## Velocity, Acceleration, Speeding Up and Slowing Down

### We all understand speed intuitively. Velocity is speed with a direction. Negative in this case does not indicate a lower value but simply which way an object is traveling. Both cars below are traveling at equivalent speeds. ### The concept and the graph analysis are challenging for many if not most students taking higher level math. This example shows how instructional strategies are not simply for students who struggle with math. Good instruction works for ALL students! ## 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 problem seen at the top. I asked him to figure out the monthly payment. He worked out the problem, overlooking the down payment. With a minimal prompt he self corrected. I followed this by “showing him the mathy way of doing the problem.” (Seen in the bottom half of the photo). He conceptually understood why the -1,000 was the first step and x had meaning.

This is a version of CRA.

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## Scaffolding for solving equations

Solving equations can be very abstract and inaccessible for students. The photo below shows a scaffolded handout that introduces students to solving two-step linear equations. The students are introduced to buying a car: down payment and monthly payment. This provides meaning for the variable (x is the monthly payment), for the constant (down payment) and coefficient (12 months – fabricated situation). This approach introduces the concept of having two steps and for which to choose. Take note of the little “PEMDAS” on the left side. I explain that solving involves using PEMDAS in reverse 