## Bubble calculator

I use the Addition and Subtraction slide rule to give students an experiential manipulative that represents what happens when we add and subtract integers. I was trying to come up with something similar for multiplication and division. I had a … Continue reading

## Making the most of factor trees

Factoring is a fundamental skill. We can reduce it to a procedural exercise by repeatedly attempting to divide by prime numbers (starting with 2), until we find that the prime number we are trying exceeds the square root of the … Continue reading

## Linear functions

Math is not real. But we use math to model reality. A commonly used model is the linear model, a kind of function. A function has the property that, given a number as input, it produces another number as output. … Continue reading

## Classroom charts

The students often create charts to explain the work they have been doing on classroom handouts. This gives them a chance to explain their work, and is important in reinforcing what they have learned, practicing literacy skills, and being comfortable … Continue reading

## 2007 AP Free-response Form B

Written solutions are available at the AP Exam question bank. Whiteboard screencasts for these problems: 2007 AP Free-response Form B, problem 1 2007 AP Free-response Form B, problem 2 2007 AP Free-response Form B, problem 3 If you would like … Continue reading

## Number lines

Here are some convenient number line graphics you can print or insert into your own documents. Wall poster from -15 to 15, to be printed on 31 sheets of 8.5x11. -15 to 15 in PNG format -15 to 15 in … Continue reading

## Algebra Skills Practice

The spreadsheets below contain randomly generated practice questions. To generate a new practice sheet on a Mac, type command-shift-=; on Windows, press F9. Single digit integer addition and subtraction practice spreadsheet. Single digit integer multiplication practice spreadsheet. Single digit integer … Continue reading

## Polynomial Calculus

Polynomial calculus introduces the concepts of differentiation and integration through algebraic and geometric arguments. The rationale is that the notion of limits and differentials are not needed at the outset to illuminate the ideas. From the introduction to the Polynomial … Continue reading

## Addition and subtraction on a slide rule

One of the roadblocks in math is understanding how arithmetic extends to the negative integers. This seems almost certainly due to the fact that the typical student can envision concrete examples when numbers are positive, but does not have a … Continue reading