options: Solve equations and inequalities in one variable.

Work with addition and subtraction equations.

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

Create equations that describe numbers or relationships

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

Reason about and solve one-variable equations and inequalities.

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

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

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

Analyze patterns and relationships.

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.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Perform arithmetic operations on polynomials.

Represent and solve equations and inequalities graphically.

Add and subtract within 20.

Understand the relationship between zeros and factors of polynomials.

Use polynomial identities to solve problems.

Solve systems of equations.

Represent and solve problems involving addition and subtraction.

Gain familiarity with factors and multiples.

Generate and analyze patterns.

Write and interpret numerical expressions.

Use the four operations with whole numbers to solve problems.

Multiply and divide within 100.

Represent and solve problems involving multiplication and division.

Use properties of operations to generate equivalent expressions.

Work with radicals and integer exponents.

Rewrite rational expressions.

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

Interpret the structure of expressions.

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

Write expressions in equivalent forms to solve problems.
problem_activity: Warm-up
The purpose of this algebra talk is to elicit strategies and understandings students have for evaluating an expression for a given value of its variable. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to evaluate expressions.
Launch
Give students a minute to see if they recall that
\(x^2\)
means
\(x \boldcdot x\)
(which they learned about in an earlier unit in this course), but if necessary, remind them what this notation means.
Display one problem at a time. Give students 30 seconds of quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.
Representation: Internalize Comprehension.
To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory; Organization
Student Facing
If
\(x\)
is 6, what is:
\(x + 4\)
\(7 - x\)
\(x^2\)
\(\frac13 x\)
Student Response
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Activity Synthesis
Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:
“Who can restate ___’s reasoning in a different way?”
“Did anyone have the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to _____’s strategy?”
“Do you agree or disagree? Why?”
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: 12