Mathematics Grade 7
Educational Links

Strand: RATIOS AND PROPORTIONAL RELATIONSHIPS (7.RP)

Analyze proportional relationships and use them to solve real-world and mathematical problems (Standards 7.RP.1-3).

Standard 7.RP.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ^1/2/_1/4 miles per hour, equivalently 2 miles per hour.

• Chapter 4 - Mathematical Foundation (UMSMP)
  This is Chapter 4 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Proportional Relationships and Solving Problems.
• Chapter 4 - Student Workbook (UMSMP)
  This is Chapter 4 of the Utah Middle School Math: Grade 7 student workbook. It focuses on these topics: Proportional Relationships and Solving Problems.
• Cider versus Juice - Variation 1
  This task asks students to compute multiple unit rates, aligning with standard 7.RP.A.1. The problem also has a real-world context, which requires students to compare two rates in different units in order to reach a conclusion on buying two different products.
• Cider versus Juice - Variation 2
  The goal of this task is to apply proportional reasoning to determine which of two ways of buying apple juice/cider is a better deal. This task is a second variation to 7.RP.A.1, 7.RP.A.2.b Cider Versus Juice - Variation 1. This version offers a less directed approach to one of the questions posed in that task.
• Cooking with the Whole Cup
  While the task as written does not explicitly use the term "unit rate," most of the work students will do amounts to finding unit rates. A recipe context works especially well since there are so many different pair-wise ratios to consider.
• Drill Rig
  The purpose of this task is to provide a context for multiplying and dividing signed rational numbers, providing a means for understanding why the signs behave the way they do when finding products.
• Dueling Candidates
  The goal of this task is to have students examine some properties of ratios (and fractions) in an important real world context. Students will gain practice working with ratios while investigating some of the complexities of voting theory.
• Estimating: Counting Trees
  This lesson unit is intended to help educators assess how well students are able to solve simple problems involving ratio and direct proportion, choose an appropriate sampling method, and collect discrete data and record them using a frequency table.
• Grade 7 Math Module 1:Ratios and Proportional Relationship (EngageNY)
  In this 30-day Grade 7 module, students build upon sixth grade reasoning of ratios and rates to formally define proportional relationships and the constant of proportionality. Students explore multiple representations of proportional relationships by looking at tables, graphs, equations, and verbal descriptions. Students extend their understanding about ratios and proportional relationships to compute unit rates for ratios and rates specified by rational numbers. The module concludes with students applying proportional reasoning to identify scale factor and create a scale drawing.
• Grade 7 Math Module 4: Percent and Proportional Relationships (EngageNY)
  In Module 4, students deepen their understanding of ratios and proportional relationships from Module 1 by solving a variety of percent problems. They convert between fractions, decimals, and percents to further develop a conceptual understanding of percent and use algebraic expressions and equations to solve multi-step percent problems. An initial focus on relating 100% to the whole serves as a foundation for students. Students begin the module by solving problems without using a calculator to develop an understanding of the reasoning underlying the calculations.
• Grade 7 Unit 3: Ratio and Proportional Relationships (Georgia Standards)
  The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. They learn to express different representations of rational numbers (e.g., fractions, decimals, and percents), discover how to identify and explain the constant of proportionality, and represent proportional relationships and scale drawings within real-world contexts. The Big Ideas that are expressed in this unit are integrated with such routine topics as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year.
• Holes
  After watching a clip of the movie Holes from Walt Disney Pictures students will answer a series of questions, such as "If Stanley and X-Ray both dig one hole per day for a year, how much extra dirt will Stanley have dug than X-Ray?" and "How many times could that extra dirt fill one of the holes X-Ray digs?"
• Molly's Run
  This task asks students to solve a problem in a context involving constant speed. This task provides a transition from working with ratios involving whole numbers to ratios involving fractions.
• Molly's Run, Assessment Variation
  This task is part of a set of three assessment tasks that address various aspects of 6.RP domain and help distinguish between 6th and 7th grade expectations.
• Ratios and Proportional Relationships (7.RP) - 7th Grade Core Guide
  The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 Cluster "Analyze Proportional Relationships and Use Them to Solve Real-World and Mathematical Problems." / Standards 1, 2 and 3.
• Sale!
  The purpose of this task is to engage students in Standard for Mathematical Practice 4, "Model with mathematics." The teacher might use this task after formally teaching 7.RP.1-3. Students could be given the task and asked to collaborate in small groups to solve the questions posed using all the formal instruction on ratio and proportional reasoning.
• Stock Swaps, Variation 2
  Given the price of two stocks to be swapped, students must determine how many shares of stock they need to offer to get an even swap.
• Stock Swaps, Variation 3
  Given the price of two stocks to be swapped, students must determine how many shares of stock they need to offer to get an even swap.
• Temperature Change
  The goal of this task is to provide a context for interpreting the expressions that match the last part of the standard 7.NS.2.b, ''Interpret quotients of rational numbers by describing real-world contexts,'' though in this case the numerator and denominator are integers. Because of the context, students will also gain experience working with rates.
• Thunder and Lightning
  The purpose of this task is to work on performing unit conversions in a real world context about the speed of sound.
• Track Practice
  This task asks students to find the unit rates that one can compute in a context.

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http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.