Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students should be able to know and apply the multiplication and division properties of whole number exponents to generate numerical or algebraic expressions with whole number exponents.
Students should be able to distinguish between a power and exponent. Many students confuse the two. Power is not the exponent; it is the combination of the base and the exponent together.
Students should be able to define or give an example of a monomial.
This lesson is only meant to cover part of the Standard MAFS.8.EE.1.1 This lesson will focus strictly on the multiplying and dividing properties of whole number exponents and only on ones resulting in positive non-zero exponents.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be familiar with exponents and the following vocabulary:
base; exponent; cube; square (Students may not understand the use of the terminology cube and square, with respect to exponents.)
Students should be able to evaluate numerical expressions involving whole number exponents.
Students should be able to reduce fractions by eliminating common factors from the numerator and denominator.
Students should be able to expand exponent monomials to monomials composed of the products of its bases.
Guiding Questions: What are the guiding questions for this lesson?
How can we break down this multiplication / division problem to something simpler? What would the problem look like if we wrote an equivalent expression without exponents?
Where have you seen something like this before? Is this a fraction? How did we simplify fractions? - cancel out common factors (that equal 1)
Essential question to be visible to the students before, during and after the lesson:
"How do I simplify expressions containing powers being multiplied and divided?"
Teaching Phase: How will the teacher present the concept or skill to students?
After reviewing the Formative Assessment, the teacher will put the following on the board:
Then ask the students to express using exponents.
Some students may say it is x to the 5 to the second. If so, point out that the existing exponent of 2 will only apply to the last x and none of the others.
Some students may say that it is x to the 4th times x to the 2 or x squared. "That's true, but we can actually express this with only one base of x and not 2. How do you think we could do that?"
You are wanting to get them to see that if they expand the x squared and count up the x's, they are multiplying a total of 6 x's and therefore it is the same as .
write on the board:
If you count the x's, do you get the same number that you would by adding the exponents? - yes
Ask the students to write the initial expression in different ways (shown after the equal sign).
How would we simplify the following?
Some students may write 16 times 8; others may work it out to 128. Some may write .
How could we write this with one base and exponent, instead of two?
We're looking for them to answer 2 to the 7th power. How did you get 7?
What if I had the following:
How would I simplify that to have only one base and one exponent?
Hopefully by now, they have caught on that you are adding the exponents.
Write the following on the board.
Can we add the exponents here to simplify the expression?
If yes - What would the new base be? 10 to the 5th? 7 to the 5th? 7 to the 6th? Isn't 2 to the 3rd equal to 8; isn't 5 squared equal to 25? Do any of these look like they are equal to 8 times 25?
If no - Why not? - The bases are not the same
When we expand the expression, we get This is not 5 number twos being multiplied.We can't just add the exponents, they are not like bases. The only way we could simplify this is by working out 2 to the 3rd and 5 squared and multiplying the results.
What about the following?
Can it be simplified? - no, they are not like bases
So, what can we say about multiplying factors that have exponents?
"We can add the exponents of like bases being multiplied."
Write the following on the board.
This is a fraction. Is it in its simplest form? - No
What does it simplify to? - 3/5, 0.6
How did you get 3/5? - I divided the numerator and denominator by 3.
What do they call that three that you divided by? - common factor
When you first started learning how to simplify fractions, you were asked to write out the factors of the numerator and denominator. Like this:
Then you were told you could cancel out any factors that both the numerator and denominator had in common, since 3/3 equals 1. In this case, it was the 3.
Why were you able to cancel them out? - because three divided by three is equal to 1, and 1 times anything is itself. You may want to remind students that this is using the multiplicative identity property of 1.
What are the factors of ? - 5 x's or
What are the factors of ? - 2 x's or
So, if I have that is the same as
Cross out the common factors, what do you get?
Does there appear to be any relationship between the exponents we started with and the exponent we ended with? Notice how we "took away" 2 x's from the bottom and the top, since x/x = 1.
What did we do when we multiplied bases? - added the exponents of the like bases
What do you think we are going to do when dividing powers? - subtract the exponents
Do you think it will work for bases that aren't the same? - no
Provide the problems below.
Note how the first question uses the division symbol instead of the fraction bar.
Note how the second example uses coefficients. See if the students can figure out how to work these. Give them the hint of "Use the commutative property of multiplication."
Note how the third one has an x with what appears to be no exponent. This helps point out to the students that when there is no exponent, there is actually an "understood" exponent of 1. The same is true with the 4th one.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
The Guided Practice is incorporated in the Teaching Phase.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Students complete a scavenger hunt that includes 16 exponent questions. The directions for how to do the scavenger hunt are included in the file, along with an answer sheet, printable scavenger cards with the 16 problems listed on it, and a sample answer sheet that can be used by the students.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will stop the class a few minutes before the end of class and ask them the following questions.
What do we do when we multiply powers with like bases? - Add the exponents Why?
Does the same apply to non-like bases? - No
What do we do when we divide powers with like bases? - Subtract the exponents. Why?
Does the same apply to like bases? - No. Why?
What do we do with the coefficients of powers being multiplied? - Multiply them to form the coefficient of the resulting power. Why?
The following day's bell ringer (opening activity) should include examples of multiplying and dividing powers.
Administer the Summative Assessment, when appropriate.
A summative assessment could be made using some of the questions from the scavenger hunt along with some of the following questions.
1. If you had a million dollars () in one hundred dollar bills (), how many bills would you have? ans:
2. Simplify: ans:
3. Simplify: ans:
4. Simplify, express your answer using exponents: ans:
5. Simplify: ans:
6. Simplify: ans:
7. Simplify: Ans:
Write an equivalent expression without using exponents
The teacher will use the students' responses to guide instruction.
During the lesson:
The teacher will monitor students' responses and ask guiding questions to understand their thinking and advance their reasoning.
As students complete the scavenger hunt assignment, the teacher will periodically check their work for accuracy and understanding, asking guiding questions to promote their conceptual understanding.
Feedback to Students
The teacher will use the responses to adapt instruction.
The teacher will monitor the students' responses and probe their thinking with guiding questions.
As students complete the scavenger hunt assignment, the teacher will periodically check their work for accuracy and understanding. The teacher will provide appropriate feedback as needed.
Students will be provided with the correct secret message at the end of the exercise, which will let them know if they have been getting the problems correct or not. The problems in the exercise are designed, so that the common mistake made on one problem will lead to the answer of another. If the student skips problems as the result of a wrong answer, they will end.