Helping Students REMEMBER the Difference in ‘LOOK’ Between Positive and Negative Slope

No Mistakes

Some ideas just slap you in the face. I got slapped this morning as I was flying home from LA to Albuquerque. Those little cocktail napkins they hand out with “beverage service” often give me the urge to write. So this morning, nerdily enough, as I sipped my orange juice at 30,000 feet above the […]

SAT and ACT Preparation

SAT & ACT Prep

Every once in a while I get a call like this: “Hi, this is ____. My son is taking the SAT on Saturday. Can you, like, help him get ready for the test so he can score real high?” “Real high.” That’s what I wonder if the parent is. I’ve been tutoring students to prepare […]

Journey to the LCM … and Beyond!

In this blog/video I want to take you a little bit deeper into the world of … the LCM! Yes, that fascinating little mathematical entity is beckoning us to explore it further. Several readers wrote to me after I posted my LCM “trick,” saying they want to see me demonstrate WHY this “shortcut” works. One […]

Problem of the Month – January 2013

Twelve is the first number with two pairs of factors (2 x 6 and 3 x 4). Primes, on the other hand, have no pairs of factors other than the trivial pair of one and the prime number itself. Considering that contrast, here’s an interesting fact about primes and the number 12. Add 12 to […]

Cultivating original thinking

Intuitive proof that the two differently shaped triangles are congruent

An interesting thing happened today. A girl I was working with, who’s had virtually no schooling in geometry, made a brilliant “leap” in a geometry problem. This student was starting a unit on fractions, and the curriculum was describing a standard way of conceptualizing fractions. The book was showing that if you divide a given […]

Stop the Shotgun Approach to Learning Algebraic Rules

Shotgun View of Algebraic Rules

Once in a while I have to hold back my chuckles when I’m tutoring. Here’s a classic situation:  a student is looking at part of a problem that has the expression:  x times x. He says he thinks the answer is (in order): “2x” Then “2x squared” Then “Zero?” … and on and on. I call this the […]

Temperature for Positive and Negative Numbers

Celsius temperature scale

Kids struggle with positive and negative numbers … that’s a given. But I’ve recently hit on a reliable way to eliminate the confusion … temperature. Using a temperature scale as a model for solving integer problems has several advantages: 1)  It’s a system students already know from everyday life. 2)  The relationships among positive temperatures, […]