Perimeter, Area, Volume, and All That: A Study of Measurement

CONTENTS OF CURRICULUM UNIT 19.05.06

  1. Unit Guide
  1. Introduction
  2. Demographics
  3. Objectives
  4. Rationale
  5. Unit Content
  6. Area Models with Whole Numbers
  7. Basic Arithmetic Rules of Addition & Multiplication
  8. The Associative and Commutative Rules for Multiplication
  9. The Commutative Rule of Multiplication
  10. The Extended Distributive Rule
  11. Teaching Strategies
  12. Activities
  13. Appendix
  14. Bibliography
  15. Endnotes

When Your Plan to Multiply Polynomials is FOILED

Tierra Lynn Ingram

Published September 2019

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Objectives

This unit is intended to be a one to two-week (5 -10 instructional days) unit based on scheduling, pacing calendars etc. I will not start this unit until my scholars show a solid understanding with the 5 stages of place value and the law of exponents. I would like to increase my students’ fluency, precision and solid understanding of polynomial operations using area models for multiplication. I would like them to demonstrate multiplying polynomials using the box method as a way to classify the various terms and degrees of polynomial (magnitude of exponent). My hope is that, by reintroducing the associative and commutative rules of multiplication, I will enable my students to successfully find area and surface area of geometric figures.

I will be introducing this unit in parallel with Algebra I Module 1 Topic B: Structure of Expressions, in the curriculum as presented in the Eureka/EngageNY curriculum instructional materials. By focusing on multiplying polynomials using the box method and justified by both the associative and commutative rules, scholars will gain a strong grasp on polynomial operations, and solving problems involving them, specifically area models. All standards in my unit are compiled of grade level Common Core State Standards (CCSS) as noted in the Appendices, and will follow the pacing calendar as provided by the District of Columbia Public Schools. This unit comprises three topics:

  1. the area model for multiplication,
  2. the box method using exponential notation (5th stage of the five stages of place value),
  3. geometric illustrations of the associative and commutative rules for multiplication.

There are 4 overall objectives that I would like my scholars to master, they are as follows:

  1. Justify how the associative and commutative rules prove their calculations of products of polynomials to be correct.
  2. Demonstrate multiplying polynomials using area models and the box method.
  3. Find the area and perimeter of a rectangle with polynomial side lengths.
  4. Create an area model using algebra tiles and create an equation involving the appropriate polynomial operations.

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