Category Archives: Problem Solving

Sharing: Multiple Representations of Systems

One of the realizations that I made at NCTM was that the idea of multiple representations is still new to some people and that I need to start sharing more.1 This is one of my “worksheets”2 from last fall that … Continue reading

Posted in General, Math, Problem Solving | Tagged , | 4 Comments

Maximum return?

Today I issued a challenge to my 8th period class:  Which group can construct an open box with the largest volume? I explained that the box was to be constructed out of an ordinary sheet of paper – 8.5×11 inches … Continue reading

Posted in Math, Problem Solving, teaching | 8 Comments


We’re in the “World of Functions” unit in IMP4. This may be my favorite unit in the whole curriculum. Instead of a separate sections on linear, quadratic, radical, rational, exponential, …, we’re studying functions. Delving deeper into the relationship between … Continue reading

Posted in Math, Problem Solving | Tagged , | 8 Comments


One of my classes is at an impasse. They all agree that having proportional sides does not guarantee similarity in a quadrilateral (yay for the students who thought to grab a rhombus and a square from the tub of shapes … Continue reading

Posted in Math, Problem Solving | Tagged , , | 15 Comments

Questioning Techniques

This recent comment1 regarding students who are afraid of being wrong, reminded me of a resource I recently shared at a PD session for math teachers. These questions are a good starting point for creating classroom discussions in a math … Continue reading

Posted in Math, Problem Solving | Tagged , , | 2 Comments

One Graph, So Many Questions

I’m not sure where I first saw these types of questions. It was either at  Dan Greene’s1 or the Pre-AP Mathematics site2. Sadly, it was not in a textbook. Here3 is one I made last week. I plan on using … Continue reading

Posted in Math, Problem Solving | Tagged , , | 12 Comments

Proof Update

Things have gone much better the past two days with the trig proofs. Much much better. Yesterday, I asked for volunteers to put up the solutions. Not every problem was done correctly (most were though). Having the students explain their … Continue reading

Posted in First Year, Math, Problem Solving | 8 Comments