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.img_2465
  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).

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″.IMG_2065
  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.


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.


The Case of the Missing Blink Cards (Age 8)

The Activities

  1. Topic: Measurement. Book: Measuring Penny by Leedy. Lisa gets a homework assignment to measure something in a variety of ways. She decides to measure her dog Penny.
  2. Topic: Sorting, Patterns, Charts. We have a card game called Blink, which has cards of six different colors, with six different shapes, and five different numbers (1 – 5). Here are some sample cards.

    Blink cards

    We calculated that there should be 6 * 6 * 5 = 180 unique cards. However, the Blink deck only contains 60 cards.  I asked the kids to figure out which cards are missing, and if there’s any pattern.

  3. Topic: Protractors, Measurement, Triangles. Each kid got a protractor, and  triangle I had drawn before circle. We measured each angle, and then added them up to see what we got.

How did it go?

We had 4 kids this week. Overall, it was a fun, focused circle.

Measuring Penny

We had read this book over a year ago. Some kids remembered it, but 3 out of 4 kids wanted to hear it again. This time I took several different breaks to discuss the book. For example, when they talked about ‘nonstandard units’, I measured one of the kids’ hair in number of “Corey Hands”. We also measured everyone’s ears in centimeter. The kids had a great time with the book, and stayed focused and interested.

Missing Blink Cards

We had told the kids about the missing cards several weeks ago, and they all remembered that there are supposed be 180 cards.  We recalculated it again, just to be sure.  Then I asked if we could figure out which cards are missing?  I started them off by sorting through the cards and showing that there were only two cards that had red lightning bolts on them.

The kids took over from there. At first they just randomly picked a color and shape, and looked for the matching cards. Soon this became unmanageable, so one of the kids suggested moving to the floor, and making a separate row for each color, and use columns for the shapes. This resulted in the following chart:


I then asked the kids several questions about the cards, which were easy to answer with this chart. How many of each color are there? 10.  How many of each shape? 10.

How many of each number? This one was trickier because the chart is not sorted by number. One kid wanted to rearrange the chart, but instead we went row by row looking for each number. We found there are 12 of each. We also found that for each color, there are two of each number.  During this time, two kids counted the attributes, and two kids were keeping notes.


One kid’s notes.

Next I asked how many cards are missing from each row? The kids looked at their chart, and said two are missing from each row. We then calculated there must be 12 missing cards total. But that would make only 12 + 60 = 72 cards, not 180, like we calculated.

I should have asked the kids where the other cards were, but instead I just showed them how to update the chart to sort by number too.  So we had a row for each color, and a column for each number/shape combination. Two kids helped me fix the chart:


The new chart.

Then we counted the missing cards in each row. This time we found there are 20 cards missing in each. 20 * 6 = 120 + 60 = 180!

Triangles and Protractors

I handed out several big triangles I had drawn with sharpie before circle. The kids used protractors to measure the three angles, and then add them up.


Using the protractor was still challenging for the kids, but they all made progress when I helped them. The kids added angles up to 180 four or five separate times. We also got 182  and 183 a couple times. Weirdly, when I did it myself, I got 188 for a triangle…Not sure why.  But the kids actually noticed that it was near 180 all the time, so we may be almost ready for the proof that they must always be 180.


My daughter measuring a triangle.

Seven Days Old to Seven Years (Age 8)

The Activities

  1. Topic: Time. Book: A Second is a Hiccup, by Hutchins. This is a sweet book about how much a kid can do in second, day, week, year. It’s pretty simple, but I made it more challenging for the big kids by asking computational questions like: “How many seconds are there in one hours? How many hours in two days?”
  2. Topic: Measurement. Use ribbons to measure the kids’ ears, wrists, hands, feet, and height. Add the new measurement to the chart we’ve been keeping for the last couple years.

    Two years of measurements.

    3. Topic: Decision Trees, Programming. First show the kids a simple decision tree for sorting cards into three piles: A, B, and C. Trace through the tree for some sample cards as a group. Then give each kid a stack of cards to sort using the tree.  Next try some harder decision trees. Then deal 6 cards into two stacks, A and B, and try to write a decision tree that puts each card into the right pile.


    An easy decision tree.

    Here a the other trees: Tree 1,  Tree 2, Tree 3, Tree 4, Tree 5.


How did it go?

We had 4 kids this week. There was a lot of energy, but the kids were pretty focused, and I only had to give a few behavior warnings to my daughter.

See How We’ve Grown

The kids were excited to take their measurements again.  Measurement error was again a big factor, as some kids ears and wrists magically seemed to shrink. Height and foot size seemed more accurate, probably because those measurement changed the most. The kids grew between 3 cm and 5 cm this year.  We discussed questions like: how much did you grow this year? How much have you grown since the beginning of circle? Who has the biggest feet? Smallest ears?

I also showed the kids a picture of my daughter when she was seven days old, along with an impression of her foot.  It’s so amazing how quickly they grow up.


My seven day old girl.


Playing Card Decision Trees

Last week, the kids tried to classify cards into piles using a simple programming language. The syntax of the language proved to be pretty confusing to the kids, especially the parentheses. Syntax has often been trickier than expected in the past too.

We decided to repeat the same activity, but use decision trees instead of a programming language to sort the cards. All four kids quickly caught on to how to trace a given tree.  Some kids also started to notice unreachable branches of the trees…for example:IMG_0002

The second “8?” is always “no”, so you never put any cards in pile C.  Several kids noticed this, and were excited to point it out.

Next, I made two piles cards and asked kids to help write a decision tree to sort the cards. I intentionally picked each divisions, for example, pile A might have all hearts in it, so you can make a simple tree: “Hearts?” yes -> A, no -> B.  After they were comfortable, I dealt out six random cards, and we worked together to make a tree. With random cards, you are likely to need more than one question.

At this point, I asked the kids if they were ready for their own set of harder cards. Everyone said “yes” (always a good sign), so I dealt out six cards in two piles to each kid. If a kid was stuck, I suggested a starting question.  All 4 kids were able to make progress on this.  I think all 4 quickly came up with trees that *almost* worked, except for one card.  I helped them find the place in the tree where the card went to wrong pile, and suggested that they add a new question there, to make the card go to the right place.


One kid’s decision tree for six random cards. Yes, her handwriting is better than mine!

All four kids were able to fix their trees and correctly sort all six cards.

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.IMG_20160110_173859

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.

Spending a Million Dollars (Age 7)

The Activities

  1. Topics: Multiplication, Division: Perfectly Perilous Math, Challenge 3 — if you spent 50 cents every second, how many days does it take to spend 1 million dollars (to nearest day).IMG_1742
  2. Topic: Combinations: We continued the pumpkin activity from last week.  Last week, they had made a bunch of pumpkins but hadn’t checked for duplicates.  This week, we tried to come up with strategies for finding all the duplicates.  Also, I started with the simplest version of the problem (circular eyes, nose, and mouth), and then gradually added elements (non-symmetric parts, multiple choices), computing how many different combinations there were each time.
  3. Topics: Logic, Measurement: Perfectly Perilous Math, Challenge 4 — if you have one bucket that holds 3 quarts, and one that holds 5, how can you measure exactly 4 quarts using just those two buckets?  We worked as a group to solve this problem using various containers and beads (instead of water).

How Did It Go?

We had all five kids this week. All the activities this week were group activities, which turned out to be a problem. Most of the time, only two or three of the kids were actually working on solving the problem; the others were drawing, making paper airplanes, or otherwise not paying attention. Kid A grabbed and crumpled another Kid B’s paper, and later in circle (unrelatedly) Kid B threw a container of beads at Kid A, which we all had to help pick up. I think another issue was that the problems were all pretty hard; the kids working on them did a good job, but it discouraged the other kids.  One of the kids who drew during the Million Dollars activity said they couldn’t help because they didn’t know how to do multiplication, and then was very attentive for the remaining two problems.

Spend a Million Dollars

One of the kids is a lot better at large multiplication than the others, so that kid did most of the computations.  Another kid helped figure out what the right numbers to multiply were.  The kids figured out how many seconds were in a day, but then they were planning to multiply by 50 (cents) — they didn’t realize that 50 cents was half a dollar.  They also needed help figuring out how to divide 1 million by 43,200 — they know the method of repeated addition/multiplication, but I think their number sense suffers a lot past 1,000.  They got pretty close to getting the right answer, but I had to a help a lot for the final few steps.

Pumpkin Combinations

One of the kids suggested sorting the mouths by orientation, and then by type of mouth.  A different kid decided to implement this, but changed it to have 1 column for each of the combinations of 4 mouths.  Some of the other kids helped sort (there were about 35 pumpkins total), and eventually the pumpkins were all in columns.  There were still 8-9 pumpkins in each column, and they mostly stopped making progress at this point, besides finding a few duplicates ad hoc.  I suggested putting the circle eyes above the triangle eyes, but they didn’t take to this idea.

Then I switched gears a bit and started with a problem with circle eyes, nose, and oval mouth.  This meant there was only one possible pumpkin, which the kids figured out right away.  Then I made the nose triangular.  There were answers of both 2 and 4; the 4 answer was reasonable because they showed how you could put the straight edge in any of the 4 directions (although two of them make pretty weird noses).  I said we should only allow the two directions, and then added triangular eyes.  They got 4 right away.  Then I added a smiley/frowny mouth, and it got much harder.  I got answers of 4, 6, and 8.  6 is an interesting answer, because you could think of that if you considered varying each dimension one at a time.  I had the kids try to write out all the combinations — I really should have had them to all 4 for the previous problem first, because the key insight here is that if you group the faces by smiling vs. frowning, you have the same set of 4 faces from the round mouth case, once for each mouth.  In the end, one kid was able to figure out that there should be 32 different answers for the previous week’s problem, but wasn’t able to figure out which faces were still missing.

Tricky Buckets

The beads worked okay, although one of our containers was more like 2.6 than 3, so the measurements didn’t quite come out right.  Also, we ended up picking up a bunch of beads because of the bead-throwing incident.  One of the kids figured out a solution right away using a third bucket; and then they were able to come up with the 2-bucket solution with only a bit of help.  I asked a follow-up question about a 5 and 7 bucket (trying to make each of 1, 2, 3); the kid who had done the best on the first part was able to make progress and solved 2 and 3 but not 1.

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.