Counting without Seeing (Age 5)

The Activities

  1. Topic: Zero, Multiplication, Addition. Book: A Place for Zero by Lopresti. This book covers the additive and multiplicative properties of zero in a very flavorful and engaging way.
  2. Topic: Counting. We used the Base 10 Blocks to count to 100 by 10s, and 1000 by 100s and 10s.IMG_20151129_175021
  3. Topic: Search, Pan Balances, Inference. I showed the kids a box that contained some number of plastic leaves.  I asked them to figure out how many leaves were in the box without opening the box.  I gave them a pan balance, and an identical, empty box.IMG_20151129_174846


How did it go?

There were only 3 kids at circle this week due to Thanksgiving travel.  It was a really good, focused circle.  All three kids paid attention and took turns very nicely.

A Place for Zero

The kids really enjoyed this book, about poor Zero who has no place in numberland. One kid predicted that Zero would be paired with a One to make 10 (which turned out to be true).

The book first shows how any number + Zero = the number.  Next Zero headed off to multiplication land to try to multiply himself.  At this point, I paused the book, and used Base 10 Blocks to teach the kids about multiplication.  Two of the kids had not done multiplication before, but I explained that 2 * 3 means you make 2 groups with 3 items in each group, and then count how much you have.

We did a couple small problems like that, and then I asked how much would 0 * 7 be? Two kids thought it should be 7.  My son said it would be 0.  I said, well, if we make Zero groups each with seven cubes, how may cubes do we have?  The kids agreed that would probably be zero, but were not super convinced.  I figured that 7 * 0 was probably easier to explain.

I said, “If I give you 7 bags which each have 0 pieces of candy in them, how much candy did you get?” All three kids immediately saw that they would have no candy.  After circle, I quizzed one girl, in front of her mother: “What’s 1,000,000 times 0?” and she instantly said “0”, and went on to explain that 1 million bags, each with no candy, makes 0 pieces of candy. 🙂

After we got a bit of intuition about multiplication, I finished the books, and the kids were all excited to see that 0 multiplied by any number made 0.  They also loved seeing 0 and 1 pair up to make 10 and lots of other big numbers.

Base 10 Blocks

After the book, I had the kids try out some big addition problems, like 22 + 33, using base 10 blocks.  First you make 22 by getting two 10-bars, and 2 unit cubes.  Then make 33, and combine the two piles and count the result.  All three kids were able to do this.

My son looooves addition and multiplication, so these problems were too easy for him, but he was thankfully very patient during this activity.  He begged the other kids to give him a hard problem, and the hardest one they thought of was 100 – 2.  My son said 98, and we all checked that he was right by counting 2 higher than 98.

Next we used 100 squares to count by 100 to 1000.  Then we used 10 bars to count by 10s to 1000. The kids each made 100 out of 10 bars, and I carefully added it to our stack, so in the end we had a block of 10 bars the same size and shape as the 1000 cube.

Counting Without Seeing

Next I showed the kids the pan balance, and said they should use it to figure out how many plastic leaves were in a treasure box (without opening it). If they could get it right, they would each earn a treasure.

They quickly got the idea of putting a handful of leaves in the empty box and weighing it vs the treasure box. They were very good at interpreting the result, knowing that if their box weighed more than the treasure box, then they should take out some leaves.  They even understood that they should only adjust it by a few leaves if the boxes were close in weight.

At one point, it looked like the boxes weighed the same, but the kids wanted to test to make sure, so they first added one leaf (too heavy), then took away two leaves (too light), then added back a leaf to get a match.

To find our answer, we opened up the kids’ box and made piles with 5 leaves in each. We had 41 leaves.  We then checked the treasure box, and found 41!! Everyone cheered!


Flowers, Stars, and Crabs (Age 5)

The Activities

  1. Topic: Comparisons: Book: Anno’s Math Games II by M. Anno, Chapter 2.  This chapter has a number of side-by-side similar pictures, and you have to find the similarities and differences.
  2.  Topic: Logic: We did “Boole Says” again — I said something like “Stand up if you are a boy OR are wearing socks.”  This time, the kids each got to come up with a command, and we also did some commands using “not” (“stand up if you are NOT wearing socks”).
  3. Topics: Patterns, Geometry: We used pattern blocks to draw pictures.  I named 2 or 3 different kinds of shapes (e.g., triangles and squares), and then each kid made a picture using those shapes.  Each time, we each went around and said what we had made.  We did about 5 rounds total.
  4. Topics: Scale, Astronomy: We explored The Scale of the Universe 2 web app for a while.  This is a visualization of the universe from the smallest scales (Planck length) to the largest (size of the observable universe).  Starting at human scale, we scrolled both bigger and smaller and discussed what we saw.

How Did It Go?

This circle went really well, the kids were very interested in all the activities.

Anno’s Math Games II

We spent a while finding all the differences in the most complicated of the activities.

Boole Says

The kids enjoy anything involving standing up and sitting down over and over :).  They did a pretty good job following the commands, a few of the kids got confused by AND vs. OR sometimes, but the other kids helped them.  When the kids were giving their own commands, I think every single one of the commands included themselves; and several of them ONLY included themselves.  One of the commands was “Everyone wearing flowers stand up”, and one of the kids didn’t realize they had flowers on their tights until everyone else pointed it out.

Pattern Block Pictures

The kids enjoyed this activity a lot.  There were a lot of flowers.  One kid’s pictures were noticeably different from the others — for example, one picture was a pretty good crab.  There were a few pictures that the kid didn’t know what it was.

The Scale of the Universe

The kids voted to go bigger first.  One of the kids has done a lot of astronomy things in the past, and was able to identify a bunch of the objects, such as the Lunar Lander, Apollo rocket, etc.  Smaller turned out to be less interesting — pretty quickly all you’ve got is particles, which aren’t too exciting.  The kids’ favorite thing was scrolling through the whole thing really fast, which looks like going through a tunnel because the way there are smaller and smaller concentric circles.


20 Statements (Age 5)

The Activities

Corey was gone this week, so one of the other parents stepped in and led circle.  These are their notes.

  1. Topic: Logic: Book: Anno’s Math Games II by M. Anno, first chapter, about a transformation machine (i.e., “function”).
  2. Topic: Logic: A kid would pick a card with an animal on it.  I made a series of statements, and they had to say true or false, until I was able to figure out what animal it was.
  3. Topic: Logic: To practice the use of AND and OR,  I made up a bunch of statements like “stand up if you’re five and have long hair”, “stand up if you are a boy and don’t have socks on”, etc.
  4. Topic: Logic: We did a logic puzzle, borrowed from Boole2School.
    On Halloween,  four strange characters visited your school:
    a witch, a goblin, a ghost and a black cat. Each of them went into exactly one of these rooms: classroom 2, classroom 3, classroom 4 and the staff room.
    The goblin stole a notebook.
    The cat painted her paws.
    The ghost hid in a desk. .
    The witch left a present.
    Clue 1: Nothing was stolen from classroom 4.
    Clue 2: The ghost hid either in classroom 2, or in the staff room.
    Clue 3: Classroom 2 was not visited by a goblin.
    Clue 4: No notebooks or paints are ever kept in the staff room.
    Clue 5: The black cat did not prowl through classroom 4.

    Where did each of them go?

    IMG_20151108_184225 IMG_20151108_184328

  5. Topics: Logic, Puzzles: Fox, goose, grain puzzle: a boat, only 2 things can be transported across the river at a time, if you leave the fox with the goose or the goose with the grain, the goose/grain will be eaten.

How Did It Go?

Anno’s Math Games

All kids really liked the magical machine.  They figured out the patterns fairly well, and liked the “reverse time machine”, i.e. if they went in it would make then babies.

20 Statements

The first round went well, everyone took turns and I was able to figure the animal out fairly quickly.  Second round became disorganized, two kids always tried to help by telling me the animal.

Boole Says

The kids enjoyed this.  Two of them always liked to stand up, but after a few statements they paid closer attention with more success.

Halloween Logic

This was a good puzzle. I had them write in the name of their school.  This got their attention, but one of them became concerned if this really happened in their school.  I read them the clues and filled out the first part of the table, after that we went around and everyone filled in part of the truth table.  At the end, they were quite surprised and curious when the table revealed who went to which classroom. One kid was very good at interpreting the clues for the truth table.

Furry Monsters Hate Raisins (Age 5)

The Activities

  1. Topics: Arithmetic, Counting: Book: Math for All Seasons by G. Tang.  We read about half the pages, solving each problem.
  2. Topics: Combinations, Venn Diagrams, Attributes: The kids made pumpkins using 2 different kinds of eyes, 1 kind of nose, and 2 kinds of mouths, each with 2 orientations (right-side up or upside-down) — download templates here.  The goal was to make as many different pumpkins as possible.  After that, we made Venn diagrams with attributes like “Half-circle Eyes” or “Upside-down Mouth”.IMG_1740
  3. Topic: Logic: We solved several Halloween-related logic story problems.  We’ve done this activity before with this circle, but this time we did all seven puzzles instead of just three.IMG_1741
  4. Topics: Estimation, Counting: We have a small plastic skeleton bucket (about the size of a baseball).  One at a time, I filled the bucket with several different types of item: glass beads, paper clips, etc.  For each item type, he kids all guessed how many there were in the bucket, and then we counted as a group.

How Did It Go?

We had four kids this week.

Math for All Seasons

The kids liked counting the items.  I don’t think they ever did the clever counting methods until after I suggested it.

Pumpkin Combinations

The kids did a pretty good job coming up with different pumpkins.  I taped each one to the wall after checking whether it was different.  There were a few duplicates which we fixed by turning one of the parts upside down (since we were using glue sticks, this was easy to do).  They ended up making 18 of the 32 possible pumpkins; they didn’t get blocked, they just got tired of making pumpkins.  Around this time, one of the kids started to get distracted and remained that way for the rest of this activity and the next as well.

The Venn diagrams went pretty well — they weren’t all that great with the overlaps, but they understood the idea.  We did a three-circle Venn diagram, and they did alright with that as well.

Halloween Logic

I still helped them some, keeping things moving, but they were much faster than last time we did this (in March).  They were more likely to guess and fix things later, and they understood all the clues right away.  So we were able to get through all 7 of the puzzles.  Two of the kids (including the distracted one) thought the clue “Furry monsters hate raisins” was hilarious.

Skeleton Estimation

They guessed low every time, except for a guess of 90 for small plastic acorns when the answer was 36.  In general I’ve found that they almost always guess too low.  They were particularly far off for paper clips (largest guess was 60, answer was 179).  They enjoyed counting the items as a group.

Cargobot for Pre-Readers (Age 5)

The Activities

  1. Topic: Tallying, Counting. Book: Tally O’Malley by Murphy. In this book, a family plays a counting game where each person picks a color of car, and then makes a tally mark when they see a car of that color. The book shows how to ‘bundle’ the marks together with the fifth mark.
  2. Topic: Tallying, Number Recognition. I put tiles with the numbers 1 – 100 in a bag. Each kid picked a digit from 1-9. Then we took turns drawing numbers out of the bag. If the number contained your digit, you got a tally mark.

3. Topic: Programming. We played Cargobot with our hands today. Cargobot is an on-line programming game where you control a robot arm, moving it left or right and picking up or dropping boxes. We played this using our own arms, and colored stones as the commands.


Your arm starts above the blue dot. The program of stones moves both boxes to the square closest to the blue dot.

4. Topic: Attributes, Set. We played a couple rounds of Set with just the solid cards.

5. Topic: Attributes, Venn Diagrams. Using the fairytale bingo cards, we categorized cards in two ways: Things that Fly vs Thing that go in Water. Girls vs Scary Things.

Girls vs. Scary Things. The witch and the three bears fit in both categories.

Girls vs. Scary Things. The witch and the three bears fit in both categories.

How did it go?

There were only 3 kids this week.


The kids all enjoyed the book. They were interested to see who would win the family’s games. Drawing numbers out and making tallies was good practice for them. I had the kids read out the name of each number they drew. There was lots of excitement when someone drew 22, since it gave the kid who had chosen ‘2’ two more tallies.


First I demonstrated how to use the stones to make a program.  Then I gave each kid one box, and asked them to move it to the square closest to the blue dot.  It took each kid a couple tries, but soon they caught on.  They were all pretty good about fixing bugs and not giving up…though my son was a bit more fragile than the others.

As each kid finished, I gave them a new task. Move two boxes to the square closest to the blue dot.  One girl quickly wrote the program, but it turned out she had expected to be able to pick up two boxes at once.  My son teased her saying of course you can’t pick up two!  I assured her that her program worked and made sense, but I asked her to update it so it would work if you could only hold 1 box at a time.

Next I checked my son’s program. It turns out that he expected that the hand could hold 2 boxes, but that it would take two ‘red’ bead to pick up two boxes. He was very upset when I tried to explain that the hand could only hold one bead at a time.

Meanwhile, the girl had a new idea. She suggested we should take the program that moves one box, and do it twice instead.  I said this was a good idea, and helped her add a second line to her program, that was identical to the first one. We tested out the program, and found that the second time the hand ended up going too far left.  She fixed it by removing one green bead from the second line. I asked why it hadn’t worked, and we figured out it was because the hand originally started above the blue dot, but after dropping the first box, the hand was above the square where the box was dropped.

Next my son and the other kid both independently had the same idea that we should repeat the first program. We all worked together to try it, and then fix it.

This activity went very well, except that the kids all wanted me to check their programs with them at the same time.  I’ll have to figure out some way to remove that bottleneck. Perhaps the kids can work in pairs to check each other’s programs, now that they get the basic idea.


I let the kids vote for the next activity. Two kids voted for Set, and one voted for Venn Diagrams.  In Set the kids were fairly even, though there were many incorrect Sets picked up still.

Venn Diagrams

One kid said Venn Diagrams was boring, and I said I thought they would be fun. Once we started, everyone seemed pretty into it.  There was some disagreement on the Girls vs. Scary Things category, because one kid wanted to put the Castle and the Crown in the ‘Girls’ circle, but the other kids didn’t.

After we categorized all the squares I asked questions like: How many scary things were there? How many scary girls? How many things that were not scary and were not girls? These were all pretty easy. The only hard one was “How many things were either girls or were scary but were not both?” Some kids wanted to count the scary girls, some said they didn’t understand the question.

Venn Fairy Tales (Age 5)

The Activities

  1. Topic: Word Problems: Book: The Case of the Missing Zebra Stripes, “Henry’s Tale”.  We stopped to solve all the riddles in this story.
  2. Topic: Numbers: Using a deck of cards from 1-104 (e.g. Slide 5), we did several activities.  First, I gave each kid 10 random cards and asked them to find the largest one.  Then I asked what the largest one was overall.  Next I gave them each a stack of cards and asked them to find all the 50’s.  After that, they had to find all the numbers that ended in 2.  Finally, they needed to find pairs of cards that were flipped (e.g., 68 and 86; also 55 by itself).
  3. Topics: Odd One Out, Venn Diagrams, Attributes: Using a set of fairy tale character cards, I dealt sets of 4 cards, and then asked the kids to come up with ways to group them (e.g., these are animals, the others aren’t).  There were usually 3-4 different ways the kids came up with per set.  After doing that for a while, using big paper circles to make a 2-circle Venn diagram, I asked them to place all the cards where one of the circles was “Magic things” and the other was “Animals”.

How Did It Go?

We had 4 kids this week.

Henry’s Tale

The riddles were a good level for the kids; they solved them all but it took a while.

Number Cards

There’s still a wide variety of abilities for recognizing numbers; most but not all of the kids now recognize two-digit numbers. The kids found the numbers 100+ to be very amusing. Finding mirror images was pretty hard. One of the kids convinced everyone else to help find the number they were looking for. At one point, two different kids were each looking for the other’s card. One kid decided they really wanted to find the sum of all the cards, which actually was one of the activities in the big kids circle!

Venn Fairy Tales

The kids did a good job coming up with different ways to group the cards. The most interesting one was when we had gone up to 6 random cards, and the kid decided to split into “real” vs. “not real” — but 5 of the 6 cards were (probably) in the wrong group! (Gingerbread Man => real, Golden Goose -> real, Flute Player => not real). The Venn diagram went well, they didn’t use the overlapping region though until I asked them specifically where the dragon should go. We had to have a vote about whether the queen was magical or not (she looks like the wicked queen from Snow White).

Pompeii Money (Age 5)

The Activities

  1. Topic: Lines, Shapes. The Case of the Missing Zebra Stripes by Time-Life Books. (Page 40 – 47). This section was about lines: parallel, intersecting, shapes.
  2. Topic: Money, Addition. I showed the kids glass beads that I said were money from a different country.  Green beads were worth $3, red beads were $2, and yellow beads were $1. First I handed out small handfuls of money, and helped the kids add it up.  Next we figured out how much more money each kid needed to have $20. Finally, I opened up a Math Circle store where the kids could spend their money on tiny toys.

    My kids playing 'store' after circle.

    My kids playing ‘store’ after circle.

  3. Topic: Attributes. I taught the kids Set.  We only used the solid colored cards. First I explained what a Set is: a set of three cards where all three cards either match or are different for each attribute.  Next we looked at two cards and figured out what 3rd card would make a set.  Finally we played Set, laying out 9 cards at a time. Each kid would raise their hand if they thought they saw a Set.

    Each row is a Set.

    Each row is a Set.

How did it go?

Pompeii Money

The kids all said they had seen money before.  I told them that we would play with pretend money from a different country.  I asked what our country should be called? One boy immediately proposed “Bumpitup” which he said was a country that had been destroyed by a volcano.  I asked if he meant “Pompeii”, and he said yes.

I showed the kids the values of the different colors of money, then handed a few beads to each kid.  The kids really varied in their ability to add up the money.  Two of the kids just wanted to count the beads, not add up the dollar amount.  They seemed to understand what was going on, but needed one-on-one help to add 3+3, etc.  Another kid could pretty much do it on their own, with just a little help.  My son could quickly add it all up himself.

We did two rounds of adding small groups of money.  Everyone soon understood that greens were the best, since they were worth three.  Next I worked with the kids to add money so that each had $20.

I asked “What’s the fun thing about money?” One kid said the fun was that you can use money to buy more money.  I then opened the store, which had small stickers and toys available for $2, $5, or $10.  The kids took turns picking an item and paying me the correct amount (often needing help).


My son had played Set before, but the other kids had not.  We practiced finding Sets, and then eventually played a couple rounds. If one kid fell behind, I let that kid have extra time (and clues) to find the next Set.  All 4 kids caught on by the end of circle, and were excited to play.