- Topic: Maps: Book: Mapping Penny’s World by Loreen Leedy.
- Topics: Logic, Maps: My Little Ponies are at Disneyland, and the kids have to figure out which section of Disneyland each pony is currently visiting. Each puzzle involves 6 ponies, and for each of the 2 sets of ponies, I had an easier and a harder puzzle. Below, there is a picture with the solution for each puzzle, followed by the clues for that puzzle. The map and clues are in this powerpoint, and these are the ponies.
- All ponies with a single hair color went to Fantasyland or Tomorrowland.
- One unicorn is north of the yellow pegasus, and the other is south.
- The purple unicorn is north of the other purple pony.
- There are no other ponies with the pegasi.
- No pony went to Fantasyland or Frontierland.
- Each pony went to a different place.
- The pegasi went to “lands”.
- The purple ponies are next to each other.
- The unicorns are next to each other.
- The orange-haired pony is north of the yellow-haired pony.
- 2 ponies went to Fantasyland.
- 2 Ponies went to Mickey’s Toontown
- One unicorn went to Adventureland, and the other went to Frontierland.
- Each blue pony is north of a white pony.
- The pegasi are together.
- No ponies went to Critter Country or Main Street U.S.A.
- Each pony went to a different place.
- The white ponies are next to each other.
- The ponies with 2 hair colors went to Tomorrowland, Adventureland, and New Orleans Square.
- Unicorns don’t like New Orleans.
- An earth pony (no horn or wings) went to Fantasyland.
- The blue ponies are next to each other.
- Topic: Proofs, Numbers: Prove there is no largest number.
- Topic: Programming: Another set of programs to trace. The new thing this time was the combination of loops and self-assignment of variables. We used the same worksheet.
Box_A = 3
Box_B = 5
Box_A = Box_A × Box_B
Box_B = Box_B + Box_A
Box_A = 0
Do 5 times:
Box_A = Box_A + 1
Box_A = 0
Box_B = 2
Do 5 times:
Box_A = Box_A + Box_B
Box_A = 2
Box_B = 1
Do 4 times:
Box_A = Box_A + Box_B
Box_B = Box_B – Box_A
How did it go?
All 6 kids attended this week.
Mapping Penny’s World
The kids said “yay” when the book came out, since we had read several Penny books before. They didn’t comment on the book afterward though.
Ponies go to Disneyland
I divided the kids into two groups of three (Team X and Team Y), and then went back and forth helping each group.
The kids are quite good at reading now, they only had problems with a few words (pegasi, for example). All of the kids were able to read most of the clues. They all understood which direction was north, south, east, west. But the concept of “Pony A is north of Pony B” was kind of tricky (Kid A got it backwards at one point).
The easy puzzles in each set weren’t too hard. One of them had a clue “One of the unicorns is north of the yellow pegasus, the other is south”. This turned out to uniquely identify where the yellow pegasus was, but it was kind of tricky — Kid A got confused, either with directions or got the clue reversed. The other one had some pretty clear clues and was easy to just do a couple swaps to fix (although Team Y did have the wrong answer — they hadn’t obeyed one of the rules, which was fixable through a simple swap). The hard problems were hard primarily because you had to keep a lot of information in your head in order to remember what legal swaps were (putting ponies on the board and then swapping them to try to satisfy the constraints was definitely the right thing to do). Kid A (on Team X) was doing a good job with this, she usually remembered what was okay to swap. Team Y had a lot of problems with this. They kept forgetting, even with lots of reminders from me, what were legal swaps subject to all the rules so far. There was one point where they just needed to swap Rainbow Dash for another pony, but they kept trying a bunch of swaps that broke a rule.
Team X stayed on task most of the time (with a little help from Corey towards the end), but the other group lapsed into playing with the ponies a couple times while I was helping the other group. Team X was able to make progress while I wasn’t there, and solved at least one while I was at the other table. Team Y didn’t make much progress while I wasn’t there. Team X ended up solving all the problems, while Team Y only solved 3.
I’m not sure how much Kids B and C contributed to the solving, but they both read some of the clues, and I saw Kid B add at least one pony to the map.
One thing that was very clear is that the right strategy is to put out a possible solution and then try to fix it. A question for the future is how to make logic puzzles where it’s easier for the kids to check the constraints themselves. Even though they could read pretty well, it was still not that easy for them to go through and check all the rules. If we had the constraints it in a simple graphical language, then I could probably be more hands off and hopefully they would themselves get in the habit of checking the constraints frequently, which is I think what they need to do to get better at holding them in their heads better.
No Largest Number
First they said that you could keep counting and counting. To make it more formal, I introduced the idea of proof by contradiction, and asked what the opposite of “There is no biggest number”. Kid A said “There is a biggest number”. Kid B said something about “There is no smallest number.” I said, “Suppose there is a biggest number. Let’s call it fibble. Is there a bigger number?” Very quickly, I got “Fibble-1” from Kid C and “Fibble + Fibble” from Kid D. Corey was standing by and said “but maybe fibble + fibble is the biggest number?” I said “But we assumed fibble was the biggest number.” Proof by contradiction is a subtle idea, and they probably didn’t quite understand it, but it was still a good conversation.
There wasn’t anything new this week, but we did combine loops with self-variable setting, which makes things much more difficult and interesting. These programs were noticeably trickier than the previous week’s. Kid A was the only one who got to problem #4 before time ran out. One problem had multiplication, and the kids initially complained they couldn’t do multiplication; but as soon as they realized is was 3 X 5, at least a couple of kids immediately said 15.
The kids are all now very proficient at setting boxes to constants, and usually at printing things out. But assignment to a variable involving an expression with other variables is still tricky. Kid A had particular problems with complicated assignments, particularly inside loops; but Kid A was also the quickest at figuring out how to do the rest of the iterations of the loop after doing it 1 or 2 times. A number of the kids needed to be walked through a number of iterations of each loop — one thing we need to introduce is making a tick mark next to every instruction as you execute it, so you can keep track of where you are. One thing I saw this week that I hadn’t seen before (but Corey had) was mixing up string literals with semantic values, and names of variables with string literals. Kid B had the most problems with variable names, at one point writing “Box A” as the value of Box A, and another time printing “Box A” as output at one point. Kid C had trouble with the statement ‘Print “Odd numbers: “’. First, Kid C started to output “Print”, and then once I said that you weren’t supposed to print “Print”, started printing the actual odd numbers 1 3 5 7. Despite some challenges, I do think most of the kids understood that the program to print even numbers was adding 2 each time, and most of the kids were able to “production line” their evaluation after a few iterations.
Problem #4 involved adding and subtracting some small negative numbers; Kid A was working on this immediately after circle, and it turned out to be really hard, especially when coupled with a somewhat tricky loop. So, we need to do more on negative numbers before trying this. Also, the solution (accidentally) ended up being “Kid C ate -3 cookies in 2 minutes.” We asked Kids A and D what this meant. Kid D first said that it meant Kid C ate 3 crumbs, and then changed to 0 cookies. Kid A, with a bit of help from me, said it was throwing up cookies.
As usual, the kids all were very into sentences like “Kid D has 20 toes” (Kid D showed us their 10 toes) and “Kid A has 5 arms”.