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

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving addition and subtraction.

Write and interpret numerical expressions.

Use the four operations with whole numbers to solve problems.

Create equations that describe numbers or relationships

Gain familiarity with factors and multiples.

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

Rewrite rational expressions.

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.

Perform arithmetic operations on polynomials.

Add and subtract within 20.

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

Multiply and divide within 100.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand the relationship between zeros and factors of polynomials.

Use properties of operations to generate equivalent expressions.

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

Work with addition and subtraction equations.

Interpret the structure of expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve equations and inequalities graphically.

Write expressions in equivalent forms to solve problems.

Analyze patterns and relationships.

Represent and solve problems involving multiplication and division.

Generate and analyze patterns.

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

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

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

Solve systems of equations.

Use polynomial identities to solve problems.

Solve equations and inequalities in one variable.
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: 16