# What Makes a Good Pre-AP* Mathematics Problem?

After reading the goals of the Pre-AP* mathematics program, seeing how AP* problems can be adapted for use at other levels. After examining exemplar problems for particular TEKS, we hope you have a better understanding of what makes a problem or activity particularly appropriate for use in the Pre-AP mathematics classroom. Below you will find some of the criteria that the committee used in selecting the problems and activities for this document.

A good Pre-AP mathematics problem or activity

- has a clear connection to the vocabulary, skills, concepts, or habits of mind necessary for success in AP mathematics courses;
- goes beyond a minimalist approach to addressing the TEKS;
- can serve multiple purposes, such as addressing an Algebra I TEKS, reviewing a middle school geometry skill, and introducing an AP Calculus concept;
- should go beyond simple drill and recall (There should be a greater emphasis on analysis, application, and synthesis of material.);
- requires students to engage in an extended chain of reasoning (Problems should require more than one step and might cover more than one topic.);
- might be completely different from problems that the teacher has demonstrated in class, though based on the same concept (Students are expected to apply their knowledge in novel situations with very little teacher direction.);
- requires students to develop their reading and interpretation skills using verbal, graphical, analytical, and numerical prompts;
- asks students to communicate their thoughts orally and/or in writing (Students must be able to justify their work in clear, concise, and well-written sentences.);
- stretches the students in ways that might make them uncomfortable (The solving of problems might take several attempts. They might have to hear someone else's explanation (preferably one of their peers) before they begin to develop understanding.);
- should be graded based on the process and methods as well as the final answers; and
- might require the thoughtful use of technology.