In the challenge, students teams will build a racer from given materials that travels as far as possible down a given ramp and across the floor.
Students will discuss factors that might influence how far a racer travels, and the class will explore the influence of weight on distance traveled.
Each team will gather data for their car with varying weights, and graph the data on a distance vs. added weight graph. They will use this data to predict distance traveled for other weights.
The cycle is designed to take two 55minute class periods.
The mathematics foci are developing an understanding of statistical variability; summarizing and describing distributions (via the mean and dot plots); and representing and (qualitatively) analyzing quantitative relationships between dependent and independent variables. Standards of Mathematical Practice 1 (Make sense of problems and persevere in solving them) and 6 (Attend to precision) are particular foci.
Prior Experience:
 Constructing dot plots (also known as line plots}
 Construction with hot glue gun
 Plotting points on coordinate plane
 Calculating arithmetic mean (average)
Learning Cycle Wrapup:
Teacherled summary discussion: Lead a discussion about things that students have figured out through this cycle. Be sure to discuss and record ideas, and draw out students to explain more. Be sure the following areas are raised, by either students or teacher:

Ways to make a racer that rolls well

Methods of changing how far the racer will roll, including by varying weight

Ways to record data (including in a table)

Recognition that data varies: the racer didn’t always go the same distance, even when you didn’t change anything

Average (mean) as a way to describe a “typical” value

Graphing data as a way to spot trends and patterns

Language to describe trends and patterns, e.g. “The distance went up with increasing weight, until it got too heavy” (refined from “the dots go up”)

Using trends in graphed data to predict

Thinking about the limits of that kind of prediction (predicting in between data vs predicting beyond data)

Assessment:
Progress in Standards for Mathematical Practice (SMP) assessment
Growth in SMP 1 (Make sense of problems and persevere in solving them) and SMP 6 (Attend to precision) should be assessed via teacher observation and monitoring during the team work phases of the lessons. Keep notes at the student level about

Student perseverance: are students struggling with problems longer? Is that struggle productive? What evidence do you see of this?

Attending to precision of language: are students getting better at describing observations and discoveries to each other in more precise, meaningful language? (e.g. “The distance traveled went up as the weight increased” as opposed to “they go up”)

Mathematical precision: Are students using appropriate precision in measuring, recording, and graphing so that the constructed graphs are useful for predicting? Do you see them refining their work to increase precision?

Pedagogy note: “Attend to precision” does not mean “be more precise;” but rather, “use precision appropriate to the task.” So arguments over measurements at the 1/16inch level represent too much attempted precision here, because our tools and apparatus don’t have that level of repeatability; but measurements to the nearest foot are too imprecise because they may obscure differences.

Progress in Mathematical Content Assessment
Some possible assessment items:

Given a table of data for a hypothetical situation (either someone else’s racer or a totally separate situation), predict the “dependent variable” for some values of the independent variable that are not represented in the table. Best to include some value of the independent variable that are outside of the realm of reasonableness for the situationfor example, in the racer situation, 50 pounds of weight or “your weight (you sitting on the racer)”

Given someone’s notes on four trials of of some task, with one clear outliere.g. Sabah ran the 50meter dash four times, and her partner recorded her times with notes:

8.4 seconds

13 seconds, tripped at the beginning

9 seconds, started in a crouch

7.9 seconds, right before lunch

What would you say is Sabah’s “typical” 50meter dash time? Explain why you chose that time, and explain some reasons why Sabah doesn’t run in exactly that time each time she runs. (one possible solution: 13 seconds thrown out because the trip made it nontypical, average other three times; times vary because of wind, tiredness, people shouting, etc.)
Progress in Maker Mindset Assessment
In team work and discussion times, observe for and record instances of:

Students willing to try things when they aren’t sure they will work, then trying to fix issues (rapid prototyping)

Students learning from others’ discoveries (scouting)

Students effectively sharing their own and listening to/taking on others’ ideas in their teams (group work)

Students making predictions, with reasoning (Guess what will happen)

Students keeping good documentation
Teacher Reflection:
Make some notes for next time:
 Did students all have access to the activities?
 Did I maintain cognitive demand/productive struggle by resisting doing the students’ thinking for them?
 Did the activities provide opportunities to fail, and then learn from those failures?
 Did the activities help the mathematical ideas of average, graphing data, and predicting more meaningful and accessible to my students?
 What should I try next time to increase the productive struggle my students exhibit in this cycle?
Credits and Sources:
Sonoma State writing team: Ben Ford, Carol Keig, Brigitte Lahme, Kathy Morris
Project Make the Way teacher pilottest teams