- 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.
- 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.
- 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.
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.
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.
- Topic: Time: Book: At The Same Moment, Around The World by C. Perrin. After we read the book, I asked the kids for different places they had visited and we figured out what time it was there. Also I asked why sleeping was more difficult after a long trip.
- Topic: Probability: We did probability charts with two six-sided dice. Each kid had a chart, and repeatedly rolled the dice and filled in a box (from bottom to top) for that number. Once one of the numbers gets to the top (5 rolls) that number “wins”. Most of the kids did 2-3 charts, and then we checked to see what numbers had won most often.
- Topic: Puzzles: Each kid got a Tower of Hanoi set, and they tried to solve as many discs as they could.
How Did It Go?
We had four kids this week. The kids were all very engaged the whole time.
At The Same Moment
The kids got the idea of the book and liked naming the places they had been. All of them have been on very long trips so the idea of time zones and figuring out the time in another place was pretty natural for them. They were also quite familiar with jet lag, particularly the ones who had gone halfway around the world.
This is always a popular activity and this week was no exception. One of the kids immediately asked why there was a 13 and 14. The kids went at wildly different speeds — in the 20 minutes we did this activity, one kid finished 4 and another finished only 1. The kids are pretty good at adding up the dice now, but some still need to think a bit for the bigger numbers. At one point, one kid noted that someone else’s chart looked like a pyramid (which is exactly what it looks like “in expectation”). As expected, we had lots of charts with 6, 7, and 8 winning; I asked them why and they didn’t have a good answer. One kid noticed that a different kid had two winning charts with “8”, so I asked whether it mattered who rolled the dice. The kid said “I don’t know” and then “I don’t think so?”
Tower of Hanoi
The kids really made a lot of progress during circle. Two of them started with 5, solved 6 without too much trouble; one of them finished 7 by the end of circle while the other almost did. Another kid started with 4, and after getting the hang of it solved up to 6. The final kid had a lot of trouble with 4, so I helped them with 3, then 4, and they were able to solve 5 by the end of circle. They all worked hard solving the problems and were clearly getting the idea of moving piles in order to clear up the discs they needed to move.
- Topic: Puzzles: Book: Taro Gomi’s Playful Puzzles for Little Hands. Still haven’t quite finished, this time it was mostly mazes.
- Topics: Number Line, Number Recognition. We revisited higher/lower number guessing again, mostly from 1-100. As usual, the theme of the game was a bear who wants to steal our picnic food. But the bear print-out was missing so kids took turns standing next to the wall and using their finger as the bear. I did a few numbers, and then each kid took turns thinking of their own number. At the end, we had a discussion about what makes a good or bad guess, and then I did one from 1-1000.
- Topics: Combinatorics, Geometry: Using wooden pattern blocks, find as many ways as possible to make a 2×2 diamond.
- Topic: Logic: We did the Seven Flipped activity from youcubed.org. Starting with 7 shapes face-down (we used Scrabble tiles), you could flip 3 tiles at a time. The goal is to flip all the tiles face up. After they solved that, I switched to 7 tiles, flip 4 at a time (which is impossible) and then 5 tiles flip 2 (also impossible), and we discussed why it might be impossible.
How Did It Go?
We had all five kids this week.
There is a very wide range of abilities in this game. By the end, three of the kids completely understood how the game worked, and during the discussion two of them worked together to figure out that they should guess half-way in between each time. One of the other kids usually made proper guesses, but the final kid frequently made guesses outside of the current range (even when they were just reminded of what the current range was). I also made a couple “illegal” guesses when I was playing, but was called out on it. 1-1000 is still pretty challenging even for the kids that get it.
The kids weren’t as in to this activity as I expected. A couple of them went off task pretty quickly, building whatever they felt like. One kid tried hard to use the skinny white diamonds, which doesn’t work. Another kid was trying but kept building diamonds that were 3 units on the side. One kid tried for a while to use squares, without success, but then eventually figured out a key insight for building different diamonds, which is that you can swap two adjacent triangles for a diamond, or vice-versa. So that kid generated more than half of the variants we found.
The kids each had their own set of tiles. There was lots of cheating, but it didn’t matter because I would just ask them to show me again. At first the kids decided it wasn’t possible, but after a few minutes one of the kids figured it out. Another kid watched them demonstrate, and then the two of them taught the other three. Then I switched to 7/4. There were lots and lots of claims of having done it, but it’s impossible :). After a while, I asked them to try 5/2 instead. A couple of the kids started to get the idea that it was impossible. I myself made a bunch of moves on this problem with the kids watching, and we kept track of how many were face up. With a hint the kids noticed is was only 0, 2, and 4. I made a set of maybe 11 tiles with 6 flipped up, and then showed them all the possible moves (2 down -> 2 up, 2 up -> 2 down, and 1 up, 1 down -> 1 down, 1 up), and they saw that it could only be +2, -2, or 0. One or two of the kids might have understood this proof that 5/2 is impossible.
- 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.
- 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.”
- 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.
- 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.
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.
The kids figured out the answers pretty quickly. Interestingly, different kids figured out the second one from the first.
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).
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.
- Topic: Puzzles. Book: Taro Gomi’s Playful Puzzles for Little Hands. The kids still love this book, though they’re getting slightly impatient. The most interesting page this week was one where you’re supposed to trace two different shaped mazes with two hands at once. Each kid wanted to try it more than once.
- Topic: Logic, Puzzles. The kids played Tower of Hanoi, first with two discs, then 3, 4, 5, 6, 7. Before moving to a higher number of discs, I usually asked them to solve the current puzzle twice. To solve the Tower of Hanoi you have to move a stack of discs from the left peg to the right peg following two rules: you can only move one disc at a time, and you cannot put a larger disc on top of a smaller one.
How did it go?
This was our first circle in a few weeks, due to holidays and vacations. This week we only had two kids, due to summer break. This made for a very easy and relaxed circle. I was able to spend time with each kid, working on the Tower puzzle. I gave quite a bit of advice to each one to help them solve the seven disk problem. Eventually the kids noticed that solving the 7 disc problem requires first solving the 6 disc problem, then the 5, 4, 3, 2 disc problem. By the end, they were quite confident about solving the 4 disc puzzle, and could also independently solve 5 discs. Higher than that started to get complicated and required help from me.
- Topics: Logic, Puzzles: Book: Still More Stories to Solve by G. Shannon, stories 6-8.
- Topics: Optical Illusions, Geometry: We did several activities from The Usborne Optical Illusions Activity Book, by S. Taplin. The first activity was about coloring a diamond grid — the well-known illusion about two different ways to see a pattern of cubes. The second activity involved a pattern with several rows of arrows, odd rows point left and even rows pointing right — once colored, it can either look like, say, red arrows pointing right on a blue background, or blue arrows pointing left on a red background. The third activity was a circle of dots which when connected in the specified way generated a circular hole in the middle in the shape of a circle. I extended this activity by showing the kids how to draw a line drawing of a star: Draw a cross on a sheet of graph paper, and then draw a line from (0, X) to (12 – X, 0) for all X.
Only a few misplaced lines
Sometimes it’s hard to remember to move both sides of the lines
How Did It Go?
We had all five kids this week. I realized 15 minutes before circle we should have done an activity involving Pokemon, and indeed there was a lot of talk about Pokemon Go during circle while the kids were coloring. We’ll definitely do something about Pokemon soon.
Still More Stories to Solve
The first puzzle was a variant of “This sentence is a lie.” — awfully hard for an 8-year-old to guess. The second was about a king saying “Don’t do X until you see my face” (meaning, “until we meet again”) and then someone sees the king’s face on a coin so they do it earlier. With some clues the kids realized that people’s faces were on money, and then they figured out the answer exactly. The last one also went pretty well, they needed a lot of hints but they figured it out.
The first two only went ok, the kids were fine coloring the pictures, but then they weren’t impressed by the illusion at all. For the cube one, I’m not sure if they were actually seeing it both ways, or if they were just uninterested; it’s very hard to tell the difference. Most kids said something similar for the arrows: they said “They go both ways.” One kid was quite sure that they were blue arrows going left, because the top and bottom row were red, so red looked like the background. I added a row of blue arrows to the top, and then they said that the arrows didn’t go either way.
The third activity (circle of lines) was fine, not too hard and a nice-looking result — but still not that much excitement. However, the star-shaped pattern was much more interesting to them. It was tricky to do correctly — many of the kids repeatedly forgot to move one of the endpoints of the line. In the end, all of the kids asked for me to make another cross on grid paper so they could take it home and try it again. At first, I was doing the wrong thing — connecting (0, 12) to (1, 0) when I should have connected (0, 11) to (1, 0). One very interesting thing about this activity is that there are several closely connected curves. Besides the one we did, there’s also one where the length of the line you draw is constant (draw all possible lines of length 12 connecting the X axis to the Y axis), and there’s also connecting (0, X) to (1/X, 0), which makes a hyperbola.
- Topics: Logic, Puzzles: Book: Playful Puzzles for Little Hands, by Taro Gomi. This is the third time we’ve done puzzles from this book.
- Topics: Tesselations, Geometry, Patterns: Each kid made a square-based tessellation by starting with a 3 inch square of poster-board, drawing an inset on two adjacent sides, cutting it out, and taping to the opposite side. They each kid filled a 8.5 x 11 sheet of paper with the tessellation and colored it.
A rather ambitious tessellation
How Did It Go?
We had three kids this week. We took it pretty easy this week after the month long break.
This continues to be a great book, lots of interesting fine details in the “What’s different?” puzzles.
I started by showing them how to make a tessellation and how to trace it. Two of the kids made fairly simple tessellations, one made a very complicated one. I cut them all out and taped them. The two kids with easier tessellations started getting distracted and chatting part way through, so all three kids ended up nearly finishing. Two of the kids picked rainbow colors.