PCMI 2010 SSTP: Reflecting on

Teaching

Day 2: Steppin’ it up

The Stair Step Problem

Stage 4Stage 3Stage 2Stage 1

•How many small squares at the 5th, 10th, nth stage?

•Work privately first, then with a partner.

•Find as many solutions as you can.

•Post your solutions on POSTER PAPER.

Look at the solutions posted by other pairs. As you look at other solutions, if you have a question/comment that should be raised, post it with a sticky note. Post at least one or two sticky notes. (10 minutes)

Looking at the Stair Step prpblem

Time to take off your “student hat,” and put on your “teacher hat!”

Suppose you are going to use the Stair Step problem in your classroom next week. Your goal is to help students make connections between geometric solutions and algebraic solutions to the problem.

Using this problem in your classroom

1. What specific points would you want to make clear for your students?

2. What solutions, misconceptions, or confusions do you anticipate in your students’ work?

Table Discussion: record on poster paper (25 min)

Your group has identified specific points to make clear, and anticipated student responses.

How will you prepare your class for a rich discussion that :◦ deepens their understanding of the algebraic

geometric connections,◦ fosters good discourse, ◦ and highlights/dispels common misconceptions?

Whole Group Discussion:

How will you◦ deepen their understanding of the algebraic

geometric connections,◦ foster good discourse, ◦ and highlight/dispel common misconceptions?

What questions will you create to◦ help kids who can’t get started? ◦ guide them if they get off track?◦ Push/extend solutions?

How will you sequence/use student solutions to further the discourse?

Whole Group Discussion: