6.RP.1 - About the Math, Learning Targets, and Increasing Rigor
Grade 5 AGL Ratio and Proportion
6.RP.1
Full Standard
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.”
Learning Targets (I can)
- Describe ratios as relating parts to a whole.
- Describe ratios as relating parts to parts.
- Identify part-to-part ratios when the parts being compared do not comprise the whole (3 squares, 2 triangles, and 4 circles has a part-to-part ratio of 3:2, 2:4, etc as one shape is discounted in the comparison).
- Represent ratios using tape diagrams, double number lines, and ratio tables.
- Solve problems involving ratios.
About the Math
Ratios and proportional relationships are foundational for further study in mathematics and science and useful in everyday life. Students use ratios in geometry and in algebra when they study similar figures and slopes of lines, and later when they study sine, cosine, tangent, and other trigonometric ratios in high school. Students use ratios when they work with situations involving constant rates of change, and later in calculus when they work with average and instantaneous rates of change of functions. (Progressions of the Common Core State Standards Links to an external site., Common Core Standards Writing Team, 2011)
A ratio is a number that relates two quantities or measure within a given situation in a multiplicative relationship. Ratios can express comparisons of a part to a whole, for example, the number of boys in the class to the entire class. A ratio can also relate one part of a whole to another part of the whole, for example, if we were to compare the number of boys to the number of girls within a class. These ratios compare two measure of the same type of thing. A ratio can also be a rate. When a ratio is a rate, it is a special type in in which two different quantities or things are compared. Common rates include miles per gallon and wages per hour. Often times a unit rate is given that shows the measurement of one unit. For example, tickets to the show are $12 per person. How much will a family of four cost to go to the show? The unit rate is $12 to 1 and the multiplier is 4. It is important that students see many contexts for applying their understanding of ratios.
The following mathematical connections link ratios and fractions:
- Ratios are often expressed in fraction notation, although ratios and fractions do not have identical meaning.
- Ratios are often used to make part-part comparisons, but fractions are not.
- Ratios and fractions can be thought of as overlapping sets.
- Ratios can often be reinterpreted as fractions.
Essential vocabulary for this standard includes: proportion, ratio, and relationship. Visit the online dictionary Links to an external site. or visual math dictionary Links to an external site. for vocabulary support.
Progression of Standard within Grade 6 (5 AGL)
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
| Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
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Progression of this Standard Across Grades
This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.
| Grade 5 | Grade 7 |
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TASKS
These tasks can be used with small group or whole group instruction.
- I have 7 orange balloons. How many more green balloons would have to be added so that the ratio is 1 orange balloon for 2 green balloons? Explain your thinking.
- Create 2 pictures or situations showing the ratio of 5/8.
- In the cafeteria, 100 milk cartons were put out for breakfast. At the end of breakfast, 27 remained. What is the ratio of milk cartons taken to total milk cartons? What is the ratio of milk cartons remaining to milk cartons taken?
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
Module 8 • Ratio And Proportion
Describe Ratios and Use Ratios to Solve Problems:
Additional Tasks
These links provide instructional ideas connected to this standard. [NOTE: NCTM membership required for access to Illuminations lessons.]
- Games at Recess Links to an external site.(Illustrative Math)
- Lesson 2.1 -Introducing Ratios and Ratio Language Links to an external site. - (Illustrative Math)
- Lesson 2.2 - Representing Ratios with a Diagram - Links to an external site. (Illustrative Math)
- Lesson 2.3 - Recipes Links to an external site. - (Illustrative Math)
- Lesson 2.4 - Color Mixtures Links to an external site.( Illustrative Math)
- Lesson 2.5 - Defining Equivalent Ratios Links to an external site. (Illustrative Math)
- Which Cup is Lighter Download Which Cup is Lighter (Lesson Collection)
- Ratio Relationships Download Ratio Relationships (Lesson Collection)
- The Golden Ratio Links to an external site. (NCTM Illuminations Lesson)
- Defining and Writing Ratios Links to an external site. (MSDE Lesson Plan)
- Unit Rate Links to an external site. (MSDE Lesson Seed)
- Ratio Concepts and Reasoning Links to an external site. (MSDE Full Unit)
- Bad Date Links to an external site. (Math Snacks video clip)
Tasks From Print Resources
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
| Book Thumbnail | Book Title | Grade | Pages |
|---|---|---|---|
| Teaching Student-Centered Mathematics | 3-5 | Birthday Cupcakes, Activity 11.1, Page 200 Which Has More, Activity 11.2, Page 202 |
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Hands-On Standards Common Core
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6 | 8-11 (Lesson 1) 12-15 (Lesson 2) |
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Groundworks: Algebraic Thinking |
5 | 24-31 (In the Drawer) |
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Centers
These print resources can be used during independent or center time. These resources could also be used as lesson seeds.
INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.
- Writing Ratios Links to an external site.
- Writing Ratios a Links to an external site.
- Writing Ratios b Links to an external site.
- Writing Ratios c Links to an external site.
- Write and Reason About Part-to-Part Ratios Links to an external site.
- Write Part-to-Part and Part-to-Whole Ratios Links to an external site.
- Write Part-to-Part and Part-to-Whole Ratios_2 Links to an external site.
- Solve Problems Involving Ratios Links to an external site.
- Solve Problems Involving Ratios_2 Links to an external site.
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Learning Targets
- Describe ratios as relating parts to a whole.
- Describe ratios as relating parts to parts.
- Identify part-to-part ratios when the parts being compared do not comprise the whole (3 squares, 2 triangles, and 4 circles has a part-to-part ratio of 3:2, 2:4, etc as one shape is discounted in the comparison)
- Represent ratios using tape diagrams, double number lines, and ratio tables.
- Solve problems involving ratios.
Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading.
Rubric for Tasks Links to an external site.
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Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.