Description



Lesson Title: “Using Properties of Exponents”

Author’s Name: Sharon Parker

Teaching Partner(s): Leandro Schuab

Date of Lesson: 3/21/2011

Length of Lesson: 50 minutes.

Grade Level: 8th (Honors Algebra 1)

Source of the Lesson: Larson, R., Boswell, L., Kanold, T. D., Stiff, L. Algebra 2. McDougal Little: Florida Edition 2004

1. Florida Sunshine State Science Standards Addressed

|Benchmark Number |Descriptor |

|MA.912.A.1.3 |Simplify real number expressions using the laws of exponents. |

2. Concepts

Exponents can be very useful, especially in the modern age. There are computers for a lot of the calculations, but you must be able to understand exponents a little in order to do that. There really isn’t that often that you can’t use a calculator, but it’s the concept of exponents that students should learn. Really understanding the properties should help the students understand the concepts behind the exponents. Exponents are just a quicker way of writing multiplication. When something is multiplied by itself multiple times, you can just rewrite it using exponents. For the example of the fractal, using exponents makes it much more simpler than it would be if you had to make sure you multiplied enough times. The exponent is especially useful to use for scientific notation.

3. Materials List and Advanced Preparations

• Set of cards for each group of four with letters a to n on them randomly, but the same as the other groups. (14 cards)

• Picture of fractal from Marston. (if have time you may even make a small fractal…)

• Exit Slip for each student.

• Pre-Test for each student

4. Performance Objectives

Students will be able to:

• Use properties of exponents to evaluate and simplify expressions involving powers.

• Use exponents and scientific notation to solve real-life problems.

5. Safety Considerations

No safety Considerations

Lesson Plan in 5E format:

|ENGAGEMENT | |Time: 5 minutes |

|What the Teacher Will Do |Probing/Eliciting Questions |Student Responses and |

| | |Misconceptions |

|Give students pretest | | |

|Show the students the picture of the Menger |“What do you think of when you see this?”|[fractals] |

|fractal from the Marston Library. Then show | |[exponents] |

|them the sample one level fractal. | |[patterns] |

| | |[repetitions] |

| |“What is a fractal?” |[fraction] |

| | |[something that breaks apart forever] |

| | |Most likely the students do not know what a fractal|

| | |is… |

| |Explain how a fractal is a shape that the| |

| |parts of the shape is a smaller copy of | |

| |the whole. Show in the Menger fractal | |

| |where this is equivalent. | |

| |Explain what a level 3 Menger sponge |[figure out how much each level is made of. Then |

| |would be. “How could we figure out how |you multiply how many levels there are] |

| |many squares it would take to make a | |

| |level 3 Menger sponge?” | |

| |So there are 20. And 3 levels so 20x20x20| |

|EXPLORATION | |Time: 15 minutes |

|What the Teacher Will Do |Probing/Eliciting Questions |Student Responses and Misconceptions |

| |“What are exponents?” |[They are like 3^4] |

| | |[They are a number multiplied by itself |

| | |however many times the exponent is.] |

| |“What are the parts of an exponent?” |Base and exponent |

|Do a few examples first |“What is 2^4?” |2x2x2x2 |

| |“What is a^4?” |axaxaxa |

| |“What is 5^m? |5x5x….x5 m times |

| |What is 3^-4? |1/(3^4) or 1/(3x3x3x3) |

|Do this one first as an example aᵐ•an am+n | | |

|=[am+n] | | |

|Product of Powers Property |We want to find another expression that |[Expand it out] |

| |is equivalent to aᵐ•an. What are some |[Multiply] |

| |ways to do this? |[students could also have no response] |

| |So what does aᵐ and an |a multiplied m times and a multiplied n times |

| | |so axaxax…xa x axax…xa |

| | |m times n times. |

| |So how could we rewrite this? (or how |If they are multiplied together there is a |

| |many a’s do we have? |multiplied m and n times so it’s m+n a’s |

| |So how could we rewrite the expression? |[am+n] |

|Before starting the activity remind the | | |

|groups about the Amazing Race. Let them | | |

|know that they will be doing an activity | | |

|where they can earn some more money for. | | |

|For each match they match correctly they | | |

|will earn 10 dollars worth of Indonesian | | |

|money. | | |

|Split the students into groups of four. |“Out of these there are pairs so that |The students will talk among the groups and |

|(The groups that they are working with for |each has a match so that the two matches|figure out which go with which. They will have|

|the Amazing Race project-their table) Give |are equivalent. Figure out which ones |to come up with reasons why they do. |

|the students a set of cards. (see below) |are pairs and then give an explanation | |

|Have them match which expressions are |for why they represent the same | |

|equivalent. Then have them show |expression. When working with these, if | |

|justification for it. |there is a variable in the denominator | |

| |assume that it isn’t zero.” | |

|Walk around the room as they are doing | | |

|this. | | |

|EXPLANATION | |Time: 20 minutes |

|What the Teacher Will Do |Probing/Eliciting Questions |Student Responses and |

| | |Misconceptions |

|(moved up to exploration) | |The students should be writing all this done on a |

|Have two students come up at a time and give | |separate sheet of paper. |

|them each a property to work on. Go over | | |

|quickly after they show their justification. | | |

|Power of a Power property |So what is (am)n equivalent to? And why? |[amn, because you have n a to the m’s. So you have|

| | |m a’s and n of those than it’s m times n a’s.] |

|Power of a Product Property | |[ambm, if you have m a times b’s you have ababab… |

| |So what is (ab)m equivalent to? And why? |if you separate the a’s and the b’s than you have |

| | |m a’s and m b’s, from the cumulative property of |

| | |multiplication. |

|Negative Exponent Property |So what is a-m equivalent to? And why? |[1/am, because you multiply it by m less a’s. So |

| | |it’s like you divide it by a’s] |

|Zero Exponent Property |So what is a0 equivalent to? And why? |[1, this means you don’t multiply by any a’s so |

| | |it’s like multiplying by one.(if a isn’t zero)] |

|Quotient of Powers Property |So what is am /an equivalent to? And why? |[am-n, if you have m a’s in the numerator and n |

| | |a’s in the denominator, then if a isn’t zero, an a|

| | |in the top and in the bottom simplify to one. So |

| | |you can subtract the number of a’s in the top from|

| | |the a’s in the bottom.] |

|Power of a Quotient Property |So what is (a/b) m equivalent to? And why? |[am/bm, similar to multiplication, if you have an |

| | |m number of a/b’s multiplied together, you will |

| | |have m a’s in the top and m b’s in the bottom. |

|Show the class the list of properties so they |Evaluate the expression. Tell which | |

|can use them. Give the students a problem to |properties of exponents you used. | |

|do. Complete as many as time allows. |1) (6^-3)^2 |1)1/46656 |

|Do the first together as a class and then let |2) 8^-1x8^4 |2)512 |

|the students all try it on their own. |3)3^3/(3^-5) |3)6561 |

| |Simplify the expression. Tell which | |

| |properties of exponents you used. | |

| |1) (x^4y^5)/(x^2y^3) |1)x^2y^2 |

| |2) -4x^0y^-5 |2) -4/y^5 |

| |3)(4x^3y^-1)/(20x^6y^5) |3)1/(5x^3y^6) |

|ELABORATION | |Time: 5 minutes |

|What the Teacher Will Do |Probing/Eliciting Questions |Student Responses and |

| | |Misconceptions |

|(moved this section up…) |We want to figure out how well Indonesia is|5.4X10^11/2.3x10^8= |

|GDP of Indonesia: 540,000,000,000=5.4X10^11 |doing as a country as we are traveling over|5.4x10^3/2.3= |

|Population of Indonesia: 230,000,000= 2.3x10^8 |there. So we need to figure out GDP per | |

| |person. How could we do that? |2,347 |

|GDP of US 307,000,000=3.07X10^8 |Let’s compare it to the US. What would our |1.41x10^13/3.07X10^8= |

|Population of US 14,100,000,000,000=1.41x10^13 |GDP be? |1.41x10^5/3.07= |

| | | |

| | |45,928 |

| |Which country is doing better? |US |

| |“Are there any specifications to what n can|[It has to be an integer, either positive or |

| |be?” |negative. Not usually use zero though, because |

| | |that would just be one, and you wouldn’t need it.]|

| |“So how do you think this would apply to |You would do it the same way as with exponents. |

| |multiplying and dividing numbers in | |

| |scientific notation?” | |

| | | |

| | | |

| | | |

|EVALUATION | |Time: 5 minutes |

|What the Teacher Will Do |Probing/Eliciting Questions |Student Responses and |

| | |Misconceptions |

|See attached. | | |

Exponent cards.

aᵐ•an am+n

(am)n amn

(ab)m ambm

a-m 1/am

a0 1

am /an am-n

(a/b) m am/bm

Pre Test Student Name__________________________________

1. Evaluate

(6)^0x(6)^3x(6)^-4

2. Simplify the given expression

[(y^-1)(x^2)]/[(2x)^3(x^-1)]

Post Test. Student Name_________________________________

1. Evaluate and show which properties you would use.

2^3x2^-2/3^-1

2. Simplify the given expression

[(x^4)(y^2)(y^-1)]/[(x^3)(y^-2)]

3. In 1999 the national debt of the United states was about $5,608,000,000,000. The population of the United States at that time was about 273,000,000. Suppose the national debt was divided evenly among everyone in the United States. How much would each person owe?

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download