# Design Your Own School Bus

How many students can ride on a school bus?

If you could design your own school bus, what would it look like inside? How many rows of seats would there be? How many students would sit in each row? How many students could ride your bus at once?

- You might use rows of squares to represent where each student sits on the bus.
- Does your school bus have a center aisle for walking? Would you have an aisle on your bus? How can you include that in your representation?
- How can you find the total number of students that can ride on the bus without counting each seat individually? Where do you see groups of students in your representation?

- Is it possible to design a different school bus that fits the same number of students as your school bus? What could it look like?
- Can you design a school bus that would seat exactly 48 students? How many rows of seats would the bus have? How many students would sit in each row on the bus?

This open-ended activity gives students an opportunity to design their ideal school bus. Students may customize their designs according to their own preferences, within reasonable limits. (Standard school buses have space for 4 to 6 students per row with an aisle in the center and up to 12 rows.) Some students may interpret the students on the bus as one group, while others may interpret the students on the bus as two separate groups separated by the center aisle, or others may see each row as a group. Students may engage in a range of mathematical skills as they investigate this task. Depending on the grade level of your students, you may see students using skills such as working with equal groups of objects, creating informal representations of arrays (rows and columns of squares or other shapes), writing an expression or equation to match a picture, and solving using repeated addition, counting, or multiplication.

Students may use the apps in a variety of ways while solving this problem:

- The Number Frames app can be used to represent the seats or students on the bus using counters (as shown here) or simply using the frames themselves to represent the seats or students (as shown here). This app allows students to customize frames to include up to 12 rows and up to 12 columns.
- The shapes in the Pattern Shapes app can be organized in equal rows to represent the seats or students (as shown here).
- The Geoboard app can be used to outline groups of squares to represent seats or students (as shown here).

As students design their school buses, encourage them to include expressions and equations as part of their work. Extend their thinking by asking questions: *What is a reasonable number of students in each row of a school bus? What is a reasonable number of students in each row? About how many students do you want to be able to fit in your bus? How can you make a picture that shows equal rows? I see that you wrote the expression 5 + 5 + 5 + 5 to represent your seats. Where do you see the number 5 in your picture? How did you know how many times to add the number 5? Can you think of a different expression to match your picture?*