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.


Spoons Full of Beads (Age 8)

The Activities

  1. Topic: Estimation. Book: Betcha by Murphy. In this book two friends estimate the number of various objects, e.g. cars on a block, people on a bus. It ends with guessing the number of jelly beans in a large jar.
  2. Topic: Estimation. Guess how many beads will fit on each of three different spoon sizes. First the kids guessed by just looking at the spoon. Then we piled on the beads, and I let them make a second guess based on the beads on the spoon. Then we counted to see how many there really were.
  3. Topic: Building. Next I gave each kid the small size of spoon and challenged them to fit as many beads on the spoon as they could.
  4. Topic: Charts. Each kid tracked a different attribute of a Pokemon: color, height, hit points, number of abilities. We flipped over 10 random Pokemon cards and each kid updated their chart. Then we looked at our charts and predicted how the chart would change when we add in the next 10 Pokemon cards.

How did it go?

We had four kids this week, and it was a rowdy but good-natured circle. Several kids got off topic at various points but they generally came back on track after some warnings from me. This morning was my daughter’s 8th birthday party, and she had come home completely exhausted and grumpy. I was quite worried she would want to sit out circle again, but she actually did ok, though she was gigglier than usual.


The kids all enjoyed the book, and played along making their own guesses. The spoon activity was also fun. It was a bit tough to get kids to actually make their guesses, but once they were written down, everyone enjoyed helping to put the beads on the spoon and counting the beads to see who was closest.

We started with the medium sized spoon, and they realized the smaller one would hold fewer, and the bigger one more. Their second guesses (after seeing the beads on the spoon) were generally more accurate than the guess based just on the spoon.

Piling Beads on Spoons

The kids were not satisfied that I had really gotten the maximum number of beads on each spoon, so I gave them a chance to do better. I gave each kid a small-sized spoon and we sat on the floor piling beads on the spoon.  Initially we had gotten 30 beads on the spoon. I managed to get 39 on during this activity, which is one more than the 38 that had fit on the medium sized spoon. Two other kids got 34 and 36 beads. At first my daughter was messing around and giggling but eventually she got quite serious and managed to get 41 beads on her spoon, beating me by two.  The last kid never really tried and mostly threw beads around the room or put them in pockets.IMG_20160731_170549

Pokemon Charts

4 of the 5 kids are obsessed with Pokemon Go, so last week David promised them a Pokemon activity. We thought making charts of various Pokemon attributes would fit into this lesson because we could predict the attribute distribution after some Pokemon to the chart. However, this turned mainly into a looking at Pokemon and making tally marks activity. Not sure how much we really learned here, but the kids enjoyed it.  Two kids did notice that their attributes were closely related: nearly every pokemon with 40 or fewer hit points is also shorter than two feet.  We also noticed that nearly every Pokemon card has two attacks. A few have one attack, and none seem to have three or more attacks.IMG_20160731_173211

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.

A New World Record! (Age 7)

 The Activities

  1. Topic: Subtraction: Book: Shark Swimathon by S. Murphy.
  2. Topic: Sorting: The kids sorted numbered cards from 1 to 104, trying for a new world record.
  3. Topics: Charts, Graphs:  We simulated a race between a tortoise and a hare, where the hare tortoise started in Box 8 and moved 1 square a turn and the hare started in Box 0 and moved 2 squares a turn.  First we each made a table of the positions of the tortoise and hare at each step (in two columns), and figured out when the hare would pass the tortoise. Then we plotted these positions with time as the X axis and position of the Y axis, using different symbols (X vs. O) for the tortoise vs. hare.  Then, we added two more even faster animals, which started at 0 after some number of steps.
  4. Topic: Programming: We did a new kind of programming based on the iOS game CargoBot (which I highly recommend).  In this game, you control a claw arm which can move Left, Right, or Down; when it moves Down, it grabs a block if it doesn’t currently have one, and drops its block if it doesn’t. The goal is to move the blocks from a given starting position to a different given ending position.  This week, the first problem was to flip a tower over onto the adjacent space (note that there can be several colors of blocks).  The second problem was to move a tower two boxes over, WITHOUT flipping it.

How Did It Go?

We had all five kids this week.

Shark Swimathon

Pretty straight-forward math (simple two-digit subtraction), but the kids liked the story about the sharks.


This was the first time in a while we had all five kids for the card sorting activity.  They’ve now got the radix sort strategy down pretty well (i.e., putting cards directly where they should go).  There was still some unnecessary work (moving cards around to make space, even though it was ok if the cards overlapped) and not everyone contributed the whole time.  But the kids beat the previous record by a substantial margin, successfully sorting all 104 cards in 5:40.

Graphing the Race

I had a race track with numbers 0-40 and a couple of markers for the animals.  We simulated the race until the hare caught the tortoise.  The kids are pretty good at tables now and had no problems recording the positions.  They also noticed the pattern and started adding to their tables without using the simulation.  The graphing was tricky for them, as it has been in the past, but I think it went better than it has before.  For one thing, they again noticed the pattern, so they didn’t have to count from scratch for each new point.  They did often make mistakes like going right 1 and up 3 instead of right 1 and up 4 (for the ostrich).  In retrospect, I should have make the Y axis be time, going down, and the X axis be position.  Then each row would correspond to a snapshot of the race.  I did explain that each column was a snapshot of the race, I’m not sure if they understood.  This was the first time we’ve gotten nice graphs of straight lines, and the kids were pretty into it and probably would have kept going for a while with new animals.

Cargo Bot

The kids picked this up faster than I expected.  One kid immediately started using L, R, and D as short-hand, which we’ll explicitly suggest in the future since it saves a lot of time.  About half the kids solved or nearly solved the first problem on their first try, getting the pattern of RDLD.  For the others, I simulated using my hand their instructions and they saw the bugs in their programs.  One of the kids solved the first problem quite a bit faster than the others and started work on the second; they got a solution that moved the tower over 2 spaces but inverted the order of the blocks.

Hysterical Programming

The Activities

  1. Topic: Pie Graphs, Percentages: Book: The Grizzly Gazette by Murphy
  2. Topic: Programming:
    1. Trace a program:
      Box_X = 0
      Do 4 times {
      ___Print Box_X
      ___Box_X = Box_X + 3
      Print Box_X
    2. Write a program that prints the numbers 1 – 10.

      One student's program that prints 1 - 10.

      One student’s program that prints 1 – 10.

  3. Topic: Spatial Reasoning, Compasses:
    1. Practice drawing circles using the compasses.
    2. Draw a stop light, Draw a snowman.IMG_1345
  4. Topic: Logic: Hand out the first two logic puzzles from Perplexors Level A, and work through them with the kids.

How did it go?

We had all 6 kids this time.  Circle was more difficult than usual this time, partly because 2 of the kids came pretty and late, and partly because my daughter was crying during most of circle.

She puts a lot of pressure on herself to do well in circle, especially on programming activities, so when her first try to write the program didn’t work, she got very upset.  Eventually I sent her to her room to calm down.

While she was gone, I had an interesting conversation with the other kids.  One of the kids thought my daughter was crying because the problem was hard so she didn’t want to try it again. Another kid thought she was crying because she wanted to solve the problem but there wasn’t enough time for me to help her on it.

After she came back, she slowly calmed down, but still was quite fragile throughout circle.

Book: Grizzly Gazette

This was a fun book about a girl named Corey who was in a camp election. The kids were really invested in figuring out how many votes Corey would need, and reading the pie charts for the candidates.


First the kids traced through the program above that prints 0 3 6 9 12.  Two of the kids got it completely independently, and two more got it with a bit of help. The other two didn’t really understand it, but unfortunately I didn’t have time to go through it with them, especially since a couple kids had come late.

Next I handed out paper and pencils and asked the kids to write a program that would print the numbers 1 through 10.  One kid answered immediately: Print “1 2 3 4 5 6 7 8 9 10”.  I showed everyone his program and said that that would work.

I asked if the kids could write the same program, with a loop.

My daughter answered first with:

Box_X = 0
Do 9 times {
___Print Box_X
___Print Box_X + 1

I traced this through with a couple of kids, and we found that this prints “0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1” I suggested that the problem was that she was not updating the value of Box_X. At this point, my daughter got very upset, and cried through the rest of the activity 😦

A couple more kids came up with plausible answers that had small bugs, or unsupported statements. For example, one girl wrote:

Box_X = 0
Do 9 times {
___Print Box_X

(Add is not a command in our language)

Eventually, one girl came up with a working program!

This was definitely a hard activity for everyone. The kids worked hard at it, but there are still some who need more practice tracing loops before they’ll be able to write their own.


One of the girls in circle LOVES compasses, so she was really excited when I got them out. All the kids started trying to draw circles, but compasses are hard to use! Some kids really had trouble drawing any circle.

After some practice, I asked the kids to draw a stoplight.  The kids realized they had to draw three circles of the same size in a vertical column. One kid’s first attempt had overlapping circles, but he fixed them.

Next the kids tried to draw snowmen. They all figured out how to draw three circles of different sizes, but they had trouble lining them up right. Either the circles overlapped, or they were too far apart.


I gave each kid a copy of Puzzle #1 from Perplexors Level A.  The puzzle was about three teachers (Ms. Rok, Ms. Roll, Mr. Rapp) who taught three subjects (reading, writing, arithmetic), and gave out rewards (brownie points, red letters, gold stars).  There were three clues to figure out what each teacher taught and which rewards they used.

All the kids enjoyed this activity, though it was not easy for them.  Several kids noticed non-obvious conclusions for each game. For example, if Mr. Rapp did not teach writing or arithmetic, then he must teach reading.

My Pretend Birthday Party 3

The Activities

  1. Topic: Charts. Book: What Do You Like? Math Concept Reader
  2. Topic: Charts.  My birthday was last week! The kids helped me plan a pretend birthday party by voting on different items using various charts and graphs.
    1. What drink?
    2. What snack?
    3. Where should the party be?
    4. What game?
    5. What kind of cake?
    6. IMG_1333IMG_1332
  3. Topic: Search, Number Ordering. The evil, made-up Easter Goblin loves to steal eggs. She thinks of a number between 1 and 40, and if you don’t guess it in time, she gets an egg. I started by letting the kids have 10 guesses to find the number. For example: Is it 30? No, it’s higher than 30.  Then I used a number line to help them keep track of which numbers it could be.
    The dastardly Easter Goblin vs the Math Circle kids.

    The dastardly Easter Goblin vs the Math Circle kids.

    The number line showing that the number must be between 20 and 25.

    The number line showing that the number must be between 20 and 25.

    How did it go?

    I led the younger circle this week, and all 5 kids attended.  The kids were very engaged in all the activities, and did a good job waiting their turns.

What do you like?

This is a simple Math Concept reader that describes a group of kids planning a neighborhood block party. It’s pretty dry, but the kids were interested in the graphs and charts and voting.

My Pretend Party!

I’ve planned a pretend party each of the last two years with the older kids. This is the younger kids first chance.  Before circle I had prepared 5 different types of charts for voting. During circle, the kids helped me fill in the chart, suggesting what types of cake, etc we should vote on.  The kids really enjoyed this part…everyone was constantly raising their hands, ready to contribute.

Next we passed each chart around to each kid so they could vote on each topic. We had a chart where you write you name under the option you choose, make a tick mark next to your two favorites, fill in a box in a bar chart, and write your name + write an X in the box you choose.

At the end of circle, I handed one chart to each kid, and had all the parents and the kids from the older circle vote. Each kid had to explain what their chart’s topic was, and how to vote.

In the end, my pretend party was a Pump It Up, with chocolate cake and crepes and fruit. We’ll drink water, and play soccer at my party.  Sounds fun!

The kids were a bit sad when they learned they would not get to actually go to this party, but they sang me Happy Birthday and we shared a pretend cake.

The Easter Goblin Guessing Game

I told the kids about the made up Easter Goblin who steals eggs and keeps them in her purse. My daughter and I had made some nice construction paper eggs before circle. The eggs were taped on the wall between the Easter Goblin, and a picture I drew of the 5 Math Circle kids.

Each round the Easter Goblin (me) wrote down a secret number between 1 and 40.  The kids got 10 guesses to figure out my number. If they did, then Math Circle got an egg. Otherwise the Easter Goblin got one.

The first couple rounds I had a number line out on the table, but didn’t really help them figure out the possible range for the answer.  We had guesses like: 20? no, lower. 30? no, lower.  Also, one of the kids loved to guess huge numbers like 100 million or infinity.

After this, I started tracking the range of possible numbers using two glass beads on the numberline. This helped the kids a lot, and I only gave them 6 guesses.

The kids did understand that they should only guess numbers in the range, but they still need practice with number recognition. They are not sure if 27 is twenty-seven or seventy-two.  When we do this again, I’ll make sure all the kids are seeing the number line rightside-up.

The kids loved beating the Easter Goblin, and they won 5 of the 6 eggs (one time I gave them extra guesses).

Kitties, Cubs, and… Goatlings?

The Activities

  1. Topic: Patterns: Book: A-B-A-B-A- A Book of Pattern Play by B. Cleary.
  2. Topic: Patterns: We made rows of colored glass beads in different patterns.  I gave a starting pattern with 5-6 beads, which they copied and then continued the pattern.  They also each made up a pattern on their own.  Here’s the grid we put the stones in.IMG_1312
  3. Topic: Logic: We did three Halloween-themed logic puzzles.  For example, in the first one, there were 4 monsters and 4 candy buckets, and you have to figure out which one goes with which.  One of the clues is “The ghost likes orange”.  The full set of pictures and clues is available here (including 4 extra clue sets we didn’t do).
  4. Topic: Verbal Discussions: I named a bunch of animals and asked the kids what the baby animals of that type were called.
  5. Topic: Counting: Book: Skip Counting with Meerkats by T. Steffora.
  6. Topic: Counting: We counted by 2’s and 3’s as a group taking turns going around the circle.
  7. Topics: Shapes, Charts: We have a large two-dimensional table with colors on the rows and shapes on the columns.  The task was to place the Attribute Blocks onto the chart.IMG_1314
  8. Topic: Origami: Each kid made the cat from Easy Origami by J. Montroll.

How Did It Go?

All the kids attended.  The kids were mostly attentive through out, although there was the usual “Is it time to go play?” starting about 40 minutes in.

A-B-A-B-A- A Book of Pattern Play

A decent introduction to simple patterns.

Glass Bead Patterns

All of the kids were able to complete all the patterns I made, (which went up to cycle length 4).  They weren’t fooled by an all-blue pattern.  One of the kids said they wanted to make their own pattern, so I gave them time to do that.  One kid used the columns of the grid for their own pattern instead of the rows.

Halloween Logic

The kids did well on this activity.  On several occasions, they remembered an important relevant clue from earlier in order to solve a puzzle.  However, they weren’t quite ready to solve the puzzles on their own — I still needed to ask leading questions several points, particularly on the 3rd (and hardest) puzzle.  The kids were pretty good at following the instructions, but there were a few times where someone said something like “I think the cat likes the hat because a cat can’t use a broom.”

Animal Babies

The kids knew a reasonable number, including kitty, puppy, calf, cub, and duckling.  They didn’t know foal/colt, piglet, tadpole, or gosling.  The most interesting guess was “goatling”.

Skip Counting with Meerkats

One of the kids knew the animals in the pictures were meerkats, from Happy Hollow (or rather, “Danny the Dragon place”).

Counting by 2’s and 3’s

The majority of the kids still aren’t very good at counting by 2’s or 3’s — two can do it reliable, three can’t.

Attribute Block Chart

I was impressed by the kids performance on this task, I remember Circle 1 having some issues, but all the kids got the idea and were able to do it.  Initially a number of the shapes were placed incorrectly because the kids didn’t want to put more than one shape in each box, but once I showed them stacking was ok, they placed all the rest of the shapes without problems.  The kids also put all the shapes back into the box afterwards.


The kids are decent at making folds, but the idea of making a fold from point A to point B, or so that an edge lines up with a given point, is tricky for them.