Power in Numbers

Exponents and Powers Curriculum Guide

Susan Jones

Introduction:

According to the GED testing service, test takers struggle with “applying rules of exponents in numerical expressions with rational exponents to write equivalent expressions with rational exponents.”   (https://www.gedtestingservice.com/uploads/files/09738c12fe4e4accd9a16bab7cb99a3c.pdf )  

Students do “fairly well” with simple squares and square roots, but there is a “sharp drop-off” when things get more complicated.

These are questions included in the “no calculator” portion of the test.

These skills are Mathematics Standards Level D in the College and Career Readiness Standards for Adult Education (https://www.educateiowa.gov/sites/files/ed/documents/CCRStandardsAdultEd.pdf ) under “Expressions and Equations.”

This curriculum guide will offer opportunities to build the deeper understanding necessary to understand the rules of exponents such as         (xm)^n = x^(mn)   .

Write and evaluate numerical expressions involving whole-number exponents. (6.EE.1)

Know and apply the properties of integer exponents to generate equivalent numerical expressions.  (8.EE.1)

While it may be sorely tempted to “save time” and skip to the procedural lessons, this is what leads to “sharp drop offs.”  Students will remember the simpler patterns and impose them on the more complex ones, incorrectly.   This concept is an ideal one for learning the real, understandable connections between what makes intuitive sense and more complicated math.  

Resources for teaching Exponents

Author/Provider	LINK	Resource	Purpose/Use
Susan Jones, YouTube Channel  CC-BY	https://youtu.be/D8vhO-6Blw8	Introduction to ExponentsVideo (3:19)    Captions edited for timing & accuracy	Introduction to “squaring” numbers from concept of using multiplication to measure area.       The purpose is to build a concrete, conceptual foundation for understanding exponents instead of immediately teaching the procedure.
Susan JonesGoogle Drive	https://docs.google.com/document/d/1wQSWaTg0mnw5zJTzSRaGvVxgYp7Ju3Hv3KMgta4OtPI/edit?usp=sharing	Connecting Representatons Exercise  - Squares	This exercise asks students to arrange representations of squared numbers together.  The most basic one only has representations of squared numbers, such as: ’three squared”     3 x 3                  3^2 (with actual superscript notation)
Susan Jones, Youtube Channel	https://youtu.be/dxr47mZkRUM	Exponents Intro – Part 2Video (4:24)  with edited captions.	This video reviews the meaning of squares and includes meaning of cubes, with concrete, visual conceptual foundation.   It can stand alone.
Susan Jones, Google Drive	https://docs.google.com/document/d/1scYfFi_ZiVFqyMYInmKc9LSEr8U5W2V2FeBZ6SbVREs/edit?usp=sharing	Connecting Representations Exercise - Cubes	Similar to “squares” exercise. Teachers can make more challenging ones (and I will  be).   If this is a new format for students, then starting simple will mean they can focus on the routine.   The “Connecting Representations” routine can be used w/ all levels of math.  (See “Connecting Representations in Math” from the National Council on Teachers of Mathematics )
Susan Jones, YouTube Channel	https://youtu.be/LsoK5v5f3Dc	The Power of ExponentsVideo (1:51)  w/ captions	Short!    Doesn’t include building from addition and multiplying, but emphasizes the notation and that exponents “have their own rules.”  Only discusses second power.
OpenUp Resources CC-ByIllustrative MathCC-BY	https://im.openupresources.org/6/teachers/1/17.html While many Illustrative Math lessons are linked to from oercommons, this one is not. I have contacted OpenUp Resources about this; in the meantime I have uploaded the PDF files to my site here:       Teacher Presentation  Student Task  Practice Problems    Cool Down	Squares and CubesThis is lesson 17 in a unit about area and surface area but can stand by itself.                This lesson provides a solid foundation for the next lesson where the advanced properties are explored.   It addresses standard 6.EE.2c	Introduces the idea of “perfect” squares  and cubes  visually (concretely if manipulatives are used).
OpenUp Resources CC-ByIllustrative MathCC-BY	https://im.openupresources.org/8/teachers/7.html   Lessons 1-7 Lesson One:   “Exponent Review” Condensed Lesson Plan  Teacher Presentation  Student Task Statements  Practice Problems  Student Cool Down     Lesson Two: Multiplying Powers of Ten   Condensed Lesson Plan  Teacher Presentation  Student Task Statements  Practice Problems  Student Cool Down      Lesson Three:   Powers of Powers of Ten   Condensed Lesson Plan  Teacher Presentation  Student Task Statements  Practice Problems  Student Cool Down     Lesson Four: Dividing Powers of Ten       Condensed Lesson Plan  Teacher Presentation  Student Task Statements  Practice Problems  Student Cool Down     Lesson Five:  Negative Exponents with  Powers of Ten   Condensed Lesson Plan  Teacher Presentation  Student Task Statements  Practice Problems  Student Cool Down     Lesson Six:    What about Other Bases?   Condensed Lesson Plan  Teacher Presentation  Student Task Statements  Practice Problems  Student Cool Down   Lesson Seven:   Practice with Rational Bases   Condensed Lesson Plan  Teacher Presentation  Student Task Statements  Practice Problems  Student Cool Down	Lesson One: Exponent ReviewThis begins with exponent “review” – but  includes more advanced applications than the earlier lessons, including raising fractions to powers.          Lessons 2 through 5 use powers of ten to develop the more complicated rules for exponents including negative exponents.   Lesson six explores other bases.   Lesson seven has complex practice applying the rules.
Lumen Learning (No strings attached)	https://www.oercommons.org/courses/rules-for-exponents/view	Rules for exponents	Thorough but abstract explanation with videos and practice exercises for the advanced rules.   The video explaining raising a power to a power shows this by expanding; the lessons include how to avoid common errors.   This is more condensed and symbolic  than the “Open Up” resources and assumes students already understand the concepts and notation of exponents.
Sue JonesCC-0	https://www.dropbox.com/sh/uixqva9l0vbv0ve/AABGkRdgebDegiYe1ngsuxOFa?dl=0	Publisher and PDF files of posters of first, second and third powers	I have 0 to 5 powers from 0 to 3 on my wall, and often refer to them when students have questions.
Sarah Carter	https://mathequalslove.blogspot.com/2013/10/ms-hagans-book-of-exponent-rules.html	“Ms. Hagans Book of Exponent Rules”	Description of activities for learning exponents and pictures of notes for students.   It may emphasize procedure / mnemonics too much for some students.