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  • Factoring Numbers

    Factoring, as used in elementary school,  is the act of changing a number into numbers that multiply to produce the original number. For example, 12 can be factored to 3×4. 3 and 4 are called factors of 12. In the photo above, a “factor tree” is used to help identify the factors. I have often…

  • Corresponding Angles in Stain Glass

    Found this (above) cool example of corresponding angles (see photo below for explanation). This window photo could be a nice introduction to this type of problem by printing it out on paper and having students match angles as the teacher shows the photo on the Smart Board or screen.

  • Introduction to Slope

    Introduction to Slope

    Slope is one of the the most important topics in algebra and is often understood by students at a superficial level. I suggest introducing slope first by drawing upon prior knowledge and making the concept relevant (see photo above).  This includes presenting the topic using multiple representations: the original real life situation, rates (see photo…

  • Hands on Approach to Factoring out the GCF

    Factors are “things being multiplied”, e.g. 2 and 3 are factors of 6. Factoring polynomials like 5×2 + 15 above is one of the most challenging algebra topics, especially for students with special needs. To make these problems more accessible a more concrete approach is possible. The photo above shows how finding a greatest common factor…

  • Addressing the Concept of Addition Part 2

    In a previous post I presented an approach to teach and assess the concept of addition. This document shows all the steps I use including the one shown in the photo above.

  • Assessing the Concept of Addition

    Teaching students to add appears to be a very linear, skill driven endeavor. Hidden in this is the concept of what it means to add and how to assess this conceptual understanding. Here is an approach to address and assess the concept of adding. In the photo above a student is prompted to pull both…

  • A Meaning Making Approach to Word Problems

    A Meaning Making Approach to Word Problems

    Here is a typical story or word problem. Dakota helped her father bake cookies. They baked 9 sugar cookies and 3 chocolate chip cookies. How many cookies did they bake total? When solving word problem the focus is often on following steps, e.g. read the problem and identify important information. There is also a focus…

  • Making Discount Meaningful

    Educators teaching math typically start with the “mathy” stuff first. For example, for finding the sales price teachers may start with showing students the steps to calculate (photo below). I start with the concept, either with a pictorial representation or actual objects to represent the underlying concept. In the photo above, I show an object (related to…

  • Conceptual Understanding Before Getting “Mathy”

    All too often math topics are introduced first with the skills and steps. This is backwards. The photo above shows how I introduced solving equations a high school student with autism using the concept as an entry point. We discussed what was involved in buying a car, including payments (no interest) then I posed the…

  • Analogies: Making Math Meaningful

    Math is an esoteric subject for most people. Good instruction makes information meaningful. One method for making information meaningful is to connect new information to prior experience. In this situation the new information involves determining whether shapes are similar (see photo below). One example of student prior experience with this topic would be shrinking people…