Standards in Unit:

NC.6.EE.9 Represent and analyze quantitative relationships by:

• Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another.
• Analyze the relationship between quantities in different representations (context, equations, tables, and graphs).

NC.7.RP.1 Compute unit rates associated with ratios of fractions to solve real-world and mathematical problems.

NC.7.RP.2 -Recognize and represent proportional relationships between quantities.

1. Understand that a proportion is a relationship of equality between ratios.
   1. Represent proportional relationships using tables and graphs.
   2. Recognize whether ratios are in a proportional relationship using tables and graphs.
   3. Compare two different proportional relationships using tables, graphs, equations, and verbal descriptions.
2. Identify the unit rate (constant of proportionality) within two quantities in a proportional relationship using tables, graphs,
3. equations, and verbal descriptions.
4. Create equations and graphs to represent proportional relationships.
5. Use a graphical representation of a proportional relationship in context to:
   1. Explain the meaning of any point (x, y).
   2. Explain the meaning of (0, 0) and why it is included.
   3. Understand that the y-coordinate of the ordered pair (1, r) corresponds to the unit rate and explain its meaning.

NC.7.RP.3 Use scale factors and unit rates in proportional relationships to solve ratio and percent problems.

Summary of Unpacking for Each Standard:

NC.6.EE.9 - The purpose of this standard is for students to understand the relationship between two variables, which begins with the distinction between dependent and independent variables. The independent variable is the variable that can be changed; the dependent variable is the variable that is affected by the change in the independent variable. Students recognize that the independent variable is graphed on the x-axis, and the dependent variable is graphed on the y-axis. Through the representations of equations, tables, and graphs, students begin to really understand the concept of how numbers are related by equations.

NC.7.RP.1 - This standard addresses the unit rate for the first time as the rate that can be used to determine equivalent ratios. Students will be able to define and compute 2 unit rates for any multiplicative relationship, including those with fractions. Then, they can apply these unit rates to solve problems.

NC.7.RP.2 - To master this standard, students will solve problems involving conversions, percents, and circle graphs relating to proportional reasoning. Nearly all problems in this standard will exist in a real-world context, and they can involve fractions and decimals in the computations. Scale factors and unit rates are the preferred methods of solving these problems, but if algorithms are developed conceptually (such as the use of cross-products), they can ultimately be used to solve.

NC.7.RP.3 - To master this standard, students will solve problems involving conversions, percents, and circle graphs relating to proportional reasoning. Nearly all problems in this standard will exist in a real-world context, and they can involve fractions and decimals in the computations. Scale factors and unit rates are the preferred methods of solving these problems, but if algorithms are developed conceptually (such as the use of cross-products), they can ultimately be used to solve.

Prerequisite Skills:

• Coordinate Plane/Origin
• Unit Ratios and Rates
• One-Step Equations
• Percents
• Definition of Triangles
• Percent Proportions
• Converting (fractions, decimals, percents)

Future Skills:

• Writing expressions in different forms
• Slope/Equations of Lines
• Transformations/Dilations on the Plane

Key Vocabulary:

• Constant of proportionality
• Independent variable
• Dependent variable
• Discrete data
• Continuous Data
• Unit rates
• Ratios
• Complex Fractions
• Proportion
• Proportional relationships
• percents
• commission
• discount
• gratuity
• markup/markdown

Unit Test/Cornerstone Tasks

Unit Test: Schoolnet #2502865

Open-Ended Questions for Test: Unit 1a Open-Ended Test (Links to an external site.)Links to an external site.

Tasks: 1. The Price of Bread (Links to an external site.)Links to an external site.

1. Choose a rate from the word problems listed on this worksheet. (Links to an external site.)Links to an external site.

Determine the Constant of Proportionality, Independent Variable, and Dependent Variable. Create a table, graph, and equations to represent the relationship. Describe the 0,0 point and identify where to find the answer to the word problem in your graph.

MTSS/Remediation Resources

Math Topic/DPI Bucket: Unit Rate/Rational Number Reasoning

Engage NY F2F Intervention: Grade 6, Module 1 (Links to an external site.)Links to an external site., Topic C

Edgenuity Online Intervention: Grade 6 Applying Ratios and Rates Unit

Math Topic/DPI Bucket: Constant of Proportionality/Rational Number Reasoning

Engage NY F2F Intervention: Grade 7, Module 1 (Links to an external site.)Links to an external site., Topic B