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Lesson plan

Lesson 3: Rectangle Madness

teaches Common Core State Standards 6.NS.A http://www.corestandards.org/the-standards
teaches Common Core State Standards MP8 http://corestandards.org/Math/Practice/MP8
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards MP6 http://corestandards.org/Math/Practice/MP6

Lesson 3: Rectangle Madness

This lesson is optional. In this exploration in pure mathematics, students tackle a series of activities that explore the relationship between the greatest common factor of two numbers and related fractions using a geometric representation. The activities in this lesson build on each other, providing students an opportunity to express the relationship between the greatest common factor of two numbers and related fractions through repeated reasoning (MP8). Thus, the activities should be done in order. Doing all of the activities would take more than a single class period—possibly as many as four. It is up to the teacher how much time to spend on this topic. It is not necessary to do the entire set of problems to get some benefit from the activities in this lesson, although more connections are made the farther one gets. As with all lessons in this unit, all related standards have been addressed in prior units; this lesson provides an optional opportunity to go more deeply and make connections between domains.

Lesson overview

  • 3.1 Optional Activity: Squares in Rectangles (15 minutes)
    • Includes "Are you Ready for More?" extension problem
  • 3.2 Optional Activity: More Rectangles, More Squares (30+ minutes)
  • 3.3 Optional Activity: Finding Equivalent Fractions (30+ minutes)
    • Includes "Are you Ready for More?" extension problem
  • 3.4 Optional Activity: It’s All About Fractions (30+ minutes)

Learning goals:

  • Coordinate diagrams and expressions involving equivalent fractions.
  • Interpret and create diagrams involving a rectangle decomposed into squares.
  • Recognize that decomposing rectangles into squares is a geometric way to determine the greatest common factor of two numbers.

Learning goals (student facing):

  • Let’s cut up rectangles.

Required materials:

  • graph paper

Glossary:

  • Access the complete Grade 6 glossary.

Standards:

  • This lesson builds on the standards:CCSS.4.MD.A.3MS.4.MD.3CCSS.5.NF.B.3MS.5.NF.3CCSS.6.NS.B.4MS.6.NS.4

 

 

 

 

 

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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