Critical Thinking

Using Mathematical Modeling to Strengthen Decision-Making Skills

By assessing scenarios inspired by Shark Tank, students can harness their critical thinking skills.

April 4, 2023
Michael Dwyer / Alamy

The ABC television show Shark Tank naturally models the scope, terminology, and real-life application for modeling mathematics and simultaneously challenges the idea of what an entrepreneur looks like and where they come from. Blending these features into a lesson creates a unique fusion between math applications and diverse business representations. This establishes space for learners to see themselves embedding decision-making skills into meaningful math tasks. Implementing this type of lesson can minimize the times your middle school students say, “When am I ever going to use this in real life?” because they’re learning about realistic and applicable situations. 

Unlike most traditional exercises that strive for one correct solution, an entrepreneur pitch lesson delivers the opportunity for middle school students to explore multiple choices with varying consequences. Requiring them to make numerically based decisions can spark an open dialogue that broadens learners’ vocabulary and provokes respectful math debates. To encourage students’ purposeful critical thinking and discourse, I follow a five-part lesson outline. 

Part 1: Initiation

Preselect or fabricate an appropriate pitch with multiple offers. Share or watch the initial segment, including the entrepreneur’s product and their valuation offer. Pause here to launch the first discussion, slowly developing basic reasoning skills into higher-order thinking. You may choose between a brief turn and talk or rapid writing strategy, but certainly return the class to a whole group discussion to share ideas. Here are some questions to initiate the process.

  • Would you invest in this business, and why or why not?
  • What information would you want to know before deciding to invest?
  • What questions would you ask the entrepreneur to evaluate how successful their business is? (Think of at least two.)
  • What factors do you think are considered to determine the value of a business?

While leading the group discussion, be overtly intentional about bridging connections between explicit math taught in class and the implicit math utilized in real-life business structures. Introduce relevant vocabulary such as retail and wholesale costs, gross profits, net profits, royalties, lines of credit, interest, and more. Be mindful to scaffold terms to meet your students’ needs, and provide a handout or anchor chart displaying these terms in relation to the questions that students posed. 

Part 2: Guided Instruction

Use the entrepreneur’s valuation offer to model your chosen method or strategies for calculating the value of a business. Elicit a union between modeling proportional relationships in percentages and calculating the valuation of a real business. 

Whether you’re utilizing tape diagrams, using double number lines, or setting up for direct computation with fractions, decimals, and percents, I recommend a gradual release approach where you review three examples before checking for understanding and transitioning students to their critical-thinking task.

Part 3: Critical-Thinking Task

Share all of the offers the entrepreneur received with your students. Depending on your time constraints, you may want to narrow the offers down to two. 

Instruct students to calculate and critique each offer (individually or in small groups) and discern which one they believe is the best choice. Students working in small groups will bring forth opportunities for verbalizing mathematical reasoning through discourse. Have students not only verbally explain their reasoning to their partners but dive deeper—require a written response that explains their choice and references their calculations to support their reasoning.

If you prefer your students to work independently, a written response captures their reasoning, from outspoken to reserved, and you can elect for students to share their responses aloud. During this critical-thinking task, you can circulate the classroom to offer your students guided feedback and support as needed. 

Part 4: Closure

For closure, review the valuations from each offer that the entrepreneur received. Be sure to address any common errors and misconceptions discovered while surveying the classroom. Provide students the opportunity to share which offer they chose and why. It’s important to normalize flexibility and remind students that it’s OK to change their opinion when presented with more viewpoints and data. 

Finally, show or reveal the entire pitch, exposing which offer, if any, was accepted. Ask students to write a short reflection that illustrates their reaction to the reveal, and note any changes of opinions about the valuations discussed in class. Remind students to specify if their offer was chosen and to articulate any errors or misunderstandings they previously held or made. 

Part 5: Assessment and Feedback

Assessment and feedback occur throughout the entire lesson. Students demonstrate informal feedback by participating and recording their responses to the initiation questions in part 1. In part 2, students are informally assessed throughout the gradual release of responsibility. After modeling three examples, take note and provide feedback for students who accurately calculated the business valuations and for those who need more support. Be sure to check in frequently, or establish a small group for the learners who need more support during part 3. 

Formal assessment takes place through the written responses in parts 3 and 4. Students are assessed for accuracy in calculating the valuation of each offer, and their written responses are assessed using a math writing rubric. General math writing rubrics can be found online, but I created one specific to this activity

This rubric scores students on the overall clarity of their response, selecting an offer, and justifying their reason with supporting mathematical data. Students who compare offers versus citing only one offer will score higher. Additionally, students who incorporate relevant vocabulary terms also receive a higher score. 

As math teachers, we can highlight the difference between solving for the correct answer in class and the relatable dilemma of making the best decision by asking the right questions and understanding your situation through what you have to offer. Entrepreneur-focused lessons (via Shark Tank) help to naturally provide the scope, terminology, and real-life application we desire our students to recognize and attain.

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  • Critical Thinking
  • Math
  • 6-8 Middle School

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