Big Numbers, Small Numbers

CONTENTS OF CURRICULUM UNIT 18.04.04

  1. Unit Guide
  1. Introduction
  2. Demographics
  3. Objectives
  4. Unit Content
  5. Product Rule for Exponents (The Basic Rule of Exponents)
  6. Quotient Rule for Exponents
  7. Defining Negative Powers
  8. Defining the Power of Zero
  9. Power Rule for Exponents
  10. The Order of Magnitude
  11. Teaching Strategies
  12. Classroom Activities
  13. Sample Problems
  14. Teacher & Student Resources
  15. Appendix
  16. Bibliography

Closing Deficits Exponentially: Addressing Base Ten & Small Numbers Using Exponents

Tierra Lynn Ingram

Published September 2018

Tools for this Unit:

Appendix

Standards

Common Core State Standards (CCSS)

This unit will include standards from the CCSS throughout this unit. These standards will focus on using the properties of exponents to represent large and small numbers using scientific notation. We will concentrate on understanding the influence of Base 10 and exponents to ensure students can use scientific notation to represent such numbers.

Essential Standards

  • MATH.CONTENT.8.EE. A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32× 3-5 = 3-3 = 1/33 = 1/27.

Related Standards

  • MATH.CONTENT.8.EE.A.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.
  • MATH.CONTENT.8.EE. A.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology
  • MATH.CONTENT.5.NBT. A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
  • MATH.CONTENT.5.NBT. A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
  • MATH.CONTENT.5.NBT. A.3.A Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
  • MATH.CONTENT.5.NBT. A.3.B Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Standards of Mathematical Practice

  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

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