options: Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
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: 9