Purpose
Students investigate the essential question, “How can math expressions, equations, and inequalities help us make decisions in a real-life situation?” through a Decision Detectives launch that builds on their prior learning with clue cards, mini challenges, and a class puzzle. They apply variables, equivalent expressions, substitution, equations, and inequalities to create a poster, slideshow, comic, or short video that solves a real-life problem and clearly explains their reasoning. Students revise their work after feedback on the first draft and near-final version, focusing on mathematical accuracy, reasoning, and readability. Midway and at the end, they reflect on a helpful strategy and a challenge they solved before presenting their products to a fifth- or seventh-grade math class.
Learning goals
Students will use variables to model real-life decisions by writing, reading, evaluating, and generating equivalent expressions. They will solve equations in the forms x + p = q and px = q and use substitution to test whether values make equations or inequalities true. Students will create and revise a poster, slideshow, comic, or short video that clearly explains their mathematical reasoning, using feedback from two critique checkpoints. Through the Decision Detectives launch, midpoint and final reflections, and an exhibition for a fifth- or seventh-grade math class, students will answer: How can math expressions, equations, and inequalities help us make decisions in a real-life situation?
Products
Students will create a Decision Detective evidence sheet from launch challenges showing how expressions, equations, and inequalities guide real-life choices. They will develop a poster, slideshow, comic, or short video that uses variables, equivalent expressions, substitution, and an equation or inequality to solve and explain a real-life decision. Students will revise a draft plan and near-final product using peer feedback on mathematical reasoning and readability, while completing midway and final written or recorded reflections about a helpful strategy and a challenge solved. The final product will answer the essential question and be presented to a fifth- or seventh-grade math class.
Launch
Begin with a “Decision Detectives” challenge in which teams rotate through clue cards about choosing the best plan for a class celebration, using expressions, equations, and inequalities to compare costs and limits. At each station, students solve a quick challenge, test possible values by substitution, and collect a clue for a final class puzzle. Teams combine their clues to defend the best choice, then discuss: “How can math expressions, equations, and inequalities help us make decisions in a real-life situation?” End by inviting students to brainstorm real-life decisions they may investigate in their choice-based product.
Exhibition
Host a “Decision Detectives Showcase” for a visiting 5th- or 7th-grade math class. Display posters and comics in a gallery walk, set up slideshow stations, and screen short videos while each creator explains the real-life decision, variable, calculations, and solution. Visitors leave brief feedback on whether the math reasoning and final recommendation are clear and convincing. Students then write or record a final reflection naming one successful math strategy and one challenge they solved.
