Airplanes Are Faster Than Worms (Even Magic Ones)

The Activities

  1. Topic: Counting: Book: I Spy Two Eyes: Numbers In Art by L. Micklethwait.
  2. Topic: Numbers: Using the 100 tile board, I picked about 15 random numbers, and then one kid at a time I named a visible number, which they then had to find and add to the board.  I then added another random number to replenish the 15.
  3. Topics: Transitivity, Verbal Discussions:  I asked the kids questions of the form “If a elephant is bigger than a horse, and a horse is bigger than a dog, which is bigger, an elephant or a dog?”  Some of the problems, like this one, the answer was obvious from the real world; some, you couldn’t tell (e.g., “John taller than Sam, Sam taller than George”); and some were intentionally counter-factual (“Worm faster than car, car faster than airplane”).  I gave each kid the chance to pick a theme for one transitivity problem.
  4. Topic: Programming:  With the help of a parent volunteer, I split the kids into two groups.  Within each group, one kid was the robot (taking turns) and the other 1 or 2 kids made the programs (we used colored gloves as described in earlier circles).  First, they made up whatever programs they wanted, and then I gave them several simple programs to do (go to the wall and back, walk in a square, spin around twice).
  5. Topic: Addition: Book: What’s New At The Zoo?  An Animal Adding Adventure by S. Slade.
  6. Topic: Measurement: I prepared strips of cardboard ranging from 3 cm to 24 cm, which I laid out on a table.  Each kid got a ruler, and I gave each one a different length strip they needed to find.  Each kid found about 3 different lengths.

How Did It Go?

All 5 kids attended.

I Spy Two Eyes

Each page had a work of art with between 1 and 20 of some particular item.  Once we got into the harder pieces I had the kids take turns finding and counting the items.

Tile Board

The kids were pretty good at finding the numbers, but still need practice at finding the number on the board.  We did about 4 times around the table adding numbers to the board.  Then I let them add as many as they could in 2 minutes, but some kids started adding numbers to random places, so we stopped early.  Our son has had a lot of practice with numbers, so I had him sit on the floor and gave him a pile of numbers to sort; and then each time he finished the current set, I would give him a few more to add to his sorted list.


The kids were definitely inclined to use real-life intuition.  For example, for the question “John’s father is taller than John, John’s mother is taller than John, who is taller, the father or mother?” they said the father was taller.  But some of them did explain that it was because fathers are usually taller than mothers.  By the end, I think they did notice the difference between A > B and B > C; vs. B > A and C > A.  The one puzzle that really gave them problems was “A worm is faster than a car, and a car is faster than an airplane, which is faster, worm or airplane?”  A couple of the kids are really into airplanes, so they were sure airplanes were faster.  I said “But it’s a magic worm” and “It’s a slow plane and a fast car”, but even after all that they still were convinced the airplane was faster.  On the other hand, they did pretty well on puzzles like “A grasshopper is yummier than an ant, an ant is yummier than a cockroach”, where there was no real-world knowledge to apply.


Splitting into two groups worked well, with 4 kids making a program for 1 kid, some of the 4 would probably have gotten restless, but with only 1 or 2 kids writing the program, and only 1 or 2 turns to wait before being the robot, they stayed engaged.  As before, the gloves are very helpful for left vs. right.  The other group that I wasn’t leading made very long programs that took the robot into another room.

What’s New At The Zoo?

This book was a series of addition problems, ranging from easy (1 + 2) to harder (8 + 12).  We practiced doing addition by counting up — e.g., 8 + 5 is done by counting 9, 10, 11, 12, 13; keeping track of the number of counted numbers on your fingers.

Measuring Strips

The kids were pretty good at this.  There was some confusion between inches and centimeters though.  They did a good job making sure to line up the strip with 0 at one end, so they were usually correct in their measurements.


Staying Late for Sudokus

The Activities

  1. Topic: Money, Addition: Book: Pigs Will Be Pigs by Axelrod. This book is about a family of pigs that hunt through their house for money to go to out to eat for dinner.
  2. Topic: Programming: First, work together with me to trace a program:
    Box_X = 10

    Print “I can count backwards!”

    Do 10 Times {
    ___Print Box_X
    ___Box_X = Box_X – 1

    Print “All done!”

    Next the kids had to write their own programs:

    1. Write a program that prints: “The witch laughed Ha Ha Ha Ha Ha Ha Ha”
    2. Write a program that prints: “Happy Happy Happy Happy Birthday to You!”
    3. Write a program that prints “2 4 6 8 10 12 14 16 18 20”

      One student's solutions to the programming questions.

      One student’s solutions to the programming questions.

3. Topic: Logic, Puzzles, Sudoku: I handed out a separate Unifix Soduku puzzle to each kid.  I have 500 Unifix Cubes, so it was enough for all the kids to do their own puzzle.IMG_20150426_174858

How did it go?

We had all 6 kids at circle this week, it was a loud, rambunctious, but happy circle.

Pigs Will Be Pigs

I had enough paper money and coins that we could make a stack of all the money that the pigs found in the book.  The kids were all excited to handle real money.  The book does not say how much total money the pigs had, so the kids added up our big stack and found 34.67, which matches the amount in the back of the book.

We also figured out how much money the pigs spent: $7.99 * 4.  Two kids suggested multiplying 8 by 4, and then subtracting 4 cents, so that’s what we did.  I’m not sure if all the other kids understood why that would work.

At this point, the kids were getting restless, so I skipped the last question, which is how much money did the pigs have left after they ate.


At the start of this activity I reviewed what had happened last time.  All the kids agreed that if something is too hard, they should keep trying and not give up or cry.

I started by tracing through the above program with all the kids. I really emphasized the start and end of the loop, since several kids had been unsure which lines were part of the loop.  I went around the circle asking each kid what the next line did and where the program went next.  By the end of this, all the kids seemed to understand the loop, even the two kids who had struggled with this in the past.

Next I handed out paper and pencil to write answers to the Happy Birthday program.  One kid finished first.  Their program was: “Happy Happy Happy Happy Birthday”.  I pointed out that the program did not tell the computer what to do with those words, so the kid changed it to “Print ‘Happy Happy Happy Happy Birthday'”.  That worked, so I challenged the kid to solve the same program with a loop, which they did after a few tries and a couple syntax corrections.

The other kids successfully wrote the loops with minor syntax problems. No one got too upset when I asked them to fix their programs.

The Witch program was also easy for most of the kids, though one girl initially wrote a program that printed “Ha ha ha ha laughed the witch”.

I then handed out the 2 4 6 8 10 program, and said it was a bonus problem, so it’s ok if you don’t get it right.  Eventually 4 of the 6 kids did successfully solve it, with a loop. Almost all of them had a few corrections before getting it quite right. Interestingly, they all figured out that they should add 2 to X each time.


The kids all loved the Unifix cubes.  Some had seen Sudoku’s before, and some hadn’t.  I started going around to each kid to help with their puzzle.  Some kids tried to just put blocks down and adjust the placements if the puzzle didn’t work.  I encouraged them to instead keep track of the possible colors, but putting a stack of blocks on the square.

At the end of circle, the kids did not want to stop working on their puzzles, so all the parents came in to try to help their kids.  These 6-color Sudokus are actually pretty challenging, so even with a parents help many kids didn’t finish.  However, it seemed like all the kids like the puzzle, so we’ll try it again.  Next time I’ll probably work through one whole puzzle while the kids watch, before I hand out individual puzzles.

Robot Hugs

The Activities

1. Topic: Big Numbers: Book: How Big is a Million? by Milbourne.

2. Topic: Numbers, Base Ten Blocks: Give each kid a number like: 6, 19, 34. Make that number using Base Ten Blocks to reinforce quantity to each kid. Some kids were ready for much bigger numbers like 2022, or 676.

3. Topic: Programming: A parent volunteer was a robot. The kids got to write programs for the robot, like “Bump the robot into the wall”, or “Walk the robot over to the table”.


The robot wore a purple glove on the left hand and a blue glove on the right.


The robot commands. The turns were colored to match the robot’s gloves.

4. Topic: Measurement: Book: Super Sand Castle Saturday by Murphy.

5. Topic: Measurement: Measure various household objects using Unifix blocks.

One student's measurement chart.

One student’s measurement chart.

How did it go?

I led the younger circle this week, four kids attended.

How Big is a Million?

The kids all liked this book. They had no idea how big a million is.  At the end of this book, there is a huge fold-out poster that shows a million stars.  The kids were all very impressed by how big it was.

Base Ten Numbers

I got out a bunch of unit cubes, 10-bars, and hundred squares. The kids all started playing with the material, for example, laying out out 10 units next to a 10 bar. I asked them how many 10-bars it took to make a 100-square.  My son answered but the others were not sure.  I lined up 10-bars on top of a square until it was filled, and we saw it to 10 10-bars.

I handed out papers with various one digit numbers written on them. 5, 6, 8, and asked the kids to get that many blocks.  They all successfully did this.

Next I gave out two digit numbers like 19, 13, 21.  These were much, much harder for the kids. A couple of the kids do not know what number ’19’ is…they call it ninety-one or one-nine.

Several of the kids do not know how to say ’34’. They say 3-4 or forty-three, instead of thirty-four.  I helped the kids use 10 bars to make their numbers. Next time I should make them count it one by one and then trade in for 10 bars.

My son has a lot practice with numbers, so he was able to make big numbers like 675 and 2022 by himself.  Which was good, because it kept him busy while I worked with the other kids.

Parent Robot Programming

One of the parents volunteered for this.  The parent put a blue glove on their right hand and a purple glove on their left hand.  I showed the kids what each command would do, and then asked the kids to write a program to bump the robot into a wall.

Immediately one of the kids put down 8 ‘straight’ arrows.  We read the program to the robot, and she bumped right into the wall!

Next, the daughter of the robot tipped backward in her chair and fell down. The robot immediately comforted her daughter. After she calmed down a bit, we decided to write a program to walk the robot over to the girl.  We didn’t have a ‘hug’ command, but we let the robot hug her daughter anyway 🙂

The kids all caught on pretty quickly.  Using colored gloves really helped.  The kids could quickly see which turning card to use.

The last program we wrote was to walk the robot around the kitchen island.  This was going pretty well, except my son got tired of the activity and started throwing the cards around.  Also, we ran out of ‘straight’ arrows, so couldn’t make it all the way around.


The last activity was measuring using unifix cubes.  I gave each kid a chart with several named objects. Then we sat around the table and each kid measure how many Unifix cubes long each object was.  After connecting the right number of cubes, they counted the cubes and wrote down the number in their chart.

Each kid measured two or three objects. Then all the kids went over to the coffee table to measure how tall it was.  It was 24.5 cubes tall, so some kids answered 24, and some answered 25.

Finally, we connected together everyone’s stick of 24 cubes. The kids were really excited when they saw the cubes were taller than me.

Speedy, Zippy, and Zoomer

The Activities

  1. Topics: Area, Measurement: Book: Sam’s Sneaker Squares by N. Gabriel.
  2. Topics: Area, Measurement: I printed out a variety of outlines of shapes (download here).  The kids had to figure out the area of each shape, using 1.5″ by 1.5″ square tiles (actually, they were a mix of 1.5″ by 1.5″ tiles and 1.5″ by 3″ tiles, from the board game “Caverna”).  We also discussed how you could figure out the area without explicitly counting.
  3. Topic: Logic: I discussed the following problem (courtesy of Kevin Bourrillion): Anne and Bob have each watched Frozen at least once.  I know how many times they each have watched, and I tell them that one of them has watched one more time than the other.  They then have the following conversation:
    • Anne: I don’t know how many times you have seen Frozen.
    • Bob: I don’t know how many times you have seen Frozen either.
    • Anne: Oh, now I know how many times you have seen Frozen.
    • Bob: Oh, then I now know how many times you have seen Frozen as well.

    The problem is to figure out how many times Anne has seen Frozen. (Note that Bob does not update his beliefs after hearing Anne’s first statement, otherwise there are two answers).

  4. Topic: Logic: We did 4 different logic puzzles from Mindware Math Perplexors: Basic Level.  Each kid had their own print-out.  The first two I read the clues to the kids (I only gave them the bottom half of each logic sheet), the next two they read on their own.
  5. Topic: Games, Attributes: We played half a game of Set, with two teams of three.

How Did It Go?

All six kids attended.

Sneaker Squares

Several of the kids already knew you could use multiplication to compute area.  This series has a nice mix of math and entertainment.

Measuring Area

I tried to get them to guess ahead of time the area, they mostly just wanted to start filling up without guessing.  It was about a 50/50 split for kids who thought the 4×4 square was bigger/smaller than the 6×2 rectangle.  Some of the shapes you could have been clever, e.g. using symmetry, but they almost entirely brute-forced it.  A follow up could be to have much bigger shapes where brute force takes too long.

Frozen Logic

I started by discussing a simpler version, where Anne immediately says “I know how many times you have seen Frozen.”  The kids got close but didn’t quite solve this without help.  Then I asked a version where Anne doesn’t know but then Bob does.  At first they got it wrong, but then one of the kids said you should cross off 1 for Anne (just like you would in a logic puzzle).  From here we were able to work out the solution to the full problem.

Logic Puzzles

A few of the kids had trouble with the first couple problems, but most of the kids solved the last two on their own with little help — they can all read the clues on their own now.  One of the problems involved turtles with nicknames Speedy, Zippy, and Zoomer, which the kids thought was funny.  This activity went much quicker than I expected, so we had time to play…


At first here was a LOT of incorrect, fast, loud guessing, some card touching/grabbing.  After a bit I came up with a rule that worked pretty well, which was that 1) they couldn’t touch the cards when naming a set, and 2) if they got it wrong, then that team couldn’t guess again until the other team had a chance (or after a certain amount of time, about 10 seconds).  Also, if they were having too much trouble finding sets, then I would name it and get it :).  Mostly they had trouble with sets where all the attributes are different, which isn’t surprising.  In the end, one team had 4 sets, one had 3, and I had 4.

Jump, Jump, Floopsy!

The Activities

  1. Topic: Counting: Book: Prairie Dogs Perching: Counting By 3s by A. Tourville.
  2. Topics: Numbers, Counting: We recently bought a 100 tile board, so we did a few activities with it.  First, taking turns, I pointed to a number and had the kid say the number.  Next, still taking turns, I gave a random number tile to the kid and had them place it on the board.  Finally, we used the colored tiles to count by 3’s.
  3. Topics: Combinatorics, Combinations: We had print-outs of Easter Eggs with two halves, top and bottom, to color.  There were four colors of crayons, you could use the same for top and bottom, and the rule was you couldn’t personally make the same combination twice (it was okay if you repeated what someone else did).  Each time someone finished an egg, I taped it to the wall.
  4. Topics: Reflections, Symmetry: I had printed out individual squares with letters in large font, and then folded them along a line of symmetry.  Taking turns, the kids had to guess what letter it was.  We used a hand-mirror to check before I unfolded it (by holding the folded symmetry line flush against the mirror at a 90 degree angle).  Then, I drew a couple half shapes (e.g., semi-circle) on a piece of paper and asked each kid to draw a completed reflection.  We discussed the several different ways to reflect each shape.  Finally, each kid drew their own shape which I reflected in the mirror.
  5. Topic: Counting: Book: How Many Sharks in the Bath? by B. Gillham.  Each page had 4 counting problems, and a place on the right with numbers 0-10 so you could point to your answer, so I did “counting twister” where one by one 4 different kids answered the questions and then held their finger on the answer.
  6. Topic: Programming: We did “Dance Programming” with 4 instructions: Jump, Up, Down, and Spin.  The kids stood in a line facing me, and I explained each of the instructions.  Then, I gave them sequences of up to 4 instructions, which they did (sometimes I did it as well, but not always so they couldn’t just copy me).  Next, I introduced the idea of functions and gave them two, “Moopsy” which was “Jump, Jump, Jump”; and “Floopsy”, “Spin, Down, Up”.  I then gave them some programs including these two functions plus basic instructions.  Finally, each kid gave me a program with up to 5 instructions that I had to do.

How Did It Go?

All 5 kids attended.  There was a bit of “when will circle be done?” after the egg coloring, but they liked the reflections and dance programming enough that it stopped after that.

Prairie Dog Counting

There was a lot of counting by 3’s in this book, I had the kids count along with me on many of the pages.

100 Tile Board

The kids are in pretty different places on recognizing, saying, and finding numbers above 20.  Some don’t know to say “fifty-four” for 54, saying “five four” instead.  Most of them didn’t realize that the rows went by tens, in increasing order; and most don’t have the sense that 84 is large and 18 is small.  But they were all happy to try and find the numbers on the board, so this activity went well, and they were improving as we went on.  After we had done two rounds of placing random tiles on the board, I gave them each 3 to place on the board (and then gave more to the kids who finished first).  The skip counting also was pretty helpful, some of the kids who have trouble counting by 3’s in the air were able to do it on the board.

Easter Egg Coloring

The kids got the idea right away.  After a while, a couple of them started looking for eggs that were new on the wall (as opposed to just making sure they were new for themselves).  In the end we got 13 different eggs out of 16, not bad.  They seemed to understand the difference between top red/bottom blue and top blue/bottom red.  We also got a few “rainbow eggs” that didn’t follow the rules — I made the mistake of taping those to the wall in a different place, which didn’t discourage making them.


At first, for each letter, after the kid guessed I would first show it held up against the mirror, then unfold it.  They were all surprisingly good at this activity, and we got through a whole pile of ~ 20 letters.  They also were pretty good at completing the shapes that I drew.  4 kids completed a semi-circle as a circle, the 5th reflected vertically.  I drew half a diamond, which was harder — most of the kids drew a triangle, while one drew an X.  I also drew a random shape which was harder still, but several of the kids successfully reflected it.  The kids were not as into drawing their own shapes as I expected, and they mostly didn’t get the idea of drawing half shapes (so, for example, one shape was a house, rather than a half-house).

How Many Sharks in the Bath?

Since the kids were doing the counting, each page took a little while; so we only did about half the book.  It was interesting watching the kids arrange themselves so they could all touch their numbers at the same time.

Dance Programming

Everyone liked this activity and followed along with the instructions; some of them were definitely able to follow successfully, but some may have been copying other kids.  Similarly, some of them understood the functions, but probably not all.  I got a little dizzy doing the kids’ programs :).

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.

1 Trillion Easter Eggs

The Activities

  1. Topic: Ratios: Book: Beanstalk: The Measure Of A Giant by A. McCallum.
  2. Topics: Combinations, Combinatorics:  I had printouts of eggs with the top and bottom separated by a line.  First, I gave them 3 colored markers and asked “If you have 3 colors, how many ways can you color the eggs?” (Answer: 9).  Then I asked about 5 colors, without actually giving them 5 colors, to see if they could figure out the pattern without actually doing the coloring.IMG_1328
  3. Topic: Multiplication: I had a bag of plastic Easter eggs with a slip of paper with a number from 1-9 inside each one.  At first, each kid drew out two eggs and had to figure out the product of the two.  After a few rounds of this, they started drawing out three eggs and multiplying them all together.
  4. Topic: Tesselations: Using pattern blocks, we worked together to make this pattern:IMG_1329

How Did It Go?

Four kids attended this week.  Everything went pretty smoothly this week.  At the end of circle, all the big kids went and voted on the birthday party activity in the little kids circle.

Beanstalk: The Measure of a Giant

This book was about ratios and was a good level for the kids.

Egg Coloring

When I asked about 3 colors, several of the kids immediately began coloring, and quickly found all the combinations.  They clearly have gotten better at looking what’s missing rather than just trying random combinations.  I asked how many there would be with 5 colors, the most popular answer was 15 (5 * 3).  Then I arranged the eggs into a grid (as shown above) with same color tops in the rows and same color bottoms in the columns.  I asked them questions about how many were there if you only had 2 colors and 1 color, and arranged the eggs in expanding “rings” to show what gets added each time you add a new color (this suggests another activity, proving that n^2 = sum of first n odd numbers).  I also pointed out how each column and row corresponded to a bottom/top color.  Finally, I asked what shape the chart was for each of 1, 2, 3 colors, and how many eggs on each side; at this point one of the kids saw that the pattern was to make an n x n square.  When I asked about 10 colors, I still got two kids saying 3 * 10, one saying 10 * 10, and one saying “I don’t know.”  After a bit more discussion they all decided it was 10 * 10.  I also asked 1000 colors and 1 million colors just for fun.

Egg Multiplication

A couple of the kids have already memorized their multiplication tables, so the two number multiplication was very easy for them.  However, three numbers was much more complicated.  In particular, they definitely don’t have the idea of multiplying place by place.  One of the largest multiplications was 9 * 9 * 6, quickly reduced to 81 * 6.  I gave them lots of hints for what 80 * 6 was: first I asked what 8 * 6 was (immediately got 48), and then using Base Ten Blocks, I said “If 6 * 8 unit blocks is 48 unit blocks, what is 6 * 8 ten blocks?”  No one ever realized the answer was 48 ten blocks — someone eventually added 80 6 times in their head to get the answer.  They were able to say that 48 ten blocks was 480 once I pointed out that 6 * 8 ten blocks is 48 ten blocks.


I had come up with this pattern when experimenting (playing) with the blocks one day, and thought it was both pretty and somewhat challenging.  At first, they didn’t get the rules and had trouble expanding the pattern.  But once I pointed out that the yellow was surrounded by blues and whites, and the green was surrounded by blues and whites, after some practice they were able to continue expanding the pattern.