Overview
Designing with Math is a project-based learning strategy that invites students to apply mathematical concepts through real-world design challenges. Rather than working through abstract problems on paper, students engage in meaningful, hands-on projects where they plan, build, and test solutions to practical issues. This approach empowers students to act as designers and problem-solvers, using math as a tool to make informed decisions. This practice works well as culminating tasks, giving students the opportunity to apply what they've learned in a meaningful, real-world context.
Through this practice you will be able to:
- Facilitate real-world problem solving led by student thinking.
- Increase student engagement and ownership.
- Support deeper understanding by making connections to real examples.
Materials
Materials for this activity may vary based on the task that students are working on. Below you will find some examples of materials:
- Measuring tools (e.g., tape measures, rulers, meter sticks)
- Graph/grid paper and sketching materials
- Calculators or math apps
- Design supplies (e.g., cardboard, paper tubing, glue, scissors, markers)
- (Optional) Project planning templates
- Access to relevant charts or data related to the task
- Display materials for final presentations (e.g., poster board, digital slides)
Day Before Prep (~55 min)
Design Challenge Selection (10-20 minutes): Select a design challenge that aligns with your current math unit (e.g., slope of ramps, area and volume of gardens or rooms, exponential growth of money, or transformations and symmetry). This task can also be completed by asking students to design a challenge related to the math concept. Be sure to try any tasks that you give to students and document any anticipated student actions or misconceptions. See the Additional Inspiration section for a few examples. To build student buy-in and ensure the challenge feels relevant and engaging for your students, consider involving them in the selection process. You might:
- Ask students what real-world problems or topics they're curious about
- Present a few potential design prompts and have students vote on the one they'd most like to explore
- Brainstorm ideas together and refine them as a class.
Prepare Support Materials (10 minutes): Identify or prepare any charts, templates, or tools students will need for calculations.
Set up Classroom (10 minutes): Arrange materials and workspaces for group collaboration.
Develop Guidelines (15 minutes): Establish clear project guidelines and expectations (rubric, timeline, group roles)
Determine Timeframe (5 minutes): Determine how much time will be allotted for students to complete the task.
Note: To maximize impact without overwhelming instructional time, we recommend using this practice no more than once per unit to reinforce key concepts. Alternatively, it can be used once per quarter as a larger project experience. Frequency can be adjusted based on the complexity of the challenge and your students' needs.
Conducting the Practice (~90 min)
Introduce the Challenge (10 minutes): Present a real-world design scenario connected to the math unit. Frame it as a problem that needs solving with creativity and precision. Below is a sample of how to introduce and frame this practice with your students. This example is generic and should be modified to fit the task that you are giving to students:
"In this project, you'll be using math the same way designers, engineers, and problem-solvers do every day to create solutions that work in the real world, not just on paper. This challenge gives you a chance to think about how math shows up in spaces around you and how you can use it to improve things people care about. Whether it's building something accessible, saving resources, or planning smarter systems, this activity connects math to issues that matter and helps you see how math is part of everyday decision-making."
Group and Plan (15-20 minutes): Organize students into small groups and introduce the group roles. Then, have them define the problem, ask clarifying questions, and begin initial sketches or brainstorming.
Research and Calculate (20 minutes): Support students in identifying the math they need and as they gather measurements, make calculations, and test the feasibility of their ideas.
Design and Build (30-45 minutes): Students create models, diagrams, or prototypes using available materials. Encourage them to try various methods, revising sketches and recalculating as needed.
(Optional) Present and Reflect: Each group shares their solution, including the math behind their decisions. Lead a class discussion or assign a written reflection on what students learned and how math played a role.
Note: Depending on the complexity of the challenge and the depth of the math involved, this project could be stretched across multiple class periods. Consider breaking the work into phases (e.g., planning, building, testing, reflecting) to support sustained engagement and learning.
Pitfalls to Avoid
- Vague Problem Scenarios: If the design challenge is unclear or not grounded in a real context, students may struggle to engage. Ensure the problem is concrete and relevant.
- Insufficient Math Focus: Avoid letting the building or artistic aspect overshadow the mathematical thinking and processes. Prompt students frequently to explain the "why" behind their numbers.
- Overly Complex Projects: Keep the scope manageable. Too much complexity can overwhelm students and detract from the learning goals.
- Unequal Participation: Some students may dominate while others disengage. Assign group roles or check in regularly to ensure collaboration.
What to Look For
- Students actively discussing and applying math concepts in context
- Evidence of calculations integrated into sketches or models
- Groups revising their designs based on mathematical reasoning
- Engagement and ownership of the task from all group members
- Clear articulation of how math informed their design decisions during presentations
Additional Inspiration
This practice was developed in collaboration with WestEd.