Curricular Microteaching Lesson Plan

 Chris, Snow, Danielle 

Lesson Plan:

• Subject: Pre-Calculus 11, Powers with Rational Exponents

• Total time 15 mins

• Lesson breakdown: short lecture followed by a hands on activity and gallery walk to see other students solutions

Lesson Objective:

• By the end of this lesson you will be able to evaluate an expression that has a rational number in the exponent

Intro: (2 mins)

• Let’s recall what a rational number is (give some examples and some non-examples)

• Can give the class the opportunity to show what they know and define a rational number if they remember

• Definition: a number that can be written as a fraction of two integers where the denominator (bottom number) is not zero

• Example: 5/2, -3/1, non-example: sqrt(2), pi

Short Lecture: (8 mins)

• Let’s remember our exponent rules

• Can give the class the opportunity to show what they know and share exponent rules they remember (ask them which ones they remember)

Product Rule	am • an = am+n
Quotient Rule	am / an = am-n
Power of a Power Rule	(am)n = amn
Power of a Product Rule	(ab)m = am • bm
Power of a Quotient Rule	(a / b)m = am / bm
Zero Exponent Rule	a0 = 1, a≠0
Negative Exponent Rule	a-m = 1 / am

• Next, introduce rational numbers in the exponents. Lead an investigation with the students and help them discover a reasonable definition for these values

• Start by drawing a graph of y = 2x and plotting what we know (integer exponents)

• Ask students to think about 21/2. What could that mean? Is it nonsense? If it exists, where should it be plotted? Can we make it consistent with the above properties? Give them time to discuss, then collect them for an answer (It is √2. They can recognize this with either the product rule or the Power of a Power rule)

• Extend to any unitary fraction exponent (1/n). How can they use the Power of a Power rule to determine this value? (nth root of 2)

• Finally, consider any fractional exponent (m/n). How can they again use the Power of a Power rule to define any such value? (Split the m and the 1/n up to get the rational exponent law. There are two ways to do this.)

• Write out the law explicitly; add it to our list of other laws

• x takes the place of 2 from our investigation. It must be positive though (mention that we will discuss why “at a later date”)

• Mention that it is consistent with the rules that we already know!

• Do some examples on the board, maybe one easy one more difficult: 62/5, 84/3

• Questions for extending learners: What issues arise if x is negative? How could we come up with a reasonable definition of an irrational exponent?

Hands on Activity: (5 mins)

• Break students into three groups

• Each group will have the same set of expressions with rational numbers in their exponent

• The goal of the activity is to get students to place the numbers in ascending order from lowest to highest

• After about 4-5 minutes stop and get students to walk and look at other groups solutions

• At the very end share the correct solution on the board with all three groups

• During this time encourage questions, all three instructors are walking around talking with groups and answering questions

Backup Exercise:

The largest square in this diagram has side length 8 cm. Calculate the side length and area of each of the two smaller squares. Write the radicals in simplest form.