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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Appendix

Common Core State Standards (CCSS)

This unit was created with the intent of addressing specific Common Core State Standards (CCSS). These CCSS will provide emphasis on specific learning objectives and outcomes of students.

Essential Standards

  • MATH.CONTENT.HSA.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
  • MATH.CONTENT.HSA.SSE.A.1.A Interpret parts of an expression, such as terms, factors, and coefficients.
  • MATH.CONTENT.HSA.SSE.A.1.B Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.

This unit is primarily focused on the arithmetic rules of addition and multiplication. These rules are used in justifying adding and multiplying polynomials of various degrees.

Related Standards

  • MATH.CONTENT.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2+ y2).

  • MATH.CONTENT.HSA.SSE.B.3.C

Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

  • MATH.CONTENT.HSA.SSE.B.4

Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.

Standards of Mathematical Practice (SMPs)

  1. Make sense of problems and persevere in solving them
  2. Reason abstractly and quantitatively
  3. Construct viable arguments and critique the reasoning of others
  4. Model with mathematics
  5. Use appropriate tools strategically
  6. Attend to precision
  7. Look for and make use of structure
  8. Look for and express regularity in repeated reasoning

My students will have used the SMPs throughout their experience through this unit. As they are introduced to and explore through the various teaching strategies, they will be demonstrating characteristics from SMP #4, 5, 7, and 8. As students work on/through the planned activities their understanding will be evident through exhibiting characteristics of SMP #1, 2, 3, and 6.

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