# Recognize and represent proportional relationships between quantities.

a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [7-RP2a]

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [7-RP2b]

c. Represent proportional relationships by equations. [7-RP2c]
• Example: If total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

d. Explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0.0) and (l,r) where r is the unit rate. [7-RP2d]

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ACOS 2009 Correlation
• 2 - Solve problems involving decimals, percents, fractions, and proportions.
• 8 - Determining the distance between two points on a scale drawing or a map using proportional reasoning.

• 4 - Write an algebraic equation that represents a pattern shown in a table, graph, or chart.
• 4.1 - Recognizing the relationship between numerical patterns in tables and their respective graphs on the coordinate plane.
• 11 - Solve problems involving ratios or rates, using proportional reasoning.

• 12.1 - Applying proportional reasoning to identify similar and congruent shapes.
• 12.3 - Determining ratios of perimeters and areas of similar triangles, trapezoids, and parallelograms.

CMP2 Correlation
 Book Investigation Objective Comparing & Scaling 2 7-RP2 7-RP2a 3 7-RP2b 4 7-RP2 7-RP2b 7-RP2c Moving Straight Ahead 1 7-RP2a 7-RP2c 7-RP2d 2 7-RP2a 7-RP2c 7-RP2d 3 7-RP2c 7-RP2d 4 7-RP2c 7-RP2d Stretching & Shrinking 4 7-RP2c 5 7-RP2c Variables & Patterns 1 7-RP2c 2 7-RP2c 7-RP2d 3 7-RP2c 4 7-RP2c Common Core Investigations 1 7-RP2 7-RP2a 7-RP2b 7-RP2d

Resources
North Carolina's Lessons for Learning
Murphy to Manteo - 7G1, 7RP2
• I can compute actual lengths from a scale drawing.
• I can compute fractional parts and use them for real world problems.
Changing Surface Areas - 7G6, 7RP1, 7RP2
• I can solve real world problems involving surface area of cubes.
• I can draw a model for a proportional relationship.
• I can compute unit rate.

My Humble Opinion
Skills
1. Test for equivalent ratios in a table
2. Test for equivalent ratios by graphing
3. Graphing points on a coordinate plane
4. Identify the constant of proportionality in tables
5. Identify the constant of proportionality in graphs
6. Identify the constant of proportionality in equations
7. Identify the constant of proportionality in diagrams
8. Identify the constant of proportionality in verbal descriptions
9. Represent proportional relationships by equations
10. Explain what a point on the graph of a proportional relationship means
Vocabulary
1. Origin
2. Proportional
3. Equivalent
4. Unit rate