 # Standard 1 : Understand ratio concepts and use ratio reasoning to solve problems. (Major Cluster)

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Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

### General Information

Number: MAFS.6.RP.1
Title: Understand ratio concepts and use ratio reasoning to solve problems. (Major Cluster)
Type: Cluster
Subject: Mathematics
Domain-Subdomain: Ratios & Proportional Relationships

#### Related Standards

This cluster includes the following benchmarks
Code Description
MAFS.6.RP.1.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
MAFS.6.RP.1.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid \$75 for 15 hamburgers, which is a rate of \$5 per hamburger.”
MAFS.6.RP.1.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

1. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
2. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
3. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
4. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
5. Understand the concept of Pi as the ratio of the circumference of a circle to its diameter.
(1See Table 2 Common Multiplication and Division Situations)
 Clarifications:Examples of Opportunities for In-Depth Focus When students work toward meeting this standard, they use a range of reasoning and representations to analyze proportional relationships.

#### Related Access Points

This cluster includes the following access points.

#### Access Points

 Access Point Number Access Point Title MAFS.6.RP.1.AP.1a: Write or select a ratio to match a given statement and representation. MAFS.6.RP.1.AP.1b: Describe the ratio relationship between two quantities for a given situation using visual representations. MAFS.6.RP.1.AP.2a: Determine the unit rate in a variety of contextual situations. MAFS.6.RP.1.AP.3a: Use ratios and reasoning to solve real-world mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations). MAFS.6.RP.1.AP.3b: Solve unit rate problems involving unit pricing using whole numbers. MAFS.6.RP.1.AP.3c: Solve one-step real-world measurement problems involving whole number unit rates when given the unit rate ("Three inches of snow falls per hour, how much falls in six hours?"). MAFS.6.RP.1.AP.3d: Calculate a percentage of a quantity as rate per 100 using models (e.g., percent bars or 10 x 10 grids).

#### Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

#### Original Student Tutorials

 Name Description Equivalent Ratios: Help Lily identify and create equivalent ratios in this interactive tutorial. Farmers Market: Ratios, Rates and Unit Rates: Learn how to identify and calculate unit rates by helping Milo find prices per item at a farmer's market in this interactive tutorial. Helping Chef Ratio: You will organize information in a table and write ratios equivalent to a given ratio in order to solve real-world and mathematical problems in this interactive tutorial.

#### Assessments

 Name Description Sample 4 - Sixth Grade Math State Interim Assessment: This is a State Interim Assessment for sixth grade. Sample 3 - Sixth Grade Math State Interim Assessment: This is a State Interim Assessment for sixth grade. Sample 2 - Sixth Grade Math State Interim Assessment: This is a State Interim Assessment for sixth grade. Sample 1 - Sixth Grade Math State Interim Assessment: This is a State Interim Assessment for sixth grade.

#### Educational Game

 Name Description Flower Power: An Ordering of Rational Numbers Game: This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!

#### Perspectives Video: Expert

 Name Description Statistical Sampling Results in setting Legal Catch Rate : Fish Ecologist, Dean Grubbs, discusses how using statistical sampling can help determine legal catch rates for fish that may be endangered. Download the CPALMS Perspectives video student note taking guide.

#### Perspectives Video: Teaching Ideas

 Name Description Sling Psychrometers for Measuring Relative Humidity!: Dave Rodriguez demonstrates the use of a sling psychrometer to compare wet and dry-bulb temperatures to determine relative humidity. Download the CPALMS Perspectives video student note taking guide. Bicycle Mathematics: Speed and Distance Calculations: Cycling involves a lot of real-time math when you use an on-board computer. Learn about lesson ideas and how computers help with understanding performance. Download the CPALMS Perspectives video student note taking guide. Robot Mathematics: Gearing Ratio Calculations for Performance: A science teacher demonstrates stepwise calculations involving multiple variables for designing robots with desired characteristics.

#### Student Center Activity

 Name Description Edcite: Mathematics Grade 6: Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

#### Teaching Ideas

 Name Description Communicating about Numbers-SeaWorld Classroom Activity: Students communicate mathematical ideas and visually represent ideas by constructing charts, graphs, and scale drawings based on information cards about various marine animals. Baby Whale Formula-SeaWorld Classroom Activity: In this problem solving activity, students will practice measuring and making calculations in the context of providing nutrients to a baby whale that was rescued. Space Math: Estimating the Speed of a Tsunami: Students use real-world data from the 2011 Pacific Ocean earthquake and tsunami to estimate the speed of the tsunami as it crossed the Pacific Ocean. Students will also need to work through the issue of time zones and the International Date Line. Calculating Sharks-SeaWorld Classroom Activity: Given data about sharks and the amount of food they eat, students will be able to solve for the unknown in percentage problems. Given information about a shark's growth, students will be able to graph coordinates and interpret a linear graph. Given the conversion factor, students will be able to convert from metric to English units.

#### Text Resource

 Name Description Hitting Streaks Spread Success: This informational text resource is intended to support reading in the content area. Although scientists haven't determined a specific reason why one baseball player's hitting streak improves his whole team's performance, they have observed a very real mathematical pattern. There may be many reasons for the phenomenon, but no one has found them out yet.

#### Tutorials

 Name Description Ratio Word Problem: Centimeters to Kilometers: In this video, watch as we solve this word problem using what we know about equivalent ratios. Ratio Word Problem: In this video, a ratio is given and then applied to solve a problem. Finding a Percent: In the video, we find the percent when given the part and the whole. Percent of a Whole Number: This video demonstrates how to find percent of a whole number. Percent Word Problem: You're asked to find the whole when given the part and the percent. Percent Word Problem: Use long division to find the percent in this tutorial. Converting Decimals to Percents: This video demonstrates how to write a decimal as a percent. Solving Unit Rate Problem: This video demonstrates solving a unit rate problem using equivalent ratios. Solving Unit Price Problem: This video demonstrates solving a unit price problem using equivalent ratios. The Meaning of Percent: This video deals with what percent really means by looking at a 10 by 10 grid. The Meaning of Percent over 100: This video demonstrates a visual model of a percent greater than 100. Converting Speed Units: In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.

#### Video/Audio/Animations

 Name Description Understanding Percentages: Percentages are one method of describing a fraction of a quantity. the percent is the numerator of a fraction whose denominator is understood to be one-hundred. Atlantean Dodge Ball (An entetaining look at appropriate use of ratios and proportions): Ratio errors confuse one of the coaches as two teams face off in an epic dodgeball tournament. See how mathematical techniques such as tables, graphs, measurements and equations help to find the missing part of a proportion. Atlantean Dodgeball addresses number and operations standards, the algebra standard, and the process standard, as established by the National Council of Teachers of Mathematics (NCTM). It guides students in: Understanding and using ratios and proportions to represent quantitative relationships. Relating and comparing different forms of representation for a relationship. Developing, analyzing, and explaining methods for solving problems involving proportions, such as scaling and finding equivalent ratios. Representing, analyzing, and generalizing a variety of patterns with tables, graphs, words, and, when possible, symbolic rules. Bad Date (A Real World Application of Ratios): In this video from Math Snacks, a women goes on three dates, after which she analyzes the ratio of how many words she speaks compared to the number of words her date speaks. By attaining a 1:1 ratio of words, she attains her "Happily Ever After." (Apparently, in her eyes, this is the only desirable quality in a man that really matters.) A learner's guide, teachers guide, and transcript of the video is included.

#### Virtual Manipulatives

 Name Description Mixtures: In this online activity, students apply their understanding of proportional relationships by adding circles, either colored or not, to two different piles then combine the piles to produce a required percentage of colored circles. Students can play in four modes: exploration, unknown part, unknown whole, or unknown percent. This activity also includes supplemental materials in tabs above the applet, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet. Planet Size Comparison: Ratio: Images of two planets selected on two drop-down menus with a display of their respective diameters and the applicable ratio.

#### Worksheets

 Name Description Ratios and Rates - Using Ratio Tables to Make Comparisons: This resource is made up of a sequence of worksheets and is useful for a different look at how ratios work. It uses ratio tables extensively and is good for open discussion with classes. This resource might work well for struggling students. This was developed by Dr. Stephan and Mr. McManus at LCMS. Splash of Math - SeaWorld Classroom Activity: This resource allows students to assume the role of an ethologist provide 4 activities that challenge students to apply mathematics to solve complex real-life problems:Activity A: Watch the Whales - Determine average speed, distance, and percentage of time at the surface of gray whales. Activity B: Time Tally - From observations of a dolphin determine total time and percentage of time of certain behaviors. Activity C: Deep Divers - Determine average dive depth, diving time, and surface time of an elephant seal. Activity D: Breaches of the Humpback - Graph data and make a prediction from the graph. In this activity, the students will practice problem solving skills to solve complex real-life problems.

#### Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

#### Original Student Tutorials

 Title Description Equivalent Ratios: Help Lily identify and create equivalent ratios in this interactive tutorial. Farmers Market: Ratios, Rates and Unit Rates: Learn how to identify and calculate unit rates by helping Milo find prices per item at a farmer's market in this interactive tutorial. Helping Chef Ratio: You will organize information in a table and write ratios equivalent to a given ratio in order to solve real-world and mathematical problems in this interactive tutorial.

#### Educational Game

 Title Description Flower Power: An Ordering of Rational Numbers Game: This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!

#### Student Center Activity

 Title Description Edcite: Mathematics Grade 6: Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

#### Tutorials

 Title Description Ratio Word Problem: Centimeters to Kilometers: In this video, watch as we solve this word problem using what we know about equivalent ratios. Ratio Word Problem: In this video, a ratio is given and then applied to solve a problem. Finding a Percent: In the video, we find the percent when given the part and the whole. Percent of a Whole Number: This video demonstrates how to find percent of a whole number. Percent Word Problem: You're asked to find the whole when given the part and the percent. Percent Word Problem: Use long division to find the percent in this tutorial. Converting Decimals to Percents: This video demonstrates how to write a decimal as a percent. Solving Unit Price Problem: This video demonstrates solving a unit price problem using equivalent ratios. The Meaning of Percent: This video deals with what percent really means by looking at a 10 by 10 grid. The Meaning of Percent over 100: This video demonstrates a visual model of a percent greater than 100. Converting Speed Units: In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.

#### Video/Audio/Animations

 Title Description Understanding Percentages: Percentages are one method of describing a fraction of a quantity. the percent is the numerator of a fraction whose denominator is understood to be one-hundred. Atlantean Dodge Ball (An entetaining look at appropriate use of ratios and proportions): Ratio errors confuse one of the coaches as two teams face off in an epic dodgeball tournament. See how mathematical techniques such as tables, graphs, measurements and equations help to find the missing part of a proportion. Atlantean Dodgeball addresses number and operations standards, the algebra standard, and the process standard, as established by the National Council of Teachers of Mathematics (NCTM). It guides students in: Understanding and using ratios and proportions to represent quantitative relationships. Relating and comparing different forms of representation for a relationship. Developing, analyzing, and explaining methods for solving problems involving proportions, such as scaling and finding equivalent ratios. Representing, analyzing, and generalizing a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.

#### Virtual Manipulative

 Title Description Mixtures: In this online activity, students apply their understanding of proportional relationships by adding circles, either colored or not, to two different piles then combine the piles to produce a required percentage of colored circles. Students can play in four modes: exploration, unknown part, unknown whole, or unknown percent. This activity also includes supplemental materials in tabs above the applet, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.

#### Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.