options: Understand solving equations as a process of reasoning and explain the reasoning.

Perform arithmetic operations on polynomials.

Work with radicals and integer exponents.

Represent and solve equations and inequalities graphically.

Add and subtract within 20.

Solve systems of equations.

Generate and analyze patterns.

Multiply and divide within 100.

Understand the relationship between zeros and factors of polynomials.

Understand properties of multiplication and the relationship between multiplication and division.

Reason about and solve one-variable equations and inequalities.

Use properties of operations to generate equivalent expressions.

Gain familiarity with factors and multiples.

Rewrite rational expressions.

Write and interpret numerical expressions.

Analyze patterns and relationships.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Write expressions in equivalent forms to solve problems.

Understand the connections between proportional relationships, lines, and linear equations.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Work with equal groups of objects to gain foundations for multiplication.

Interpret the structure of expressions.

Understand and apply properties of operations and the relationship between addition and subtraction.

Represent and solve problems involving addition and subtraction.

Represent and analyze quantitative relationships between dependent and independent variables.

Work with addition and subtraction equations.

Solve equations and inequalities in one variable.

Use the four operations with whole numbers to solve problems.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Create equations that describe numbers or relationships

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve problems involving multiplication and division.

Use polynomial identities to solve problems.

Analyze and solve linear equations and pairs of simultaneous linear equations.
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)


correct_option_index: 2