Middle School Math Lesson

The Locker Problem: Patterns, Factors, and Collaborative Reasoning

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6th–8th Grade (Mixed)BTC Style / Thinking ClassroomsCCSS.MATH.CONTENT.6.NS.B.4, CCSS.MATH.CONTENT.MP.3, CCSS.MATH.CONTENT.MP.750 min

Learning Objective

Students will collaboratively investigate a systematic problem, identify a pattern, and justify their reasoning using mathematical structure (factors and perfect squares).

Lesson Overview

Students work in random groups at vertical surfaces to explore the classic Locker Problem, discovering that only perfect square-numbered lockers end up open. The progression moves from acting it out with small numbers to generalizing the pattern using factor-pair reasoning.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors per group)
Erasers or paper towels
Random grouping cards or app
Printed locker tracking grids (optional, for groups that want them)
Sticky notes for gallery walk

Scaffolded Task Progression

1Task 1

There are 5 lockers, all starting closed. 5 students walk by: Student 1 toggles every locker, Student 2 toggles every 2nd, Student 3 every 3rd, Student 4 every 4th, Student 5 every 5th. Make a table on your board showing the state of each locker after each student passes. Which lockers are open at the end?

2Task 2

Extend your table to 10 lockers and 10 students. Which lockers are open at the end? Add a column: 'Number of times toggled.' Look at the open lockers — what do they have in common?

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