Unit 1: Ratios and Proportional Relationships (6.RP)

Unit 1: Ratios and Proportional Relationships (6.RP)

Big Ideas:

Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems: Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates. (CCSC Grade 6 p. 39) Overview (Big Ideas), Enduring Understandings, Essential Questions, Common Misconceptions:

HCPSS Curriculum Framework Grade 6 Unit 1.docx

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Common Core Content Standards:

Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.A.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."

HCPSS UDL Lessons: Which cup has a lighter color?

6.RP.1 Which cup has a lighter color, conceptual reasoning.doc

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6.RP.1 UDL Checklist Which Cup.docx

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Ratio Relationships

6.RP.1 Lesson Ratio Relationships.doc

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6.RP.1 UDL Checklist Ratio Relationships.docx

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PARCC Assessment Limit/Clarification: This standard is part of the major content cluster assessed on PARCC. Students' prior understanding of an skill with multiplication, division, and fractions contribute to their study of ratios, proportional relationships and unit rates.

PARCC/UTA Dana Center Prototype Assessment Item: "Inches and Centimeters" (6.RP.1, 6.EE.9, MP 2)

Web Resources: NCTM Illuminations Lesson: Students learn about ratios, including the "Golden Ratio", a ratio of length to width that can be found in art, architecture, and nature. Students examine different ratios to determine whether the Golden Ratio can be found in the human body.

NCTM Illuminations Lesson: By using sampling from a large collection of beans, students get a sense of equivalent fractions which leads to a better understanding of ratios and proportions.

Lesson: This site provides lesson activities involving a number line to help students understand equivalencies among rational numbers.

Task: Games at Recess. Students write sentences to compare the number of boys and girls playing different games at recess.



Task: Ratio of Boys to Girls. Students analyze a part-whole relationship and build connections between fractions and ratios. Tape diagrams are illustrated as a solution strategy.

Task: Voting for Two, Variation 1. Students analyze a part-part relationship to determine how many votes each candidate received for class president. Ratio tables are illustrated as a solution strategy.

Task: Voting for Two, Variation 2. Students extend their thinking from Voting for Two, Variation 1.

Task: Voting for Two, Variation 3. Students extend their thinking from Voting for Two, Variation 1 and 2 by exploring part-whole relationships as well.

Text Resources For Lessons/Tasks: Lobato, J.E., Ellis, A.B, Charles, R.I., & Zbiek, R.M. (2010). Developing Essential Understanding of Ratios, Proportions, & Proportional Reasoning for Teaching Mathematics in Grades 6-8. Reston, VA: National Council of Teachers of Mathematics. p. 20.

"Reflect 1.3" Task p. 20: In this task students determine various ways to mix blue and yellow paint to make the same shade of green paint.

"Figure 1.14" Task p. 22: Students analyze the ratio of orange concentrate to water in orange juice.

"Reflect 1.4" Task p. 29: Students interpret the rate at which water is being pumped into a swimming pool.

"Clown and Frog: Task p. 79: Students compare the various speeds of Clown and Frog.

Van de Walle, J.A., & Lovin, L.H. (2006). "Chapter 18: Proportional Reasoning." Teaching StudentCentered Mathematics. Boston: Pearson. p. 248-268.

NCTM Journal Article Lesson Ideas/Resources: Billings, E.M.H. (2002). Cocoa: Teaching Notes. Making Sense of Fractions, Ratios, and Proportions: 2002 Yearbook of the NCTM. p. 38-40. [Potential math task: Cocoa Reasoning Problem]

Langrall, Cynthia. (December 2000). "Three Balloons for Two Dollars: Developing Proportional Reasoning." Mathematics Teaching in the Middle School. Vol. 6. No. 4. p. 254-261.

6.RP.A.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 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 a 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."

HCPSS UDL Lesson: Gas Mileage

6.RP2&3b Gas Mileage.doc

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6.RP.2&3b UDL Checklist Gas Mileage.docx

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PARCC Assessment Limit/Clarification: This standard is part of the major content cluster assessed on PARCC. Students' prior understanding of an skill with multiplication, division, and fractions contribute to their study of ratios, proportional relationships and unit rates.

Web Resources: NCTM Illuminations Lesson: Students experiment to find out how many jumping jacks, how many times you can sing ABCs, or hop on one foot in one minute and then use that rate to figure out how many of each of those you can do in 60 minutes (or some other time amount).

NCTM Illuminations Lesson: Students use real-world models to develop an understanding of fractions, decimals, unit rates, proportions, and problem-solving.

Task: Mangos for Sale. Students explore whether a given situation may be represented by more than one ratio.

Task: Price per Pound and Pounds per Dollar. Students develop the concept of unit rate and explore it in a grocery store setting. Ratio tables are illustrated as a solution strategy.

6.RP.A.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.

3a. 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.

HCPSS Math Tasks: World Series of Pop Culture

6.RP.3a Task World Series of Pop Culture.doc

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Grocery Store Gas Points

6.RP.3 Task Grocery Store Gas Points.doc

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HCPSS Disciplinary Literacy Lesson Seed: Pencils

6.RP.3a Disc Lit Lesson Seed Pencils.docx

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PARCC Assessment Limit/Clarification: This standard is part of the major content cluster assessed on PARCC. Students' prior understanding of an skill with multiplication, division, and fractions contribute to their study of ratios, proportional relationships and unit rates. When students work toward meeting standard 6.RP.A.3, they use a range of reasoning and representations to analyze proportional relationships. Web Resources: PowerPoint Presentation on Tape Diagrams & Double Number Line Graphs, designed by Dr. Tad Wattanabe (former Towson University professor). NCTM Illuminations Lesson: Students measure the heights and shadows of familiar objects and use indirect measurement to find the heights of things that are much bigger in size, such as a flagpole, a school building or a tree.

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