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The Pigeonhole Principle Problems

Classroom Resource Information

Title:

The Pigeonhole Principle Problems

URL:

https://math.uchicago.edu/~tghyde/Math%20Circle%20--%20Pigeonhole%20Principle.pdf

Content Source:

Other
Trevor Hyde, The University of Chicago Mathematics Department

Type:

Assessment

Overview:

This assessment provides three difficulty levels of problems related to the Pigeonhole Principle: Warm-up (easiest), Workout (more difficult), and Challenge (most difficult). An answer document with explanations for each problem is provided here.

Content Standard(s):

Mathematics
MA2019 (2019)
Grade: 9-12
Applications of Finite Math

10. Use the Pigeonhole Principle to solve counting problems.

Unpacked Content

Evidence Of Student Attainment:

Students:

Solve problems using the Pigeonhole Principle to solve problems such as determining the number of socks needed to be pulled out of drawer to guarantee a match if there are 5 distinct pairs of socks in the drawer.

Teacher Vocabulary:

Pigeonhole principle

Knowledge:

Students know:

How to construct counting models.

Skills:

Students are able to:

Solve a combinatorial problem using the Pigeonhole principle.

Understanding:

Students understand that:

If m>n and there are m pigeons (or any object) and n pigeonholes (or any position), there must be at least one pigeonhole with more than one pigeon.

Diverse Learning Needs:

Tags:

counting, logic statement, pigeonhole principle

License Type:

Custom Permission Type
See Terms: https://grad.uchicago.edu/about-us/privacy-notice/
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses

Accessibility

Text Resources: Content is organized under headings and subheadings

Comments

This resource provided by:

Author:

Hannah Bradley

ALEX Classroom Resource

The Pigeonhole Principle Problems