Unit _5
Ratio and Proportion
Mathematics
Grade 6
School Year: 2013-14
Unit Duration: Six Weeks
Domains—Students
Ratio and Proportional Relationships (6.RP.1.2.3)
Expressions and Equations (6.EE.9)
 Understand ratio concepts and use ratio
 Represent and analyze quantitative
reasoning to solve problems.
relationships between dependent and
independent variables.
Standards for Mathematical Practice
 Make sense of problems and persevere in solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in repeated reasoning.
Overview/Rationale
Grade 6 will end with unit 5, Ratio and Proportions. This important sixth grade unit comes at the end of the year
since the content will have a great amount of influence on one of the major topics in grade 7, analyzing
proportional relationships.
Standard(s)
(6.RP.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.”
(6.RP.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 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.”
(6.RP.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.
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.
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?
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the
quantity); solve problems involving finding the whole, given a part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when
multiplying or dividing quantities.
(6.EE.9)— Use variables to represent two quantities in a real-world problem that change in relationship to one
another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other
quantity, thought of as the independent variable. Analyze the relationship between the dependent and
independent variables using graphs and tables, and relate these to the equation. For example, in a problem
involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d
= 65t to represent the relationship between distance and time.
Interdisciplinary Standard(s)
Technology Standard(s)
8.1.A
Common Core Science Grade 6-Grade8
The use of technology and digital tools requires
knowledge and appropriate use of operations and
Common Core History & Social Issues Grade 6-8
related applications.
4.A.1: Demonstrate effective input of text and data
Common Core Reading Informational Text
using an input device.
4.A.2: Create a document with text formatting and
graphics using a word processing program.
4.A.3: Create and present a multimedia presentation
that includes graphics.
4.A.4: Create a simple spreadsheet, enter data, and
interpret the information.
4.A.5: Determine the benefits of a wide range of
digital tools by using them to solve problems.
Technology Common Core Standards
Essential Question(s)
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If we didn’t have variables, what would we use?
What purposes do variable expressions serve?
What are some advantages to being able to describe a pattern using variables?
Why does the order of operations exist?
What other task/processes require the use of a strict order of steps?
How many parts does a number have?
What is the best way to compare amounts or sizes?
Why is it useful to know how to combine and separate parts of numbers?
How do you apply finding factors and multiples to real life?
Why do we need different ways to say the same thing?
When is it appropriate to use estimates and when should you compute exactly?
What is a real-world situation that can be modeled using positive and negative rational numbers?
What is the absolute value of a number and when do we use it?
How does the number line extend in order to incorporate negative numbers?
How does the coordinate plane extend in order to incorporate negative numbers?
How do you know which quadrant a coordinate pair will be in?
How do you decide which of two numbers is greater when both numbers are positive? Both are
negative? One number is positive and one number is negative?
Why is being able to convert rational numbers between fractions, decimals and percents important
Why is it important to be able to relate absolute value inequalities to real world situations?
Why is it useful for me to know the absolute value of a number?
What are opposites and how are they shown on a number line?
How do I compare and order integers?
What are opposites and what characteristics do they have on the number line?
How are opposites and absolute value related?
How can I use models to prove that opposites combine to 0?
What real life situations combine to make 0?
How are the characteristics of a polygon different from other shapes?
How do we use polygon shapes in the real world?
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How can a frequency table be used to determine the number of outcomes of given event?
How can a line plot be used to determine the number of outcomes of a given event?
How does using a frequency table or line plot make understanding the data easier to understand?
Enduring Understandings
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Algebraic expressions can be used to generalize properties of arithmetic.
Variables can be used as unique unknown values or as quantities that vary.
Algebraic expressions may be used to represent and generalize mathematical problems and real life
situations.
Use values from specified sets to make an equation or inequality true.
Develop an initial conceptual understanding of different uses of variables.
Graphs can be used to represent all of the possible solutions to a given situation.
Many problems encountered in everyday life can be solved using proportions, equations or inequalities.
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In this unit plan, the following 21st Century themes and skills are addressed.
Check all that apply.
21 s t Century Themes
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Global Awareness
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21 s t Century Skills
A
Creativity and Innovation
Environmental Literacy
T
Critical Thinking and Problem Solving
Health Literacy
E
Communication
E
Collaboration
Civic Literacy
Financial, Economic, Business, and
Entrepreneurial Literacy
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Student Learning Targets/Objectives/SLOs
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Indicate whether these skills are E-Encouraged, T-Taught, or AAssessed in this unit by marking E, T, A on the line before the
appropriate skill.
Explain the relationship of two quantities or measures of a given ratio and use ratio language to
describe the relationship between the 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.”
Use rate language in the context of a ratio relationship to describe a unit rate a/b associated with a
ratio a:b with b≠0. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of 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.”
Use ratio and rate reasoning to solve real world and mathematical problems which include making
tables of equivalent ratios, solving unit rate problems, finding percent of a quantity as a rate per 100.
Use ratio and rate reasoning to convert measurement units (manipulate and transform units
appropriately when multiplying or dividing quantities).
Use variables to represent two quantities that change in relationship to one another in a real world
problem and write an equation to express one quantity, thought of as the dependent variable, in terms
of another quantity, thought of as the independent variable.
Analyze the relationship between the dependent and independent variables in an equation using
graphs and tables. For example, in a problem involving motion at constant speed, list and graph
ordered pairs of distances and times, and write the equation d = 65t to represent the relationship
between distance and time.
Assessments
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NWEA--Diagnostic
Exit Tickets, Do Nows, skill check list, --Formative (Monitor student progress)
Model Curriculum Unit Testing, Unit Project, Extended Response Questions—Summative
(evaluate student learning)
Authentic Tasks, Math Notebook, Other Evidence
Interactive Assessment Practice
CMP2 Testing Activities Grade 6
Instructor Code: amk-5500
Student Code: amk-0099
Grade 6 Math Skill Practice
Interactive math skill builders - Sixth grade at I4C
6th Grade Math Test Skills Practice
Portfolio
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Authentic Tasks
Extended Response Questions
Short Response Questions
DOL Samples
Enrichment
Test Box
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Unit Tests
Quiz Samples
NWEA Data
SAMS Data
Differentiated Activities
Bit & Pieces I: Pg. 52 #53
Bits & Pieces I: Pg. 67 #41-- #43
Shapes & Designs: ACE #29-35
How Likely is it?: Pg. 19 #32; Pg. 36 #35; Pg. 53 #33- #35; Pg. 67 #24.
Covering & Surrounding: Pg. 31 #18.
Data About Us: Pg. 43 #11
Value Student Backgrounds to Improve Performance
Be aware of and draw from your ELL students' prior knowledge. You should:
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Make sure ELL students know that their experiences and culture are
valued. This will help their attitudes and increase their motivation.
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Focus on meaning. When your ELL students share answers and present
ideas, remember to focus on the meaning they are conveying, not on their
grammar and usage.
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Be flexible with student use of native language. You may want to have
the ELL student record answers or solution steps in their own native
language. You can have their work translated, if desired. This will help
ELL students focus on the concepts and reasoning involved, without
being slowed or hindered by their developing language skills.
Readings:
ELL
Helping English Language Learners in the Classroom
Intervention
Instructional Strategies
Activities/Experiences
Key Terms
Readings
US Department of Education--Intervention--What Works!
Strategies to help struggling students
Teaching and Learning Actions
Compare & Contrast: Venn diagrams, Number line placement, plot and graph
comparison
Note Taking: Student organized notebook by unit.
Reinforcing Effort & Providing Feedback: Using rubrics to guide student work;
display student work with relevant comments.
Homework & Practice: Focus practice on difficult concepts; Homework is an
extension of class work. Word problems that require student to choose the
correct strategy.
Setting objectives & Providing Feedback: Specific objective and DOL for each
lesson; Rubrics comparison as feedback. (Given a word problem, the student will
be able to complete the division algorithm to find the solution)
Generating & Testing Hypotheses: Using a general rule to make a prediction.
(Rounding to add/subtract/multiply/divide decimals)
Cues, Questions, Advance Organizers: Use of lists, tables to collect data, the
efficient use of an algorithm.
Rate Ratio Lesson: Illuminations
Feeding Frenzy Activity: Illuminations
Interactivate: Cartesian Coordinate System
(For More Activities--Connect to TE Resource Wiki)
Resources
Content Vocabulary
Percent
Proportion
Rate
Ratio
Rational number
Tape diagram (bar models, strip
diagrams, Singapore Strip)
Unit Ratio
Quantity
Academic Vocabulary
Compose
Decompose
Context
evaluate
Visual
Relationship
Interpret
Value
Verbal model
Numerical data sets
observations
Progression through the Grades
University of Arizona Progression documents to support the Common Core
Kansas Assoc. of Teacher of Mathematics--Flip Books
“Flip Books” are intended to help teachers understand what each standard
means in terms of what students must know and be able to do. It provides only a
sample of instructional strategies and examples. The “Flip Books” support a
teacher’s goal to guide students in understanding and making sense of
mathematics.
Supporting Text
Connected Math 2
Supplemental Materials
Video/Presentation Links
Teacher Resource Links
Student Resource Links
6.RP.1: Bits & Pieces I. Inv. 4.
Working with Percents;
6.RP.2: CC Transition Kit. Inv. I.
Ratios and Rates
6.RP.3: Bits & Pieces I: Inv. 3.
Moving Between Fractions and
Decimals; Inv. 4. Working with
Percents.
Shapes & Designs: Inv. 2. ACE 29-35
How Likely Is it?: Inv. 1. A First Look
at Chance; Inv. 2. Experimental and
Theoretical Probability, Inv. 3. Making
Decisions with Probability; Inv. 4.
Probability, Genetics, and Games.
6.EE.9: Covering & Surrounding. Inv.
2. Changing Area, Changing Perimeter;
Data About Us. Inv. 2. Using Graphs to
Explore Data; CC Transition Kit. Inv.
2. Number Properties and Algebraic
Equations.
Ready Common Core Math 6—Student Workbook
Lesson 1: Ratios
Lesson 2: Understand Unit Rate
Lesson 3: Equivalent Ratios
Lesson 4: Solve Problems with Unit Rate
Lesson 5: Solve Problems with Percents
Lesson 21: Dependent and Independent Variables
Math Connects, Course 1: Problem-Solving Practice Homework Book
http://www.mathplayground.com/mathvideos.html
http://math.pppst.com/
Translate ratios into rates - for teachers | LearnZillion
Creating and graphing equations in two or more variables | LearnZillion
Plotting x.y Relationships: Khan Academy
Rates & Ratios: Khan Academy
(Connect to TE Resource Wiki)
CMP2 Transition Kit
Pearson Transition Kit Grade 6
Connected Math Online:
http://www.phschool.com/cmp2/
Master Codes: CMP2 Student Grade 6: amk 0099 Teacher: amk 5500
Sadlier-Oxford Online Practice & Activities
Rate Ratio Worksheets: Math-Aids
Worksheets: Softschools
Thinking Blocks - Model and Solve Math Word Problems
Quantitles Grade 6 Database
(For More Resources Connect to TE Resource Wiki)
Rate Ratio Proportional Practice: Internet4Classrooms
Interactivate: General Coordinates Game
Submitted by: ____________________________________
Date:
Curriculum and Instruction Administration:
Approved
Date: March 11, 2014
Board of Education:
Approved
Date: March 25, 2014