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How far apart do parking space dividers need to be?
What we had in mind
  • Algebra Students
  • One 60-minute class period
  • Students who have some experience using variables to represent quantities in a context
Goals of this activity
Students will be able to...
  • Use arithmetic computations to inform their use of algebraic symbols (SeeCommon Core SMP8)
  • State the meanings of variables in context
Supported Devices
About this activity

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.

How the activity works:
1. Guesses
Students drag parking lines into a lot to make four even spaces. Students have no trouble stepping over this bar. This ensures students understand the goal of the task.
2. Numbers
Now students use arithmetic to calculate the space width for three lots. They get a sense of the parts that change (the width of the lot, the width of the parking lines) and those that don’t (dividing by the four spaces).
3. Variables
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 variable equations, it works for all parking lots.
4. More Variables
Now the number of dividers changes. Students need to update their equation to evenly space any number of dividers.
The Student Experience
Students can input arithmetic expressions (not just one number). What happens when you input (35–6)/4?

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.

Keep an eye out forstudents who are guessing and checking at the numbers phase of the lesson. This strategy, while useful for getting started, will not generalize to variables. Ask guessers to say how they could know in advance that their numbers will work.

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.

Students who are struggling at this phase may need to go back to their arithmetic expressions in the previous phase. Connecting these two phases is the important work of Central Park.
The Teacher Experience

While students are working, use the teacher view to identify students to talk with. For example:

Help slower-working students adjust their responses rather than starting from scratch with each error.
Keep an eye out for students who skip the written prompts to get to the next fun interaction. Students need to reflect!
Look at the equations of flagged students. These students may need help relating their computation work to their algebraic expressions.
Make sure students notice that they can enter fractions or arithmetic expressions such as 32 - 4.
If some students agree and some disagree, a good discussion can be had! If everyone disagrees, take on the opposing role yourself. Force your students to persuade!
    Keep an eye out for interesting algebraic expressions. You can:
  1. Click on a part of the lesson to display it and all the student responses,
  2. Click on a student response to auto-fill the input box, and
  3. Click on Try It! to execute the input.
Pro Tip!Copy and paste a couple of responses into a word processor or presentation slides in order to isolate them to bring to the attention of the class.

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

Tips from Teachers