options: Work with addition and subtraction equations.

Use polynomial identities to solve problems.

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

Represent and solve problems involving multiplication and division.

Multiply and divide within 100.

Reason about and solve one-variable equations and inequalities.

Use properties of operations to generate equivalent expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Interpret the structure of expressions.

Create equations that describe numbers or relationships

Solve equations and inequalities in one variable.

Represent and solve problems involving addition and subtraction.

Add and subtract within 20.

Write and interpret numerical expressions.

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

Analyze patterns and relationships.

Understand the relationship between zeros and factors of polynomials.

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

Use the four operations with whole numbers to solve problems.

Rewrite rational expressions.

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

Solve systems of equations.

Represent and solve equations and inequalities graphically.

Generate and analyze patterns.

Write expressions in equivalent forms to solve problems.

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

Perform arithmetic operations on polynomials.

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

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

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

Work with radicals and integer exponents.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Gain familiarity with factors and multiples.
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: 30