Concrete-Representation-Abstract


  • Grumpy Cat Multiplication

    Grumpy Cat Multiplication

    If you find this helpful, maybe consider making a small donation to help build an accessible playscape for children with disabilities. Here is a CRA approach to multiplication that can be individualized. I created this one for a student who loves cats. Here is a link to the Jamboard. You make a copy by clicking…


  • Grumpy Cat Multiplication

    Grumpy Cat Multiplication

    If you find this helpful, maybe consider making a small donation to help build an accessible playscape for children with disabilities. Here is a CRA approach to multiplication that can be individualized. I created this one for a student who loves cats. Here is a link to the Jamboard. You make a copy by clicking…


  • Division of Fractions with Cookies

    Division of Fractions with Cookies

    Division of fractions may be one of the most abstract concepts in middle school math. Here is an approach to address the concept using a Google Jamboard (you can make a copy which allows you to edit it), which would be a foundation for the ensuing steps. I will preface this approach by stating the…


  • Division of Fractions with Cookies

    Division of Fractions with Cookies

    Division of fractions may be one of the most abstract concepts in middle school math. Here is an approach to address the concept using a Google Jamboard (you can make a copy which allows you to edit it), which would be a foundation for the ensuing steps. I will preface this approach by stating the…


  • Dividing a Binomial

    Dividing a Binomial

    If you have taught algebra, you have likely experienced this error. We know many students will make this type of error and we can help many students avoid it by being proactive. Below are excerpts from a Google Jamboard that can be used to unpack the underlying concept of the division or simplifying shown above.…


  • Plotting Points Introduction

    Plotting Points Introduction

    Plotting points is surprisingly challenging for some students. Here is an approach originated by one of my former math teacher candidates in a methods class I taught. This approach uses the analogy of setting up a ladder. First, determine where to position the ladder, then climb the ladder. (brilliant and not my idea). Plot the…


  • Plotting Points Introduction

    Plotting Points Introduction

    Plotting points is challenging for some students, even in high school. This approach uses the analogy of setting up a ladder for the x-value and climbing the ladder for the y-value. Jamboard with Ladder This activity is conducted on a Google Jamboard with moveable objects (see photo at the bottom on how to access it).The…


  • Intro to Reading Scatterplots – Used Mustangs

    Intro to Reading Scatterplots – Used Mustangs

    One step in reading and analyzing scatterplots is simply identifying what the dots on the graph represent. If students do not understand the dots (including the position) how can they analyze. An approach I have used is start by having students create their own scatterplot for mileage and price of used cars they shop for…


  • Reading Scatterplots with Ford Mustangs

    Reading Scatterplots with Ford Mustangs

    One step in reading and analyzing scatterplots is simply identifying what the dots on the graph represent. Students who do not understand the meaning of the points, including the position, will struggle to interpret the graph. This post outlines a Jamboard activity to support interpretation of the points. Overview I present the scatterplot of used…


  • Multiplication with Integers: a Meaning Making Approach

    Multiplication with Integers: a Meaning Making Approach

    I previously tackled the difference between the ” – ” symbol used to represent a negative and a subtraction problem. This post gets into multliplication through the context of buying a Wendy’s frosty. One comment to preface what is presented here. Negative numbers are abstract and challenging for many students. Multiplying by negatives is even…