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  • Rate of Change in Real Life

    Rate of Change in Real Life

    61 cents per ounce is a rate of change. Graph the line modeled by this (y intercept is 0) and it becomes slope of the line. In referring to algebra we often hear, “when will I ever need this?” My response is “all the time!” Our job as teachers is to make this connection for…

  • Analyzing a Graph

    Students can hit a road block at the steps that appear to be very simple. For example, in the problem below the students are prompted to find the highest point on the graph. Many think the graph refers to the entire coordinate plane and they pick 5 as the high point. It is the highest point…

  • Color Coding for Calculus

    This is an example of color coding (highlighting) to help make a calculus problem accessible. You don’t have to know calculus to see that the yellow sections (left and right of the 0) are going up while the green section is going down. Color coding breaks a whole into parts that are easier to see…

  • Interpreting Slope Intercept

    Slope is one of the most important topics covered in high school algebra yet it is one of the least understood concepts. I have two observations about this. First, slope is often introduced with the formula and not as a rate of change. Second, students intuitively understand slope as rate of change conceptually when presented…

  • Excel Software as Accommodation

    I had a 7th grade student with PDD-NOS who was tested at a kindergarten math level. He struggled  with graphing. I taught him to use Excel on the computer to generate graphs and gave him a standing direction to use it whenever we had a graph to complete. The top photo below shows a warm-up…