It is officially a thing now to post a photograph from our classrooms every day of the school year. I can’t keep up with that.
But I have written about the importance of differentiating between diagrams and decorations. And I have a swanky new iPad (Thanks TED-Ed!) So I’ll aim to get a diagram from my teaching up here each week. Some will be mine. Some will be my students’. Some may represent thinking transparently. Others may be more challenging to interpret.
All will be examples of representing mathematical thinking with pictures.
Today we worked on the Oreo problem in College Algebra. Specifically, given information freely available on the Nutrition Facts labels on regular and Double Stuf Oreos, and given the assumption that Double Stuf Oreos are in fact doubly stuffed, we asked:
Where are there more calories in an Oreo? In the wafers or in the stuf? And how many calories are in each?
Along the way, I drew this diagram to represent a student’s words. The A, B, C and D were his letters, as were what they referred to. I just drew the picture for all to see.
And what are the red X’s?
Those represent the student’s thinking. He was comparing a double stuf Oreo (right) to a regular one (left). When you get rid of the equivalent of a regular Oreo (red x’s), you are left with one unit of stuf. When you do the same with the calorie figures, you now know the number of calories in one unit of stuf.
This is equivalent to the algebraic technique of eliminating one variable in a system of two equations, two unknowns. We built that connection in class.