MA.6.A.2.1Archived Standard

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Use reasoning about multiplication and division to solve ratio and rate problems.

Remarks

Example: Four items cost $5.00 and all items are the same price. Explain how to find the cost for 9 items.
General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 6
Body of Knowledge: Algebra
Idea: Level 3: Strategic Thinking & Complex Reasoning
Big Idea: BIG IDEA 2 - Connect ratio and rates to multiplication and division.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 3: Strategic Thinking & Complex Reasoning - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC , GR item(s)

  • Clarification :
    Students will find solutions to real-world and mathematical ratio and/or rate problems.
  • Content Limits :
    Rates involving money should be limited to the nearest cent.

    Ratios may be presented in words or symbols (e.g., 2 to 3, 2:3, 2 out of 3, or 2/3).
  • Stimulus Attributes :
    Items should be set in a real-world or mathematical context.

    Stimuli in GR items must indicate the place value to which answers should be rounded.

    Graphics can be used in some items, as appropriate.
  • Response Attributes :
    Answers in items involving real-world situations may require students to round answers depending on the context of the item.
Sample Test Items (2)
  • Test Item #: Sample Item 1
  • Question: Karla and Becky were practicing free throws. Karla attempted 24 free throws and was successful 8 times. Becky attempted 20 free throws and was successful 5 times. At these rates, how many more successful free throws would Karla make than Becky if they each attempted 180 free throws?
  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 2
  • Question: Marissa drove 770 miles in two days to visit her friend. On the first day, she drove 8 hours at an average speed of 55 miles per hour. She continued to drive at the same rate on the second day. How many hours did Marissa drive the second day?
  • Difficulty: N/A
  • Type: GR: Gridded-Response

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

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

Lesson Plans

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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

Type: Lesson Plan

Teaching Idea

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.

Type: Teaching Idea

Worksheet

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.

Type: Worksheet

STEM Lessons - Model Eliciting Activity

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

Student Resources

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

Parent Resources

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