Who has the biggest ears?

The Activities

1. Topic: Measurement: Book: Magnus Maximus, A Marvelous Measurer, by Pelley.
2. Topic: Measurement: Measure various body parts: wrist, ears, height, etc. Sort the kids by different attributes.
3. Topic: Logic: Story sequences with missing pictures.

Preparation

We bought some ribbon for the boy measurement activity. We also made charts for the kids to glue their ribbons to.  Here’s the PowerPoint of the chart.

How did it go?

Measuring

First I had the kids sort themselves by various attributes: height, hand size, foot size, wrist circumference. It was funny watching them compare themselves. For example, for foot size, they decided to have both people sit on a chair facing each other and put their feet together, but they didn’t have a third person come look at the feet, and it’s hard to see your own feet that well.

Next I gave them each a sheet with centimeter spaced lines, space for each of the 4 things we measured, and a space for name and height.   Another parent and I helped cut ribbons that matched the kids hand, foot, etc.  I was surprised that some of the kids’ feet are longer than the width of a sheet of paper, so the ribbons hung off the end when glued down.

At the end I brought down a picture of my daughter as a newborn, with the cast of her foot, and we measured it.

Story Sequences

The kids have already mastered basic story sequences, where there are six picture cards telling a story, and they have to put them in the right order. We made it a bit harder by randomly removing one of the cards, and asking the kids to figure out what was missing.

The kids were quite good at this, and made good guesses about what card might be missing. Everyone seemed pretty engaged, except one kid who asked, “When is math circle over?”

Super Bowl of Math

The Activities

In honor of the Super Bowl, today we had a football-themed circle.

1. Topic: Counting by 2s, 3s, and 4s. Book: Spunky Monkeys on Parade, by Murphy.
2.  Topic: Addition: Football scores.  Football plays can score either 3 or 7 points (field goal vs touchdown).
1. How could a team score 10 points?
2. 9 points?
3. 20 points?
4. 11 points?
5. 0 points?
3. Topic: Least common multiples:
1. Count by 3s.
2. Count by 7s.
3. Some number you said both times…what’s the first number you said in both sequences?
4. How about 3 & 5?
5. 2 & 4?
4. Topic: Addition: Football game simulation.  Two teams: Seatle Seahawks and Denver Broncos.  If you get to the endzone, you get 7 points. Otherwise the field goal kicker comes on, and you get 3 points. Who wins the game below
1. Broncos: Start on 50 yard line. The quarterback throws the ball 20 yards.  Then the Broncos run the ball 15 yards.  Then they pass the ball 15 yards.  Do they score?
2. Seahawks: Start on their own 20.  Throw 45 yards.  Run 20 yards.
3. Broncos: Start on Seahawk’s 30. Run 10, Throw 15.
4. Seahawks: Start on their own 40.  Throw 35 yards. Run 25 yards.
5. Topic: Addition: Bean bag toss addition: The kids compete in Math Circle ‘football’. There’s a chart with different numbers written on it. The kids each throw 3 beanbags and then add up the numbers the beanbags land on. The highest sum wins the round.  We’ll play several rounds.

Preparation

I made a really beautiful poster board football field…Luckily it was fun to make, because the math activity didn’t really justify the time it took.

The bean bag chart was easy to make, I just drew random boxed on the posterboard, and taped it to the ground.

How did it go?

We had 4 kids at circle.

Football Scores

First I told the kids how you can score 3 or 7 in football. They figured out 3 + 7 = 10 easily.  For 9, they asked for the Base Ten Blocks, and then figured out 3 + 3 + 3.  For 20, one of the kids immediately said “That’s easy! 2 7s plus two 3s”. She then explained that she doubled her answer from 10.  To get 11, they worked for a few minutes with blue blocks, and noticed that 3 + 3 + 3 wouldn’t work, and 7 + 3 wouldn’t work.  I asked what that could mean, and they said it must be impossible.

Least Common Multiples

The kids really loved counting by X…I gave them each paper and pencil, and they wanted to go on and on writing numbers: 3, 6, 9, 12, etc..  Unfortunately, they don’t yet know how to put space between numbers, so it was quite hard to identify which numbers appeared on both lists.

Football Simulation

All the kids decided they wanted the Broncos to win.

Broncos run the ball 15 yards.  Then they pass the ball 15 yards.  Do they score?

At first there was confusion about whether ‘runing the ball 15 yards’ meant the ball should end up on the 15 yard line.  Soon the kids figured out that you had to count by 10s or fives from whatever line you were one.  Some of the kids seemed persistently a bit confused by this, though there was lots of cheering and excitement when the Broncos would score, and sadness when the Seahawks scored.

Bean Bag Toss

At first the kids didn’t want to do this, but after the first round, they didn’t want to stop 🙂  They each took turns throwing 3 bean bags, and I’d write their numbers (20 + 11 + 5) on the paper, and then they’d go to the table and add it up using base ten blocks.

They did this in interesting ways…mostly by making each of the three numbers, and counting every block. Even if they made a number using 10 bars, they would sometimes count the individiual cubes when adding it up.  I showed some of them during this time how to line up the cubes to make 10 bars, and at the end I noticed one of them did her last sum that way by herself.

Robot Turtle Turmoil

The Activities

1. Topic: Powers: Book: Anno’s Magic Seeds by Mitsumasa Anno.  This book is about doubling the amount of seeds you have each year.  We acted out part of the book using the Base Ten Blocks.
2. Topic: Weight: Weigh out a number of ounces of playdough, then make that digit with the playdough. For example, one kid weighed out 1 ounce of play dough and formed a ‘1’ out of it.  I got this idea from the book Games For Math by Kaye.
3. Topic: Programming: Robot Turtles Board Game. This is a board game where each kid controls a turtle and writes short programs to walk the turtle around barriers to get to a jewel.

Preparation

This circle took very little prep time.  Mostly I just had to gather together the materials (play dough, a scale, the base 10 blocks, Robot Turtles).

How did it go?

Anno’s Magic Seeds

This book starts with the main character getting 2 magic seeds. Then he eats one and plants the other (which grows 2 seeds the next year), and he does this 3 times in a row!  The kids started to ask me if anything else would ever happen. One of the kids said it was a very boring book.

Then finally Anno plants both seeds and the amount of seeds quickly grows.  The kids easily figured out 3 + 3 = 6, and 5 + 5 = 10.  None of the kids could do 9 + 9 in their heads so I got out the Base 10 Blocks, and showed them how to put a row of nine blocks, and then another row on top. Then the kids happily counted by 2s to 18.  Next we had to 17 + 17, which we worked together to solve.  Now we had to do 33 + 33.  For this I got out the 10 bars, and one of the kids very quickly looked at the two rows and said it was 66 (the 10 bars are awesome!).  Then we did 64 + 64 with the 10 bars, but by now, some of the kids were playing their own games with blue blocks. They protested loudly when I suggested stopping the book, so I then read the rest of it without acting it out.

Playdough Numbers

The kids were excited to work with playdough, and everyone wanted to help me weight it out.  However, no one seemed to get the point, which is to help build a feeling for weight.  Some of the kids took a verrry long time to make their digits.

Robot Turtles

This is a cool board game that teaches programming to kids age 3 – 7.  It turns out that kids that young can have trouble playing nicely.  Overall the kids really enjoyed the game, but we had our fair share of turmoil:

• One kid crying because she didn’t get the right color turtle.
• Two kids insisting they would both try to steer their turtles to the same jewel.
• One kid getting trapped in a corner by another kid’s turtle.

Most of the kids did figure out how to write programs to make their turtles go where they wanted.  The kids were also excited to learn about the Laser cards in the future.

Plastic Leaves vs. Poker Chips

The Acitivities

1. Topic: Counting: Book: Hands Down by Dahl
2. Topic: Tesselations: Make a tesselation out of the following shapes, using Shape Pattern Blocks.
1. Hexagons, skinny diamonds, squares.
2. Hexagons, triangles, diamonds.
3. Hexagons, skinny diamonds, triangles.
4. Hexagons, diamonds, trapezoids.
5. Triangles, trapezoids, diamonds.
6. Diamonds, squares.
7. Hexagons, triangles.
8. Skinny triangles, squares, diamonds.

My daughter tries to cover the paper rectangle using hexagons, skinny diamonds and squares.

3. Topic: Multiplication: Have the numbers 1 – 100 on the wall. Assign each kid a number, X, and a color of marker. The kid then counts by ‘X’, and colors in a box above the numbers they get.  For example, one kid will be assigned ‘5’, and color in a segment of 5, 10, 15, 20, etc.
1. Which numbers have the most colored in boxes? (most factors). The least?
2. When counting by ‘X’ how many numbers did you color in from 1 – 100?
3. Counting by 4 always hits the counting by 2 numbers. Why?

Each kid used a different colored marker to color in the number factors. For example, 2 used light blue, so 2, 4, 6, 8, have a light blue section.

My daughter colors in her numbers.

4. Topic: Weight:  Divide the kids into pairs. Each pair gets a different unit we’ll use to weigh different objects in the Pan Balance. The units are poker chips, letter tiles, and plastic leaves.  Have 4 objects that we will weigh. Each pair should guess how many of their units will weigh the same as the object.  Then they use the pan balance to get the exact answer, and fill in the answer on a chart.
1. Which object weighed the most?
2. Which unit of measure weighed the most?
3. How many letter tiles does it take to equal 1 poker chip?  How many leaves?

Plastic leaves in the Pan Balance.

Preparation

For the tesselations, I tried out the shapes to find combinations that could tesselate nicely. For the factors, I printed out the candlestick numbers so that each kid could color in a sector for the numbers they count.  For the pan balance activity, I picked out the units of measure, and the objects we would weigh.

How did it go?

This circle was much wilder than usual.  We had all 6 kids, and it was tough to keep them all engaged.

Multiplication / Factors

First I gave assigned each kid a number, starting with 2.  All the kids were quite excited to do this activity.  I gave them 10×10 grids where they would mark their numbers. After I checked their work, they could go color on the candles on the wall.  Many of the kids noticed patterns while doing this.  The kid with ‘2’ saw that she had to color every other column. The kid with ‘3’ noticed diagonal lines in the 10×10 grid.

The kids flew through the low numbers, but it started to get hard when we did counting by 12 and 13. The kid with ’13’ got pretty frustrated.  The kid with ’12’ did ok, but ended up being off by one row.  One kid cried because someone else had the pink marker she wanted.  At that point, I decided we had colored enough numbers.

We went over to look at the candles. The kids all agreed that counting by 2s would color the most candles.  I asked them how many you would color when counting by 2s and they started to count the blue lines, but then it got confusing because the ‘2’ kid had accidentally switched from evens to odds around 47.  This confused the counters so they didn’t end up with an answer.

We kept the candles up on the wall for a month after circle, and my 3-year-old son LOVED the candles. He would constantly count from 1-100 while pointing at the candles.

Weighing

This activity did not go as well as I’d hoped. I divided the kids into 3 teams of 2, and each team was supposed to guess how many of their objects would weigh the same as my big object. Then each team got to use the pan balance to find the answer.  However, weighing took a long time, and the other kids got restless.  Also, some kids played around during the weighing. I ended up cutting this short and moving on to tesselations.

Tesselations

I had prepared bags with construction paper rectangles that should be covered by the shapes in the bag. No duplicate shapes could touch.

Half of the kids worked hard on this one, and half played around.  Some kids finished several bags of shapes, while other kids spent time swapping shapes with their neighbors.  One of the kids mentioned how she did *not* want to work on a tricky one.  Thankfully, this sentiment has been very rare in circle, and I hope it will stay that way.

Corey’s Pretend Party, Take Two

The Activities

1. Topic: Multiplication: Book: Too Many Kangaroo Things To Do by Murphy.
2. Topic: Charts: Planning Corey’s pretend birthday party.  Kids will come up with possible venues, drinks, snacks, games for my birthday. Then we’ll all vote on them using different types of charts: bar chart, ranking charts, X votes, tick marks.  Then we’ll figure out the winners and compare to last year’s results for my pretend party

What game should we play at my party? Robot Turtles, Busytown, or the Adding Game?

3. Topic Story Problems: Solve Corey’s 6 birthday problems (I recently turned 34). We had 6 kids at circle, so team #1 solved problems A – C, and team #2 worked on D – F.
1. Corey moved to California when she was 18.  How many years ago was that?
2. Daisies have 10 petals. Roses have 7 petals. Corey has 34 petals. What flowers does she have?
3. It’s impossible to make a square out of 34 cubes. How many more cubes do you need to be able to make a square?
4. I get \$4 per week. I really want to buy a book that costs \$34. How many weeks do I have to save?
5. David is turning 34 in November. How many more months does he have to wait for his party?
6. Make a rectangle out of 34 squares. How long are the two sides of the rectangle?

Preparation

Before circle, I use graph paper and sharpies to make the various empty charts.  I also came up with the birthday story problems.

How did it go?

The Pretend Party

The kids really enjoyed coming up with choices for each chart. They listened carefully while I explained how to vote on each chart, and happily took the charts around to the parents and other kids to get their votes.  They were a bit wild while we figured out who had won, and I warned some of them for singing during the wrap-up.

The only tricky chart was the ranking chart, where you ranked your drink choices with 1,2, and 3.  I asked the kids how you could tell who won that one.  One kid said it should be the one that got the most #1s.  Another kid said it would be the one with the highest total. The kids quickly realized it should be the lowest total.

Birthday Story Problems

The kids were in two teams of three. One of the kids was not paying attention but did not disrupt the other two teammembers.  All the other kids worked hard on these.

Corey moved to California when she was 18.  How many years ago was that?

This was the hardest for the kids.  I suggested they should make 34 to figure it out.  After collecting 34 blocks, the kids removed 18, and then counted the remaining 16.

Daisies have 10 petals. Roses have 7 petals. Corey has 34 petals. What flowers does she have?

First the kids tried 3 10s, but they saw they couldn’t get 34.  They were a bit puzzled, so I hinted that maybe they could not use 3 daisies.  Then they switched to 1 daisy and 1 rose.  Kid #2 added another daisy = 27.  Kid #3 added another daisy: 37.  They all took away that daisy and Kid #1 suggested trying a rose instead, and they got 34!

It’s impossible to make a square out of 34 cubes. How many more cubes do you need to be able to make a square?

The kids worked together to make a 5×6 shape.  I pointed out that a square has to have the same length sides, and then they added in the last 4 blocks and saw they needed 2 more.

I get \$4 per week. I really want to buy a book that costs \$34. How many weeks do I have to save?

First Kid #4 tried to solve it by counting by 4s but they got a bit turned around and didn’t know how many they had counted.  Then Kid #4 and #5 made groups of 4s, and counted together by 4s until they got to 36.  I asked what the answer was, and the kids counted the groups and got 9, with \$2 left over.

One of the kids was having some trouble, and said, “I can’t solve this problem because I haven’t learned money yet.”

David is turning 34 in November. How many more months does he have to wait for his party?

This was very easy for them. The only problem was they didn’t initially know what month to start with.  I asked them what month it is right now, and one kid said March. Then the kids said the months in order together while one of them counted on her fingers.

Make a rectangle out of 34 squares. How long are the two sides of the rectangle?

Unfortunately I only had enough Base Ten Blocks for one set per group, so one kid worked on this while the others watched.

My Daddy Has Twice As Much Money As That!

The Activities

2. Topic: Sorting: As a group, sort 103 numbered cards in 15 minutes.
3. Topic: Money: Find all the ways to make 1 cent, 5 cents, 10 cents, and 25 cents.
4. Topic: Puzzles: Towers of Hanoi: Work on 4, 5, 6 disc puzzles.  The object is to move all the discs to the rod at the other end, but you can only move one disc at a time, and cannot put a larger disc on top of a smaller one.

A 4-disc Tower of Hanoi puzzle.Sort 103 numbered cards in 15 minutes. This time the kids only sorted 60 cards.

Preparation

For the money activity, I had a bag of cleaned up coins of various denominations.

Somewhere online I found super-cheap Towers of Hanoi puzzles (~\$4 each), so I bought 6 so each kid could use their own.

How did it go?

We had 5 kids at this circle.

Sorting

This is really a fascinating activity and I have very interesting video of the kids working on this.  This time I gave the kids a few minutes to strategize before starting, but they didn’t want to talk at all.

3 of the kids spread all their cards out face up on the ground. But Kid #4 and Kid #5 held on to their cards.  They quickly laid out cards 1- 25. But then the first 3 kids got bored while waiting for Kid #4 and #5 to find cards in their hands.  So Kids 1-3 started picking random cards.  This slowed the group down drastically.  The problem is that the kids page throught cards in their hands one at a time, without sorting them at all, so it takes forever.

Kid #3 actually sorted the cards ina pile for 40s, 50s, and 60s, but didn’t pay attention to the other kids, so missed it when they called for 40s.

They ended up sorting 60 cards in 15 minutes, which is worse than the last time they did this.  I asked them why they did worse this week. They had no insights.  Then I asked if there were times when they went faster or slower today.  Kid #4 said they went fast in the 30s and I asked why. She said because there were more of them. I said “are there?” and she said no.  I pointed out that they had going faster in the beginning when cards were on the floor.

Money

There was a lot of excitement when I brought out a bag of coins.  Several kids said basically “My daddy has twice as much money as that!”  They all grabbed a big pile of coins and starting stacking, sorting and talking. After a bit of this, I brought out a money chart where I had taped each denomination on a paper and written the name and amount of each.  Several kids said they wanted to make a chart like that.

The kids quickly saw there is only one way to make 1 cent.  They also got 2 ways for 5 right away. 10 cents took a bit longer, and 25 cents was hardest. Several of the kids would drift off into their own world and not suggest any ways to make 25, unless I explicitly asked them.

Towers Of Hanoi

The kids were excited to see the Towers again, especially Kid #1 who had begged her parents to buy her a Towers of Hanoi app so she could practice. Kid #1 easily finished 5,6,7,8 discs. I *think* all the moves were legal, but I wasn’t watching too closely.

Kid #2 did 4 and 5 discs easily, but got really frustrated on 6. It didn’t help that Kid #3 kept pointing out that Kid #1 was doing more discs than Kid #2.

Kid #3 – 5 solved 4 discs, and worked hard to get 5.

The Infamous Easter Goblin

The Activities

Today we had an Easter-themed Math Circle!

1. Topic: Probability: Book: Probably Pistachio by Murphy
2. Topic: Logic: There’s a beautiful egg hidden behind a door numbered 1 – 36. The kids get 10 guesses to find the egg, or else the Easter Goblin gets it. They can ask yes/no questions like: Is it higher than 10?
3. Topic: Combinations: You have a row of 5 Easter eggs. How many different ways can you color 3 out of 5 eggs. i.e. you could color the first 3, or the first 2 + the last one.
4. Topic: Addition: Draw 3 plastic Easter eggs out of a bag. Each egg contains a one or two digit number. Add the numbers together, and the kid with the highest number wins the round.

Preparation

For the Easter Goblin activity, I colored a few cute paper Easter eggs that the kids would want to save from the silly Easter Goblin (a clipart female goblin).  We printed out a bunch of sheets with 5 egg-shaped ovals on them for the combinations activity.  For the easter egg addition, I used all the left-over plastic easter egg shells, and filled each with a number on a scrap of paper, instead of candy.

How did it go?

We had 4 kids this week.

Easter Goblin

First the kids got 10 questions to find the hidden egg, hidden behind a door numbered 1 – 36. The first kid asked if it was in a door higher than 14. ‘No.’ The next kid asked if it was in a door less than 5.  ‘No.’  The 3rd kid asked if it was number 9.  ‘No.’ The first two kids immediately groaned and said it was not a good question.  I asked why, and they said it’s because it only crossed off one number.  One kid observed that you should ask something more in the middle. Then the 4th kid asked if it was in door number 7.  The first 2 kids again groaned. 🙂

The kids loooved this game, and kept begging for more rounds, but I moved on to the next activity after 4 rounds.

Combinations

We did a variation of this activity with the kids a long time ago, and they were not very good at it. This time they had much better strategies. Kid #1 jumped to the lead quickly finding 6 ways to color 3 out of 5 eggs. Kid #2 was right behind.  One strategy #1 and #2 used was to reverse each novel pattern they found, so they would get two at a time.

Kid #2 then moved to the lead, finding a 7th way. This annoyed Kid #1, who sat on the floor for the rest of the activity, making very little progress, but not bothering anyone. Suddenly Kid #3 found a new pattern and had 9 different ways. Kid #4 was just trying all different things, without worrying if some of the patterns were repeats.

Finally Kid #3 found the 10th and last way. Then we compared the other kids papers to find the ones they had missed.  It turned out that Kid #4 unknowingly actually had all 10 patterns among the 26 rows they had colored.