options: Use properties of operations to generate equivalent expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Use the four operations with whole numbers to solve problems.

Reason about and solve one-variable equations and inequalities.

Multiply and divide within 100.

Work with radicals and integer exponents.

Represent and solve problems involving addition and subtraction.

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

Work with addition and subtraction equations.

Solve equations and inequalities in one variable.

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

Perform arithmetic operations on polynomials.

Create equations that describe numbers or relationships

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

Understand the relationship between zeros and factors of polynomials.

Generate and analyze patterns.

Represent and solve equations and inequalities graphically.

Add and subtract within 20.

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

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

Analyze patterns and relationships.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Gain familiarity with factors and multiples.

Use polynomial identities to solve problems.

Represent and solve problems involving multiplication and division.

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

Rewrite rational expressions.

Write and interpret numerical expressions.

Solve systems of equations.

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

Interpret the structure of expressions.

Write expressions in equivalent forms to solve problems.
problem_activity: Optional activity
This activity gives students an opportunity to interpret the graph of a line in context, including the meaning of a negative slope and the meaning of the horizontal and vertical intercepts.
Launch
3 minutes of quiet work time, followed by 2 minutes to confer in small groups to verify answers.
Reading: MLR6 Three Reads.
Use this routine for Elena’s situation to support reading comprehension for students. In the first read, students read the problem with the goal of comprehending the situation (e.g., Elena is paying back her brother every week.). In the second read, ask students to look for quantities represented in the graph (e.g., at week 0, Elena owes him
$
18; at 6 weeks, she has paid him back completely). In the third read, ask students to brainstorm possible strategies to answer the question: “What is the slope of the line and what does it represent?” This will help students reflect on the situation and interpret the slope in the given context.
Design Principle(s): Support sense-making; Maximize meta-awareness
Student Facing
Elena borrowed some money from her brother. She pays him back by giving him the same amount every week. The graph shows how much she owes after each week.
[IMG]
Answer and explain your reasoning for each question.
What is the slope of the line?
Explain how you know whether the slope is positive or negative.
What does the slope represent in this situation?
How much did Elena borrow?
How much time will it take for Elena to pay back all the money she borrowed?
Student Response
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Anticipated Misconceptions
Students may interpret money owed as negative. In this setup, the axis is labeled so that money owed is treated as positive.
Activity Synthesis
Ask students to share answers to each question and indicate how to use the graph to find the answers. For example, draw a slope triangle for the first question: the slope is -3 rather than 3, because the number of dollars owed is decreasing over time. Label the vertical intercept for the amount Elena borrowed and the horizontal intercept for the time it took her to pay back the loan.


correct_option_index: 20