Let’s Start a Math Circle!

Inspired by the book “Math from Three to Seven” by Alexander Zvonkin, my wife and I decided to start a math circle for our 4-year-old daughter.  We invited 5 of her friends from preschool to meet at our house once a week for an hour.  All 5 said yes!

We have two main goals:

1) Show the kids that math is fun

2) Challenge the kids to solve problems different from problems they’ve never seen before

We plan to start each circle with a math-themed picture or chapter book and work through two or three math activities each week.  Some activities will be individual, others will be done in small or larger groups.

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Wiggly Princesses

The Activities

  1. Topic: Division: How Hungry Are You? by Napoli
  2. Topic: Pigeonhole Principle: Give the kids 11 dogs and 10 bones. Ask the kids to feed all the dogs.  Once they see there are not enough bones, suggest different ways of feeding the dogs (i.e. yellow dogs with yellow bones, etc), and see how long it takes before they decide it is impossible.  For this, I used colored wooden cubes for the dogs, and paper bones cut out of colored construction paper.
  3. Topic: Counting, Inference: I got this idea from “Math from Three to Seven” by Alexander Zvonkin. Tell the kids a story, and act it out as you go. I used blue poker chips for the princes, and orange chips for the princesses.  The plates were blue or orange construction paper squares.
    1. Once upon a time there were a king and a queen and they had great ball in their castle. They invited many princes and princesses who had lots of fun. The queen wanted to count them but they kept moving and even leaving the room.  (move the chips around if the kids try to count them).  The king had an idea to have the orchestra play music, and the princes and princesses started to dance together. (put the chips in couples). There was one extra prince but he wasn’t sad, he danced by himself.
    2. Are there more princes or princesses?
    3. Then it is time for dinner, the princes and princesses sit down to matching plates…one color for the princes, and different color for the princesses. (put the chips next to corresponding plates). But the food is not ready, so they go outside to play.
    4. The cook wants to make ice cream for the princes and lollypops for the princesses, how many should she make?
  4. Topic: Sets, Shapes: Use the small Attribute Blocks.
    1. Put a large string circle out. Ask the kids to put the following items in the circle:
      1. blue blocks
      2. hexagons
      3. red, thick blocks
      4. thick, triangles
    2. Put out 2 string circles:
      1. thick in one, thin in the other.
      2. squares in one, circles in the other
      3. triangles in one, blue in the other

        The kids’ answer to blue shapes in one circle, triangles in the other.

How did it go?

How Hungry are You?

The book was hard to read because it had so many characters.

Give a Dog a Bone

I gave the kids ‘dogs’ that were different color and sizes of cubes.  The bones were cut from paper.  I asked the kids to give each dog a bone.  They worked together to assign dogs to bones and found there were was one extra dog.  I asked them to try again, and they did, and again one extra.

Both times the leftover dog was a small black cube. I suggested assigning the small black cube first, which they did, but two kids started arguing about who could hold the purple bone.  I ended up taking away that bone and the dog that went with it.  Then we had one extra dog again.  The kids suggested giving the purple bone to it, which I did, but pointed out that I still had the one extra dog.

We tried one more time and still there were too many dogs.  The kids said it was because there were more dogs than bones.  So I asked the kids to count.  The kids are not very good at counting so 2 kids counted and got 10 bones, but they weren’t sure if there were 11 or 12 dogs.  Either way, we agreed there were more dogs than bones.

The Wiggly Princesses

The girls were excited to have princesses and wanted to touch them all.  I told them how the king and queen were wondering if there were more princes or princesses.  The kids suggested counting, but I kept moving the pieces around while they counted. I said they were playing.

One of the kids told the princes and princesses to stay still so they could be counted. She started to count but after a few numbers I started moving the chips again, saying the princes and princesses weren’t listening.

Then I told them the king and queen decided to have a dance, and I said that usually one prince and one princess would dance together.  The kids started arranging the chips into couples. There was some fighting because the girls didn’t want to let go of the orange princess chips.  We found there was one extra prince.  The kids agreed this meant there was one more prince than princess.

Next the cook called everyone to dinner.  I gave a stack of orange and blue paper squares that were the plates.  I asked the kids to give each chip a matching plate.  They went to work, with some arguing. One kid was convinced that the princes and princesses should eat in pairs, but the other kids didn’t care.

Next the cook realized the food wasn’t ready, so the princes and princesses went off to play in the garden.  The kids helped pick up the chips, leaving the plates behind.  The girls only wanted to pick up the orange princess chips. Luckily the boys were willing to pick up the princes.  I took away the chips, and said the cook needed to know how many princes and princesses there were, since he wanted to make ice cream for the princesses and lollypops for the princes…But everyone’s outside!

One kid said we could count the plates, so I had the kids line up the orange and blue squares and count then.  One kid counted the blue plates and got 13. Kid #2 counted 11 orange plates, and Kid #3 counted 12 orange.  Kid #4 said, “Yeah 12 must be right because we know there is one more prince than princess”.

Then the kids put the chips next to their plates so the princes and princesses could have their desserts.  Then we picked everything up with the all the girls fighting to pick up the most princesses, and the boy picking up all the princes.

All the kids were really engaged in this activity and loved the story aspect, and touching all the shapes to tell the story.

Attribute Sets

I got out the small attribute blocks and asked the kids to put all the blue shapes in the circle.  They quickly did it, with little fighting.  I asked if anyone wanted to count and 3 of the girls counted.  Kid #1 is the most dependable counter.  Kid #2 tends to count the same shapes repeatedly, while Kid #3 moves her finger faster than she says the numbers.  We got varying answers from the kids, but we didn’t worry much about it, just picked the number the most kids got.

Next I asked for triangles in the circle.  There were not as many triangles so 2 kids got upset that there was no triangle for them.  I took one back out of the circle and let them put it back in.  Again we counted.

Kid #4 told me it wasn’t fair because she had never gotten to go first at counting, I said was sorry about that.  Kid #5 said she also had never gone first.  So I decided both #4 and #5 could count first right now.  They started counting, and they got very confused since they were both counting at once, and ended up getting 21.  Next Kid #1 counted and got something like 9. Kid #2 said 10 and Kid #3 said 13. Inconclusive.

The kids started getting antsy now, so I said I had a tricky one.  I asked for blue triangles in the circle.  They quickly did this, though someone put a red triangle in, which the other kids said was wrong.

Now I had each kids take a turn with things like: yellow hexagons in the circle, blue and red rectangles in the circle etc.  It seemed pretty easy, though one kid was still not comfortable with the idea of thick vs thin and waited for the other kids to do those.

Again the kids got too excited so I said it would be different now.  I put two circles of string down and asked the kids to put red shapes in one and blue in the other, which they did.  I asked what shapes were not in a circle, and they said yellow ones.

Next I asked for triangles in one circle and blue shapes in the other.  They started doing this but Kid #1 started protesting loudly when someone put a blue triangle with the other triangles, saying “But that’s blue!” She had been working on the blue shapes so was very concerned when the triangle went away.

I had them put it with the triangles and when we were done I pointed to the blue string and asked if all the blue shapes were there.  The kids said yes.  I asked again, are they ALL here?  and then they pointed out the two blue triangles in the other string.  So we moved them to the blue string.

Then I asked if all the triangles were there and they said no, the two blue were not, so we moved them back.  Then Kid #2 said “but now all the blue shapes are not there!” and so everyone laughed as I moved the blue triangle back and forth.  Kid #3 suggested putting the blue triangles in between the two circles, which is what we did.

She Got to Count First Last Time!

The Activities

  1. Topic: Addition: Book: Math Fables Too by Tang. We did #3, 5, and 10. The kids liked this book but it wasn’t very mathy.
  2. Topic: Sets, Attributes. Given a pair of Attribute Blocks, identify the differences between them. For example, a thick, big, blue square vs a thick, small, blue, circle.  Differences: Size and Shape.
  3. Differences: Size, Color, Thickness.

    3. Topic: Patterns, Spatial Reasoning: Make simple patterns on the Pegboard, and have the kids extend the pattern.  Make a butterfly on the pegboard, and have the kids copy it.

    Two patterns that the kids extended.

    A cocoon on the left. A butterfly on the right.

How did it go?

We had 4 kids at circle this week.

Attribute Blocks

The kids took turns identifying differences between pairs of shapes. They were all pretty good at this, though there was some confusion between hexagons and octagons.

At the end of this activity, I told the kids they could all touch the shapes.  Everyone grabbed a bunch, and two kids started arguing because they both wanted to count all the shapes.  Eventually they counted the shapes together.

Now the kids started to get really wild, and my daughter started whining about wanting another cookie and pouting when I wouldn’t let her.

At this point I asked the kids if there were more blue shapes or yellow ones.  Kid #1 counted them both and decided there were more blue.

Aret there more triangles or circles? Kid #2 and #3 started arguing again about who should get to count.  I said it was Kid #3’s turn, but she didn’t want to count triangles, she insisted on counting red shapes. So I let Kid #2 count them, but she decided to count red shapes also.  This was a tricky situation as both kids were really arguing, and Kid #3 was putting her hands on Kid #2.

Pegboard

The pegboard is a key material in “Math from Three to Seven” by Alexander Zvonkin.  However, he only had 2 or 3 kids in his circles, while we have 6.  Based on today, I think the pegboard does not work well for larger groups of kids, since everyone wants to touch it at once, and only one kid can use it at a time.

The kids loved touching the board, and were fully capable of continuing patterns like: red, yellow, red, yellow.  Or blue green green blue green green.

Next we made cocoons. I made a line of four pegs in one color, and asked the kids to make the same line in another color.  Finally we turned the cocoons into butterflies by changing one line into a square and having the kids make the other wing.  This was easy for everyone.

After this the kids wanted to add antenae to their butterfiles, which I allowed.

Corey’s Pretend Party

The Activities

  1. Topic: Charts: Book: “What do you like?”  This book is about kids voting to plan a party, and using various types of graphs to find out what wins.
  2. Topic: Charts: Show the kids 6 different ways to vote on features for my pretend birthday party: Food, Drink, Ice Cream Flavor, (Party Favor), Location, Game. Each kids votes on each item, and then takes on of the charts around to the parents so they can vote too.  Afterward, we’ll figure out which item won each vote, and compare it to the kids in the book.

    Which game should we play?

    What food should we have?

  3. Topic: Probability: Probability Race. Which number will be the first to be rolled 5 times on two dice?  Kids roll two dice, and color in the square corresponding to the sum of the dice.

    Probability Race.

  4. Topic: Sequences, Logic: Story Sequence cards. Arrange story pictures in the order they happened.

How did it go?

Five kids attended circle this week.

My Pretend Party

I told the kids that we were going to plan a pretend birthday party for me.  I read a book called ‘What do you like?’ about kids planning a block party. Each time the kids in the book voted, I had our kids vote too.

 The first was to vote for the party location: park, house, or Pump It Up.  You voted by writing your name under the one you wanted. All the kids voted for Pump It Up.

 The next vote was for the snacks at the party: pretzels, popcorn, carrots, cheese, apples.  You voted by putting a tick mark next to the one you want.   

The next vote was for drinks: oj, lemonade, milk or water. You voted by drawing a circle in a horizontal line next to the thing you want. I picked water. The kids were split on milk or lemonade.  One kid seemed to be voting based on the color of the circle (milk was a pinkish circle).

The next vote was for the game at the party: tag, musical chairs, or treasure hunt.  You voted by coloring in a rectangle above the one you wanted, making a bar chart.  I voted for musical chairs, most kids voted for treasure hunt.  There was a lot of excited discussion about the various choices, for example Kid #1 said that they played musical chairs at Kid #2’s party, and Kid #3 said he had never done a treasure hunt before.

The final vote was for a kind of ice cream: mint, mango, chocolate, or vanilla. You voted by writing your name on a line and filling in a circle for the one you want, lined up with your name. Like a scan tron.  The kids had a hard time with this type of chart, they didn’t want to skip circles, so they would fill in circles that were on lines for other people’s names.

Next, I gave one chart to each kid and spread them out across two tables. Then I had the parents rotate through the stations and the kid explained how to vote to the parent.  The kids enjoyed this.

After everyone voted, we came together and looked at each kid’s chart to see what had won, counting up the votes.  Everyone was really engaged in this activity.

Probability Race

We reviewed the result of last week’s race (6 had won).  We started rolling, and the kids were pretty good about letting the person whose turn it was count the dots. We only had to roll about 12 times before 5 won the race.

Story Sequences 

One story showed: 1. bottle of bubbles,  2. a boy blowing one bubble, and  3. a boy with many bubbles in the air.  Kid #1 ordered them as 2,3,1, and I told the story: “Once a boy blew a bubble. The he blew more bubbles.” The kids filled in the last bit, saying the boy ran out of bubbles or the bubbles all popped.  Kid #2 said there was another way to do the story and ordered them 1,2,3, explaining that the boy hadn’t opened the bubbles yet.

The next pictures were: 1. chicken looking at egg, 2. egg hatching, 3. chick eating worms, 4. big chicken.  Kid #3 ordered them as 1, 2, 3, 4, and told the story herself.

The next pictures were: 1. person mixing batter 2. person rolling dough, 3. person cutting cookies, 4. plate of cookies.  Kid #4 was unsure at first, but then organized them 1,2,3,4 and told the story coherently.  I pretended to feed the cookies to the kids, which caused a moment of wildness as everyone insisted they must eat the heart cookie.  I said there were enough because they were pretend cookies, and eventually they calmed down.

Building a Watermelon

The Activities

  1. Topic: Evens and Odds, Division: Book: Splitting the Herd by Harris. The kids will act out the book with the wooden cows we have.
  2. Topic: Combinations: Given a chain of 5 circles, how many different ways can you color in zero circles? 1 circle? 2 circles? 4 circles? For example, OXOOX and XXOOO are two ways to color 2 circles out of 5.
  3. Topic: Probability: Kids will roll two dice, compute the sum and fill in a box in a chart.  We’ll end up with a 6×6 grid of all possible sums of two dice.
  4. Topic: Sequences: Kids arrange the story cards in order.

How did it go?


Splitting the Herd

This is a really fun book that involves Emma’s 10 cows getting into her neighbor Kirby’s pasture and mixing in with his 10 cows.  The two neighbors split the cows into two groups of 10.  The next night 2 cows run into the neighbor’s pasture, and they split them into two groups of 6, and send 6 back home. The kids saw no problem with this.  Then again two cows run over, and they split the 8 cows.  At this point one kid said “But Kirby only has 4 cows!” and the kids agreed this was unfair. Again 2 cows run over, and now there are 5 cows to split, which can’t be done so Kirby and Emma get married.  I didn’t know how to explain why the cow division ended up wrong, so I talked about how Kirby and Emma should have remembered that there were still some cows in Emma’s field.

Circle Coloring Combinations

Given a chain of 5 circles, how many ways can you color in zero circles? 1 circle? 2 circles?

3 of the kids had seen this activity at an earlier circle. One of them remembered she had been able to get 8 different colorings.

This was new to the other 2 kids. I started by coloring in one circle in the chain: XOOOO. I asked Kid #1 if he could make a different chain by coloring in one bead, but he colored in the same bead as me.  So I asked another kid, who found a new way: OOXOO. We continued taking turns until the kids had found 5 different ways to color in one circle.  Then I asked Kid #2 to find another, and after awhile she gave up, and I suggested maybe 5 was all of the ways.

Then I gave each kid a sheet with rows of 5 circles on it, and told them to color in two beads in each chain. One kid got 7 different ways, another found 6. One kid got 5 ways…she had trouble because she felt that reflections were the same, for example: XOXOO and OOXOX.

One kid was stuck so I stood by the kid and tried that each row was a chain and we should color two beads in each. The kid colored one in each row, and sometimes seemed to think the chains should be vertical.  The last kid was more interested in playing with puppets after circle and in telling me her plans to color all the circles in different colors when she got home.

Then I gave the kids a new paper and asked them to color 4 beads in each chain. 3 of the kids got 3 or more different colorings.

Probability Charts

By now, we’ve done probability race about 5 or 6 times. We decided the kids might be ready to learn *why* some rolls are more common than others (i.e. 7 is the most likely roll).  I made a chart like this:

1 2 3 4 5 6
1
2
3
4
5
6

The plan was to write the sum of the two dice in the appropriate box.

The kids all remembered probability race, and were happy to roll dice and count the dots.  I showed them how to fill in the chart, but only one kid seemed to understand. We filled in the results of 12 rolls, and then stopped because the kids got restless.

 Story Sequences

The kids all loved this activity. The only problem was a bit of restlessness during other people’s turns. Also, some of the kids wanted to tell the other kids how to arrange the cards.  For this circle, we used a bunch of story sequences that we found on the internet and printed out.

  • Kid #1 had a boy throwing a ball for a dog.  At first she was intimidated because it had 6 cards, but she started organizing them and corrected herself where she was wrong.
  •  Kid #2 got a frog growing up from an egg.  She organized them all correctly, but she had the frog with a tail as the last card.  I told the story as she had arranged it and at the last card I said “then the frog grew a tail”.  All the kids said that sounded good, but then I said I would change something.  Kid #1 immediately swapped the adult and the tail frogs.
  • Kid #3 had pictures of building a snowman, and then a melted heap of snowman parts.  She put the melted heap first, and said that that was before the snowman was built.  Kid #4 said she’d arrange it differently: her story was: First there’s a snowman, then all it parts disappear, then it gets a face, then it melts (she was not joking).  Then I let Kid #2 have a turn and she organized them as expected with the melted picture last.
  • Kid #4 had one with 3 cards: A man with a watermelon, a man with watermelon in half, man and kids eating watermelon.  Kid #4’s story was: 1. watermelon in half. 2. man with whole watermelon 3. eating:  “A man builds a watermelon, then he cuts it and they eat it.”  Kid #1 reorganized in the expected order.
  • Kid #5 had: A: A girl with dog pulling her scarf.  B: Girl waving at dog with scarf. C: Boy chasing a dog with scarf. D: Boy giving scarf to girl.  Kid #5 arranged it as D A B C.  Everyone was tired so I ended circle here.

After circle, Kid #5 wanted to show dad the story cards and tell the story. Also several parents told me about their kids wanting to start math circles and playing pretend math circle at preschool.

Sometimes Math is Like Pulling Teeth

The Activities

  1. Topic: Counting, Addition, Subtraction: Book: Red Riding Hood’s Math Adventure, by Harcourt. This is an interactive book where the kids get to decide how many cookies to give to various fairytale characters. After each page ask:  How many cookies do you have? How many have you given away? How many total cookies were given away, and are left?
  2. Topic: Logic: Logic puzzles from “Thinking Skills age 4-6” by Shapiro. Given 4 pictures of things (like pets or houses), and a few clues, figure out which item the clues refer to.  First use the clues in the book.  Then make it a bit harder by giving clues and asking if the kids have enough info:
  3. Topic: Logic, Puzzles: Boat problem. You have one boat that can fit 2 items and a group of items that need to cross the river.  Each boat trip must contain at least one person to drive the boat. If a cow and a carrot are left alone on the riverside with no person to watch, the cow will eat the carrot.  How can you get the following groups across:
    1. 2 cows and 2 people
    2. 1 person, 2 cows and 1 carrot.  (not possible)
    3. 2 people, a cow, and a carrot.
    4. 1 person, a carrot, a rabbit, a lion

How did it go?

We had a Saturday math circle this week, with only 3 kids. My daughter had had a very long day before circle, including having one of her teeth pulled at the dentist.

Red Riding Hood’s Math Adventure

Each girl got 12 construction paper cookies.  They were red, pink or blue. Kid #1 and #2 picked pink and red, but then my daughter got extremely upset and threw the blue cookies on the ground.  She kept crying so I had to send her away to David.

Each page has a character which asks for cookies. The girls can give 0, 1, or 2 cookies, and characters’ replies change based on the choice.  I asked each time how many cookies each girl had left and they counted successfully.

Then my exhausted daughter came back and took the blue cookies. She gave the next character 6 cookies. This inspired Kid #2 to give all her remaining cookies. The girls enjoyed telling the ‘bad’ characters like the wolf and troll that they got no cookies.

At one point Kid #1 said my daughter sounded like a baby because she was crying so much. So she started crying again.

After the end of the book, I asked if anyone wanted to try counting all the cookies together.  Kids #1 and #2 wanted to.  First Kid #1 counted and laid out all the cookies.  She got 34.  Then Kid #2 counted the laid out cookies and got 36 (interestingly, she did skip and double count some cookies but ultimately got the right answer).

Logic Puzzles

There were several groups of objects, for example, 4 frogs, some green, some brown, some with blue spots, some with purple spots.  I gave a couple clues and the kids had to figure out which one matched all the clues.

The kids had no problem with this at all.  They were able to follow clues like “It has purple” or “It cannot fly” and combine the clues to figure out the right answer.

Next I had my own set of clues for the same pictures, and after each clue I asked the girls if they knew the answer yet.  The only confusion was that Kid #2 thought my clues were *in addition* to the old clues.  After I clarified that we were looking for a different person’s pet she understood.

Finally, I used the same pictures but had the girls ask yes/no questions to figure out the pet.  I assumed they would naturally ask yes/no since I had played lots of Guess Who with my daughter.  However, Kid #2’s first question was: “Which one is your pet?”.  I managed to describe yes/no questions to them and then they were able to solve each problem.

Once Kid #2 asked: “Does it have white?” for a set of picture where there was no white and another kid giggled because she saw this.  Another time a kid asked “Is it looking up?” hoping to distinguish between two frogs, but they were both looking up, so she changed her question to “Is it looking up and its mouth is open?”

Boat Problem

All 3 girls were able to immediately solve the 2 cows, 2 people problem.

Next they tried 1 person, 2 cows, and 1 carrot, which is actually impossible.  After trying a bunch of different things they started to claim that it couldn’t be done. So I added in another person, and asked if they could do it now.  Kid #1 was able to solve it.

Next was 1 person, a carrot, a rabbit, and a lion. Kid #2 started this one.  She first took the rabbit across.  Then came back to get the carrot, and then was stuck. Kid #1 also got stuck in the same way. Then she started to lose interest, and I said that it was actually possible.  This brought back her interest.

Finally Kid #3 tried.  She first took the rabbit across.  Then got the lion.  Then she said “I’m scared, I don’t want the lion to eat the rabbit!”.  But I said the rabbit was safe as long as the person is there.  Then I suggested she could take out the lion put the rabbit in the boat.  After she did that, she solved the rest of the problem easily.  Kid #1 saw that it would work and said “She’s solving it, yay!”

Then I asked #1 and #2 if they wanted to solve the problem too.  And they both said no.

Graphing

This activity is also from Thinking Skills, age 4-6.  The graphing activity involved counting a number of objects and then coloring a bar chart with the number.  The objects were dolls, balls, and trains.  Everyone wanted to do dolls.  So I randomized who went first and it was Kid #3.  She picked dolls.  Kid #1 immediately said she would not do the activity, and stood to the side pouting. Kid #2 also said she wouldn’t do it. Kid #3 counted the dolls and filled in the chart, but the other girls still refused to participate.

I dismissed the circle, and the girls ran upstairs.  There was more drama when my daughter ran to get her new sparkly shoes and Kid #2 said that she had shoes that were even sparklier than that.  She was sad that Kid #2 said this, so I told her to tell her friend that.  She said “It makes me sad when you say your things are more beautiful than mine”.  Kid #2 looked sad at hearing this but did not want to apologize and went off by herself for a little bit.

Which Princess has the Most Toes?

The Activities

  1. Topic: Doubles, Addition: Doubles Fun on the Farm by Freese.
  2. Topic: Shapes, Charts: We have a bag with an assortment of Attribute Block shapes.  There are two activities.
    1. Put your hand in a bag, find a shape.  Then, without looking say what size, shape, and color 🙂 it is.  Next, I specify a size and shape, and each kid needs to find it without looking.  Then the kid puts it in the right box of the shape/color chart.

      The shape and color chart.

  3. Topic: Sequences, Transitivity: 
    1. This is from “Math from Three to Seven” by Zvonkin. To go to work, I drive to the train station, get on the train, get on a bus, then walk to my desk.  How do I get home?
    2. A plane is faster than a car, car is faster than bike. Is a plane faster than a bike?
    3. Jim is taller than Fred. Fred is taller than Susan. Who is taller, Susan or Jim?
  4. Topic: Logic: Some stole the princess’s jewel. I gave the kids a lineup of 4 clipart characters, and also 4 name labels. The kids have to figure out which name goes with each character so they can identify who stole the jewel.
    1. 4 girls, different heights.
      1. The person with the red hat stole the jewel.
      2. Anne is the shortest person.
      3. Dinah is the tallest.
      4. Cara  is taller than Betsy.

        The Girls Lineup

    2. 4 boys with different amounts of hair.
      1. The thief is bald.
      2. Cody is has less hair than Ben.
      3. Cody has less hair than Alex.
      4. Cody has more hair than Dan.

        The Boys Lineup


How did it go?

We had 4 kids at circle this week.

Doubles on the Farm

This is a simple book where two kids see farm animals and do 1+1 = 2, 2 + 2 = 4, and so on. Once we got to 3+3=6, one kid predicted that next would be 4+4=8. Then the kids all said next would be 5+5. Before turning the page, I asked how much that was. The kids thought for a bit, and then one suggested it would be 10.

When we got to 7+7, the kids asked me to stop showing the answers, so they could figure it out first. I checked the book and realized there were only 3 more sums, but 4 kids, so I asked if someone would be ok with not getting another turn.  Everyone protested.  Then I said I would do them all, but they said that wasn’t fair. One kid suggested that the parents could take turns answering, but another kid pointed out that one parent wouldn’t get a turn.  I said, “Do you think that parent will cry?” And all the kids laughed, although they agreed that they would cry if they didn’t get a turn.  So three parents double checked the last sums.

Shapes and Charts

I explained that we need to feel a shape and say what it is without looking into the bag.  I had two bags so two kids could go at the same time.  Most of the kids were pretty good at this. Next I asked 2 kids to pull out a circle, however, Kid #3 said that hexagons were her favorite so she insisted on getting a hexagon.  Kid #2 didn’t understand what I meant and pulled out a triangle.

Then I asked Kid #1 and #4 to get out a circle, which they did successfully. After that, we did another round, and all the kids did better.

Then I got a chart that had square, triangle, rectangle, circle across the top and red, yellow, blue down the side.  The empty space in the top right corner was crossed out.  The kids immediately wanted to know what could go in the empty space I said nothing went there.  I then realized that the chart did not have any hexagons (I forgot about them), so we decided to put the hexagons into the empty square.

I asked each pair of kids to take out a shape and then put it in the chart.  Kid #1 got a red triangle and she wanted to put it right on top of the triangle outline.  I showed how it needed to line up with the red patch of color, but she was unconvinced.

Kid #4 put her yellow circle on the chart with no problem.

Kid #3 got a hexagon (intentionally) and so she put it in the crossed out space.

Then the kids kept taking turns placing shapes.  Kid #4 and #2 were the only ones who really seemed to understand the chart, so we should do more chart work in the future.

At the end, the kids started to get rather wild. I settled them down by saying that I needed their help solving a mystery.  Someone stole a princess’s jewels and they needed to follow clues to figure out who.

Who stole the jewels?

Each problem started with 4 clip art suspects and 4 names written on paper.  The kids’ reading ability varies from pre-K level to fluent.  I read the clues to the kids, and they had to work together to figure which name went with each person.

On the first problem (with the girls of different heights), I told the kids that the jewel thief was the girl with the red hat.  Then I said we had to find the person’s name so we could tell the police.

My first clue was that Anne is the shortest person.  Anne is the one with the red hat, so they already knew who stole the jewel…oops! But we decided to assign the other names anyway.  Kid #4 assigned Anne to the shortest person, but Kid #2 wanted to change it and give the shortest name to the shortest person.  Next I said Dinah is the tallest. Last I said Cara is taller than Betsy and Kid #4 was able to correctly assign the names.  We all agreed Anne was the thief and we should tell the police.

The next problem was the lineup of boys with different amounts of hair.  This one was much harder.  I didn’t tell them the theif was bald, I saved it to the end.  I said all the clues, but no one could deduce anything.  Finally someone assigned Cody to the hairiest person.  I said let’s see if that possible.  I said Cody has less hair than Ben, so who could Ben be? There was no one.  So I asked if there was someone else who could be Cody?  They said maybe he was second hairiest.  So we put Ben as the hairiest but had nowhere for Alex.  Then we scooted Cody down to 3rd hairiest and put Ben and Alex ahead (no one noticed or cared that we couldn’t distinguish A&B).  Finally we put Dan down for the bald person.

Then I went around the circle having each kid verify one clue, and they all fit.  So I said…ok, the theif is bald.  And they excitedly said that Dan took the jewel. I said we’d tell the police and that I hoped Dan would give the jewels back. I said maybe the princess could just ask for the jewel and then call the police if Dan says he won’t give it back.

The quietest kid in circle was a bit lost during this activity because the other kids were super loud.

Sequences and Transitivity

“To go to work, I drive to the train station, get on the train, get on a bus, then walk to my desk.  How do I get home?”

Kid #1 shouted, you do it backwards! Then she correclty explained it, except for forgetting the original order.

The kids asked me if that is really how I go to work.  I said I walk to the garage, ride my bike to my son’s school, ride my bike to work, and then walk to my desk.  I asked how I get home.  Everyone yelled “Backwards!” but had some trouble actually saying the backward order.

“A plane is faster than a car, a car is faster than a bike. Is a plane faster than a bike?”

I asked this one to Kid #2, and who correctly said a plane is faster, but it wasn’t clear if it was just because everyone already knows planes are fast, or because of the clues.

“Jim is taller than Fred. Fred is taller than Susan. Who is taller, Susan or Jim?”

I asked this one to Kid #1 who correctly said that Jim is taller.

“Aurora has more jewels than Cinderella and Cinderella has more than Belle, who has the most.”

“Belle read more books than Aurora and Aurora read more books than Ariel, who read the most? The fewest?”

Everyone was shouting answers, mostly correct.  I asked if they thought Ariel liked to read, and I said I hoped so.  One kid said the stepsisters did not like to read.

Next I asked the only boy at circle today what he wanted a puzzle about… Trains? Thomas? Spiderman? After thinking for a few moments and looking over at all the girls, he said he liked princesses. Very sweet of him 🙂  So I said “Belle has more toes than Cinderella, Cinderella has more toes than Snow White. Who has the most toes?” The kids all laughed at this one, and he answered correctly.

I asked if anyone could think of a princess who really had no toes.  One kid said Ariel, because she is a mermaid.

After circle my daughter wanted to play the jewel thief game more and said it was her favorite part of circle.