550 Tubes of Toothpaste (Age 7)

The Activities

  1. Topic: Money: Book: Sluggers’ Car Wash by S. Murphy.
  2. Topics: Money, Optimization: I made an inventory with 4 different items, each with a buy price and sell price (e.g., Toothpaste had a buy price of $1 and sell price of $3; Toaster $25/$30; My Little Pony $20/$20; iPad $100/$150).  The kids each had $1000 and owned a store, and they had to decide how to stock their store in order to make the most profit (using a chart with item name, number of that item, total cost, total revenue).
  3. Topic: Programming: We did more CargoBot (see previous weeks for overview).  This time the problem was to use as few instructions as possible to make one block each in boxes A, B, and C to a stack on box F (they were allowed to use functions).

How Did It Go?

We had 4 kids this week.

Slugger’s Car Wash

This book is a pretty good introduction to the idea of profit vs. revenue, the kids liked it.

Stocking a Shop

This activity was pretty new to them, it took a while before they understood what they were supposed to do.  One particularly tricky part was that some of them wanted to make up their own buy and sell prices — they didn’t understand for a while that they didn’t have control over the prices, only how many of each to buy.

All the kids chose the items in their shop randomly (with some preference for things they liked, such as My Little Pony and iPad).  Most of them also didn’t spend all $1000 of their money — the only one who did used Toothpaste (which cost $1 each) to use up the rest of their money, buying 550 tubes.  That kid ended up with the biggest profit by quite a bit, because the revenue/cost ratio was much higher for toothpaste than for the others.  The final tricky part of this activity was the the multiplication was somewhat tricky for them.

At the end, I asked for each item how much they would make if they bought just that item, and we saw that Toothpaste was by far the best.  I asked why stores didn’t just have 1 thing, and someone said “Because no one would go to that store.”  I also asked why people didn’t just buy the Toothpaste for $1 instead of $3, and with a bit of hinting one of them mentioned delivery being hard.


Most of the kids made a brute-force solution first, without any functions — one tried to use functions from the start, but this turned out to be difficult.  After a few of them did the brute force, they started looking for repeated sequences.  All the kids had an improved solution, but the number of symbols used varied.  No one quite got to the optimal number of symbols — probably because the optimal solution (at least the one I came up with) actually had some wasted work at the end (which means that it’s hard to see the shared structure when you have to add extra symbols).


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