## Carrying Compost

By Lily Thiboutot, February 27, 2017

### Grade Level

- Middle School

### Category

- Summer Design Institute

### Subject Area

- Mathematics

### Lesson Time

2 class periods, 50 minutes each

### Introduction

**Carrying Compost**is a design-based lesson which engages students in the real-world application of 7

^{th}grade geometry calculations in order to better understand the problem their teacher has, and compels them to collaborate on a construction plan which, again, requires the use of 7

^{th}grade geometry as well as consumer mathematics in order to evaluate, test and communicate their product. The challenge is to design a means by which the teacher can carry her at-home compost bin to school without use of a car, in order to contribute the composted soil—a source of vital nutrients and a soil conditioner, fertilizer, etc—to the school’s new garden plot. Background:

**Compost**is the result of letting food waste break down and become soil. Compost piles are very stinky and, when moved, sometimes leak liquid. The

**school garden**was proposed by the science department last year and could be starting as a curricular supplement as soon as next school year. The

**compost container**the teacher keeps compost in is a cylinder with a height of 28 inches and a diameter of 20 inches.

### National Standards

The Common Core Standards connected to this lesson are:
http://www.corestandards.org/Math/Content/8/G/C/9/
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
http://www.corestandards.org/ELA-Literacy/SL/6/1/
Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and expressing their own clearly.

### Objectives

- Students will be able to understand and address the needs of their audience
- Students will encounter a cylinder in a real-world context and have the opportunity to appreciate how mathematics helps them research and understand a relevant, every-day problem
- Students will authentically conceptualize the volume of a cylinder as they inquire about the weight of a full backyard compost bin
- Students will use the design process to formulate their ideas, express themselves to peers, and collaborate on a single prototype

### Resources

Classroom projection equipment is necessary for the ActivInspire/Powerpoint materials to be displayed and referenced. An iphone or ipad is necessary to photograph and quickly display prototypes for viewing on the projector screen.

### Materials

“Carrying Compost” Flipchart (for ActivInspire) or PDF
DITC bags
Design Challenge Proposal Form - Handout

### Vocabulary

Compost: decayed organic material used as a plant fertilizer.
Cylinder: a solid geometric figure with straight parallel sides and a circular base.
Diameter: a straight line passing from side to side through the center of a body or figure, especially a circle or sphere.
Radius: a straight line from the center to the circumference of a circle or sphere.
Volume: the amount of space that a substance or object occupies, or that is enclosed within a container.

### Procedures

**FIRST DAY – at or near the beginning of geometry unit**

*Students should be sitting in groups of 3-6 for this lesson.*

*Allow 20 minutes to perform procedures 1-7, and 25 minutes for procedures 8-13.*

- Introduce the design day with a review of the design process (see flipchart/pdf). Begin with reference to the many things in the room that were designed for a specific purpose (students’ chairs v. the teacher’s chair, your watch and the clock on the wall and the clock interface of an iPhone, a pair of scissors, etc.). Ask students to imagine a time before scissors existed and explain that to design the first pair of scissors--as well as every other pair of scissors that’s been designed since then!—humans had to go through a
*process.*The process involves (reference the graphic):

- Tell students that you’ve begun to research a problem related to our school and you realized that knowing 7
^{th}grade math made your research much easier. It all started when you heard the school was considering a school garden that science classes would take care of and learn from. Make sure students understand what compost is, and then explain that you thought of your at-home compost bin and how you’d like to contribute the soil from your compost bin to the school garden because it is nutrient rich and good for growing new plants. - The volume of the compost cylinder is . Use h = 28 and r = 10 (half of diameter) and demonstrate the volume calculation while students simply watch.
- After calculating that the volume is 8, 792 cubic inches, find out if anyone knows how heavy that is. They don’t? That’s what we have conversions for! Display the computer on the board as you google “8,792 cubic inches to gallons,” and you’ll show that the volume of the compost is about 38 gallons.
- Question students about carrying 38 gallons of anything and make sure they agree that their teacher is going to need some help getting that stinky compost to school.
- Define the problem: (Insert teacher name here) needs to carry 38 gallons of stinky, juicy compost from her apartment to school without her car.
- Take questions from students about the problem. If no one asks, be sure to mention how far you live from school, tell them whether or not using a bike is an option, and comment on the terrain between your apartment and school.
- Allow students 3 minutes to brainstorm in their groups.
- Provide a DITC materials bag to each group and allow them 7 minutes to build. Float around the room and engage groups by questioning and commenting.
- Instruct groups to clean up their unused materials and put them back in the bag. While they do this, about 3 minutes, photograph each prototype with a tablet or iphone so you can project those images or email them quickly to yourself in order to project them.
- Tell students that you will show a photograph of each group’s solution and that group will take exactly 2 questions from the class and answer them.
- Use the last 10 minutes of the lesson for the question and answer session, first showing the design process graphic again and connecting the discussion they’re about to have with the evaluate/test phase of the process.
- End the lesson with “If you had 5 more minutes to work on your prototype, how would your solution change?”

**SECOND DAY – at or near end of geometry unit**

- Conduct a 5-minute (or less) discussion where students recall what the design process is, what the design challenge was from the beginning of the unit, and how defining the problem required math. Tell students that they will begin their work today by doing the math (volume of a cylinder) that was demonstrated to them in the first design lesson.
- Show each prototype photo (from FIRST DAY) and allow groups to each take two questions from the audience. Curb the discussion to 5-10 minutes total.
- Ask for a show of hands: who has an idea for their solution that is different and better than the prototype they made with their group? Tell them that today is about their individual ideas coming to fruition, and pass out the Design Proposal Form handout.
- Allow students to work independently for 15-20 minutes. Refer to “Assessment” section for notes on differentiating the lesson when students struggle with independent work and/or still need to master the mathematics concepts.
- Transition your students out of independent work time and give them the next 10 minutes of class to present their proposal to their table group. If groups are 5 students each, manage the time so that each student gets to speak for 2 minutes.
- In the last 5 minutes of class, conduct a large-group discussion in response to the question: “Which solution do you think your teacher would be likely to choose and why?” Be sure to facilitate such that students are considering their user (their teacher!) and defending their ideas with an understanding of the user’s priorities. This discussion is your chance to bring the design process full circle!

### Assessment

Check the math! Review the proposal form handout for understanding of the problem and for students’ calculations using the volume formula, accuracy of dimensional measurements in their sketch, and success adding up the budget items. Guide students through the proposal if they are struggling, providing examples and connecting them to peers they are known to work well with. When it is clear that a student has not yet mastered volume calculations, they will be provided with extra practice on circle area calculation as an alternative assignment.

### Enrichment Extension Activities

Connect students to websites where designs similar to theirs are already marketed (ie; a Burley, which is a pull-behind carrier for attaching to bikes) and ask them to develop a competitive marketing message.
Direct students toward further research on school-based gardens and have them design a composting center to be housed on-site.

### Teacher Reflection

Design-based teaching was a very successful way to introduce the concepts of 7

^{th }grade geometry. The actions of the design process were relevant to students, so they saw and later reflected about the value of learning and practicing volume calculations. There are still students struggling with the skills of squaring numbers and naming the dimensions of a cylinder, such as finding radius when only the diameter is labeled. In the future I may not provide an alternative assignment for these students but instead use an alternative instructional method that supports them to complete the same work as their peers. If I model the volume calculation for them again and provide more direct instruction and prompting then that lower-performing group can still participate in and enjoy the relevance of the design challenge.