The first thing you have to understand is that asking people to model with mathematics makes them mad. Not in all contexts, though! At a social gathering with a generally amiable and curious group of people, you might try floating a question like:

• I wonder if graduates of more expensive universities tend to earn more in their careers?
• Do you think the time it takes a pendulum to swing back and forth depends on how heavy it is?
• What do you think is the most efficient way to get 2,000 calories a day?

Continue reading “Making Authentic Modeling Possible”

Six months ago, I hated trigonometry.

By Becca Phillips

In fact, when my daughter missed a week of school, she announced on her first day back, “Someone has to teach me trig because I missed the whole thing.” Her father jumped in, “That’ll be me. Your mother hates trig.”

At least that used to be true. I have since made peace with my least favorite topic, in large part because of my experiences with the Illustrative Mathematics Geometry course. Let me tell you ways that the IM Geometry course has helped.

Continue reading “Making Peace with the Basics of Trigonometry”

By Kate Nowak

When I was teaching high school mathematics, my local colleagues and I spent a whole lot of time creating problem-based lessons. We were convinced that this style of instruction was a good way to learn, but the textbooks in use at our school simply contained definitions and theorems, worked examples, and practice problems. One day I was talking to my dad about how much time I had been spending lesson planning. His response was, “People have been teaching geometry for, what, 3,000 years? Shouldn’t the lessons be, like, already planned?”

Continue reading “Presenting IM Algebra 1, Geometry, Algebra 2”

are best thought of as a sequence of if-then statements: If $x$ is a number such that $3x + 2 = 5$, then $3x = 3$; if $3x = 3$, then $x = 1$. Continue reading “Truth and Consequences Revisited”