options: 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.

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.

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

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.

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

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.

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

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

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.
problem_activity: Optional activity
The purpose of this optional activity is to practice using a proportional relationship in another context. The chosen numbers make the unit rate a useful tool to answer the questions.
Launch
Remind students of the value of a quarter and a dime.
Student Facing
4 quarters are equal in value to 10 dimes.
How many dimes equal the value of 6 quarters?
How many dimes equal the value of 14 quarters?
What value belongs next to the 1 in the table? What does it mean in this context?
| number of                         quarters | number of                         dimes |
|--------------------------------------------|-----------------------------------------|
|                     1                      |                                         |
|                     4                      |                   10                    |
|                     6                      |                                         |
|                     14                     |                                         |
Student Response
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Student Facing
Are you ready for more?
Pennies made before 1982 are 95% copper and weigh about 3.11 grams each. (Pennies made after that date are primarily made of zinc). Some people claim that the value of the copper in one of these pennies is greater than the face value of the penny. Find out how much copper is worth right now, and decide if this claim is true.
Student Response
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Activity Synthesis
Ask students for the value that belongs next to the 1 in the table. Invite several students to explain the significance of this number.
Speaking: MLR8 Discussion Supports.
To provide a support students in precision of language when describing proportional relationships from a table, provide sentence frames for students to use, such as: “_____ is equal in value to _____, because . . . .”
Design Principle(s): Cultivate conversation


correct_option_index: 1