# Research

There are several challenges to the FACT Project.  The first is that the Classroom Challenges were intentionally designed to be paper-based activities.  Our goal is to write software that enables these challenges to be replicated on a computer screen, that understands what the students have written in response to Classroom Challenges, and then asks students questions that will push their mathematical reasoning deeper.

Nine Classroom Challenges (CCs) have been chosen as a part of the preliminary research.  Details on the Challenges in their paper-based forms can be found on the Mathematics Assessment Project (MAP) site.  The problems are as follows:

1. Interpreting Distance Time Graphs
2. Estimating Counting Trees
3. Sharing Traveling Costs
4. Boomerangs
5. Increasing and Decreasing Quantities by a Percent
6. Solving Linear Equations in One Variable
7. Solving Real-Live Problems – Baseball Jerseys
8. Steps to Solve Equations
9. Modeling with Linear Equations

We give an example of one of the problems, Boomerangs, below.

Optimization – Boomerangs:

This question has students look at a real-world problem involving optimization.  They must interpret the situation and represent the constraints and variables mathematically, choosing the appropriate methods, exploring the effects of systematically varying the constraints, and interpreting the data to identify the optimal case. Click on the image to enlarge and read the problem. Example Responses: