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Problem Solving Classroom

Tips from a Master Teacher (This is a work in progress.)

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Feel free to send in problems that I can add to this page. Just go to the contact page, and send the problem along with a solution.

A Source of Your Problems

One of the obstacles in creating a problem-solving classroom is that there are not a lot of great support materials available. The articles in this site will help guide you in creating some of your own problems, but I also decided to create this library of problems of different types and lengths. These are all free to teachers to use with their students in their own classrooms. You can check out this article on what makes a good problem. You can also read this article that describes the types of problems you’ll find here.

Social Distancing Squared

Social Distancing Squared

Four benches are arranged in a square, and four people sitting on the benches have to maintain a 6-ft safe distance as they all slide along the benches. Where can they sit? Where can they not sit? This set of problems gives a fresh twist on min-max type problems involving Pythagorean Theorem expr...
Course(s): Geometry

Difficulty: 3/5

Length: long

Topics: Pythagorean Theorem

Snakes on a Plain

Snakes on a Plain

This is one of my favorite problems! I discovered it while flying back from Wichita where I had presented a workshop. I noticed the snaking rivers on the plains below and wondered about the mathematics. If I modeled the "snakes" with semicircles, would there be an ideal number of snakes that woul...
Course(s): Geometry

Difficulty: 3/5

Length: long

Topics: circles, pi, circumference, literal equations

Invisible Runner

Invisible Runner

An observer sees a sprinter hidden behind another sprinter four lanes away. He or she models a problem using similar triangles and proportions. This leads to an understanding of how much faster the outside lane runner is traveling and to an estimation of the difference in finish times. This is a ...
Course(s): Geometry

Difficulty: 2/5

Length: short

Topics: similar, similarity, proportions

Tile Style

Tile Style

Algebra is about pattern recognition and using linear models to represent relationships. (Read “The Essence of Algebra” in the Articles.) This diagram shows the four related ways that things worth analyzing or investigating can be represented. Students should practice moving flexibly from one rep...
Course(s): Algebra 1

Difficulty: 2/5

Length: short

Topics: patterns, equations, linear

Pirates, Portraits & Perspective

Pirates, Portraits & Perspective

Students develop the mathematics for creating a portrait in which four people of different heights all appear to be the same height. As with any Exploration, they start by building a model of the most basic version of the problem. Then they ask what-if questions and challenge assumptions in the m...
Course(s): Geometry

Difficulty: 3/5

Length: medium

Topics: ratios, proportions, similarity, similar triangles

To Catch an Elephant

To Catch an Elephant

This is a similar triangle problem where all the parameters are not already prescribed for the students. They have to identify the pertinent data and create a diagram that shows how similar triangles and proportions can be applied. Students have to figure out where to place an elephant and a pair...
Course(s): Geometry

Difficulty: 2/5

Length: medium

Topics: similarity, proportions, similar triangles