Submitted by: Jenna Murpree. Alicia Todt, Tracey Townsend, Erin Leggs, Matt Hampton
School: Math PD, 3/31/14
Content Standard(s):
Expressions and Equations Work with radicals and integer exponents.
CCSS.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.
Task Description:
Students will be introduced to an open-ended question about some different appearances of expressions in
exponential forms. (THREE’S A CROWD, Choose the one that does not belong! WHY?) The expressions will be
formed in a way that promotes thinking about exponential forms with negative powers.
(could include, but not limited to: open-ended question, thought-provoking problem, picture, link to video, or “Act 1”)
Possible Approach(es) or Solution(s) to the Problem:
The answers are unlimited… some students may give “incorrect” explanations at first, but that’s is ok.
Encourage any answers as long as the students give a valid explanation as to WHY the expression they chose is
different from the other two.
Examples of TRUE/VALID responses…
Possible reasons for A being the most unique/different…
 The only one with 8 and 6
 The only one with two exponents/powers
 The only one with two positive exponents/powers
Possible reasons for B being the most unique/different…
 The only one with a negative exponent/power
 The only one that shows ONE “x”
 The only one that does not have a fraction bar
 The only one that does not show multiplication/division
Possible reasons for C being the most unique/different…
 The one with the most “x” variables shown
 The only one that shows a dot as a multiplication symbol
 The only one that does not show any numbers
Examples of INVALID responses… (but, still accept them for now and discuss later)
 A/B/C is the biggest/smallest number!
 B is a negative number
What is the
overarching
mathematical idea
being developed?
Students will come to realize through discussion and exploration that…
 Negative exponents do not necessarily mean “negative number answers”
 Negative exponents occur as a result of multiplying or dividing terms with
“like bases.” Example, you cannot add/subtract “powers” when dividing the
following expression because the bases are not like.
5

What connections are
made to other math
concepts (if any)?
Describe how you use
this task to develop the
concept. When during
the concept
development did you
use this?
What facilitating
questions will you ask
students when they
need help? Be specific.
How will solution(s) be
shared or assessed?
𝑥
𝑦6
When multiplying you “add” and when dividing you “subtract” the powers of
“like bases.”
 When dividing/multiplying exponential expressions with like bases, you may
end up with “negative” exponents.
 In the case of a negative exponent, it is preferred to write as a fraction with
positive exponents.
 Students will become familiar with using terms such as, NUMERATOR,
DENOMINATOR, COEFFICIENT, EXPONENT, BASE, POWER… etc. when
describing expressions with exponents
There are not “a lot” of real world connections… but this skill involves…
 Laws/rules of operations with exponents
 Four functions (+/-/x/÷)
 Cross canceling
 Properties of multiplication/division

This task will be used a “prompt” to begin meaningful discussion and assess
background knowledge of exponential expressions. This can be used FIRST in the
lesson. (For example, the last of three warmup questions that will “spring board” the
students into discussion of a new topic)
Subsequent tasks (similar ones with different expressions) can be used throughout
the unit, getting slightly more difficult with each day.
Which of the three has the biggest value?
Many will have a different opinion at first. Some will realize that they are
equivalent/congruent in value. You can allow students to prove this using a
calculator. This would be a good time to go over the exponent keys on a calculator.
Have students test the truth of this by inserting different values of “x” in each place it
appears in the expression.
Open-ended group discussion. Encourage/acknowledge all answers given, valid or
invalid. Follow up discussion can be “think pair shared” etc. Have students answer
the same questions again, after hearing everyone else’s thoughts first.
Could this task be
extended? If so, how?
Follow up with other “three’s a crowd” questions.
When able to recognize differences, follow up with “Alice In Wonderland
(shrink/enlarge)” task.
Please attach or include, as needed:

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Any materials that might help someone implement your task.
Any additional files (pdf or otherwise).
Links to relevant websites.
First: (copy and paste image below to Microsoft Word to enlarge)
Second: (copy and paste image below to Microsoft Word to enlarge)