 Standard #: MAFS.6.RP.1.3

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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)

Subject Area: Mathematics
Domain-Subdomain: Ratios & Proportional Relationships
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Understand ratio concepts and use ratio reasoning to solve problems. (Major Cluster) -

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.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

Remarks/Examples

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.

TEST ITEM SPECIFICATIONS

Item Type(s): This benchmark may be assessed using: MC , EE item(s)
N/A

Assessment Limits :
Rates can be expressed as fractions, with “:” or with words. Items may involve mixed units within each system (e.g. convert hours/min to seconds). Percent found as a rate per 100. Quadrant I only for MAFS.6.RP.1.3a.
Calculator :

No

Context :

Allowable

SAMPLE TEST ITEMS (3)

 Test Item # Question Difficulty Type Sample Item 1 Tom knows that in his school 10 out of every 85 students are left-handed. There are 391 students in Tom’s school. How many students in Tom’s school are left-handed? N/A EE: Equation Editor Sample Item 2 The standard length of film on a film reel is 300 meters. On the first day of shooting a movie, a director uses 30% of the film on one reel. How long is the strip of film that was used? N/A EE: Equation Editor Sample Item 3 In a circle, which ratio is equivalent to ? N/A MC: Multiple Choice

Related Courses

 Course Number1111 Course Title222 1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1204000: M/J Intensive Mathematics (MC) (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 and beyond (current)) 7912110: Fundamental Explorations in Mathematics 1 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))

Access Point

 Access Point Number Access Point Title 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).

Perspectives Video: Professional/Enthusiast

 Name Description Amping Up Violin Tuning with Math Kyle Dunn, a Tallahassee-based luthier and owner of Stringfest, discusses how math is related to music. Coffee Mathematics: Ratios and Total Dissolvable Solids Math - the secret ingredient for an excellent cup of coffee! Gear Heads and Gear Ratios Have a need for speed? Get out your spreadsheet! Race car drivers use algebraic formulas and spreadsheets to optimize car performance. KROS Pacific Ocean Kayak Journey: Calories, Distance, and Rowing Rates Food is fuel, especially important when your body is powering a boat across the ocean. Related Resources: KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX] KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML] KROS Pacific Ocean Kayak Journey: Kites, Wind, and Speed Lofty ideas about kites helped power a kayak from California to Hawaii. Related Resources: KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX] KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML] Mathematical Thinking for Ceramic 3D Printing In this video, Matthew Lawrence describes how mathematical thinking is important for 3D printing with ceramic materials. Pizza Pi: Area, Circumference & Unit Rate How many times larger is the area of a large pizza compared to a small pizza?  Which pizza is the better deal? Michael McKinnon of Gaines Street Pies talks about how the area, circumference and price per square inch is different depending on the size of the pizza. The Science and Math Behind Sour Fizzy Candy Master candymaker Wes Raley describes the process and science behind making sour fizzy candy. Unit Rates in Swimming In this video, David Fermin demonstrates real-time estimates for monitoring swimming performance and physiology.

Video/Audio/Animation

 Name Description 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. 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.

Teaching Idea

 Name Description 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.

Formative Assessment

 Name Description Bargain Breakfast Students are given the prices of three different quantities of cereal and are asked to determine which is the best buy. Comparing Rates Students are asked to solve rate problems given the time it takes each of two animals to run different distances. Finding the Whole Students are asked to find the whole given a part and a percent. Homework Time Students are asked to convert a given rate to an equivalent rate out of 100. Making Coffee Students are asked to write ratios equivalent to a given ratio. Measurement Conversion Students are asked to make unit conversions. Party Punch - Compare Ratios Students are asked to compare ratios given in two different tables. Sara’s Hike Students are asked to solve a problem involving ratios. The Meaning of Pi Students are asked to explain the relationship between the circumference and diameter of a circle in terms of pi.

Perspectives Video: Teaching Idea

 Name Description 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. Robot Mathematics: Gearing Ratio Calculations for Performance A science teacher demonstrates stepwise calculations involving multiple variables for designing robots with desired characteristics.

Tutorial

 Name Description Converting Speed Units In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units. Finding a Percent You are asked to 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 example 2 It's nice to practice conversion problems, but how about applying our new knowledge of percentages to a real life problem like recycling? Hint: don't forget your long division! Percent Word Problem Example 3 You're asked to find the whole when given the part and the percent. Ratio word problem: boys to girls In this example, we are given a ratio and then asked to apply that ratio to solve a problem. No problem! Ratio word problem: centimeters to kilometers Let's solve this word problem using what we know about equivalent ratios. Solving Unit Price Problem This video demonstrates solving a unit price problem using equivalent ratios. Solving Unit Rate Problem This video demonstrates solving a unit rate problem using equivalent ratios. The Meaning of Percent This video talks about what percent really means by looking at a 10 by 10 grid.

Virtual Manipulative

 Name Description Converting Units Through Dimensional Analysis Using this virtual manipulative, students apply dimensional analysis (AKA factor-label method or unit-factor method) to solve unit conversion problems. There is also the opportunity to create your own unit conversion problems. 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. Percentages This virtual manipulative allows the student to enter any two of the three quantities involved in percentage computation: the whole, a part and the percent. This manipulative can also be used for the discussions of relations among fractions, decimals, ratios and percentages. 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.

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.

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! Fractions Decimals Percents Jeopardy Game In this interactive Jeopardy game, students convert fractions to decimals and percents and convert percents to fractions and decimals. Up to four teams or individuals can play the game, and members of each team or individuals can pick which category and amount they would like to answer in order to score the most points. Ice Ice Maybe: An Operations Estimation Game This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents. Various levels of difficulty make this game appropriate for multiple age and ability levels. Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals. Multiplication/Division: The multiplication and addition of fractions and decimals. Percentages: Identify the percentage of a whole number. Fractions: Multiply and divde a whole number by a fraction, as well as apply properties of operations.

Unit/Lesson Sequence

 Name Description Functions-Day Trips (National Security Agency) In this 3-lesson unit, Students explore functions as they use their knowledge of patterns and number operations to analyze function tables and graph them. Using tables and graphs, students determine which items are the best deals.

Original Student Tutorial

 Name Description Helping Chef Ratio Learn how to identify explicit evidence and understand implicit meaning in a text. You will be able to organize information in a table and write ratios equivalent to a given ratio in order to solve real-world and mathematical problems.

Worksheet

 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. Shopping and Conversion Word Problems This ready-to-print worksheet presents students with three shopping problems that challenge students to convert between smaller and larger measurement units and use all four mathematical operations. There are a total of seven questions involving these three problems, and the conversions which students must undertake involve dollars and cents, pounds and ounces, grams and kilograms, and centimeters and meters. 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.

Assessment

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

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.