options: Use properties of operations to generate equivalent expressions.

Analyze patterns and relationships.

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

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

Perform arithmetic operations on polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use polynomial identities to solve problems.

Work with addition and subtraction equations.

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

Gain familiarity with factors and multiples.

Reason about and solve one-variable equations and inequalities.

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

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

Represent and solve problems involving addition and subtraction.

Solve systems of equations.

Interpret the structure of expressions.

Multiply and divide within 100.

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

Represent and solve equations and inequalities graphically.

Represent and solve problems involving multiplication and division.

Write expressions in equivalent forms to solve problems.

Generate and analyze patterns.

Add and subtract within 20.

Understand the relationship between zeros and factors of polynomials.

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

Work with radicals and integer exponents.

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

Rewrite rational expressions.

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

Use the four operations with whole numbers to solve problems.

Write and interpret numerical expressions.

Solve equations and inequalities in one variable.

Create equations that describe numbers or relationships

Represent and analyze quantitative relationships between dependent and independent variables.
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: 25