# Kakuros are Surprisingly Hard!

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

## The Activities

1. Topic: Primes: Book: The Number Devil, by Enzenberger.

2. Topic: Measurement: Measuring the kids bodies with ribbons. We measured the kids’ ears, wrists, hands, feet and height with ribbons, and glued the ribbons onto their charts. We discussed measurement error and compared different kids’ measurements.

My daughter’s measurement chart.

3. Topic: Patterns, Fibonacci Numbers, Graphing: I showed the kids the start of the Fibonacci pattern: 1, 1, 2, 3, 5, 8, 13, 21, and asked them to figure out what came next. Then we used graph paper to draw the Fibonacci numbers as squares of each size.

One of the kids’ Fibonacci drawing

4. Topic: Logic Puzzles, Kakuro: I gave the kids a sheet of Kakuro puzzles and we worked together to solve them.  Kakuro is similar to Sudoku.  You fill in the boxes with numbers that sum to a given value (like 6), and you can’t use the same number more than one in a single column or row.

## How did it go?

#### Book: The Number Devil.

This week we read about large prime numbers, and the fact that between any number and it’s double is at least one prime.  This was really over the kids’ heads and they got confused and distracted. I think it may be time to take a break from this book and come back in a few months or so.

#### Body Measurement

Two parents and I used ribbons to measure the various body parts of the kids.  This went fine except for general loudness and high-spirits from the kids (which is no problem).  We noticed that several kids ears and wrists seem to have shrunk.  The kids said they did not think they had really shrunk. They mentioned that perhaps the parent that was doing the measuring had done it differently this time.  We discussed the idea of measurement error, and I said maybe this meant they hadn’t grown very much since the last time.

While their hands, wrists and feet were not much bigger, all the kids had grown noticeably since last July. Their growths varied from 2cm to 4 cm.

#### Fibonacci Numbers

I wrote the first few Fibonacci numbers on a sheet of paper: 1, 1, 2, 3, 5, 8 and asked the kids what should come next. First they suggested it should start back over at 1, but I said it was not a repeating pattern.  Then they guessed various numbers like 9, 10, etc with no particular reason.  Someone suggested maybe it was counting by 3, but another kid pointed out that the gap between the numbers was not always the same.

Above the original pattern, I helped the kids write the gap between numbers. We saw the first gap was 1 then 1 then 2 then 3 then 5.  The kids then caught on that the gap followed the same pattern.  We extended the pattern: 13, 21, 34, 55.  I expected these sums to be easy for the kids at this point, but all of them had some trouble with these.  Looks like it would be good to bring back the Base 10 blocks and practice some more.

After this, I got out some graph paper, and we drew a graphical version of the Fibonacci numbers. We drew a 1×1 sqaure, 1×1, 2×2, 3×3, in a spiralling pattern.  The kids did pretty well drawing the squares and figuring out where the next one should go. However, I wasn’t paying enough attention and we ended up not making the spiral.  Therefore I cancelled the second half of the activity, which was to use compasses to draw the spiral on top of the squares, and moved on.  A few kids complained because they saw the compass kits but we didn’t use them.

#### Kakuro Puzzles

I handed out a sheet of Kakuro puzzles that focused on adding numbers up to 10.  I had never done a Kakuro, but expected to be able to quickly learn it, since these were aimed at kids.  Actually it was much harder than I expected to come up with strategies.  I sat with a few of the kids and we wrote down some possibilities: this row adds to 3, so it can be 1,2 or 2,1.  Some of the kids followed along with me, some tried out their own guesses, and some were just confused.

After I had figured out 3 of the numbers in the puzzle (which had ~10 numbers), I filled them in in all the kids sheets. At that point one kid finished solving the puzzle, and that encouraged several others to have another try.  Finally they all ended up with the right answer.

We moved on and did one more puzzle. Some of the kids understood the puzzle by the end, but a couple others didn’t quite get the idea.  I think I’d be able to teach it better next time.

#### Paying Attention

2 or 3 of the kids were pretty rowdy this time, not listening to me, or not giving back the materials when it was time to move on.  I stopped circle in the middle and discussed this with the kids. They agreed that the purpose of circle is to learn Math, and we should not distract other kids. They suggested that kids who were being disruptive should get a warning, and then sit out of circle for a few minutes to calm down.  I’m planning to implement this next circle.