# Making a Trundle Wheel

*Build a trundle wheel with a paper plate and yardstick. Measure distances, plan a running course.*

## Cycle Type

Contextualized Math This is the Contextualized Math cycle type. Cycle types used to organize cycles by categories.

## Maker Mindset

During maker projects, participating productively as part of a group generally leads to better and more robust work. Pooling and building on each other’s ideas creates better maker designs and products. Likewise, solving mathematics problems or building a mathematical model is a creative process that benefits from collaboratively generating and/or vetting ideas and working together.

Maker tasks encourage trying out design ideas early to see if they are feasible. If they work, they are revised and improved upon. If they don’t, they are replaced by new ideas quickly without losing too much time pursuing dead-ends. This habit of mind also applies to mathematics. While solving math problems, students should test their ideas early. Will an idea lead to answers that is reasonable rather than too big or too small? If we are writing a general expression or equation, does it work for small cases? Can we tell without solving if a solution will be positive or negative?

During maker projects, students are encourage to scout out the projects of other groups and to incorporate and build on (or reject) scouted ideas into their own designs. Making is a social and open endeavor where all ideas are common property with the goal to create the best overall product. This habit of mind is also valuable within mathematics. Worthwhile mathematics often affords many entry points and approaches. Students can benefit from comparing their own ideas to their peers so that they can combine or adopt other’s ideas in their own mathematical work.

## CC Standards:

7.RP.A, 7.G.B.4, 7.G.A.1 ,MP5, MP6

You can find descriptions of all common core math standards at Common Core Math Standards

Students will complete the surveyor wheel challenge where they are making their own surveyor wheel using different size wheels and use it to measure various walking distances. They design a course for a 5K race on their school grounds. Through the challenge and 1 or 2 follow-up lessons, the mathematical purpose to deepen understanding and use the proportional relationship between number of rotations and distance traveled by the wheel (7.RP.A) and a greater understanding of the relationship between diameter and circumference (7.G.B.4, if students are already familiar with this relationship). They will engage in mathematical practices 5 (appropriate tools) and 6 (attending to precision).

Other mathematical purposes: Scale drawings 7.G.A.1

### Prior Experience

This maker lesson cycle can be used to gain a deeper understand about the relationship between diameter (D) and circumference (C) of a circle: $C = \pi\cdot D$. In this case students should already be familiar with this relationship. This activity is not intended to be used to introduce it.

Material | Quantity | When Used |
---|---|---|

Variety of measuring tools such as yardsticks, measuring tapes. | 1 of each per group | challenge lesson, warm-up |

Wooden yardsticks or rulers (with a hole at one end, or a drill to make holes) | 1 per group | challenge lesson, activity |

Tape | 1 per group | challenge lesson, activity |

Fasteners | 3 per group | challenge lesson, activity |

Paper plates of different sizes (typical sizes are 6-12 inches) | 3 per group (to make revisions) or 1 per group and extras that students have access to if they want to start over | challenge lesson, activity |

Piece of cardstock (index card or business cards work well) | 3 per group | challenge lesson, activity |

### Lessons:

### Learning Cycle Wrapup:

Teacher summary

### Assessment:

Progress in Standards for Mathematical Practice assessment

Progress in Mathematical content assessment

Progress in Maker mindset assessment

### Teacher Reflection:

[questions and discussion for teacher reflection after teaching learning cycle]