Talking probability with kids

My younger son has made up an elaborate dice game involving battling armies of eraser heads. He tried to explain it to me, but . . . .

  

I used his enthusiasm for his gave as motivation for a short project tonight. Instead of his game, though, I thought up a game that I could understand 🙂 The game works likes this:

You have 6 players in 6 slots. During each turn you roll a single 6 sided die. A player is removed if the number in their slot comes up.

Question 1: How many rolls do you think it will take until every player has been removed?

Question 2: Are any of the spots more or less likely to contain the last player standing?

Here are his thoughts on the two questions – it is fun to hear what a 4th grader thinks about probability:

 

Next we played the game twice to see what would happen. His guess of 12 turns wasn’t too bad 🙂

 

An escalator problem

My older son is working his way through Art of Problem Solving’s Introduction to Algebra book. He works through the problems in each section of the book and we discuss the ones that are giving him trouble. Today he had some difficulty with a problem about an escalator.

The problem is a twist on one of my favorite math contest problems from back when I was in high school – Problem 10 from the 1987 AIME:

Here’s our discussion of the version of the of the problem in Chapter 7 of the AoPS’s Introduction to Algebra:

 

At the end of the last video my son was thinking about trying to find the speed of the sister running up the escalator. Here we turn our attention to a different quantity – how many steps does that sister take?

The main idea in this part was to try to gather together then information that we know in this problem. For example, we know the speed of the two escalators (because he assumed a speed), we know how many steps the escalator has, and we know how long it takes for the sister running up the escalator to get to the top.

 

To wrap up the project, I asked my son to summarize the solution. We had jumped around a little bit to get to the solution, so I wanted him to do this summary just to make sure that he’d understood the ideas that we’d discussed during the solution: