, Adding, Sorting. I brought out a set of dominoes that went up to 6 on each end. We played two different games, suggested by the book, Dominoes, by Planet Dexter
1. Lost Domino: Pick a domino and count the spots. Then put it face down with the other dominos and mix them around. The kids take turns flipping over one domino and counting the spots to see if it is the lost domino.
2. Domino Sort: Mix the dominoes face down. Each kid takes 6 dominoes and then sorts them by the total number of dots on the domino.
3. Topic: Sorting, Teamwork. I made cards numbered from 1 – 99 out of poster board. I shuffled the cards, then gave a stack to each kid. The kids had to work together with no help from me to sort all the cards. First we did it with cards 1 – 50. After that went well, I added in cards up to 99.

## How did it go?

This was the first circle in a few weeks for some of the kids. All five kids were here. Three of the kids had just had a week-long winter break from their schools. There was a lot of energy, but they were also amazingly focused, especially during the team sorting activity. Overall, it was a great circle.

#### Domino Sorting

Lost Domino was very easy for everyone, so we played just one round.  Domino sorting with dominos with up to 6 dots per side went pretty easily for all the kids. They all wanted to add in dominoes that go up to 9 dots per side, which made the activity much harder for most of the kids. Two could still sort them independently, but the other three needed more help.  Everyone was pretty interested in this.

Each kid ended up individually sorting 1/5 of the dominoes.  I suggested that we could sort all the dominoes together in the middle, and I organized this by asking “who has a 0 domino?” “A one?” Most the of kids kept their dominoes sorted, but one kid mixed her stack up, which made it much harder for her.  Several kids kept asking me and other how many dots various dominoes had.  In the end, we had a very nice layout of the sorted dominoes.

#### Sorting Together

The kids’ number recognition has really improved in the last few months, so they were ready to try sorting a bunch of cards together. I try not to help during this activity, because I want the kids to come up with their own strategies, and own evaluations of what worked and didn’t work.

First we did cards 1 – 50. It took the kids about five minutes to sort. Most of the kids laid their cards out on the floor so they could all search for the next number. This works very well, if you are using brute search.

The kids then all really wanted to try the cards up to 99. I warned them that it is *much* harder, and that the bigger kids couldn’t do it the first time they tried. Everyone still really wanted to do it. I shuffled the cards and gave each kid a stack, the said “Go!”.  The kids worked really well together, and stayed focused the whole time, even when the big kids finished their circle and came down and ran around a bit.

Again, things went best when the kids put their cards out on the ground. Some kids did not want to do this, which definitely slowed everyone down.  I even suggested to my son that he should put down his cards, but he felt like he owned those cards, and didn’t want to share them. Eventually he did put them down, but got a bit upset when someone else picked up some of his cards. “55 is mine, I remember!”.

Two kids really took the lead in calling out what number was needed next. 4 of the 5 kids helped search for the numbers. The fifth held onto his cards mostly, but was still very focused.  One kid would find streaks of numbers (51, 52, 53, 54, 55) and hand them off to others to add to the chain. Unfortunately, this meant double the sorting work, since the numbers would get mixed up in the transfer.

After 19 minutes, all the cards were sorted, stretching all the way out of the kitchen, under the dining room table, to the wall. Everyone cheered!

We’ll have to do this again in a couple weeks, and see if they can beat their time.