Home > Math Resources > Problem Archive

# Math Resources

## Problem Archive

Using rich and open mathematical problems is a hallmark of a Japanese math research lesson. While lesson study does not have to revolve around open problems, we have found that these kinds of problems have enabled our participants to engage in deeper conversations about student learning of mathematics.

Based on a presentation by Jerry Becker at NCTM Boston, we have organized the "open" math problems in this section into 3 general categories. If not stated otherwise, the problem came from Becker's materials.

## (3) Problems that lead to many new problems.

(1) Problems with many approaches but 1 solution

1a. How many dots?
1b. Fractions, decimals and percents using an Area Model
1c. Ships in the Fog
1d. Chances Are

(2) Problems with many solutions

 2a. How "scattered" are the marbles? Problem Statement: Three students each threw five marbles, which came to rest as shown. The winner is the student with the smallest scattering. The degree of scattering seems to decrease in the order A,B,C. Devise as many methods as you can to determine the degree of scattering. Comments: We used this problem at the March, 2003 workshop. back to top

(3) Problems that lead to many new problems.