standard_description: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
problem_activity: Warm-up
The purpose of this Number Talk is to elicit strategies and understandings students have for dividing powers. These understandings help students develop fluency and will be helpful later in this lesson when students investigate negative exponents. While four problems are given, it may not be possible to share every strategy. Consider gathering only two or three different strategies per problem. It is expected that students won't know how to approach the final question. Encourage them to make their best guess based on patterns they notice.
Launch
Display one problem at a time. Give students 1 minute of quiet think time per problem and ask them to give a signal when they have an answer and a strategy. Allow students to share their answers with a partner and note any discrepancies.
Representation: Internalize Comprehension.
To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory; Organization
Student Facing
Solve each equation mentally.
\(\frac{100}{1} = 10^x\)
\(\frac{100}{x} = 10^1\)
\(\frac{x}{100} = 10^0\)
\(\frac{100}{1,\!000} = 10^{x}\)
Student Response
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Activity Synthesis
Ask students to share what they noticed about the first three problems. Record the equations with the solutions written in place:
\(\frac{100}{1} = 10^2\)
\(\frac{100}{10} = 10^1\)
\(\frac{100}{100} = 10^0\)
Ask students to describe any patterns they see, and how they would continue the patterns for the last problem:
\(\frac{100}{1,\!000} = 10^{x}\)
Tell them that in this lesson, we will explore negative exponents.
Speaking: MLR8 Discussion Supports.
: Display sentence frames to support students when they explain their strategy. For example, "First, I _____ because . . ." or "I noticed _____ so I . . . ." Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Design Principle(s): Optimize output (for explanation)


aligns: no