Wentzville School District
Curriculum Development Template
Stage 1 – Desired Results
Unit 1 - Ratios and Proportional Reasoning
Unit Title: Ratios and Proportional Reasoning
Course: Integrated 7
Brief Summary of Unit: Students will learn to identify and represent proportional relationships. In addition, students
will use the properties of proportions to make conversions between units and unit rates. Finally, students will solve
real-world problems involving ratios and proportions using multiple strategies.
Textbook Correlation: Glencoe Math Course 2 Chapter 1 (including 1-5 lab and 1-7 lab)
Time Frame: 3.5 weeks
WSD Overarching Essential Question
Students will consider…
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How do I use the language of math (i.e. symbols,
words) to make sense of/solve a problem?
How does the math I am learning in the classroom
relate to the real-world?
What does a good problem solver do?
What should I do if I get stuck solving a problem?
How do I effectively communicate about math
with others in verbal form? In written form?
How do I explain my thinking to others, in written
form? In verbal form?
How do I construct an effective (mathematical)
argument?
How reliable are predictions?
Why are patterns important to discover, use, and
generalize in math?
How do I create a mathematical model?
How do I decide which is the best mathematical
tool to use to solve a problem?
How do I effectively represent quantities and
relationships through mathematical notation?
WSD Overarching Enduring Understandings
Students will understand that…
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Mathematical skills and understandings are used
to solve real-world problems.
Problem solvers examine and critique arguments
of others to determine validity.
Mathematical models can be used to interpret and
predict the behavior of real world phenomena.
Recognizing the predictable patterns in
mathematics allows the creation of functional
relationships.
Varieties of mathematical tools are used to
analyze and solve problems and explore concepts.
Estimating the answer to a problem helps predict
and evaluate the reasonableness of a solution.
Clear and precise notation and mathematical
vocabulary enables effective communication and
comprehension.
Level of accuracy is determined based on the
context/situation.
Using prior knowledge of mathematical ideas can
help discover more efficient problem solving
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How accurate do I need to be?
When is estimating the best solution to a
problem?
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strategies.
Concrete understandings in math lead to more
abstract understanding of math.
Transfer
Students will be able to independently use their learning to:
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Use proportional reasoning to make sound financial decisions.
Use proportional reasoning to find appropriate conversions (dosages, recipes, time, etc.
Meaning
Essential Questions
Understandings
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How can you show that two objects are
proportional?
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A ratio is a comparison of two numbers or
two measurements.
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How can you identify and represent
proportional relationships?
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A unit rate shows relationship between two
different units.
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How are unit rates useful in everyday, realworld contexts?
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Proportions are mathematical sentences
identifying equivalent ratios.
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How can graphs, tables, and equations assist
in calculating and predicting unit rates?
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Once you determine a relationship between
two units, that relationship can be used to
determine unknown quantities.
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How can I determine a unit rate from a table or
graph?
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Tables, graphs, equations, and diagrams can
all be used to represent and/or analyze a
proportional relationship.
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A graph, table, or equation can be used to
determine if a relationship is proportional..
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Properties of operations on fractions extend
to complex fractions.
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Ratios can be used to show a relationship
between changing quantities, such as vertical
and horizontal change.
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Direct variation is when one variable is equal
to a constant times another variable, with no
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What strategies can I use to determine if two
quantities are in a proportional relationship?
What role does an equation play in
determining proportional relationships?
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How can cross products be used to help solve
a proportion?
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How can a proportion be set up to represent a
real-world context?
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What other methods are available to solve a
proportion?
additions or subtractions alongside.
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What are different ways we can use ratios to
find unknown measurements?
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How do I apply properties of rational numbers
to manipulate complex fractions?
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What makes a fraction complex?
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What are real world applications of rational
numbers, including complex fractions?
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How are linear functions used to model
proportional relationships?
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What does the slope of a line indicate about
the line?
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What types of real-world situations can be
represented by a direct variation?
Acquisition
Key Knowledge
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Complex fraction
Unit rate
Constant of proportionality (unit rate)
Ratio
Proportion / Proportionality / Proportional
Relationship
Equivalent Ratios
Cross products
Dimensional analysis
Rate
Direct variation
Rate of change
Constant rate of change
Constant of variation
Non-proportional
Slope
Unit ratio
Key Skills
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Determine unit rates.
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Simplify ratios involving measurements.
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Simplify complex fractions and find unit rates.
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Convert units of measure between derived
units to solve problems using dimensional
analysis.
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Identify proportional and non-proportional
relationships.
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Identify proportional relationships by graphing
on the coordinate plane.
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Compare and contrast proportional and nonproportional linear functions.
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Use proportions to solve problems including
the cross products method.
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Understand slope as it pertains to rate of
change.
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Identify constant rates of change using tables
and graphs.
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Identify slope using tables and graphs.
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Use direct variation to solve problems.
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Write ratios as fractions in simplest form.
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Create a graph based on a table or equation
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Apply various strategies to determine
proportionality of two ratios
Standards Alignment
MISSOURI LEARNING STANDARDS
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational
numbers.
(7.NS.3) Solve real-world and mathematical problems involving the four operations with rational numbers.
(Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
Analyze proportional relationships and use them to solve real-world and mathematical problems.
(7.RP.1) Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other
quantities measured in like or different units. For example, if a person walks ½ mile in each ¼ hour, compute the
unit rate as the complex fraction ½ / ¼ miles per hour, equivalently 2 miles per hour.
Analyze proportional relationships and use them to solve real-world and mathematical problems.
(7.RP.2) Recognize and represent proportional relationships between quantities
a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent
ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line
through the origin.
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal
descriptions of proportional relationships.
c. Represent proportional relationships by equations. For example, if total cost t is proportional to the
number n of items purchased at a constant price p, the relationship between the total cost and the
number of items can be expressed
as t = pn.
d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the
situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Analyze proportional relationships and use them to solve real-world and mathematical problems.
(7.RP.3) Use proportional relationships to solve multistep ratio and percent problems.
Examples: simple interest, tax, markups and markups and markdowns, gratuities and commissions, fees, percent
increase and decrease, percent error.
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
SHOW-ME STANDARDS
Goals:
1.1, 1.4, 1.5, 1.6, 1.7, 1.8
2.2, 2.3, 2.7
3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8
4.1, 4.4, 4.5, 4.6
Performance:
Math 1, 5