# Proportional Relationships

## Objective

Use different strategies to represent and recognize proportional relationships.

## Common Core Standards

### Core Standards

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• 7.RP.A.2 — Recognize and represent proportional relationships between quantities.

• 7.RP.A.2.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.RP.A.2.B — Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

• 7.RP.A.2.C — Represent proportional relationships by equations. For 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.

• 7.RP.A.2.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 (1, r) where r is the unit rate.

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• 6.RP.A.3

## Criteria for Success

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1. Analyze proportional relationships
2. Use proportional reasoning to solve real-world problems involving proportional relationships (MP.4).

## Tips for Teachers

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This is a flex lesson that can be used in a variety of ways, depending on the individual class. There are no anchor problems, as teachers can determine what specific concepts are best to look at with the whole class. The Problem Set Guidance is a collection of problems that may be used for this day.

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

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Kate is baking cookies using a recipe she found online. Several of the measurements are given in grams, but she needs them in ounces instead. The recipe notes that $8$ ounces is $226.8$ grams.

Kate uses this information to determine an equation that will convert between the two units of measurement. However, she is unsure what the equation should be. She comes up with two equations: $z=28.35g$ or $g=28.35z$, where $z$ is the number of ounces and $g$ is the number of grams.

1. Which equation correctly converts between ounces and grams? Explain your reasoning.
2. What is the unit rate and what does it represent in this context?
3. Sketch a graph of the relationship between ounces and grams.

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