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Connect ratio and rates to multiplication and division.

General Information

Number: MA.6.A.2

Title: BIG IDEA 2

Type: Big Idea

Subject: X-Mathematics (former standards - 2008) - Archived

Grade: 6

Body of Knowledge: Algebra

Related Benchmarks

This cluster includes the following benchmarks

Code	Description
MA.6.A.2.1:	Use reasoning about multiplication and division to solve ratio and rate problems.
MA.6.A.2.2:	Interpret and compare ratios and rates.

Related Access Points

This cluster includes the following access points.

Independent

Access Point Number	Access Point Title
MA.6.A.2.In.a:	Identify the meaning of common uses of ratio, such as equivalent fractions and mixtures.
MA.6.A.2.In.b:	Identify two meanings of rate: a measure of speed, including miles per hour and words per minute; and a measure of cost, including price per gallon and cost per pound.

Supported

Access Point Number	Access Point Title
MA.6.A.2.Su.a:	Recognize the meaning of a simple ratio, such as 2 to 1.
MA.6.A.2.Su.b:	Identify one meaning of rate, including how fast something moves or happens.

Participatory

Access Point Number	Access Point Title
MA.6.A.2.Pa.a:	Recognize differences in quantity in two sets of objects to 6.
MA.6.A.2.Pa.b:	Recognize changes in rates of movement (fast and slow).

Related Resources

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

Lesson Plans

Name	Description
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.
For Students by Students:	Students are presented with the task of evaluating several types of fabric based on each of its characteristics. They need to analyze their current uniform needs and decide by choosing which type of fabric will best fit their uniform needs. Then they have to write a report explaining the procedure they used to analyze their choices, reasoning for their ranking and make the requested recommendations. 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.
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

Perspectives Video: Professional/Enthusiast

Name	Description
Gear Heads and Gear Ratios:	<p>Have a need for speed? Get out your spreadsheet! Race car drivers use algebraic formulas and spreadsheets to optimize car performance.</p>

Problem-Solving Tasks

Name	Description
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.
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.

Teaching Ideas

Name	Description
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.

Virtual Manipulative

Name	Description
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.

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.

Parent Resources

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

Problem-Solving Task

Title	Description
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.

Big Idea 2 : BIG IDEA 2 (Archived)