Unit 1 Real Number System
UEQ: How do we use the properties of rational and irrational numbers and extend the
properties of exponents to rational exponents?
Lesson 1: Integer Exponents
Chapter 6 Lesson 1
Learning Goals for this Lesson:
Standards: MAFS.912.N-RN.1.1, MAFS.912.NRN.1.2, MAFS.912.N-RN.2.3, MAFS.912.N-Q.1.1
Students Will Know:
Students Will Be Able To:
That the sum and product of two rational numbers
Find the sums and products of rational and
is a rational number and an irrational number. That irrational numbers. Recognize that the sum of a
the product of a nonzero rational number and an
rational number and a irrational number is
irrational number is a irrational number.
irrational. Recognize that the product of nonzero
rational number and a irrational number is
irrational.
Lesson Essential Question:
How do the properties of rational and irrational numbers determine their sums and products?
Activating Strategy:
Have the students evaluate each expression on the processing side of their cornell notes. We will go over
the answers to the questions in Learning Activity 2.
1)
2)
3)
Key Vocabulary to Preview and Vocabulary Strategy:
Zero exponent, negative exponent, base, power, rational number, irrational number, integer, whole
number, natural number
Lesson Instruction:
Learning Activity 1:
Introduce Vocabulary: base, power, exponent, zero exponent, negative
exponent (in the numerator and in the denominator). Show and model
examples of each vocabulary term.
Assessment Prompt for LA 1:
Quick Write: Have the students write in their cornell note books the answer
to the following questions: (answer must be written in at least three complete
sentences) What is the difference between a negative exponent in the
Graphic Organizer:
Cornell Notes
Guided Notes:
Exponents and Radicals
Graphic Organizer:
Properties of Exponents
numerator and a negative exponent in the denominator? What happens to the
solution when the negative exponent is in the numerator or in the
denominator?
Differentiation:
Learning Activity 2:
Model and Explain to students how to simplify expressions that have a zero
and negative exponents. But FIRST REVIEW how to solve an expressions that
uses an exponent. For example:
= means 7 x 7 not 7 x 2.
Review the student’s answers to the Activating Strategy. Common Error:
Assignment:
Textbook Pages 392397
Workbook Pages 321326
Students forget that the exponent wants the number to be multiplied by itself
not the number that is in the exponent.
Zero – Exponent: any number raised to the power of zero will ALWAYS equal
1.
Negative Exponent: (negative number in the numerator) set the expression
equal to 1 and divide by the base/exponent, and change the exponent to a
positive value. (negative number in the denominator) set the expression equal
to 1 and multiply by the base exponent and change the exponent to a positive
value.
See examples 1 and 2 on text book page 393. Work book practice problems
on page 324.
Assessment Prompt for LA 2:
Collaborative Pairs: one student will simplify
, the other student will
simplify
. The first student will explain how they got their answer to the
other student and vis versa. If a student disagrees with the other student’s
answer, they must work together to find the correct solution.
Differentiation:
Learning Activity 3:
Model and Explain to the students how to evaluate expressions with zero and
negative exponents. Common Error: When evaluating an expression using
exponents you not only have to simplify the expression you also have to find
the solution to the expression. Remember: any number with an exponent of
zero will ALWAYS be 1. NO MATTER THE NUMBER.
Negative Exponents are another story. KNOW: if the negative exponent is in
the numerator the solution will be a fraction. If the negative exponent is in the
denominator then the solution will be a whole number.
For example:
and x=2
Step 1: put the expression
into a fraction
. Remember to change the
negative exponent to a positive value.
Step 2: Substitute the value of 2 into the expression for the value of x.
Step 3: Simplify the expression
denominator of the expression.
= 2 x 2 which is 4. Place the 4 in the
Step 4: The solution is
See example 3 on page 393 in the text book.
Assessment Prompt for LA 3:
Collaborative Pairs: one student will evaluate the expression
the other student will evaluate the expression
where p = 2,
where p is = 3. The first
student will explain how they got their answer to the other student and vis
versa. If a student disagrees with the other student’s answer, then they will
work together to find the correct solution to the problem.
Practice Assignment:
TB: 395-397
Basic: #12-23
Advanced: # 43-65
Extra Credit: # 86-93
Quick Check Homework:
24,28,34,42,52,77
Differentiation:
Learning Activity 4:
Model and Explain to the students how to simplify more complex expressions
with zero and negative exponents. Expressions with more than one variable or
part will require multiple steps to find the solution.
For example:
The expression reads 3 times
. Since the expression is NOT in parenthesis
the negative exponent is only associated with the y variable/ IF the expression
has parenthesis then the negative exponent would be associated with the 3y.
To Simplify
.
Step 1: Separate the expressions into pieces. 3 x
.
Step 2: Since the value of 3 is positive then it stays the same, but since the y
has a negative exponent then it will be set equal to 1 and divide by the
variable and negative exponent. (change the negative exponent to a positive
exponent). Then combine the expression with 3.
3x
Solution is
See example 4 on page 394 in the text book.
Assessment Prompt 4:
Think-Ink-Pair-Share: Students will see the following expression on the
board
and they must list the steps on how to simplify the expression.
Then they will share and compare with steps with the other student (partner).
Differentiation:
Learning Activity 5:
Introduce the Properties of Exponents: refer to page 331 in their work books
to see the chart for properties of exponents. Model and Explain how each
property works. Provide the students with the Properties of Exponents
worksheet from them to complete the examples and practice problems.
“Foldable or Graphic Organizer that you can use. See attached.”
Assessment Prompt 5:
Think-Ink-Pair-Share: Provide the students with the following list of
expressions. Have the students name which property of exponents they need
to use to simplify the expression, and they have them simplify the
expressions. Once the students have completed the activity they will share
their answers with their partner. If one student does not agree with the other
student’s answer then they must work together to find the correct solution.
Differentiation:
Summarizing Strategy:
Ticket Out The Door: Have the students choose three exercises from page 395 numbers 37-42, write
each expression in words and then show two different ways to evaluate each expression.