Shoes for a Three-Legged Bird (Age 5)

The Activities

  1. Topic: Addition: Book: Double Play: Monkeying Around with Addition by B. Franco.
  2. Topics: Addition, Games: The kids took turns tossing two or three beanbags onto a large piece of poster board with numbered regions.  They then had to add up the numbers of the regions their beanbags landed on, using Base Ten Blocks if they wanted to.
  3. Topics: Pigeonhole Principle, Probability:  I had a bag with 12 “shoes” (colored glass beads), 4 shoes each in 3 different colors.  We first discussed how many draws from the bag it would take to get a pair of matching shoes.  Each kid took turns drawing until they god a pair.  Then, for each number of draws, we talked about whether it was impossible, possible, or certain to get a pair.  We then repeated the whole process for a three-legged bird.
  4. Topics: Latin Squares, Puzzles:  Using pieces from Qwirkle, I made sets of 9 tiles using 3 colors and 3 shapes (so there was one of each possible combination).  Each kid got one set.  First, they had to arrange them in a 3×3 square so that each row had matching colors and each column had matching shapes.  Then, they had to arrange them so no row or column had any duplicate shapes or colors.  After they solved this, then we combined 4 of the sets to make a 36 tile set with 6 colors and 6 shapes.  Working together they had to try to build both the matching and mismatching arrangement.
  5. Topics: Alphabet, Sorting:  This was a repeat from last week, I gave each kid one random letter and they had to arrange themselves in alphabetical order.

How Did It Go?

We had four kids this week.  It was a fairly calm circle, all the kids concentrated on all the activities.

Monkey Doubling

This book is about the right level for them, they understand the idea of addition but 9+9 is still a bit hard.

Beanbag Addition

The kids liked this game quite a bit, we ended up playing for almost half of circle.  For some of the kids, I wrote down the problem they needed to solve after they tossed their beanbags, others wrote it themselves.  Most, but not all, of them knew how to write two-digit numbers.  They did better than I expected at addition — they’re all comfortable with how addition works now.  Some used blue blocks, one used fingers.  They still have some trouble counting reliably though, so there were some mistakes.  By the end they were all adding up three numbers.  Our son is really advanced at calculation, so he did multiplied his numbers instead.

Matching Shoes

The kids liked drawing the beads out of the bag and would have gladly done another round (we did two full rounds, one for the 2 shoe problem, the other for the 3 shoe).  We got a good distribution of number of draws before getting a pair/triple, and a couple of the kids were able to sort of explain why 3/6 was the most you could get without a match, so they got the right answers to impossible/possible/definitely by the end.

Latin Squares

After I gave them their sets, I said they could look at their tiles for a bit (I didn’t explain anything about what was on them); during that time, one of the kids solved the first problem (matching rows/columns) on their own!  The mismatching problem (technically, it’s probably a “double” Latin square, I suppose?) was quite a bit harder, but most of the kids were able to solve it without help; the final kid got help from the other kids.  After we joined together the sets, it turned out that getting the matching 6×6 square was harder than expected, there were a number of mistakes (always a mistake in shapes, not colors, primarily because they were going row-by-row and the matching colors were in the rows).  But they got this eventually without help.  The 6×6 Latin square is really tricky, I’m not sure the older circle can solve it; the little kids placed about 18 tiles before giving up.  It was much harder for them to figure out what was legal at any given spot than for 3×3.

Alphabet Sorting

The kids like this activity a lot.  The first time they got L, M, N, and T, and ended up M, L, N, T.  Like last week, I checked by singing the song and tapping heads as I sang; and they realized they needed to switch L and M right away.  The second one they got right on the first try.

Optimized Cargo Bots (Age 7)

The Acitivites

1. Topic: Algebra. Book: Safari Park by Murphy.  5 kids each get 20 tickets to spend on amusement park rides. Work out simple algebra problems to figure out how many tickets each kid has left.

2. Topic: Algebra. I made several worksheets with simple algebra problems. I divided them by difficulty into three levels. Level One was problems like: 3 + X = 30. A Level Two problem was 3 * X = 15.  Level Three problems were 2 * X + 5 = 25.  Here are the problem worksheets.


3. Topic: Programming. We continued with Cargo Bot programming problems this week.  Move a stack of 3 blocks from square A to square F. Then ask the kids if there are any repeated sections, and introduce sub-programs. What’s the shortest program that can solve the problem?


How did it go?

We had three kids this week. It was a quiet, focused circle.  My daughter has been crying a lot during circle recently (much to her disappointment), and she did much better this time.  What a relief! She loves circle, but gets very upset if it doesn’t go how she expects.


We did algebra problems about six months ago, and the kids are much, much better at it now. After each kid finished a worksheet, they could either move up to a harder problems, or choose to do another sheet of the same level.

My daughter decided to do two Level One worksheets before moving up. The other two kids moved up a level after each worksheet.  One girl sped through the problems, finishing her Level 3 sheet with essentially no help before the others had finished Level 2.  She worked on the other Level 3, and also the easier levels while the other two kids finished.

Two problems on Level 3 were: X * 0 = 0, and X / X = 1.   Each kid put down an answer for X, e.g. X = 3.  I asked if they were sure X was 3, and they said yes, 3 works.  I asked if X could be anything else, and eventually they realized that X could be any number.  I suggested putting a question mark down in those boxes.

Cargo Bots

There’s an App called Cargo Bots about a machine moving boxes around a warehouse. We used pen and paper to solve Cargo-Bot-like problems.  There are three commands: Left (L), Right (R), and Drop (D) which picks up or drops a box.

The first problem was easier than last week’s question…they just had to move a stack of identical boxes from square A to square F.  Two of the kids immediately wrote out correct (long) programs to do this. The third kid complained that the program would be very long.  I checked her progress, and it turned out she had written code to move the whole stack of blocks from square A to square B.  She was then going to move them all to square C.  I suggested she could move them directly to Square F.

Meanwhile, my daughter noticed repetitive parts of her program, so she replaced the strings of “L, L, L, L, L” with: “Do L 5 Times”.  She then proudly announced that her program was only 11 lines long now.  This was a great insight, but I had been planning to do subprograms with a different syntax.  My daughter was rather upset when I tried to explain that the robot arm didn’t understand the command “D L 5 Times.”  After a minute of discussion, she finally calmed down and we moved on.

Our subprogram syntax was to write a ‘1’ off to the side. Subprogram ‘1’ could contain any basic commands.  For example: 1 = “L L L L L”.  Then we could erase any string of 5 Ls in our main program with ‘1’.  To count the length of a program, you count each line of the main program, plus all the lines in the subprograms.

I then assigned a new task: Move 3 blocks from box C to box A, and try to make the shortest possible program.  Here’s my daughter’s solution:


The other two kids took a bit longer to solve this, but made good progress on their own.  One girl had two subprograms, which added up to 12 lines.  My daughter helped her try to get down to 9 lines.  In the course of the help, the girls realized that it was impossible to do it in 9 lines, and that my solution had a bug…I was missing the final ‘D’ in the main program.  This made them very happy.

Pick a Pickle (Age 5)

The Activities

1. Topic: Odd and Even. Book: Splitting the Herd by Harris. This is an interesting book about two neighbors dividing up cows that have escaped from the fence.

2. Topic: Sorting. Give each kid a number and have them sort themselves. Then give them letters to sort.


3. Topic: Adding. The kids got worksheets showing boxes with 2 dice in each. They had to color each box where the sum of the dice was 5. Each completed sheet formed a letter, which spelled out a message. Here are the worksheets.


“Pick A Prize”

4. Topic: Spatial Reasoning. I photographed some pictures I had made out of Wooden Pattern locks, and the kids recreated them.

IMG_20150718_084016 IMG_20150719_171420 IMG_20150718_084204

How did it go?

We had 4 kids this week after a couple weeks without circle, due to vacations.  The kids seemed happy to be back, and all contributed to the activities.


First the kids were randomly given numbers between 1 and 100.  The kids had to stand against the wall in sorted order. Most of the kids could correctly name a number, e.g. ’27’ is twenty-seven, not seventy-two. But only one of the kids was confident whether 27 is smaller than 72 or not.  We decided to count by tens to find out if twenty comes before seventy.

Next I said we were going to sort letters. The kids said we could use alphabetical order.  They agreed ‘A’ was first and ‘Z’ was last.  I handed out random letters to each kids and they sorted themselves against the wall. Once they were satisfied, I would sing the ABCs and tap each kid on the head when I said their letter. Often they would find out that they were not in the correct order. After two or three sets of letters, one of the kids took charge and would sing the song to herself to sort the other kids.


The kids went right to work. Some kids checked each box in order. One girl realized that 2 + 3 was 5, so she searched her sheet for all 2+3s.  Next she did 1+4. Two of the kids really zoomed through their sheets, the others took more time but did make progress.  At the end we taped the sheets to the wall in order and sounded out “Pick A Prize”. After circle each kid got to choose a small prize from my shoebox of math prizes.

Pattern Block Diagrams

All 4 kids were surprisingly good at recreating shapes from my photographs.  Each kid did at least 4 of the designs. One girl wanted to keep going even while we were picking up and getting ready to choose a prize.

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.

3178 Sprinkles (Age 7)

The Activities

  1. Topics: Angles, Geometry: Book: Hamster Champs by S. Murphy.
  2. Topics: Jeopardy, Arithmetic, Story Problems, Measurement, Programming, Sudoku: We played Math Jeopardy this week.  The problems can be downloaded here.  The topics were
    1. Arithmetic Chains: The kids had to evaluate a chain of arithmetic operations from left to right: 7 * 8 + 9 / 5 = 13.
    2. Extra Information: These were story problems that all had some extra information.  For example, John has 2 cakes, each with 7 pieces, and each piece has 227 sprinkles.  How many pieces of cake are there?
    3. Estimation: We had a number of objects of different lengths, for each question the kids had to guess the length in cm within some bound (+-1 for a 5 cm object, +- 5 for a 40 cm object).
    4. Programming: The kids had to trace a program using our standard language and execution worksheet.
    5. Sudoku: The kids had to solve 4×4 sudoku with increasingly many numbers missing.

How Did It Go?

We had all 5 kids this week.  The Age 5 circle didn’t happen this week so we both helped with the Age 7 circle.

Hamster Champs

This book was about angles.  The kids really liked it.  They loved the hamsters having to trick the cat.

Math Jeopardy

This was a very competitive game, it came down to the last question and the final difference was only 100 points.  All the kids contributed to their teams.  The way we handled the guessing was whichever team raised their hand first got to guess; if they were wrong, the other team got another 30 seconds to work on it; if they still got it wrong, the first team could guess again.

Arithmetic Chains

This was the easiest category.  The first three were quite easy, but the division caused them more problems.  65 / 5 was fairly tricky for them.  But in the end they got all of these correct.

Extra Information

The problem about the cupcakes (1000 cupcakes in 10 groups, 200 kids ate all but one from each group, how many left?) was the hardest in this group, and no one got it right.  We got 10, 999, and 800 as answers.  The 500 was answered correctly, but probably due to luck rather than fully understanding the answer.


This was the category with the most zeroes; the kids consistently under-guessed.  They usually missed by just a bit more than they were allowed to.


The 300 turned out to be the hardest for them, because they forgot how loops with multiple statements worked.  We went over that problem after no one got it right; and then they were able to answer each of the 400 and 500.  The 500 programming was the final question, and most of the kids made good progress on it.


The 200 puzzle was broken (I had made a mistake when preparing it, which is now fixed); one of the kids pointed it out almost immediately.  4×4 sudoku is easy enough that you can often guess and get it correctly on the first try.  All the kids were able to make progress.  All the puzzles were solved correctly but there was at least one incorrect guess.