options: Reason about and solve one-variable equations and inequalities.

Use properties of operations to generate equivalent expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use polynomial identities to solve problems.

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

Write expressions in equivalent forms to solve problems.

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

Use the four operations with whole numbers to solve problems.

Work with addition and subtraction equations.

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

Analyze patterns and relationships.

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

Add and subtract within 20.

Write and interpret numerical expressions.

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

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

Represent and analyze quantitative relationships between dependent and independent variables.

Multiply and divide within 100.

Solve systems of equations.

Represent and solve problems involving multiplication and division.

Solve equations and inequalities in one variable.

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

Represent and solve problems involving addition and subtraction.

Interpret the structure of expressions.

Gain familiarity with factors and multiples.

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

Rewrite rational expressions.

Create equations that describe numbers or relationships

Work with radicals and integer exponents.

Represent and solve equations and inequalities graphically.

Generate and analyze patterns.

Perform arithmetic operations on polynomials.

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

Understand the relationship between zeros and factors of polynomials.
problem_activity: Warm-up
The purpose of this Math Talk is to elicit strategies and understandings students have for expressing total lengths and areas, given some dimensions. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to combine like terms to express a total length and express an area of a rectangle in different ways using the distributive property. In this activity, students have an opportunity to notice and make use of structure (MP7) because there are opportunities to invoke the distributive property and to replace expressions with equivalent expressions.
Launch
Display one problem at a time. Give students 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.
Student Facing
A rectangle is partitioned into smaller rectangles. Explain why each of these expressions represents the area of the entire rectangle.
[IMG]
\(7(7+7+4+4)\)
\(7(2 \boldcdot 7 + 2 \boldcdot 4)\)
\(7^2+7^2+4 \boldcdot 7+4 \boldcdot 7\)
\(2(7^2) + 2 (4 \boldcdot 7)\)
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
\(\underline{\hspace{.5in}}\)
’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
\(\underline{\hspace{.5in}}\)
’s strategy?”
“Do you agree or disagree? Why?”


correct_option_index: 2