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

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

Use properties of operations to generate equivalent expressions.

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

Generate and analyze patterns.

Represent and solve equations and inequalities graphically.

Represent and solve problems involving addition and subtraction.

Create equations that describe numbers or relationships

Write and interpret numerical expressions.

Work with addition and subtraction equations.

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

Represent and solve problems involving multiplication and division.

Write expressions in equivalent forms to solve problems.

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

Add and subtract within 20.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Gain familiarity with factors and multiples.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Perform arithmetic operations on polynomials.

Reason about and solve one-variable equations and inequalities.

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

Analyze patterns and relationships.

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

Understand the relationship between zeros and factors of polynomials.

Work with radicals and integer exponents.

Multiply and divide within 100.

Interpret the structure of expressions.

Solve equations and inequalities in one variable.

Rewrite rational expressions.

Use the four operations with whole numbers to solve problems.

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

Use polynomial identities to solve problems.

Solve systems of equations.
problem_activity: Warm-up
The purpose of this Math Talk is to elicit strategies students have for solving equations in one variable, especially equations involving an expression in parentheses being multiplied by a coefficient. Developing fluency with these types of equations will be helpful in the associated Algebra 1 lesson when students substitute expressions in place of single variables and solve equations with expressions in parentheses.
In particular, students should see that to solve an equation like
\(100=10(x-5)\)
, a productive first step is to divide each side by 10.
Math Talks build fluency by encouraging students to think about expressions or equations and rely on what they know about properties of operations and equality to mentally solve a problem.
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
Solve each equation mentally.
\(100=10(x-5)\)
\(300=30(x-5)\)
\(15-971=x-4-971\)
\(\frac{10}{7}=\frac17 (x-19)\)
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: 28