options: Represent and solve problems involving multiplication and division.

Analyze patterns and relationships.

Interpret the structure of expressions.

Work with radicals and integer exponents.

Work with addition and subtraction equations.

Create equations that describe numbers or relationships

Multiply and divide within 100.

Generate and analyze patterns.

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

Solve systems of equations.

Understand the relationship between zeros and factors of polynomials.

Perform arithmetic operations on polynomials.

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

Add and subtract within 20.

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

Represent and solve equations and inequalities graphically.

Solve equations and inequalities in one variable.

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

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

Rewrite rational expressions.

Use the four operations with whole numbers to solve problems.

Gain familiarity with factors and multiples.

Reason about and solve one-variable equations and inequalities.

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

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Write expressions in equivalent forms to solve problems.

Represent and solve problems involving addition and subtraction.

Write and interpret numerical expressions.

Use polynomial identities to solve problems.

Use properties of operations to generate equivalent expressions.

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

Represent and analyze quantitative relationships between dependent and independent variables.
problem_activity: Activity
This activity is a continuation of the previous one. Students match each situation from the previous activity with an equation, solve the equation by any method that makes sense to them, and interpret the meaning of the solution. Students are still using any method that makes sense to them to reason about a solution. In later lessons, a hanger diagram representation will be used to justify more efficient methods for solving. For example, when they are using tape diagrams, they could just say “I subtracted the 9 extra markers and then divided the remaining 21 markers by 7.” Later, when working with hanger diagrams, we can press them to say “I can subtract 9 from each side and then divide each side by 7.”
For each equation, monitor for a student using their diagram to reason about the solution and a student using the structure of the equation to reason about the solution.
Launch
Keep students in the same groups. 5 minutes to work individually or with a partner, followed by a whole-class discussion.
Engagement: Develop Effort and Persistence.
Encourage and support opportunities for peer interactions. Prior to the whole-class discussion, invite students to share their work with a partner. Display sentence frames to support student conversation such as “To find the solution, first I ____ because...”, “I made this match because I noticed...”, “Why did you...?”, or “I agree/disagree because…”
Supports accessibility for: Language; Social-emotional skills
Student Facing
Each situation in the previous activity is represented by one of the equations.
\(7x+9=30\)
\(30=9x+7\)
\(30x+7=9\)
Match each situation to an equation.
Find the solution to each equation. Use your diagrams to help you reason.
What does each solution tell you about its situation?
Student Response
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Student Facing
Are you ready for more?
While in New York City, is it a better deal for a group of friends to take a taxi or the subway to get from the Empire State Building to the Metropolitan Museum of Art? Explain your reasoning.
Student Response
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Activity Synthesis
For each equation, ask one student who reasoned with the diagram and one who reasoned only about the equation to explain their solutions. Display the diagram and the equation side by side, drawing connections between the two representations. If no students bring up one or both of these approaches, demonstrate maneuvers on a diagram side by side with maneuvers on the corresponding equation. For example, “I subtracted the 9 extra markers and then divided the remaining 21 markers by 7,” can be shown on a tape diagram and on a corresponding equation. It is not necessary to invoke the more abstract language of “doing the same thing to each side” of an equation yet.
Speaking, Representing: MLR3 Clarify, Critique, Correct.
Present an incorrect match of an equation with a situation and/or diagram (e.g.,
\(30 = 9x + 7\)
with Situation 1). Invite students to clarify and then critique the error (e.g., there are 7 packs of an unknown amount of markers in Situation 1; not 9 as illustrated in the equation). Press for details, if needed. For example, students can reference “markers” in Situation 1, not “x”, as the unknown value represent by the variable
\(x\)
. This will help students reflect on the quantity of the unknown values that would be a reasonable solution and improve on their reasoning when matching an equation to a situation.
Design Principle(s): Optimize output (for justification)


correct_option_index: 23