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Number & Quantity: The Real Number System
Name: ____TEACHER COPY -Part 1_______
CCSS.Math.Content.HSN.RN.A.1
Date: ______________________ Period: _____
Explain how the definition of the meaning of rational exponents follows from extending the properties of
integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
Activity (Day 1):
Students will create foldable graphic organizers to illustrate the properties of integer exponents. Foldables
are great for introducing and organizing the properties of exponents. They provide a sense of student
ownership and investment in the curriculum. With foldables, students practice communicating data through
graphics, tables, charts, diagrams, and models. Below is an example of how to keep track of exponent
properties using foldables.
When you open each tab on the Multiplication Properties foldable, you see the actual property inside.
On the Division Properties foldable, you see a numerical example of the given property.
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Number & Quantity: The Real Number System
Name: ____TEACHER COPY -Part 1_______
CCSS.Math.Content.HSN.RN.A.1
Date: ______________________ Period: _____
Explain how the definition of the meaning of rational exponents follows from extending the properties of
integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
Group Work Activity (Day 1): Students will practice with exponents and mental math
Materials: 4 number cubes and 2 coins
Instructions:
1. Work in groups of two to four.
2. At the beginning of each round, roll three number cubes in order and flip one coin. The number cubes
rolled determines two powers. The first number cube rolled gives the base for both powers. The second
number cube rolled gives the exponent for the first power. The third number cube rolled gives the exponent
for the second power. If a head is flipped, divide the second power by the first. If a tail is flipped, multiply the
two powers.
3. Play at least three rounds. If students are in pairs, each student should have at least six problems worked
out on their paper. If students are in groups of four, each student should have at least twelve problems done.
Adjust the number of rounds by monitoring student understanding.
Example:
Let's say that you roll 2, 4, 5 and flip heads. Then your problem will look like this:
Let's say that you roll 3, 6, 1 and flip tails. Then your problem will look like this:
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Number & Quantity: The Real Number System
Name: ____TEACHER COPY -Part 2_______
CCSS.Math.Content.HSN.RN.A.1
Date: ______________________ Period: _____
Explain how the definition of the meaning of rational exponents follows from extending the properties of
integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
Properties of Exponents Partner Activity - use foldables! (Day 2):
Directions: Review properties of exponents in this partner activity using your foldables. Column one below
shows an expression involving exponents. In column two, write the name of the property or properties that
should be used. In column three, show your step in simplifying the expression. Each partner must fill in their
own worksheet.
EXPRESSION
x  x3
PROPERTIES
SIMPLIFY
6
(a 5 ) 7
(4 y ) 2
a6
a3
5
 
m
2
1270
x 3
b 2
b 4
 3
 4
y
5 4
5 7



2
2
 3a 5 


 2b 
(4ab3 ) 2
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All Rights Reserved by NewMathTeacher.Net
Number & Quantity: The Real Number System
Name: ____TEACHER COPY -Part 2_______
CCSS.Math.Content.HSN.RN.A.1
Date: ______________________ Period: _____
Explain how the definition of the meaning of rational exponents follows from extending the properties of
integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
Radicals and Rational Exponents (Day 2):
Let's look at the general patterns that emerge as we change the value of x in the following tables.
x
3
2
1
0
-1
2x
x
3
2
1
0
-1
3x
x
3
2
1
0
-1
4x
Can we make any general statements about numbers raised to the zero power?
Now, let's consider what happens when the value of x is a fraction.
Any fractional exponent in the form
can also be written in radical form as
.
Let's practice with some exponents to the power of one-half that can be expressed as square roots. Note that
if n = 2, you don't have to write the two above the radical in radical form. It's optional.
Rational Exponent Form
Radical Form
Integer
Will you be able to simplify these expressions into integers for all values of a?
If not, what type of number does a have to be for the square root expressions to simplify to an integer?
What type of number does a have to be for the cube root expression to simplify to an integer?
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All Rights Reserved by NewMathTeacher.Net