The question, “When will I ever use this?” is common in middle and high school math classrooms. While students sometimes throw this question out when they want to dig in their heels and avoid work, it’s a valid concern that teachers need to address. Adolescent motivation wanes when the intent and purpose of learning don’t seem relevant to their real lives.
Canned curriculum situations where “real-life” problems become contrived to target a particular math concept create challenges for teachers and frustrations for students. If these are the only examples, students will continue to view math as a series of equations, formulas, and graphs—all while teachers know that math holds much more potential as a beautiful and powerful way to interpret and understand the world. So how can we resolve this discrepancy and make math more meaningful and relevant to our students?
Approaches to Building Authentic Mathematical Connections
Amplify Math Vice President and former math educator Dan Meyer points to the importance of providing the mathematical necessity when solving problems. In this blog post, Meyer poses the question, “If math is the aspirin, then how do you create the headache?” To put it simply, the goal of instructional design is to create experiences for students that help them recognize that math isn’t pointless and that learning new mathematical concepts can help remove limitations to problem-solving. For example, understanding the concept of percent increase allows us to compare two quantities that have changed; knowing how to do this calculation can confirm or refute marketing claims that products contain “120% more” or contain “double stuff.” Students will want to learn the math to determine the truth of advertising to ensure they aren’t getting tricked and are spending money wisely when purchasing these products.
Educator Bruce Grip provides another perspective, offering a real-life math “sandwich” approach to applied problem solving. Grip explains the process of mathematical modeling involves quantifying real-world factors, applying math to the model to solve the problem, interpreting the result to determine if the model was sufficient, and taking action on these conclusions. That final step is critical and transforms this problem-solving process from the canned-curriculum-type word problem to a tool to understand and connect with the world. Teachers can explore Grip’s curated collection of culturally relevant mathematical modeling resources, diverse modeling lessons from the Consortium for Mathematics and its Applications, or the ideas below for real-world models to use in class.
Rich Examples of Mathematical Applications
1. The Golden Gate Bridge celebrates the 88th anniversary of its opening on May 27, 2025, but this beautiful engineering achievement is also deeply rooted in multiple high-level mathematical concepts. If you teach high school, use this opportunity to highlight the fact that the distinctive suspension cables form a catenary curve. Although a special natural exponential equation defines its shape, it is similar to a parabola, a familiar function to high school math students in Algebra 1.
- Question for exploration: Students might consider determining why the shape of a catenary is helpful and necessary to support the load of vehicles traveling on a bridge. This situation supports an authentic “need” for mathematics: to develop a model that addresses the force and movement of a suspended structure. Specifically, the curve’s equation must address how much the cable will sag at any point along its length. This video shows the bridge’s expansion at different temperatures, which might also spark conversation and further highlight the need for a strong mathematical understanding to ensure safety when holding tremendous weights above water.
- Lesson ideas: Use this elevation drawing from the Golden Gate Bridge website as a background on a whiteboard space like Figjam (reviewed here) or a sandbox in Padlet (reviewed here). Have students use drawing tools to sketch a parabola over the main curve to visualize the similarities and differences. Students can add key features of quadratic functions, such as the vertex and axis of symmetry, and explain what they represent in terms of the bridge’s architecture. Advanced students may even attempt to write the equation of a best-fit parabola using the elevation measurements.
- Extension: Consider incorporating elements of this curriculum unit from Yale-New Haven Teachers Institute on the mathematics in the design and building of bridges
2. Microplastics are a hot news topic and something many middle and high school students will find relevant and want to explore. Leaning into data science can help students understand and advocate for change to combat this environmental concern.
- Question for exploration: Have students imagine themselves as a social media influencer trying to convince followers of the grave concern of microplastics in ocean water. Data science offers students a way to collect, analyze, and interpret data and then take action by communicating what they discover. Creating data visualizations is a particularly useful way to tell a compelling story to followers.
- Lesson idea: The Stanford Graduate School of Education’s youcubed site provides a robust lesson addressing the question, “What’s in the Ocean Water?” by using Google Sheets to create a regression model. If your students don’t have access to this tool, consider LiveGap Charts (reviewed here), which does not require email registration.
- Extension: Have students use a design platform such as Adobe Express for Education (reviewed here) or Canva for Education (reviewed here) to create a video project or social media post that encourages viewers to take action based on the data they have explored.
To make math meaningful, teachers must design learning experiences that reveal its necessity in solving real-world problems. Doing so empowers students to engage with relevant issues and appreciate mathematics as a powerful tool for understanding our world.
Do you have any tried-and-true real-life problem-solving tasks that have increased student engagement in your classroom? Please share your ideas in the comments so we can continue to guide students through authentic mathematical explorations.