What we had in mind
Goals of this activity
Students will be able to...
We designed Central Park to help students make the transition from arithmetic to algebra. Arithmetic is for computation. Algebra makes the structure of our computations clear.
We want students to use their knowledge of computation to inform their algebra understanding, and we want them to see that representing their ideas with algebra can save a lot of computation time.
Central Park puts the power of algebra in the hands of students by asking them to design parking lots. At first, students place the parking lot dividers by hand. Then they compute the proper placement. Finally, they write an algebraic expression that places the dividers for many different lots.
The challenge in each phase of the lesson is to create equal-sized parking spaces, but everything else about the tasks will change as the lesson proceeds.
We give students numbers and variables. They can calculate the space width arithmetically again but it’ll only work for one lot. When they make the leap to using variables, each equation is useful for many parking lots. Variables should make sense and make students powerful. That’s our motto for Central Park.
For students to experience the power of algebra, they need to see their equations in action. Students need to see that their equations work under certain conditions, and that they fail under others. And when the equations fail, students need to be allowed to try again.
While students are working, use the teacher view to identify students to talk with. For example:
Scan students’ text answers for good discussion starters. Select a few students responses to the Eric task to highlight with the whole class.
Help students to connect their arithmetic computations to their algebraic representations. We want students to be able to ask and answer the question, How would I compute this if I knew the width of the parking lot?
Do students’ algebraic expressions match their computations? Use the evidence you find in the dashboard to focus your summary with the whole class