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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.

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

This cluster includes the following benchmarks.

Visit the specific benchmark webpage to find related instructional resources.

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

This cluster includes the following Access Points.

  • 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).
Cluster Resources

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

Original Student Tutorials
  • Una’s Unique Unit Rate Reunion: Join Una, the unicorn, as she learns the power of calculating unit rates while planning her family reunion in this interactive tutorial.

  • 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
  • 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!

Formative Assessments
  • The Meaning of Pi: Students are asked to explain the relationship between the circumference and diameter of a circle in terms of pi.

  • Finding the Whole: Students are asked to find the whole given a part and a percent.

  • Measurement Conversion: Students are asked to make unit conversions.

  • Comparing Rates: Students are asked to solve rate problems given the time it takes each of two animals to run different distances.

  • 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.

  • Sara’s Hike: Students are asked to solve a problem involving ratios.

  • Party Punch - Compare Ratios: Students are asked to compare ratios given in two different tables.

  • Writing Unit Rates: Students are given verbal descriptions of rates and asked to write them as unit rates.

  • Identifying Unit Rates: Students are asked to decide if given statements express unit rates.

  • Explaining Rates: Students are asked to explain the meaning of given rates and identify any that are unit rates.

  • Writing Ratios: Students are asked to write part-to-part and part-to-whole ratios using values given in a table.

  • Interpreting Ratios: Students are asked to explain the meaning of ratios in the context of problems.

  • Comparing Time: Students are given a scenario involving an additive comparison of two quantities, asked to write a ratio, and explain its meaning.

  • Comparing Rectangles: Students are asked to determine which of three given comparisons contains a correctly computed ratio in a context involving rectangles.

  • Book Rates: Students write and explain the meaning of a ratio and corresponding unit rate in the context of a word problem.

  • Bargain Breakfast: Students are given the prices of three different quantities of cereal and are asked to determine which is the best buy.

Lesson Plans
  • Coding Geometry Challenge # 12 & 13: This set of geometry challenges focuses on creating circles and calculating area/circumference as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor

  • Build Me a Beach House: This is a multi-day activity that reinforces science, math, and technology skills by taking the students through the design process. Students will be tasked with designing and building a structure that could withstand high winds and water as would be found close to the seashore.

  • Storm-Chasers: Weather & Climate: In this MEA, students will use their knowledge of weather to select a location for a camera crew to visit in order to get high quality video footage of severe weather such as thunderstorms, blizzards, tornadoes, or hurricanes. The decision will be made using data about important weather factors such as air pressure, humidity, temperature, wind direction, and wind speed.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

  • Water, Water Everywhere!: This lesson addresses current events regarding flooding in St. Petersburg, Florida. Students will create a water removal device from materials provided then use a 3D scanner to 3D print their devices.

  • Can You Stand the Wind and Rain?: In this lesson, students will:

    • Investigate how natural disasters have affected human life in Florida.
    • Add, subtract, and multiply multi-digit decimals using the standard algorithm.
    • Find a percent of a quantity as a rate per 100 and then solve problems involving finding the whole given a part and the percent.
  • Rate Your Local Produce Market: In this Model Eliciting Activity, MEA, the students will rank the local produce markets by using qualitative and quantitative data. The students will have to calculate unit rates of produce prices and then compare and order them.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

  • Champion Volleyball Team: Students will help create a championship volleyball team by selecting 4 volleyball players to be added to open positions on the team. The students will use quantitative (ratios and decimals) and qualitative data to make their decisions.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

  • Genetics can be a Monster!: In this lesson, students will use Punnett squares to calculate the probabilities of different genotypes and phenotypes produced by genetic crosses.

  • Cosmic Nose Cones: Students will design specific nose cones for a water bottle rocket. They will test them to find out and rate which one is most effective in terms of accuracy, speed, distance, and cost effectiveness. This information will be used as criteria for a company that designs nose cones for orbitary missions.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

  • Ares Habitation Corporation and the Search for Lunarcrete: In this Model Eliciting Activity, MEA, students will create a working model that can determine the best regolith to binder solution for a settlement on Mars. The students are contacted by a company that requests their services. Students will read about, study and create their own lunarcrete (moon concrete). Students will work as a team to evaluate the provided data and determine which solution is most effective. Students will find the unit rate of the lunacrete mixes. Finally, students will write a letter to the company defending their process giving reasons and data.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

  • Don't Chase a Car! There is a better way...: In this lesson, students will learn to solve a real world problem by using rates and ratios to calculate their running speed in MPH.

    • This is an activity that generates student interest because they get to go outside to generate and collect their own data to use in their calculations.
    • It's also a good collaborative project because students work in pairs or teams to collect their partners' times and rely on each other for accurate data.
  • All “Tired” Up: In this Model Eliciting Activity, MEA, students will utilize mathematical computation skills involving percentages and critical thinking skills to select the best tire deals advertised.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

  • Real Estate Rental Agency: In this Model Eliciting Activity, MEA, students will choose the best location for a family relocating and will find the monthly costs per month to make the best decision.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

  • Smooth Smoothie: In this Model Eliciting Activity, MEA, students will analyze data to decide what blender to use, the number of times the recipes are used and the total ingredients needed.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

  • Best Day Care Center for William: This MEA requires students to formulate a comparison-based solution to a problem involving choosing the BEST daycare based upon safety, playground equipment, meals, teacher to student ratio, cost, holiday availability and toilet training availability. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client. Students will receive practice on calculating a discount, finding the sum of the discounts, working with ratios and ranking day cares based on the data given.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

  • Recognizing Proportional Relationships to Develop Sense of Scale: This 90-minute lesson (15-minute pre-lesson, 60-minute lesson and 15-minute follow up lesson or homework) asks students to analyze proportional relationships to solve real world and mathematical problems. The examples use recipes, paint, and buildings. Students begin by working individually, then in pairs or threes, and then as a whole class. Student will need calculators, large sheets of paper to make a poster and the lesson materials.
  • Using Ratios and Reasoning to Calculate Cost of School Travel: In this 80 minute lesson, students use a real world scenario of the cost of traveling to school to make sense of ratio concepts and use ratio reasoning. This lesson has several correct approaches and uses proportional relationships. The lesson starts as independent work, involves an 80 minute lesson, and a 20 minute follow-up lesson that can also be assigned as homework.
  • Using Security Camera Angles to Find Area and Calculate Percentages: In this lesson, students work individually and then collectively using a real world situation to construct sight lines to see which areas are visible from a security camera. Students then find and compare the area of triangles and quadrilaterals and compare and calculate the percentages and/or fractions of areas.
  • Money: How to know where it is all going?: Students will apply their knowledge of percentages to create and assess household budgets.

  • Catapult a Rate: This lesson uses student created data to find the unit rate of distance per time. Students catapult three different coins, measure time and distance to find the rate of flight for each coin.

  • "Analyzing Wordless Stories" An Introduction to Solving Unit Rates: In this lesson, students will apply their understanding of ratios and prior knowledge of division to determine the unit rate for a given ratio. After some initial instruction on unit rates, students will determine unit rates from diagrams with teacher guidance, and they will determine unit rates from narrative descriptions independently.

  • The Best Domestic Car: In this MEA students will use problem-solving strategies to determine which car to recommend to Americans living in India.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

  • RATIOS: Compare This!: Students will explore ratios with models; express ratios in fraction form (simplest form), by use of a colon, and with words as a relationship between two quantities.

  • Lily's Cola TV Commercial: In this Model Eliciting Activity, MEA, given a tight budget, students need to find the number of people that can be hired to film a soda commercial. Students will make the selection using a table that contains information about two types of extras. Experienced extras earn more money per hour than novice extras; however, novice extras need more time to shoot the commercial than experienced extras. In addition, students will select the design that would be used for the commercial taking into account the area that needs to be covered and the aesthetic factor.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

  • Savvy Shopper: This unit rate culminating activity has students apply knowledge to purchasing groceries. Specifically, knowledge of how unit rates can help save money over time.

  • Equivalent Fractions and Percents: This lesson is designed to give students their very first experience with the concept and representation of percents. The activities seeks to lay a conceptual foundation for later problem solving with percents by building on students' prior knowledge of fractions with denominators of 10 or 100 and finding equivalent ratios. Throughout the lesson they use art to show the visual connection between fractions and percents. Students develop the knowledge that a percent is a part/whole ratio where the whole is measured in hundredths. The lesson gives students the opportunity to visually represent fractions and percents on a 10 x 10 grid, along with an enrichment activity if the teacher wants in expand to include decimal conversions and finding.

  • What Does a Ratio Look Like?: The class will use a PowerPoint presentation to take a stroll down the beach for some ice cream. The students must investigate how to write the number of ice cream cones in relation to the cost of ice cream.

  • PROFITS BY PROPORTIONS: Students will use proportions to determine how much to charge for a ticket to their concert performance. They will justify the price of tickets based upon the cost of facility rental and the number of tickets they anticipate being able to sell.

  • “My Favorite Recipe.” An introduction to ratios and rates.: This lesson shows how ratios can be indicated in words such as "to", "for every", "out of every." In grade 6, rates mean "for each 1," "for each," and "per." The students will use diagrams and tables to build their ability to use proportional thinking. At the end of the lesson, the students will increase or decrease recipes they find in cookbooks.
  • The Concept of Ratios: This lesson introduces students to the term ratio, its meaning and use, and the various ways in which a ratio can be presented.

  • It's Carnival Time!: This lesson uses a carnival theme that challenges students to calculate unit rates and make measurement conversions to determine the best values for food. The students will use mathematical practices as they analyze and compute math problems and explain their own process for arriving at their solutions.

  • But Mom, I Really Want an iPad!!!!!! Part 2: This is the 2nd Lesson where students are asked to solve a problem concerning the purchase of an iPad. Please see But Mom, I Really Want an iPad !! Part 1 (Resource 47500) for Lesson 1. Students are encouraged to use strategies to find equivalent ratios in their solutions.

  • Scuba Diving Mask Search: This MEA asks the students to decide which company would be the “best and the worst” to use to purchase scuba diving masks for Tino’s Scuba Diving School to provide to their diving certification students. Furthermore, the students are asked to suggest which type of scuba diving masks should be purchased in term of multiple panes – single pane mask, double pane mask, full face mask, skirt color, fit, durability, and price. Students must provide a "top choice" scuba diving mask to the company owner and explain how they arrived at their solution.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

  • Paper Route Logic: Students will be helping Lily Rae find the most efficient delivery route by using speed and distance values to calculate the shortest time to make it to all of her customers.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

  • Better Buy: 75 fl oz or 150 fl oz?: The students will clip out advertisements or use the attached PowerPoint to determine the better buy between small quantities and large quantities. The students will answer the question, "Which item costs less per unit?" and demonstrate fluency in dividing with decimals.

  • But Mom, I Really Want an iPad!!!!! Part 1: In this lesson, students are asked to find how long it will take for a girl to raise the money needed to buy an iPad. Students explore various solution strategies, including making tables of equivalent ratios and writing an equation to find equivalent ratios. A situational story is used to capture the students' interest and to help students create a visual for the relationship between quantities in a ratio.

  • Orange Juice Conversion: In this MEA, the students will be able to convert measurements within systems and between systems. They will be able to use problem solving skills to create a process for ranking orange juices for a Bed and Breakfast.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

  • Is It Fair?: In this lesson students will use their understanding of ratios and unit rate to solve problems where they must decide whether various situations are fair.

  • Happy Lawns: Lawn Care Service MEA: This Model Eliciting Activity (MEA) is written at a 6th grade level.
    This MEA asks the students to decide on a lawn mower that will provide the Happy Lawns: Lawn Care Service with the best value for their money. Students are asked to rank order the lawn mowers in term of gas tank capacity, customer rating, speed, amount of time the mower takes to cut an acre of grass, shipping, and cost of the lawn mower. Students must provide a "Best Value" lawn mower to the company owner and explain how they arrived at their solution.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

  • Summer Road Trip: Students will go on a virtual "road trip" with a partner. Using the scale on a map, students will calculate the distance traveled, the amount of gas used, and the cost of the gas.

  • Pancakes over a Campfire!: In this activity, students will learn how to set up ratios and calculate unit rates using a recipe.

Perspectives Video: Expert
Perspectives Video: Professional/Enthusiasts
Perspectives Video: Teaching Ideas
Problem-Solving Tasks
  • Pennies to Heaven: The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task. The total number of pennies minted either in a single year or for the last century is phenomenally large and difficult to grasp. One way to assess how large this number is would be to consider how far all of these pennies would reach if we were able to stack them one on top of another: this is another phenomenally large number but just how large may well come as a surprise.

  • Kendall's Vase - Tax: This problem asks the student to find a 3% sales tax on a vase valued at $450.

  • Anna in D.C.: The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.

  • Converting Square Units: The purpose of this task is converting square units. Use the information provided to answer the questions posed. This task asks students to critique Jada's reasoning.

  • Jim and Jesse's Money: Students are asked to use a ratio to determine how much money Jim and Jesse had at the start of their trip.

  • Security Camera: Students are asked to determine the percent of the area of a store covered by a security camera. Then, students are asked to determine the "best" place to position the camera and support their answer.

  • Shirt Sale: Use the information provided to find out the original price of Selina's shirt. There are several different ways to reason through this problem; two approaches are shown.

  • The Escalator, Assessment Variation: Students are provided seven choices and are asked to determine the ratios that are correct for the given context.

  • Voting for Three, Variation 1: This problem is the fifth in a series of seven about ratios. Even though there are three quantities (the number of each candidates' votes), they are only considered two at a time.

  • Voting for Three, Variation 2: This is the sixth problem in a series of seven that use the context of a classroom election. While it still deals with simple ratios and easily managed numbers, the mathematics surrounding the ratios are increasingly complex. In this problem, the students are asked to determine the difference in votes received by two of the three candidates.

  • Voting for Three, Variation 3: This is the last problem of seven in a series about ratios set in the context of a classroom election. Since the number of voters is not known, the problem is quite abstract and requires a deep understanding of ratios and their relationship to fractions.

  • Voting for Two, Variation 3: This problem is the third in a series of tasks set in the context of a class election. Students are given a ratio and total number of voters and are asked to determine the difference between the winning number of votes received and the number of votes needed for victory.

  • Voting for Two, Variation 1: This is the first and most basic problem in a series of seven problems, all set in the context of a classroom election. Students are given a ratio and total number of voters and are asked to determine the number of votes received by each candidate.

  • Voting for Two, Variation 2: This is the second in a series of tasks that are set in the context of a classroom election. It requires students to understand what ratios are and apply them in a context. The simple version of this question just asked how many votes each gets. This has the extra step of asking for the difference between the votes.

  • Voting for Two, Variation 4: This is the fourth in a series of tasks about ratios set in the context of a classroom election. Given only a ratio, students are asked to determine the fractional difference between votes received and votes required.

  • Currency Exchange: The purpose of this task is to have students convert multiple currencies to answer the problem. Students may find the CDN abbreviation for Canada confusing. Teachers may need to explain the fact that money in Canada is also called dollars, so to distinguish them, we call them Canadian dollars.

  • Dana's House: Use the information provided to find out what percentage of Dana's lot won't be covered by the house.

  • Data Transfer: This task asks the students to solve a real-world problem involving unit rates (data per unit time) using units that many teens and pre-teens have heard of but may not know the definition for. While the computations involved are not particularly complex, the units will be abstract for many students. The first solution relies more on reasoning about the meaning of multiplication and division, while the second solution uses units to help keep track of the steps in the solution process.

  • Friends Meeting on Bicycles: Students are asked to use knowledge of rates and ratios to answer a series of questions involving time, distance, and speed.

  • Games at Recess: Students are asked to write complete sentences to describe ratios for the context.

  • Mangos for Sale: Students are asked to determine if two different ratios are both appropriate for the same context.

  • Mixing Concrete: Given a ratio, students are asked to determine how much of each ingredient is needed to make concrete.

  • Overlapping Squares: This problem provides an interesting geometric context to work on the notion of percent. Two different methods for analyzing the geometry are provided: the first places the two squares next to one another and then moves one so that they overlap. The second solution sets up an equation to find the overlap in terms of given information which reflects the mathematical ideas reason about and solve one-variable equations and inequalities.

  • Price Per Pound and Pounds Per Dollar: Students are asked to use a given ratio to determine if two different interpretations of the ratio are correct and to determine the maximum quantity that could be purchased within a given context.

  • Ratio of Boys to Girls: Use the information provided to find the ratio of boys to girls. Tasks like these help build appropriate connections between ratios and fractions. Students often write ratios as fractions, but in fact we reserve fractions to represent numbers or quantities rather than relationships between quantities. In some textbooks, a distinction is made between a ratio, which is assumed to have a common unit for both quantities, and a rate, which is defined to be a quotient of two quantities with different units (e.g. a ratio of the number of miles to the number of hours).

  • Running at a Constant Speed: Students are asked apply knowledge of ratios to answer several questions regarding speed, distance and time.

  • Ratio - Make Some Chocolate Crispies: In this activity students calculate the ratio of chocolate to cereal when making a cake. Students then use that ratio to calculate to amount of chocolate and cereal necessary to make 21 cakes.

  • Lifting a Lion: "Students will work in groups to solve a real-world problem presented by the book: How Do You Lift A Lion? Using a toy lion and a lever, students will discover how much work is needed to raise the toy lion. They will use proportions to determine the force needed to lift a real lion" from TI World Math.

  • Space Math - Comparing Planets Orbiting Other Stars: This NASA lesson utilizes real world data about the size of planets orbiting other stars. Students are asked to use this data to compare the size of the planets to Earth and Jupiter. Lesson includes a visual representation and an answer key.

Student Center Activity
  • 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
  • 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
  • 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
Video/Audio/Animations
  • 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 Manipulative
  • 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.

Worksheets
  • 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.