# Seven Days Old to Seven Years (Age 8)

## The Activities

1. Topic: Time. Book: A Second is a Hiccup, by Hutchins. This is a sweet book about how much a kid can do in second, day, week, year. It’s pretty simple, but I made it more challenging for the big kids by asking computational questions like: “How many seconds are there in one hours? How many hours in two days?”
2. Topic: Measurement. Use ribbons to measure the kids’ ears, wrists, hands, feet, and height. Add the new measurement to the chart we’ve been keeping for the last couple years.

Two years of measurements.

3. Topic: Decision Trees, Programming. First show the kids a simple decision tree for sorting cards into three piles: A, B, and C. Trace through the tree for some sample cards as a group. Then give each kid a stack of cards to sort using the tree.  Next try some harder decision trees. Then deal 6 cards into two stacks, A and B, and try to write a decision tree that puts each card into the right pile.

An easy decision tree.

Here a the other trees: Tree 1,  Tree 2, Tree 3, Tree 4, Tree 5.

## How did it go?

We had 4 kids this week. There was a lot of energy, but the kids were pretty focused, and I only had to give a few behavior warnings to my daughter.

#### See How We’ve Grown

The kids were excited to take their measurements again.  Measurement error was again a big factor, as some kids ears and wrists magically seemed to shrink. Height and foot size seemed more accurate, probably because those measurement changed the most. The kids grew between 3 cm and 5 cm this year.  We discussed questions like: how much did you grow this year? How much have you grown since the beginning of circle? Who has the biggest feet? Smallest ears?

I also showed the kids a picture of my daughter when she was seven days old, along with an impression of her foot.  It’s so amazing how quickly they grow up.

My seven day old girl.

#### Playing Card Decision Trees

Last week, the kids tried to classify cards into piles using a simple programming language. The syntax of the language proved to be pretty confusing to the kids, especially the parentheses. Syntax has often been trickier than expected in the past too.

We decided to repeat the same activity, but use decision trees instead of a programming language to sort the cards. All four kids quickly caught on to how to trace a given tree.  Some kids also started to notice unreachable branches of the trees…for example:

The second “8?” is always “no”, so you never put any cards in pile C.  Several kids noticed this, and were excited to point it out.

Next, I made two piles cards and asked kids to help write a decision tree to sort the cards. I intentionally picked each divisions, for example, pile A might have all hearts in it, so you can make a simple tree: “Hearts?” yes -> A, no -> B.  After they were comfortable, I dealt out six random cards, and we worked together to make a tree. With random cards, you are likely to need more than one question.

At this point, I asked the kids if they were ready for their own set of harder cards. Everyone said “yes” (always a good sign), so I dealt out six cards in two piles to each kid. If a kid was stuck, I suggested a starting question.  All 4 kids were able to make progress on this.  I think all 4 quickly came up with trees that *almost* worked, except for one card.  I helped them find the place in the tree where the card went to wrong pile, and suggested that they add a new question there, to make the card go to the right place.

One kid’s decision tree for six random cards. Yes, her handwriting is better than mine!

All four kids were able to fix their trees and correctly sort all six cards.

# Drawing Castles and Trees (Age 6)

## The Activities

1. Topic: Addition: A Fair Bear Share by S. Murphy.
2. Topics: Numbers, Addition, Base Ten Blocks:  We did several addition problems using Base Ten Blocks.  We practiced making numbers, combining the piles, and interpreting the sum.
3. Topic: Logic: I drew some pictures of paths leading to a castle with labeled river crossings.  Each picture corresponds to a particular logical formula.  For example, for a path crossing two rivers before reaching the castle, you need a bridge at A AND B in order to reach the castle.  If there is a path that forks and crosses the same river in two places, then you need A OR B.  We interpreted a number of pictures, and then I gave them a new formula and asked them to draw a picture of it.  You can download my pictures here.
4. Topic: Decision Trees, Attributes, Attribute Blocks:  I drew some decision trees using color and shape as attributes to split on.  First we practiced sorting shapes according to the decision tree.  Next, I sorted the shapes onto A and B in a simple way (e.g., triangles on A and circles on B) and asked the kids to draw a tree that would give you that sorting.

## How Did It Go?

We had all five kids this week.

#### A Fair Bear Share

This book went well, the kids were interested in the baby bear not doing her fair share.

The kids are getting better at making numbers using blue blocks, and I think most of them understand how to use blue blocks to add two digit numbers.

#### Castle Logic

The kids did a pretty good job understanding the pictures.  They were very good at telling whether a particular configuration of bridges allowed you to get to the castle (I had little squares of paper that you could place on the drawing to show whether there was a bridge).  I used ^ and V for AND and OR, but I didn’t ask them to use these symbols later so I don’t know if they understood.

Drawing a picture was much harder.  By far the hardest part is parentheses, which is important for any mildly complicated situation.  I gave them a problem with parentheses to start, involving A, B, C, and D; one of the kids made a picture of Y ^ Z.  Then I gave them a much simpler problem and some of them got a correct picture.

#### Decision Trees

Again, the kids were pretty good at tracing a tree.  I think all of them understood this pretty well by the end.  However, drawing a tree was extremely hard for them.  Only one kid got even close (see 3rd picture above).  A big difficulty for them was that the original depth-1 tree I gave them split on colors, so when I gave them that as an example of how to draw a tree, they just copied it, including the colors, even though they needed to split on shapes.

# Donkeys and Salt (Age 8)

## The Activities

1. Topics: History of Math, Mathematicians: Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians (Volume One) by L. Reimer and W. Reimer, Chapter 1 (Thales).
2. Topic: Story Problems: Minute Mysteries 2: More Stories to Solve by T. Witkowski and J. Hirsch, Chapter 1 (Bake Sale).

3. Topic: Programming: We did the Conditionals with Cards offline activity from Hour of Code.  As a follow up, I dealt three random cards as “YES” and three cards as “NO” cards, and they had to write a conditional expression to separate the two groups of cards.

## How Did It Go?

We had all five kids this week.

#### Mathematicians are People, Too

I was a bit worried they might find this book boring, particularly since the chapters are a bit long, but the Thales chapter held their interest the whole time.  Our daughter immediately noticed that the story of the donkey and the salt was the same as one from a book of Aesop’s Fables she had listened to, and went to get the paper copy.

#### Minute Mysteries

Once you extract the relevant information, the problem to solve is “There are 180 brownies and cookies, combined.  There are twice as many cookies as brownies.  Brownies sold for 10 cents each, cookies for 5 cents.  How much money did the girls make total?”  The kids were able to solve this problem without any help at all.  One kid made two nice insights: first, that they needed to find a number X so that 3 * X = 180; and second, that the amount of money from cookies = amount of money from brownies, since there are twice as many cookies but they cost half as much.

#### Conditionals with Cards

We started with the warm-up exercise suggested in the activity, where I went to each kid in turn and then they had to do something different based on what I did.  This was very easy.  They also had very little problem with the main activity: each team takes turns flipping over a card, and then either they or the other team gets points depending on the card.  The first one (“If red, we get a point, otherwise they do”) was very easy; the second (“If red, we get a point, otherwise if <= 5, we get that number of points, otherwise they get a point”) some of them firmly understood and a others were a bit shaky.

The follow-up activity, where they had to write a program to separate two sets of cards, was quite a bit harder.  Two of the kids didn’t make much progress; another had a good initial idea but got stuck; a fourth got correct tests which together could make a correct program but they weren’t nested properly; and a fifth started slow but ended up with a correct program.

Afterwards, I realized that they would probably understand this much better if it were expressed in tree form (similar to the Choose-your-own-adventure activity we did a while ago).  We’ll revisit this activity soon and try again.

# Shrinking Ears (Age 6)

## The Activities

1. Topic: Size. Book: The Biggest Fish by Keenan. This is a simple book about a town that has a contest to see who can catch the biggest fish. The kids loved the drawing of a fish as big as a school bus.

2. Topic: Measurement, Graphs, Differences. We used ribbon to measure the kids’ wrists, ear, hand, foot and height. We compared the measurements to last year’s.

3. Topic: Estimation, Graphs, Counting. We guessed how many steps it would take to get from the kitchen to different parts of the house. Then we counted it out and compared the answer to our guesses.

•  First each kid made a guess and counted it out, to different destinations.
• Next, we each made a guess for a farther away destination (the front door), and then counted it to see who was closest. Each kid computed how far off their guess was.
• Finally, we counted how many baby steps it would take to get to that destination.

## How did it go?

This is the one year anniversary of the younger kids circle.  It was also the first circle in 4 weeks, due to Christmas vacations.  The kids had lots of energy, and were excited to see each other after so long.

#### Body Measurement

The kids were all really excited to find out who had the biggest feet/wrist/ ear.  It was a bit chaotic during the measurment phase. Another parent helped, but there was still lots of noise and excitement. Eventually everyone got their new ribbons glued down to their sheets.

As usual, there was a fair amount of measurement error. One girl’s ear appeared to have shrunk since last year 🙂

The kids were especially excited to see who was the tallest. My son won that competition by being one centimeter taller than the next kid. Interestingly, the smallest kid in circle grew the most — seven centimeters since last year. No one else grew more than five centimeters.

The kids had trouble answering, “Which measurement of yours changed the most in the last year?” They all wanted to answer whichever was their biggest measurement, even if it hadn’t changed much.

#### House Measurement

The kids all enjoyed guessing how far it would be to their target. Some of the kids were very strategic when taking their steps, taking smaller and smaller steps at the end, if necessary.

We all guessed how far it would be to the front door. The guesses were 19, 29, 30, 31, and 44. It took us 21 steps to get there.  Each kid then computed how far off their guess was, using our chart.

We had just a few minutes left in circle, and the kids were all joking about taking tiny baby steps, so I decided we would try it out. I picked a kid who had pretty regular baby steps, and then we all counted together as she walked to the front door. It took 115 steps, which was an excitingly big number to the kids.