Concrete-Representation-Abstract


  • Counting Out Total Value of Coins

    Counting Out Total Value of Coins

    The chart shown in the photo below was created and used by my former co-teacher and I to teach students in a high school life skills program how to count out the total value for coins (dimes, nickels and pennies). Here is how we implemented it. The students are given a pile of coins, set…


  • Adding Money First Steps

    The following shows steps to introducing the concept of the value of money and of adding coins. The concept of a dime is presented as 10 pennies (see below). The dime is compared to a penny, nickel and quarter using these representations. Repeated use of these representations leads into an intuitive understanding of the coins.…


  • Intro to Measurement

    The photos below are used to introduce length and area as part of a CRA approach. First a student is asked to build a Lego garage. He first builds the bottom row of a wall and the teacher asks for length in terms of how many Legos are lined up. After building a wall the…


  • CRA for Solving Equations

    This is a photo of a handout from a special ed conference shared by Dr. Shaunita Strozier (sstrozier@valdosta.edu) of Valdosta State University. It shows the use of algebra tiles to provide a concrete level of the concept of an equation and solving the equation. The photos on the left show the R or representational level of the…


  • Linear Functions with Comic Book Context

    This is a follow-up to a previous post about using comics to engage a student with autism. In the photo above the comics are on sale for $2 each which is a situation modelled by a linear function. The student finished this assignment independently, quickly and accurately (aside from the bars on the graph). (Note…


  • Real Life Relevant Context for Students with Autism

      In  a lesson on functions I provided a student with autism the input and output mapping on the left as opposed to the problems like the one on the right. This student, as I’ve written before, loves comics and superheroes and villains. He was tasked with matching (mapping) people with super powers with the organization to…


  • Cutouts for Area of Irregular Shapes

    Students have trouble with irregular shapes largely because they cannot visualize or determine the measures the dimensions of the individual parts. The photos below show a hands on activity to help students with these challenges. The students are cut out the individual shapes and write in the dimensions. This method allows them to see the…


  • Confidence Interval Analogy

    Statistics is challenging enough before getting into confidence intervals. I use an analogy to help make the concept of confidence intervals accessible. Here’s the analogy. You are looking for a female student who is in a classroom in a hallway. You don’t know which room but you do know that her boyfriend is well trained…


  • Graphs Representing Variable Relationships

    Students often struggle with the jump from 1 variable situations to 2 variable situations, i.e. functions. Visuals are an effective way to present concepts which may be abstract, e.g. functions. Graphs and visuals in general are designed to allow a big picture view of a concept. The photo above shows mileage and price for Honda Odyssess…


  • Percent Discount Scaffolded and Concrete

    I continue to be surprised at how much of a challenge computing percent discount is for students. It’s prior knowledge. If you ask them to explain what a discount is in their own words you’ll get a response like “it makes something cost less.” The students may even have mastery of computing a percent of…