# Problem Design – Jamming

Jamming is taking a concept that is connected with a common procedure, and asking a question that cannot be solved using the procedure. The question jams that concept, because it assesses whether a student understands the concept well enough to apply it without the procedure.

The word jamming comes from Ben Blum-Smith’s blog, who was referencing Cody Patterson, so no credit goes to me for this idea, but I’ve adapted it in my classroom and want to share it in my series of posts on problem design.

Some examples:

There are tons of tricks out there for factoring quadratics. Jam the concept with a question like this one, and see if students can solve it:
What integer c will make the polynomial below a perfect square?

Two great questions for elementary or lower middle schools folks–students may successfully apply the standard subtraction or mixed number multiplication algorithm to these questions, but for each what we really want is the number sense that allows a student to do these in her head.

This one is a bit more advanced, and effectively jams fraction operations (and might fall under Ben Blum-Smith’s thwarting as well).

The distance formula on the coordinate plane is a fascinating application of the Pythagorean Theorem, and a common victim to memorization without understanding. See what students can do with this:
Which points with integer coordinates are exactly 5 units away from (-3, 4)?

More fun with geometry:
What is the length of the side of a cube which has a volume numerically equal to its surface area?

Jamming is a critical step in formative assessment after students have been introduced to and had a chance to explore key aspects of a new concept. This is both valuable information for the teacher on student’s depth of understanding, and a chance for students to stretch their knowledge through non-routine problems and critical reasoning.