2016-2017 Curriculum Blueprint
Grade: 6
Course: Grade 6 Advanced
Approximate Time:
6 days
Module 6: Representing Ratios and Rates
Learning Goal
The student is expected to understand the
concept of ratio and use ratio language to
describe a ratio relationship between two
quantities. The student is also expected to use
ratio and rate reasoning to solve real-world and
mathematical problems and understand the
concept of unit rate.
Essential Questions
Unit Overview
How do you use ratios to compare two quantities?
How do you use rates to compare quantities?
How can you use ratios and rates to make comparisons
and predictions?
4. How can you use ratios and rates to solve real-world
problems?
Students will develop understanding of ratios and proportional
relationships. They will compare quantities using rates and unit
rates. Students will convert units within a measurement system,
and develop understanding of relationship between fractions,
decimals, and percent.
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2.
3.
Vertical Progression
MAFS.5.NF.2.5, MAFS.OA.2.3: In Grade 5, students can interpreted multiplication as scaling, generated two numerical patterns using two given rules, identified apparent relationships
between corresponding terms, formed ordered pairs consisting of corresponding terms from the two patterns, and graphed the ordered pairs on a coordinate plane.
MAFS.7.RP.1.2, MAFS.7.RP.1.3, MAFS.7.RP.1.1: In Grade 7, students will recognize and represent proportional relationships between quantities, use proportional relationships to
solve multi-step ratio and percent problems, and compute unit rates associated with ratios of fractions, including rations of lengths, areas and other quantities measured in like or different
units.
Module Focus Standards
Module Topics
Essential Vocabulary
Grade 6 Math Test Item Specs (Reference Sheet at End)
MAFS.6.RP.1.1: (DOK 2) 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.” [conceptual]
 Write ration notation a:b, a to b, a/b
 Know order matters when writing a ratio
 Know ratios can be simplified
 Know ratios compare two quantities; the quantities do not have to be the
same unit of measure
 Recognize that ratios appear in a variety of different contexts; part-towhole, part-to-part, and rates
 Generalize that all ratios relate two quantities or measures within a given
situation in a multiplicative relationship
 Analyze your context to determine which type of ratio is represented
Grade 6 Flipbook
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MAFS.6.RP.1.2: (DOK 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
Ratios (6.RP.1.1, 6.RP.1.3, 6.RP.1.3a, )
Core Resource:
 Lesson 6.1 (HMH book)
 Illuminations: The Ratio of Circumference to
Diameter
Additional Resource:
 CPALMS Video/Activity: Atlantean Dodgeball
 Learn Zillion: Understand Ratios and Ratio
Language
 Engage NY: Module 1 Lesson 1
 Engage NY: Module 1 Lesson 2
 Engage NY: Module 1 Lesson 3 (Tape
Diagrams)
 Engage NY: Module 1 Lesson 4
Formative Assessments:
 HMH: Online Quiz Lesson 6.1
Equivalent ratios
Rate
Ratio
Unit Rate
Higher Order Question Stems
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How would you represent _____________?
What evidence will support your solution?
What mathematical terms or symbols
should be used in this situation?
2016-2017 Curriculum Blueprint
Grade: 6
Course: Grade 6 Advanced
Approximate Time:
6 days
Module 6: Representing Ratios and Rates
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.” [conceptual]
 Identify and calculate a unit rate.
 Use appropriate math terminology as related to rate.
 Analyze the relationship between a ratio a:b and a unit rate a/b where
b ≠ 0.
MAFS.6.RP.1.3: (DOK 2) 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.
a. 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. Conceptual, application]
b. 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? [application]
e. Understand the concept of Pi as the ratio of the circumference of a circle to
its diameter. [conceptual, application]
 Make a table of equivalent rations using while numbers
 Find the missing values in a table of equivalent ratios
 Plot pairs of values that represent equivalent ratios on the coordinate plane
 Use tables to compare proportional quantities. Apply the concept of unit
rate to solve real-world problems involving constant speed
 Apply the concept of unit rate to solve real-world problems involving unit
pricing.
 Apply the concept of unit rate to solve real-world problems involving
constant speed.
 Solve real-world and mathematical problems involving ratio and rate.
 Understand the concept of Pi as the ratio of the circumference of a circle to
its diameter.
Mathematical Practices
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.3.1 : Construct viable arguments and critique the reasoning of
others.
MAFS.K12.MP.4.1: Model with mathematics.
MAFS.K12.MP.6.1: Attend to precision.
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Engage NY: Module 1 Lessons 1-4 Exit
Tickets (Copy-ready Materials)
CPALMS: Writing Ratios
CPALMS: Interpreting Ratios
Writing Connections
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Rates (6.RP.1.2, 6.RP.1.3, 6.RP.1.3b)
Core Resource:
 Lesson 6.2 (HMH book)
Additional Resource:
 Engage NY: Module 1 Lesson 16
 Learn Zillion: Understand Unit Rates
 Engage NY: Module 1 Lesson 20
 Illustrative Math: Riding at Constant Speed
 Illustrative Math: Price per pound and
pound per dollar.
Formative Assessments:
 HMH: Online Quiz Lesson 6.2
 CPALMS: Bargain Breakfast
 CPALMS: Comparing Rates
Using Ratios and Rates to Solve Problems
(6.RP.1.3, 6.RP.1.3a)
Core Resource:
 Lesson 6.3 (HMH book)
Additional Resource:
 Engage NY: Module 1 Lesson 5
 Engage NY: Module 1 Lesson 6
 Illustrative Math: Hippos Love Pumpkins
Formative Assessments:
 MARS: Maximizing Profit: Selling Soup
 HMH: Online Quiz Lesson 6.3
 HMH: Module 3 Quiz (Student Workbook)
 HMH: Module 3 Leveled Quizzes
(Assessment Resource Book)
Write to explain your visual representation.
Construct a viable argument supporting
your solution and solution pathway.
Write a precise explanation of your
reasoning.
Link to Webb’s DOK Guide
2016-2017 Curriculum Blueprint
Grade: 6
Course: Grade 6 Advanced
Approximate Time:
6 days
Module 6: Representing Ratios and Rates