Building Towers, Selecting from two colors for Guess My Tower, Clip 3 of 5: Milin introduces an inductive argument

In clip three of five, Milin, a fifth grade student, shares his inductive argument for building towers up to 3 cubes tall with researcher Carolyn Maher and his partner, Michelle I. Michelle in turn explains the generalized solution to Matt and Stephanie. During this explanation Michelle I. indicates that the argument made it easier to understand why the “doubling rule” worked. Michelle, in her explanation to Matt and Stephanie, extends Milin’s explanation from 3-tall to 4-tall. PROBLEM STATEMENT “You have been invited to participate in a TV Quiz Show and have the opportunity to win a vacation to Disneyworld. The game is played by choosing one of the four possibilities for winning and then picking a tower out of a covered box. If the tower matches your choice, you win. You are told that the box contains all possible towers three tall that can be built when you select from cubes of two colors, red and yellow. You are given the following possibilities for a winning tower: a) All cubes are exactly the same color; .b) There is only one red cube; c) Exactly two cubes are red; d. At least two cubes are yellow. Question 1.Which choice would you make and why would this choice be any better than any of the others? Question 2. Assuming you won, you can play again for the Grand Prize which means you can take a friend to Disneyworld. But now your box has all possible towers that are four tall (built by selecting from the two colors, yellow and red). You are to select from the same four possibilities for a winning tower. Which choice would you make this time and why would this choice be better than any of the others?".Robert B. Davis Institute for Learning (1993). Building Towers, Selecting from two colors for Guess My Tower, Clip 3 of 5: Milin introduces an inductive argument [video]Transcript and student work are also available.Available in QuickTime and Flash digital video formats