Provide an accurate, secondary-level problem appropriate for a problem-based learning activity in numbers or algebra by doing the following:
1. Provide a traditional procedural mathematics problem that could be improved by being transformed into a discovery problem.
a. Discuss shortcomings of using this problem when teaching for understanding.
2. Modify the problem you provided in part A1 so that it better serves students when teaching for understanding.
a. Explain how the modified problem promotes student engagement.
b. Explain how the modified problem promotes problem-solving or reasoning skills.
c. Explain how the modified problem promotes a deeper understanding of the mathematical concepts.
B. Discuss how teaching mathematics for understanding provides opportunities for all students to become mathematically proficient, as it relates to your modified problem from part A2.