options: Write expressions in equivalent forms to solve problems.

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

Generate and analyze patterns.

Use polynomial identities to solve problems.

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

Understand the relationship between zeros and factors of polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Reason about and solve one-variable equations and inequalities.

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

Work with addition and subtraction equations.

Use properties of operations to generate equivalent expressions.

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

Represent and solve equations and inequalities graphically.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Solve equations and inequalities in one variable.

Gain familiarity with factors and multiples.

Multiply and divide within 100.

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

Create equations that describe numbers or relationships

Write and interpret numerical expressions.

Represent and solve problems involving addition and subtraction.

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

Work with radicals and integer exponents.

Perform arithmetic operations on polynomials.

Represent and solve problems involving multiplication and division.

Solve systems of equations.

Interpret the structure of expressions.

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

Analyze patterns and relationships.

Use the four operations with whole numbers to solve problems.

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

Add and subtract within 20.

Rewrite rational expressions.
problem_activity: Warm-up
The purpose of this warm-up is for students to reason about powers of positive and negative numbers. While some students may find the numeric value of each expression to make a comparison, it is not always necessary. Encourage students to reason about the meaning of the integers, bases, and exponents rather than finding the numeric value of each expression.
Launch
Display one problem at a time. Give students up to 1 minute of quiet think time per problem and tell them to give a signal when they have an answer and a strategy. Follow with a whole-class discussion.
There may be some confusion about how negative numbers interact with exponents. Tell students that exponents work the same way for both positive and negative bases. In other words,
\((\text- 3)^2 = \text- 3 \boldcdot \text- 3\)
.
Students may also struggle to interpret the notation difference between two expressions such as
\((\text- 4)^2\)
and
\(\text- 4^2\)
. Tell students that the interpretation of the first expression is
\((\text- 4)^2 = \text- 4 \boldcdot \text- 4\)
and the interpretation of the second expression is
\(\text- 4^2 = \text- 1 \boldcdot 4 \boldcdot 4\)
.
Student Facing
Is each statement true or false? Be prepared to explain your reasoning.
\(3^5 < 4^6\)
\(\left(\text- 3\right)^2 < 3^2\)
\(\left(\text- 3\right)^3 = 3^3\)
\(\left( \text- 5 \right) ^2 > \text- 5^2\)
Student Response
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Activity Synthesis
Poll students on their response for each problem. Record and display their responses for all to see. If all students agree, ask 1 or 2 students to share their reasoning. If there is disagreement, ask students to share their reasoning until an agreement is reached. After the final problem, ask students if the same strategies would have worked if all of the bases were 10 to highlight the idea that powers with a base of 10 behave the same as those with bases other than 10.
To involve more students in the conversation, consider asking:
“Do you agree or disagree? Why?”
“Who can restate ___’s reasoning in a different way?”
“Does anyone want to add on to _____’s reasoning?”


correct_option_index: 23