1. The Think-Pair-Share activity (Part 1) requires students to connect representations of bases and exponents to their corresponding logarithmic expression. Accurate matches indicate that students have understood the relationships between exponents, bases, and logarithms. [IS.8 - Struggling Learners]
2. Student performance on the Lesson 1 Exit Ticket will indicate the degree to which they are able to represent logarithms appropriately. Use student errors to highlight misunderstood parts of the lesson.

Begin the lesson by showing a map of the school’s neighborhood with two paths going “toward any randomly chosen location.” One path should be a short route and one path should be a long route.

“How many of you would choose to go home using path A?” (students raise hands)

“How many of you would choose to go home using path B?” (students raise hands)

“Why did you choose that path? What elements did you take into consideration?” (students who pick path A will probably say that it’s quicker)

“We like saving time and doing things in a more efficient way. Today we are going to learn how to simplify expressions so that we save time in solving exponential and logarithmic equations. Why do we use exponents?”

Hopefully students recall that exponents are used to summarize repetitive multiplication.

“Recall that 2×2×2 is the same as 2³. A logarithm is also a type of exponent. It is the exponent needed to raise a number to get to another number. Using 2³ = 8, we say base of two raised to the third power. The logarithm is 3 and the base is 2.”

“We can rewrite the expression as 3 = log₂ 8. 3 is the logarithm, base 2, of 8. So 2³ = 8 and 3 = log₂ 8 are equivalent expressions. Remember when we write a log without a base, it is base ten. That means log 100000 = 5 is the same as log₁₀ 100000 = 5. Not including 10 as the base is similar to writing x and understanding that it is really x¹ (x to the first power).”

“Let’s look at this a bit more formally. For an exponential function in the form a=bx, then logba=x. Here are a couple examples.” Write the following on the board: [IS.6 - Struggling Learners]

If 9=32, then log39 = 2.

If 133=127, then log13127 = 3.
Similarly, if 10^–4 =  (1/10000), then log 0.0001 = –4.

Part 1

Activity 1 Hand out the Matching Worksheet (M-A2-4-1_Matching Worksheet and KEY.docx). Students should work on it by themselves for a few minutes and then they can pair up. They can use their calculators. [IS.7 - Struggling Learners]

Review the Matching Worksheet with students and then fill out the Properties of Exponents and Logarithms Notesheet (M-A2-4-1_Exponents and Logarithms Notesheet and KEY.docx).

Activity 2

After students have matched up the expressions, they should use the bottom of the worksheet to try to explain two of their matches. They should explain how they know that their matches are equivalent. They may have some difficulty with this part, but give them some think-time.

Activity 3

In partners, have students put together the Properties Puzzle (M-A2-4-1_Properties Puzzle.docx). Make copies of the page and then cut it up into the squares.

Part 2

Activity 4

When students have successfully put the puzzle together, give them a copy of the Simplifying-Evaluating Worksheet (M-A2-4-1_Simplifying-Evaluating Worksheet.docx). They should be able to complete this worksheet without a calculator.

Activity 5

Hand out the Lesson 1 Exit Ticket (M-A2-4-1_Lesson 1 Exit Ticket and KEY.docx) to evaluate whether students understand the concepts. For students who are having difficulty, use http://www.purposegames.com/game/negative-and-zero-exponents-quiz . They can take this short quiz to see how well they understand negative and zero exponents.

Extension:

1. In pairs, students write an expression and their partner has to write the equivalent expression or the simplified expression.