Animated Demonstrations

New on my Web site:→ Animated slides on the Lab Gear model for signed number arithmetic.Note that for each operation, the model is based on what students already know. For addition, you put down the first number, then the second number, and finally count. For subtraction, you put down the first number, take away the… Continue reading Animated Demonstrations

Proportional Relationships

One good thing about the Common Core middle school standards is the emphasis on proportional relationships, and the fact that they are approached in a multidimensional way. In addition to "set up a proportion and solve it", which is probably the most common way to teach this, the standards propose multiple representations and a variety… Continue reading Proportional Relationships


A correspondent writes:We emphasize the idea that students should approach problems in multiple ways.  This has caused me to wonder about patterns.  For example:students might conclude that 3^0=1 because of the pattern 3^4=81, 3^3=27, 3^2=9, 3^1=1orwhen the second difference is constant, students will conclude that the function is quadraticorwhen a function is concave up, the… Continue reading Patterns