Designing 3D Products: Candy Cartons
This lesson unit is intended to help you assess how well students are able to:
- Select appropriate mathematical methods to use for an unstructured problem.
- Interpret a problem situation, identifying constraints and variables and specify assumptions.
- Work with 2- and 3-dimensional shapes to solve a problem involving capacity and surface area.
- Communicate their reasoning clearly.
This activity will take two lessons. The lessons are structured in the following way:
- Before the first lesson, students tackle the problem individually. You review their work and write questions to help students improve their solutions.
- At the beginning of the first lesson, students respond to your questions. They then work collaboratively in pairs to produce a better solution, using their designs to construct a carton.
- To launch the second lesson there is a whole-class discussion. Then in small groups students evaluate and comment on sample solutions, followed by a whole-class discussion about the work.
- Finally, in a follow-up lesson students review and evaluate their work on the problem.
- Each student will need a mini-whiteboard, a pen, an eraser, a copy of the task sheet, Design a Candy Carton, and a copy of the Design Review questionnaire.
- Each small group of students will need a large sheet of paper for making a poster, a sheet of light, letter-sized cardboard, scissors, a glue stick, highlighter pens, and a copy of each of the Sample Responses to Discuss.
- Provide calculators, rules, protractors, pencils, grid and plain papers, compasses, and cylindrical counters (such as checkers pieces) for students who wish to use them.
- You may also want to bring a couple of cartons to the class.
- There is a projector resource to support whole-class discussions.
20 minutes before the lesson, two one-hour lessons, and 15 minutes in a follow-up lesson. Timings are approximate; exact timings will depend on the needs of your students.
This lesson involves a range of mathematical practices from the standards, with emphasis on:
- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP4: Model with mathematics
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP8: Look for and express regularity in repeated reasoning
Mathematical Content Standards
This lesson asks students to select and apply mathematical content from across the grades, including the content standards: