# Babb Abab Baaa

## The Activities

1. Topic: Subtraction: Book: Subtracting With Sebastian Pig and Friends on a Camping Trip by J. Anderson.
2. Topic: Addition: I put a bunch of slips of paper with numbers 1-9 inside of plastic Easter eggs.  Each kid drew out 2 eggs, opened them, and added them using Base Ten Blocks.  After a bit, they switched to drawing 3 eggs instead.
3. Topic: Patterns: We made a number of patterns using Rummikub tiles, which have numbers 1-13 in one of 4 different colors.  Taking turns, the kids completed the patterns in increasing order of difficulty.
1. 9,10,11, all blue
2. 2,3,4,5 alternating black and red
3. 1, 1 tile face down, 2, 2 tiles face down (in a stack), 3, 3 tiles face down
4. 1,3,5,7, all yellow
5. 2,4,6, all red
6. face down stacks with 1 tile, 2 tiles, 3 tiles
7. 1,4,7, all blue
8. face down stacks with 1 tile, 2 tiles, 1 tile, 2 tiles
9. 2,3,4, all yellow, rotating clockwise
10. 1,1,2,3,5, all yellow

4. Topic: Numbers: Zero is the Leaves on the Tree by B. Franco.
5. Topic: Numbers: We discussed some interesting zero facts.  What’s 2+0, 3+0, 1 million + 0, …; what’s 2 – 0, 3 – 0, …; and even multiplying by 0.
6. Topic: Combinations, Combinatorics: I told the kids that baby language had only two letters, A and B.  The task was to find all the 4 letter words in baby language.  The kids took turns adding new words to a list taped to the wall.

## How Did It Go?

All 5 kids attended.

#### Subtracting with Sebastian Pig and Friends on a Camping Trip

The kids liked finding the mice who had stolen all the pig’s things.  They’re still not that great at problems like 11 – 7.

This went quite well, all the kids were into it.  Most of the kids needed Base 10 Blocks to do the addition.  A couple of them needed help figuring out how to use them, but got the idea after a while.  Our son has practiced addition a lot, so I gave him multiplication problems instead.

#### Rummikub Patterns

We took turns with which kid got to touch the tiles to make the solution, but all the kids worked together to figure out the answer.  As we’ve seen in the past, counting by 2’s and 3’s is fairly easy for some kids and difficult for others.  The two trickiest ones were 1, stack of 1, 2, stack of 2, …, because they wanted to just do the stacks, and not include the numbers; and, not surprisingly, Fibonacci, they didn’t figure that one out.

#### Zero is the Leaves on the Tree

For each picture, I asked the kids why there were 0 of whatever it was (e.g., why were there 0 leaves on the tree during fall?)

#### Zero Facts

They picked up on the addition and subtraction pretty quickly, although I did need to show it on my fingers at first.  For multiplication, they wanted to say 0 * 5 = 5, not too surprisingly since that was the pattern from addition and subtraction.  It took them several explicit run throughs of “What’s 0 + 0 + 0 + 0 + 0?” before they got the pattern.

#### Baby Language

They did quite well on this, they got about 12 before I started helping them.  I wanted to make sure everyone got the same number of turns writing on the sheet, so I helped on the last few.  We were running short on time, so I didn’t ask them whether that was all of them and how could they tell.

# Walking Through Paper

## The Activities

1. Topic: Shapes, Geometry: Book: Zachary Zormer, Shape Transformer, by Reisberg.
2. Topic: Shapes, Geometry: Make a Mobius Strip. Cut a piece of paper so you can walk through it.

My daughter walks through a piece of construction paper.

3. Topic: Proofs, Geometry: Using 1×2 rectangles to try to cover various checkerboard shapes. If a shape is impossible to cover, prove why. Here are the checkerboard patterns they worked on.
1. 4×4 checkerboard.
2. 5×5 checkerboard (impossible)
3. 4×4 checkerboard with two corners missing (impossible)
4. two connected crosses (impossible)
4. Topic: Combinatorics, Geometry: Using wooden pattern blocks, find as many ways as possible to make a 2×2 diamond.

## How did it go?

I led the big kids circle this week, 5 kids attended.

#### Zachary Zormer

The kids all enjoyed this book. Afterward they were excited to make the mobius strips and walk through paper the way Zachary did in the book.  Everyone paid careful attention on both parts of this activity, and successfully completed both.

#### Checkerboard Proofs

All the kids happily covered the 4×4 checkerboard paper with the 1×2 rectangles. I handed out the 5×5 checkerboard next, and everyone thought it would be easy.  Soon they found that it was no so easy afterall.  Some kids tried moving pieces around, but there was always one square left over.

After a couple minutes of trying, one kid said they thought it was impossible. Another kid said the number of squares was odd, and the rectangles could only cover two squares.  We all counted the checkerboard squares and found there were 25.

Next I handed out the 4×4 checkerboard with two diagonal corners cut out. I pointed out that this had an even number of squares.  The kids set to work, trying various patterns. Eventually a couple kids thought is was impossible, but couldn’t explain why. I pointed out that both remaining squares were always white. I asked if one piece could ever cover 2 white squares. The kids checked and decided it was impossible. Someone asked if the leftover squares would always be white, so we counted the whites (8) and blacks (6), and finished our proof.

Finally we worked on the connected crosses. The kids quickly decided it was impossible, because as soon as you use the middle of the cross, the other squares are orphaned.

During this activity, 2 of the kids were really engaged in the proofs. The other 3 kids happily worked on covering the squares, but were more interested in silly solutions (like putting pieces diagonally), than thinking about the proof.

#### Diamond Pattern Blocks

The kids were really excited to play with the pattern blocks. One kid told my daughter that she was so lucky because she could play with them after circle 🙂

After a minute of free play, I showed them a 2×2 diamond, and asked them to find as many different ways to make that shape as possible. Two kids started in right away, and came up with many different options. My daughter didn’t actually find any…I think she was trying to use novel shapes like the square in her diamonds, which doesn’t work.  The other two kids sometimes worked on the activity, and sometime just made their own shapes.

We ended up finding 14 different ways to make the diamond. My daughter found a 15th after circle, which made her happy, since she hadn’t found any during circle.

# A Balloon Weighs Less Than Nothing

## The Activities

1. Topic: Counting, Addition. Book: Math-terpieces by Tang.
2. Topic: Comparisons, Weights, Pan Balance. Given a Pan Balance, and 7 small toys.  Which toy weighs the most? The least?  If I tie a helium balloon to one of the buckets, what will happen?

The toys we tested.

The balloon weighs less than nothing!

3. Topic: Reflections. Fill in the reflection of a pattern on a pegboard. The dark blue pegs are the mirror.  We used a real mirror placed on the dark blue line to check our work.

A simple shape, reflected over the blue mirror line.

4. Topic: Puzzles, Logic. Book: Puzzles, by Wildsmith

## How did it go?

This week I led the younger circle.  We had only 3 kids this time, so I used all the materials that require taking turns.  The scale and pegboard are both quite fun, but it’s really hard for more than 3 kids to use them at once without extreme chaos.

#### Math-terpieces

This is a pretty book with a combination of famous artwork and counting problems. The kids all enjoyed taking turns finding groups of shoes that add up to 7, or stars that add up to 10.

#### Pan Balance

The kids noticed the pan balance, and wanted to use it right away.  I brought it, and the small toys over to the table.  I gave the kids a minute to play with the toys, and then asked them which toy was the heaviest.  They weighed two toys against each other and realized the side of the scale that goes down is heavier.  We kept the heavier toy in the balance, and then tried to find another, heavier toy.  Eventually we found that the heaviest toy was the set of keys.  I asked if we should check the keys against the bluebird.  One of the kids said we didn’t need to, because we knew the keys were heavier than the strawberry, and the strawberry was heavier than the bluebird.  I said that was a good point, but we tested it anyway, just to make sure.

Next we figured out which toy was the lightest.  All the kids enjoyed putting different toys in the buckets.  They all thought it was hilarious when the buckets slammed down hard enough to come off the scale.

I happened to have helium balloon from a birthday party the previous day.  I asked the kids to predict what would happen if I tied the balloon to one side of the empty scale.  They all agreed that the balloon would make the side of the scale go down.  I tied it on, and we all saw that the balloon side went up.  I said the balloon must weigh less than nothing, which was quite funny to the kids.

#### Pegboard Reflections

I had 6 simple shapes set up on the pegboard, and the kids took turns reflecting their shape across the blue mirror line. We use a real mirror to check our work, and learn what a reflection is.

This was pretty easy for all the kids, although my son wanted to check his work in the mirror to figure out which color to use.  Everyone loved the pegboard, but as predicted, it was hard to wait for their turn, even though there were only 3 kids.

#### Wildsmith’s Puzzles

This is  a really cute book that’s a mix of counting, pictures, and logic.  There were a few interesting pages.

One page shows 3 cracked eggs, with 2 chicks and one grown hen. How many chicks should there be? The two girls figured out there should be 3 chicks, because there are 3 eggs, but my son thought maybe the big chicken hatched out of one of the eggs.

Another page shows two kittens hiding under a mother goat, in a rain storm. Why are the kittens under the goat?  The two girls laughed because the picture shows the goat’s udder. One girl suggested maybe the kittens wanted to be peed on.  Eventually my son noticed that it was raining, and suggested the kittens wanted protection from the storm.

# A Octopus Kissed A Ninja

## The Activities

1. Topic: Addition: Book: Math Man by T. Daniels.
2. Topic: Programming: We did two types of programming this week.  First, we reviewed how loops work, and practiced assigning a variable to itself inside a loop (X = X + 1).  Second, we introduced choosing a random noun/verb/number by drawing a word from a bag — a random version of Ask_a_Friend.  Download the programs here.
3. Topic: Algebra: I attempted to show the kids how to solve algebra problems involving addition and simple multiplication using Base Ten Blocks.  For example, in “X + 17 = 68”, you can first make 68, divide it into a pile of 17 and a pile of 41, and then conclude that X is 41.
4. Topic: Reflections: A while ago I drew a picture that had every uppercase letter hidden in it, duplicated and reflected.  E.g., reflecting “B” around the vertical line gives you a butterfly.  You can download the picture here.

## How Did It Go?

All six kids attended.

#### Math Man

The kids liked the part where Math Man adds a whole bunch of prices in his head.

#### Programming

Last week, many of the kids had trouble with loops that had more than one statement inside; and also with self assignment like “X = X + 1”.  We walked through a program with both of these features: “Box_X = 1; Do 5 times { Print Box_X; Box_X = Box_X + 2 }”.  I think by the end of it most of the kids understood what was going on; we’ll try another in a couple weeks and see how it goes.  Our daughter already had a firm grasp of these two concepts, so I gave her some harder problems to work on (second page of PowerPoint above).  She got the first two but got stuck on the nested loops.

As expected, the kids really liked the programs with random nouns/verbs/numbers.  For the most part, they had no problems, but one thing that turned out to be very hard/confusing was “Do Box_X times {Print “really”}”.  Almost all the kids wanted to print the number; and one of the kids ended up print “2 2 really really”.  So clearly they need more practice using variables in control flow rather than just printing them.

#### Algebra

One issue with this activity is that some of the kids can solve problems like “X + 17 = 63” in their head, but I had everyone work through it methodically.  My approach was a bit wrong, I think; I gave everyone a paper square with “X” on it, and had them make 17 and 63.  Then, I said they should split 63 into two parts, 17 and what’s left, and from that, they can conclude that X is 46.  I think it would have been better to simply have them make 63, and then break it into 17 and 46 and conclude that X = 46.  The problem is, I don’t think they grasped the idea that the two sides were the same, so the extra 17 didn’t really help.  Another problem is that it’s a bit hard to see how to extend this to X – 17 = 63; you need to make a 17 and a 63, put them next to each other, see that if you subtract 17 from this new number, you get 17, so the sum must be the answer.

There’s a different approach as exemplified in the very nice iPad game Dragonbox Algebra which I may try next time I do this activity.  The focus there is much more on the fact that both sides have to be the same.  I also like how they use pictures of monsters instead of numbers, at least at first, which helps emphasize the nature of “subtracting from both sides”.  I think Dragonbox Algebra still gets something wrong, which is that instead of opening the box and revealing what’s inside, the box instead eats the other side, which doesn’t make much sense.  So my ideal version is to have some objects hidden inside the box, emphasize that both sides have the same objects, have them isolate the box, and then reveal it to show that it has the same thing as what’s on the other side.

#### Reflection Picture

The kids really enjoyed doing this again, working together they were able to find all the letters.

# Kitties, Cubs, and… Goatlings?

## The Activities

1. Topic: Patterns: Book: A-B-A-B-A- A Book of Pattern Play by B. Cleary.
2. Topic: Patterns: We made rows of colored glass beads in different patterns.  I gave a starting pattern with 5-6 beads, which they copied and then continued the pattern.  They also each made up a pattern on their own.  Here’s the grid we put the stones in.
3. Topic: Logic: We did three Halloween-themed logic puzzles.  For example, in the first one, there were 4 monsters and 4 candy buckets, and you have to figure out which one goes with which.  One of the clues is “The ghost likes orange”.  The full set of pictures and clues is available here (including 4 extra clue sets we didn’t do).
4. Topic: Verbal Discussions: I named a bunch of animals and asked the kids what the baby animals of that type were called.
5. Topic: Counting: Book: Skip Counting with Meerkats by T. Steffora.
6. Topic: Counting: We counted by 2’s and 3’s as a group taking turns going around the circle.
7. Topics: Shapes, Charts: We have a large two-dimensional table with colors on the rows and shapes on the columns.  The task was to place the Attribute Blocks onto the chart.
8. Topic: Origami: Each kid made the cat from Easy Origami by J. Montroll.

## How Did It Go?

All the kids attended.  The kids were mostly attentive through out, although there was the usual “Is it time to go play?” starting about 40 minutes in.

#### A-B-A-B-A- A Book of Pattern Play

A decent introduction to simple patterns.

All of the kids were able to complete all the patterns I made, (which went up to cycle length 4).  They weren’t fooled by an all-blue pattern.  One of the kids said they wanted to make their own pattern, so I gave them time to do that.  One kid used the columns of the grid for their own pattern instead of the rows.

#### Halloween Logic

The kids did well on this activity.  On several occasions, they remembered an important relevant clue from earlier in order to solve a puzzle.  However, they weren’t quite ready to solve the puzzles on their own — I still needed to ask leading questions several points, particularly on the 3rd (and hardest) puzzle.  The kids were pretty good at following the instructions, but there were a few times where someone said something like “I think the cat likes the hat because a cat can’t use a broom.”

#### Animal Babies

The kids knew a reasonable number, including kitty, puppy, calf, cub, and duckling.  They didn’t know foal/colt, piglet, tadpole, or gosling.  The most interesting guess was “goatling”.

#### Skip Counting with Meerkats

One of the kids knew the animals in the pictures were meerkats, from Happy Hollow (or rather, “Danny the Dragon place”).

#### Counting by 2’s and 3’s

The majority of the kids still aren’t very good at counting by 2’s or 3’s — two can do it reliable, three can’t.

#### Attribute Block Chart

I was impressed by the kids performance on this task, I remember Circle 1 having some issues, but all the kids got the idea and were able to do it.  Initially a number of the shapes were placed incorrectly because the kids didn’t want to put more than one shape in each box, but once I showed them stacking was ok, they placed all the rest of the shapes without problems.  The kids also put all the shapes back into the box afterwards.

#### Origami

The kids are decent at making folds, but the idea of making a fold from point A to point B, or so that an edge lines up with a given point, is tricky for them.

# 15 Heads in a Row

## The Activities

1. Topic: Algebra: Book: The Yum-Yum House by Walker.
2. Topic: Algebra: Work together as a group to solve simple algebra problems.
1. y + 11 = 32
2. y + 68 = 72
3. y + 22 = 100
4. 2 * y = 40
5. 3 * y = 12
6. y / 2 = 10
3. Topic: Programming: Trace more complex programs, then try to write your own programs.

1.  Box_X = 1 Print Box_X Box_X = Box_X + 10 Print Box_X

2.  Box_Y = 1 Do 10 times { ____Print Box_Y ____Box_Y = Box_Y + 1 }
3. Write a program that prints out “Hello”.

One student’s program to print “Hello”

4. Topic: Probability: Experiment with coin flips to figure out how many flips it takes to get 3 Heads, and how many it takes to get 3 Heads in a row.

## How did it go?

I led the big kids circle this week. 5 kids attended.  At the start of circle we had a discussion about how wild circle got last week. I explained that I want kids to talk, but they should talk about the activities, not about other things. Two of the kids suggested I should say “1, 2, 3 Silent!” and then everyone should stop talking.  This worked well this circle…there was still lots of talking, but it didn’t get out of control.

#### Book: The Yum Yum House

The kids all really enjoyed this book. It has a lot of story, and a little math.  It centers around 2 kids who want to get at least 83 pieces of candy so they can make a gingerbread house that is fancier than their friend’s.

#### Algebra

I asked the kids if they had ever heard of algebra, and they all raised their hands excitedly.  Apparently all of the their schools have introduced simple problems like x + 10 = 17.  The first 3 problems about addition were very easy for the kids, though some were faster at mental arithmetic than others.

2 * y = 40 was more difficult. None of the kids had seen multiplication in an algebra problem.  Several kids were able to explain that if you make 2 groups of y blocks each, you should have 40 blocks.  They were able to guess 20, and we verified it using Base 10 Blocks.  3 * y = 12 was also quickly solved.

y / 2 = 10 was actually  much trickier. One kid really wanted to answer ‘5’ to this.  The other kids realized that it should be a number that can be broken into 2 groups of 10, and came up with y = 20 on their own.  I then showed all the kids the difference between y * 2 = 10, and y / 2 = 10.

One kid complained that this activity was too easy, though she stopped complaining when the problems involved multiplication.  Another kid kept asking if we could do programming or compasses next.

#### Programming

All the kids were excited to do programming.  I handed out the materials and the first problem.  It turns out that a statement like:

Box_X = Box_X + 10 is confusing to about half the kids. Most kids were able to get through the first program with a couple questions to me.  One kid wrote “11 11” for the output, because after the value of Box_X changed, she also changed the value that had been printed.

The second program (which should print the numbers 1 through 10), was much trickier for everyone.  Only one kid was able to do it totally independently. Two kids understood what was going on after a bit of help from me, and the last two kids were really pretty confused.

The confused kids did not understand which lines we were supposed to do 10 times, or which order to do them in.  3 kids thought they should print “1” 10 times in a row, but then I showed that we have to do Box_X = Box_X + 1 in between the prints.  Then they guessed “1” 10 times, followed by “2” 10 times.  We’ll have to work on loops a bit more.

Next I said the kids would get to write their own programs.  They were excited to do this, but my daughter started crying when she heard it should do something specific…she didn’t think she’d be able to do it.

The first program was supposed to print “Hello”.  Most of the kids quickly caught on, and several came up with interesting ways to do this.

I suggested: “Print “Hello””.  Two kids independently came up with “Box_X = “Hello”; Print Box_X”.  One kid came up with the complex program pictured above.  I like how that program uses a loop.

After this, the kids started writing their own programs to do whatever they wanted. They loved to have me follow their programs and write the output. Nobody wanted to stop, but it was time to move on to the last activity.

#### Coin Flips

I handed each kid a small cup with a quarter in it. I showed them how to flip the coin by covering the cup with their hand, shaking it, and then looking at what side the coin is showing.

First I asked the kids to write down their flips until they got 3 heads.  This took between 4 and 8 flips.  Next I asked them to keep flipping until they got 3 heads in a row. Three of the kids took 24, 28, and 25 flips, which seems reasonable.

One kid kept getting Tails, like 15 times in a row. I’m not sure if he was intentionally cheating, or not shaking the cup hard enough, or what.  Another kid kept getting Heads.  So their results were a bit suspect.

The kids explained that it is harder to get 3 heads in a row than it is to get just get 3 heads. One girl mentioned that if you get 2 heads and then a tails, then you have to start over to get 3 in a row, but the 2 heads still count if you just want 3 heads total.

# Stepping on a Dragon’s Butt

## The Activities

1. Topic: Large Numbers: Book: Millions, Billions, & Trillions by D. Adler.
3. Topic: Measurement: I bought two standard latex balloons filled with helium at the grocery store.  The problem was to figure out how many balloons it would take to lift one of the children.  The available materials were paper clips and a kitchen scale.

## How Did It Go?

All the kids attended.  Unfortunately, this circle was pretty wild; I almost stopped it early because many of the kids weren’t paying attention during the final activity.  The programming went very well and the kids liked the book, though, so it was still a moderately successful circle.

#### Millions, Billions, & Trillions

This was a pretty interesting book that talked about how big a million, billion, and trillion were.  The kids were particularly interested in how long it would take to count to each of these numbers.  One of the kids didn’t believe that a trillion dollars in \$100 bills would make as tall a stack as it would (700 miles).

#### Programming

The kids were all quite comfortable with putting things in boxes and then using them, definitely better than last time we did programming.  Nothing was too tricky, but I did vary the order that I used the boxes in, I had one where you set from one box into another, and one with a loop.  No one had any problems.  There was some variation in speed, which depended entirely on how fast each kid wrote.  The kids loved “Ask A Friend”, but it also got pretty wild.  Some of the supplied answers weren’t entirely appropriate, which is how we ended up with “[Anonymized kid’s name] stepped on a dragon’s [butt].” Needlessly to say, they thought this was hilarious.