Today I hope to to cement the connection between a situation, a table of values, the graph, and the equation. The will also begin to connect slope more explicitly with the idea of rate of change and specifically with speed for distance-time graphs.

We'll begin with an opener that reviews slope and connects it to rate of change and speed (screenshots below).

We'll then complete an activity that requires gathering some data on three people walking, entering it into an

Activity Builder, then using the data to try to come up with equations to describe their motion. The first walker will start at 0 and walk at an even pace for 10 seconds. The second walker will start at 3 feet (for example) and walk at a steady pace (hopefully slightly different pace than the first walker, we'll see). The third walker will walk a piecewise graph. Starting at 2 feet (for example), walking at a steady rate for 4 seconds, standing still for 3, then walking at a steady rate back toward the starting point for 3 seconds.

The hope is that they will not only connect the actual walk to the data tables and the graph, but they'll get a better idea of how speed relates to the graph and the idea of a domain restriction and piecewise equations. In our next class we will then revisit

Graphing Stories and the

MARS activity, coming up with equations for any of the linear graphs (including the piecewise ones).

For

homework students will take a piecewise table of values, graph it on Desmos and come up with equations, domain restrictions, and a verbal description of what may have happened, then record a short screencast of their thinking.

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