The Budget Constraint: Modeling and Solving Linear Inequalities
Shared by A STEM Educator
Students will write, solve, and graph linear inequalities from real-world constraints, and justify why the inequality symbol reverses when multiplying or dividing both sides by a negative number.
Lesson Overview
Students move from interpreting number line graphs and writing simple inequalities to solving multi-step inequalities with negative coefficients, discovering the sign-flip rule through a cell phone battery context. The anchor problem — an amusement park gift card — anchors the real-world thread throughout.
Materials
- Vertical whiteboards or large chart paper (one per group)
- Dry-erase markers (one per group)
- Random grouping cards or name-picker app
- Desmos Classroom activity (pre-loaded on student devices)
- Exit slip half-sheets (printed)
Scaffolded Task Progression
An amusement park charges $15 to get in and $3 per ride. You have a gift card worth $30. Can you go on 3 rides? Can you go on 5 rides? Can you go on 10 rides? Draw a number line showing every possible number of rides you could choose to go on.
An amusement park charges $15 to get in and $3 per ride. You have a gift card worth $30. Can you go on rides? Can you go on rides? Can you go on rides? Draw a number line showing every possible number of rides you could choose to go on.
Word bank:
- gift card: a card with a set amount of money already on it that you can spend.
- charge: the amount of money you must pay.
- per ride: for each ride; the cost for one ride.
- possible: able to happen or be true.
- number line: a straight line used to show numbers in order.
Look at the number line your group drew for the gift card problem. Write a single mathematical inequality that captures the constraint on the number of rides . Then, rewrite the original constraint in words as a complete sentence. Which inequality symbol did you use, and why is it instead of ?
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