Draft Unit Plan
6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
Overview:
The overview statement is intended to provide a summary of major themes in this unit.
This is the first time that students have formally studied ratio and proportion. The study of ratios and proportional reasoning extends
students’’ work in measurement and multiplication and division in elementary grades. Ratios and proportional reasoning are the foundation
for further study in mathematics, science and are useful in everyday life. Students will be working with ratios, rates, unit rates and percents
to solve situations in daily life.
Teacher Notes:
The information in this component provides additional insights which will help the educator in the planning process for the
unit.
x Ratios are used in geometry and in algebra when students study similar figures.
x The term ratio is used when units are the same and the term rate is used when units are different in the ratio. The CCSS uses ratio to
encompass both situations.
x The goal in sixth grade is to study ratios while leaving proportional studies for grade seven.
Enduring Understandings:
Enduring understandings go beyond discrete facts or skills. They focus on larger concepts, principles, or
processes. They are transferable and apply to new situations within or beyond the subject.
At the completion of the unit on ratio concepts, the student will understand that:
x
x
A ratio is a multiplicative comparison of two quantities.
A rate is a special ratio with a denominator of one that compares different types of measures.
Essential Question(s):
A questions is essential when it stimulates multi-layered inquiry, provokes deep thought and lively discussion,
requires students to consider alternatives and justify their reasoning, encourages re-thinking of big ideas, makes meaningful connections
with prior learning, and provides students with opportunities to apply problem-solving skills to authentic situations.
x
x
x
Is it important to know how to solve for unit rates?
What is the connection between a ratio and a fraction?
How are ratios used in the real world?
x How is a ratio or rate used to compare two quantities or values?
x Where can examples of ratios and rates be found?
x How can I model and represent rates and ratios?
x What are similarities and differences between fractions and ratios?
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
Priority Clusters in Grade 6:
According to the Partnership for the Assessment of Readiness for College and Careers (PARCC), some clusters require greater emphasis
than others. The table below shows PARCC’s relative emphasis for each cluster. Prioritization does not imply neglect or exclusion of
material. Clear priorities are intended to ensure that the relative importance of content is properly attended to. Note that the prioritization is
in terms of cluster headings.
Key:
Ŷ Major Clusters
† Supporting Clusters
 Additional Clusters
Ratios and Proportional Reasoning
ŶUnderstand ratio concepts and use ratio reasoning to solve problems.
The Number System
Ŷ

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
Compute fluently with multi-digit numbers and find common factors and multiples.
Ŷ
Apply and extend previous understandings of numbers to the system of rational numbers.
Expressions and Equations
Ŷ
Ŷ
Ŷ
Apply and extend previous understandings of arithmetic to algebraic expressions.
Reason about and solve one-variable equations and inequalities.
Represent and analyze quantitative relationships between dependent and independent variables.
Geometry
† Solve real-world and mathematical problems involving area, surface area, and volume.
Statistics and Probability
 Develop understanding of statistical variability.
 Summarize and describe distributions.
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
Focus Standards
(Listed as Examples of Opportunities for In-Depth Focus in the PARCC Content Framework document):
According to the Partnership for the Assessment of Readiness for College and Careers (PARCC), this component highlights some individual
standards that play an important role in the content of this unit. Educators may choose to give the indicated mathematics an especially indepth treatment, as measured for example by the number of days; the quality of classroom activities for exploration and reasoning; the
amount of student practice; and the rigor of expectations for depth of understanding or mastery of skills.
6.RP.3 When students work toward meeting this standard, they use a range of reasoning and representations to analyze proportional
relationships.
Possible Student Outcomes:
The following list provides outcomes that describe the knowledge and skills that students should understand and be able to do when the unit
is completed. The outcomes are often components of more broadly-worded standards and sometimes address knowledge and skills
necessarily related to the standards. The lists of outcomes are not exhaustive, and the outcomes should not supplant the standards
themselves. Rather, they are designed to help teachers delve deeply into the standards and augment as necessary, providing added focus
and clarity for lesson planning purposes. This list is not intended to imply any particular scope or sequence.
The student will be able to:
x
x
Use ratios, rates and percent in a wide variety of contexts.
Use tables, graphs, tape diagrams and double number line diagrams to represent equivalent ratios.
Progressions from Common Core State Standards in Mathematics:
For an in-depth discussion of the overarching, “big
picture” perspective on student learning of content related to this unit, see:
The Common Core Standards Writing Team (10 September 2011). Progressions for the Common Core State Standards in Mathematics
(draft), accessed at: http://commoncoretools.files.wordpress.com/2011/09/ccss_progression_rp_67_2011_11_121.pdf
Vertical Curriculum Alignment:
x
x
Vertical curriculum alignment provides two pieces of information:
A description of prior learning that should support the learning of the concepts in this unit
A description of how the concepts studied in this unit will support the learning of additional mathematics
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
x
Key Advances from Previous Grades: Between grade 5 and grade 6, students grow in their ability to analyze ratios, rates, unit rates
and percents. Students use their knowledge of decimals and fractions to:
o
o
o
x
apply their skills with multiplication, division, and fractions to contribute to their study of ratios and unit rates (6.RP).
extend their work in measurement and in multiplication and division
work with percents
Additional Mathematics: Students will use ratios, rates, unit rates and percent skills:
o
o
in grade 7 when working with proportional relationships and probability
in geometry and in algebra when studying similar figures and slopes of lines
Possible Organization of Unit Standards: This table identifies additional grade-level standards within a given cluster that support the
over-arching unit standards from within the same cluster. The table also provides instructional connections to grade-level standards from
outside the cluster.
Overarching Unit Standards
Supporting Standards within the
Cluster
Instructional Connections outside
the Cluster
6.RP.1:
Understand the concept of a ratio and
use ratio language to describe
a ratio relationship between two
quantities.
6.RP.2: Understand the concept of a
unit rate ܽȀ„ associated with a ratio a:b
with b  0 (b not equal to zero), and use
rate language in the context of a ratio
relationship.
6.RP.3: Use ratio and rate reasoning to 6.RP.3a:
6.NS.8:
solve real-world and mathematical
x Make tables of equivalent ratios
x Solve real-world and mathematical
problems, e.g., by reasoning about
relating quantities with wholeproblems by graphing points in all
tables of equivalent ratios, tape
number measurements, find missing
four quadrants of the coordinate
diagrams, double number line diagrams,
values in the tables, and plot the
plane. Include use of coordinates
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
or equations.
pairs of values on the coordinate
plane. Use tables to compare ratios.
6.RP.3b:
x Solve unit rate problems including
those involving unit pricing and
constant speed.
and absolute value to find distances
between points with the same first
coordinate or the same second
coordinate.
6.EE.9:
x 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.
6.RP.3c:
x 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.
6.RP.3d:
x Use ratio reasoning to convert
measurement units; manipulate and
transform units appropriately when
multiplying or dividing quantities.
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
Connections to the Standards for Mathematical Practice:
This section provides samples of how the learning experiences for
this unit support the development of the proficiencies described in the Standards for Mathematical Practice. The statements provided offer a
few examples of connections between the Standards for Mathematical Practice in the content standards of this unit. The list is not
exhaustive and will hopefully prompt further reflection and discussion.
In this unit, educators should consider implementing learning experiences which provide opportunities for students to:
1. Make sense of problems and persevere in solving them.
x Analyze a problem and depict a good way to solve the problem.
x Consider the best way to solve a problem.
x Can interpret the meaning of their answer to a given problem.
2. Reason abstractly and quantitatively
x Consider the ideas that ratios can be represented in more than one way.
x Does your answer connect to the question?
3. Construct Viable Arguments and critique the reasoning of others.
x Justify the process of working with a ratio to answer a question.
x Justify an argument using a table, graph, tape diagram or double line graph.
4. Model with Mathematics
x Draw a diagram that represents ratio.
x Analyze an authentic problem and use a nonverbal representation of the problem.
x Use appropriate manipulatives.
5. Use appropriate tools strategically
x Use virtual media and visual models to explore ratio and rate problems.
6. Attend to precision
x Demonstrate their understanding of the mathematical processes required to solve a problem by communicating all of the steps in
solving the problem.
x Label appropriately.
x Use the correct mathematics vocabulary when discussing problems.
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
7. Look for and make use of structure.
x Look at a table or graph and recognize the relationship that is represented in each.
x Compare, reflect and discuss multiple solution methods.
8. Look for and express regularity in reasoning
x Pay special attention to details and continually evaluate the reasonableness of their answers.
x Use of mathematical principles will help you in solving the problem.
Content Standards with Essential Skills and Clarifications:
The Content Standards and Essential Skills and Knowledge
statements shown in this section come directly from the Maryland State Common Core Curriculum Frameworks. Clarifications were added
as needed. Please note that only the standards or portions of standards that needed further explanation have supporting statements.
Educators should be cautioned against perceiving this as a checklist. All information added is intended to help the reader gain a better
understanding of the standards.
Standard
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.””
Essential Skills and Knowledge
x Knowledge of ratio as a
comparison of any two quantities
•• Knowledge of a ratio is not always
a comparison of part-to-whole; Can
be part-to-part or whole-to-whole
6.RP.2:Understand the
௔
concept of a unit rate ••Knowledge that a unit rate
emphasizes finding an equivalent
ratio with adenominator of 1.
௕
associated with a ratio a:b with b
 0 (b not equal to zero), and
use rate language in the context
Clarification
6.RP.1: ratio: Ratio is a comparison of two quantities or measures.
௔
Ratios can be expressed in the form ( ), a to b, or a:b. Ratios can be
௕
expressed as comparisons of a part to a whole, one part of a whole to
another part of the same whole, or measures of two different types
which is called a rate. Example: Part-to-whole would be the ratio of
boys to the whole class. Part-to-part would be the ratio of boys to girls.
Rate would be the ratio of miles per gallon to miles per hour.
6.RP.2: unit rate: A ratio where the denominator is 1 unit. Example: If
15 bars of soap cost $6.75,one bar would cost $.45.
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
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."
(Expectations for unit rates in
this grade are limited to noncomplex fractions.)
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.
••Knowledge of multiplicative
recursive patterns
•• Ability to use multiplicative
relationships to extend an initial
ratio to equivalent ratios; When
working backward, use the inverse
operation (division).
6.RP.3: tape diagrams: Tape diagrams are linear models used to
represent data and help students organize their thinking. Example:
Casey read 7 more books than Jamie. If Casey read 16 books, how
many books did Jamie read?
Number of books Jamie read
Number of books Casey read
difference
Jamie+7=Casey
Casey––7=Jamie
16––7=9
SoJamieread9books.
6a: Make tables of equivalent
x Ability to recognize a linear
ratios relating quantities
relationship appears when the
with whole-number
pairs are plotted on the coordinate
measurements, find missing
plane
values in the tables, and
plot the pairs of values on
the coordinate plane. Use
tables to compare ratios.
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
6b: 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?
6c: 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.
•• Ability to use division to determine
unit rate
•• Ability to introduce percent as a
special rate where a part is
compared to a whole and the
whole always has a value of 100
6.RP.6c: percent: is another name for hundredths Ratio of a number
to 100 with a percent sign. Per hundred Example: 75% =
•• Ability to solve problems using
equivalent ratios. (NOTE:
Proportions are not introduced until
Grade 7.) This is developing
proportional reasoning without
formal proportions.
6d: Use ratio reasoning to
convert measurement units;
manipulate and transform
units appropriately when
multiplying or dividing
quantities.
•• Ability to expand ratio reasoning to
units of measurement
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
Fluency Expectations/Recommendations:
This section highlights individual standards that set expectations for fluency, or that
otherwise represent culminating masteries. These standards highlight the need to provide sufficient supports and opportunities for practice
to help students meet these expectations. Fluency is not meant to come at the expense of understanding, but is an outcome of a
progression of learning and sufficient thoughtful practice. It is important to provide the conceptual building blocks that develop understanding
in tandem with skill along the way to fluency; the roots of this conceptual understanding often extend one or more grades earlier in the
standards than the grade when fluency is finally expected.
x PARCC has no fluency expectations related to ratio and proportion.
Evidence of Student Learning: The Partnership for Assessment of Readiness for College and Careers (PARCC) has awarded the Dana
Center a grant to develop the information for this component. This information will be provided at a later date. The Dana Center, located at
the University of Texas in Austin, encourages high academic standards in mathematics by working in partnership with local, state, and
national education entities. Educators at the Center collaborate with their partners to help school systems nurture students' intellectual
passions. The Center advocates for every student leaving school prepared for success in postsecondary education and in the contemporary
workplace.
Common Misconceptions: This list includes general misunderstandings and issues that frequently hinder student mastery of concepts
regarding multiplication and division of fractions.
Students may:
x confuse mathematical terms such as ratio, rate, unit rate and percent.
x not understand how to set up a table or graph.
x not understand the difference between an additive relationship and a multiplicative relationship.
Interdisciplinary Connections:
x
x
x
Interdisciplinary connections fall into a number of related categories:
Literacy standards within the Maryland Common Core State Curriculum
Science, Technology, Engineering, and Mathematics standards
Instructional connections to mathematics that will be established by local school systems, and will reflect their specific grade-level
coursework in other content areas, such as English language arts, reading, science, social studies, world languages, physical education,
and fine arts, among others.
x
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
Model Lesson Plan:
MSDE Mathematics Lesson Plan
Content/Grade Level
Background Information
Ratios and Proportional Relationships/Grade 6
Unit
Understand ratio concepts and use ratio reasoning to solve problems.
Essential Questions/Enduring
Understandings Addressed in the
Lesson
Essential Questions
x Is a ratio is a multiplicative comparison of two quantities?
x What is the connection between a ratio and a fraction?
x How are ratios used in the real world?
x How is a ratio or rate used to compare two quantities or values?
Enduring Understandings
x Knowledge of a ratio is not always a comparison of part-to-whole; can be part-to-part or whole-towhole.
x Knowledge of the difference between a ratio and a fraction.
Standards Addressed in This Lesson
6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between
two quantities.
Lesson Topic
Defining and Writing Ratios
Relevance/Connections
Students’ work with ratios and proportional relationships (6.RP) can be combined with their work in
representing quantitative relationships in real world problems that change in relationship to one another
(6.EE.9). Formal use of proportions will be covered in grade 7.
Student Outcomes
Students will:
x
Know three ways to write a ratio, 9:10, 9 to 10,
x
Develop a definition of ratio
ଽ
ଵ଴
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
Prior Knowledge Needed to Support
This Learning
Method for Determining Student
Readiness for the Lesson
x
x
x
Use ratio language to describe a relationship between two quantities
Express ratios as part-to-part relationships
Express ratios as part-to-whole relationships
x
x
Knowledge of a fraction as a part-to-whole relationship.
Knowledge of multiplication and division of fractions.
Use warm-up to determine student understanding of fractional part to whole relationship.
Learning Experience
Component
Warm Up/Drill
See NCTM Ratio, Proportions
& Proportional Reasoning pg.
Details
ସ
1. Which is another way of expressing ?
A.
B.
ଵ
ଵ
ଵ
ଷ ଷ
ଶ ଶ
ଷ
ଷ
ଵ
+ + +
ଷ
+
ଷ ଷ
ଵ
C. 1
Which Standards of Mathematical Practice
does this component address?
x Make sense of problems and persevere
in solving them
x Reason abstractly and quantitatively
x Model with mathematics
x Look for and make use of structure
ଷ
D. All of the above
2. Model answer choice A by shading the fraction bars
below.
3. How would your model look different if you shaded a
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
Learning Experience
Component
Details
Which Standards of Mathematical Practice
does this component address?
model for answer choice B?
4.
What is the value for the shaded part of the fraction bars
above?
5. What are all the possible ways of expressing the model
given in #4?
Motivation
Note to Teacher: Give students a picture of an assortment of
sports balls (see sample below).
x
x
x
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Make sense of problems and persevere in
solving them
Reason abstractly and quantitatively
Model with mathematics
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
Learning Experience
Component
Details
Which Standards of Mathematical Practice
does this component address?
Given the values 5 and 7, discuss how these values are
represented by the balls in the picture.
Activity 1
UDL Components
x Multiple Means of
Representation
x Multiple Means for
Action and Expression
x Multiple Means for
Engagement
Key Questions
Formative Assessment
Summary
Divide class into pairs or small groups; Give each group a
x
scoop of rainbow cubes.
x
x Use the cubes to write fractions that compare each
x
color to the total cubes. (Examples: red to total; blue
to total; etc.; all comparing color/part to total/whole.)
Use labels when writing these fractions. Students
should understand terminology: “part-to-whole.”
x How many red cubes do you have? Have many
yellow cubes do you have? Can we compare red
cubes to yellow cubes by writing a fraction? (Answer:
No, because the denominator of a fraction represents a
whole. This is a part-to-part relationship; one form of
a ratio, which can be written using fraction notation.
In the same way, a fraction (part-to-whole) is also a
ratio.) Students should understand terminology:
“part-to-part.”
x Define ratio (a comparison of two quantities or
measures) & the 3 ways to write it. (Example: 2/3,
2:3, 2 to 3).
x With your partner, continue to write other ratios with
the rainbow cubes. (Students should include part-topart and part-to-whole.)
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Use appropriate tools strategically
Model with mathematics
Construct viable arguments and critique the
reasoning of others
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
Learning Experience
Component
Details
Which Standards of Mathematical Practice
does this component address?
Practice writing ratios, including part-to-part and part-towhole and use of all 3 methods to write a ratio (Example: 2/3,
2:3, 2 to 3). Practice using ratio language. Ask students to
write ratios using objects in the classroom. Sample responses
could include, but are not limited to:
x Males to females
x Chairs to desks (Note: This may be a 1:1
relationship)
Group students and have each student (1) share their ratios
and (2) explain the type of relationship represented in those
ratios. Students should be able to defend their thinking.
Activity 2
UDL Components
x Multiple Means of
Representation
x Multiple Means for
Action and Expression
x Multiple Means for
Engagement
Key Questions
Formative Assessment
Summary
Closure
On a 10-question quiz a student answers 8 questions
correctly. What is the ratio of the number of questions
answered correctly to the total number questions? Allen says
the answer is 10 to 8. Is he correct? Justify your answer.
x
Construct viable arguments and critique the
reasoning of others
x
Make sense of problems and persevere in
solving them: Identify and execute
appropriate strategies to solve the problem.
Use additional scenarios to help students realize the
significance of the order in which ratios are written given a
scenario. Samples may include but are not limited to:
x Wins to losses
x Cost to number of items purchased
Have students work with a partner or in a small group. Give
each group a photograph of something that is of personal
interest, e.g. from National Geographic or any other
magazine. (Ask students to bring in a photo or a poster that
they like.) Ask them to create ratios of comparisons based on
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6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
Learning Experience
Component
Details
Which Standards of Mathematical Practice
does this component address?
objects in the photographs. Identify each ratio as part-to-part
or part-to-whole.
Have groups exchange their photographs and ratios to share
for correctness.
Interventions/Enrichments
x Special Education/Struggling
Learners
x ELL
x Enrichment/Gifted and
Talented
Supporting Information
Common Misconceptions by students:
x Fractions and ratios are the same. A ratio is just another name for a fraction.
x Students may not see ratios as a comparison of two amounts. They will likely focus on just one
quantity.
x The transition for these students will be in that they need to take into account two quantities when
applying ratio reasoning.
x Students may want to use additive properties when reasoning with ratios. However, equivalency and
reasoning with ratios must include multiplicative properties.
ଶ
ଷ
x 2 wins to 3 losses is NOT the same as 3 losses to 2 wins ( ‹•not equal to ).
ଷ
ଶ
Possible extension for enrichment:
Have students discover the value of pi. Give students a number of circles, lids, bowls, plates, Frisbees, etc.
Ask them to measure the diameter and measure the distance around the circles (see if any student calls it
circumference. Or, you can tell them that’s what it’s called.) Compare the measurement of the diameter to
the measurement to the circumference in the form of a ratio. Tell students to average all of the ratios that
they found. Have a discussion about how this is equivalent to pi.
Materials
Rainbow Cubes, Picture of assortment of sports balls, Photographs or posters
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Technology
Optional: Interactive white board
Resources
x
(must be available to all stakeholders) x
x
“Teaching Student Centered Mathematics; Grades 5-8” by Van de Walle
“Developing Essential Understanding of Ratios, Proportions, & Proportional Reasoning” by NCTM
“Good Questions for Math Teaching; Why Ask Them and What to Ask; Grades 5-8” by Lainie
Schuster and Nancy Canavan Anderson
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Lesson Seeds:
The lesson seeds have been written particularly for the unit, with specific standards in mind. The suggested activities are not
intended to be prescriptive, exhaustive, or sequential; they simply demonstrate how specific content can be used to help students learn the
skills described in the standards. They are designed to generate evidence of student understanding and give teachers ideas for developing
their own activities.
MSDE Mathematics Lesson Seed Organizer
Lesson Seeds : The lesson seeds are ideas for the domain/standard that can be used to build a lesson. Lesson seeds are not meant to be allinclusive, nor are they substitutes for instruction.
Domain: Ratio and Proportional Relationship
Standard: 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,
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double number line diagrams, or equations.
b. Solve unit rate problems including those involving unit pricing and constant speed.
Purpose/Big Idea: Finding the best unit rate for wireless phone use.
Materials: Rate sheet for three companies
Activity:
Students are looking for the best cell phone plan for their families to buy for them. They looked on line and found these phone companies published these rates
per month.
Horizon
Horizon
EZZ
EZZ
Rocket
Rocket
Talking Only
Talking & Texting
Talking
Talking & Texting
Talking
Talking & Texting
39.99
59.99
69.99
89.99
59.99
79.99
89.99
109.99
69.99
89.99
99.99
119.99
450 minutes
700 minutes
69.99
99.99
900 minutes
1400 minutes
89.99
119.99
2000 minutes
99.99
129.99
Unlimited
119.99
149.99
What information do you need to compare these prices?
DraftMarylandCommonCoreStateCurriculumUnitforGrade6MathematicsDecember2011
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Draft Unit Plan
6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
What would you do to find the unit rate for each plan?
Which plan would you choose and why?
Essential Guiding Questions: How is a ratio or rate used to compare two quantities or values?
Sample Assessment Items:
x
x
x
x
The items included in this component will be aligned to the standards in the unit and will include:
Items purchased from vendors
PARCC prototype items
PARCC public release items
Maryland Public release items
Interventions/Enrichments:
(Standard-specific modules that focus on student interventions/enrichments and on professional
development for teachers will included later, as available from the vendor(s) producing the modules.)
Vocabulary/Terminology/Concepts:
This section of the Unit Plan is divided into two parts. Part I contains vocabulary and terminology
from standards that comprise the cluster which is the focus of this unit plan. Part II contains vocabulary and terminology from standards
outside of the focus cluster. These “outside standards” provide important instructional connections to the focus cluster.
Part I –– Focus Cluster: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
௔
ratio: :Ratioisacomparisonoftwoquantitiesormeasures.Ratioscanbeexpressedintheform( ),atob,ora:b.
௕
Ratioscanbeexpressedascomparisonsof:
1. parttoawhole,onepartofawholetoanotherpartofthesamewhole.PartͲtoͲwholewouldbetheratioofboystothewholeclass.measures
oftwodifferenttypeswhichiscalledarate.
2. partͲtoͲpartwouldbetheratioofboystogirlsinaclass.
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Draft Unit Plan
6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
Measuresoftwodifferenttypesarecalledarate.Ratewouldbetheratioofmilespergallontomilesperhour.
unit rate: A ratio where the denominator is 1 unit. Example: If 15 bars of soap cost $6.75,one bar would cost $.45.
଺Ǥ଻ହ
ଵହ
=
Ǥସହ
ଵ
tape diagrams: Tape diagrams are linear models used to represent data and help students organize their thinking. Example: Casey read 7
more books than Jamie. If Casey has read 16 books, how many books did Jamie read?
Number of books Casey read
Number of books Jamie read
Jamie+7=Casey
Casey––7=Jamie
16––7=9
SoJamieread9books.
difference
percent: is another name for hundredths Ratio of a number to 100 with a percent sign. Per hundred Example: 75% =
଻ହ
ଵ଴଴
= .75
Part II –– Instructional Connections outside the Focus Cluster
dependent variable: In a function of two variables, one variable is dependent and the other is independent. In the equation y = 3x + 4, y is
the dependent variable. Its value depends on the value of x. If the value of x= 2, then the value of y is y = 3ൈ2 + 4 or y = 10.
independent variable: In a function of two variables, one variables is dependent and the other independent. In the equation y = 3x + 4, x
is the independent variable. The value of y depends on the value of x. If the value of x is 1, then the value of y is y = 3ൈ1 + 4 or
y = 7.
Resources:
This section contains links to materials that are intended to support content instruction in this unit.
http://ime.math.arizona.edu/progressions/#products
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Draft Unit Plan
6.RP.1-3: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems
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