Unit Overview
Content Area: Math
Unit Title: Proportions and Proportional Thinking
Unit: 5
Target Course/Grade Level: Seventh Grade
Timeline: 6 weeks
Unit Summary: Students will explore proportional reasoning and its application in similarity.
Students understand that two quantities are proportional when a change in one quantity
corresponds to a predictable change in the other. The topics of ratio, rate, and proportion give
students the opportunity to solve proportional relationships and to determine whether a relationship
is non-proportional. Students examine and compose scale drawings as an introduction to similar
figures. Proportional reasoning as it applies to similarity is extended to include perimeter and area
of similar figures. The emphasis is on developing an understanding of proportionality and its use in
real-world applications so that students become competent and confident in their ability to
determine if values are either directly or inversely related. Students will also learn how changes in
dimensions affect the surface area and volume of similar solids. Proportional reasoning is applied
throughout to solve real-world measurement problems.
Primary interdisciplinary connections: Language Arts and Technology
9.1 21st-Centuries Life & Career Skills
Standard 9.1 All students will demonstrate the creative, critical thinking, collaboration, and
problem-solving skills needed to function successfully as both global citizens and workers in
diverse ethnic and organizational cultures.
Strand: A. Critical Thinking and Problem Solving
B. Creativity and Innovation
C. Collaboration, Teamwork and Leadership
Content Statement:
9.1.8: A The ability to recognize a problem and apply critical thinking skills and problem
solving skills to solve the problem is a lifelong skill that develops over time.
9.1.8: B Gathering and Evaluating knowledge and information from a variety of sources,
including global perspective, fosters creativity and innovative thinking.
9.1.8: C Collaboration and team work enable individuals or groups to achieve common goals
with greater efficiency.
Leadership abilities develop over time through participation in group and or teams that
that are engaged in challenging or competitive activities.
21st Century themes and skills: Critical Thinking and Problem Solving, Collaboration, Teamwork and
Leadership, Creativity and Innovation
Mathematical Practices:
7.MP.1 Make sense of problems and persevere in solving them.
7.MP.2 Reason abstractly and quantitatively.
7.MP.3 Construct viable arguments and critique the reasoning of others.
7.MP.4 Model with mathematics.
7.MP.6 Attend to precision.
7.MP.7 Look for and make use of structure.
7.MP.8 Look for and express regularity in repeated reasoning.
Learning Targets
Domain: Geometry
Cluster: Parallel lines, Triangles and Transformations
Standard #
Standards
7.RP.1
Compute unit rates associated with ratios of fractions, including rations of lengths, areas
and other quantities measured in like or different units.
7.RP.2
Recognize and represent proportional relationships between quantities.
7.RP.2a
Decide whether two quantities are in a proportional relationship 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.
7.RP.2b
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams,
and verbal descriptions of proportional relationships.
7.RP.2c
Represent Proportional relationships by equations.
7.RP.2d
Explain what a point (x,y) on the graph of a proportional relationship means in terms of
the situation, with special attention to points (0,0) and (1,r) where r is the unit rate.
7.G.1
Solve problems involving scale drawing of geometric figures, including computing actual
length and areas from scale drawing and reproducing a scale drawing at a different scale.
7.G.6
Solve real-world and mathematical problems involving area, volume and surface area of
two dimensional and three dimensional objects composed of triangles, quadrilaterals,
polygons, cubes and right prisms.
9.1.8.A.1
Develop strategies to reinforce positive attitudes and productive behaviors that impact
critical thinking and problem-solving skills.
9.1.8.A.2
Implement problem-solving strategies to solve a problem in school or the community.
9.1.8.B.2
Assess data gathered to solve problems for which there are varying perspective (e.g., cross
cultural, gender specific, generational, etc.) and determine how the data can best be used to
design the multiple solutions.
9.1.8.C.1
Determine an individual’s responsibility for personal actions and contributions to group
activities.
9.1.8.C.2
Demonstrate the use of compromise, consensus and community building strategies for
carrying out different task, assignments and projects.
9.1.8.C.3
Model leadership skills during classroom and extracurricular activities.
Unit Essential Questions
 What are ratios and proportions and how do we
use them in our daily lives?
 How can you determine if two quantities are
proportional?
 How are ratios, proportions, and scale drawings
used in the real world?
 How are similar figures scale drawings used in
real-world situations?
 When is a linear function a direct variation?
How is direct variation different from inverse
variation?
 Why is it important to have a good
understanding of a ratio and proportion in order
to be able to convert measurements?
 How do changes in dimensions of threedimensional figures affect area and volume?
Unit Enduring Understandings
 A ratio is a comparison of two quantities by
division. A rate is a ratio that compares two
quantities of different rates and a unit rate has a
denominator of 1.
 If the ratios are not equal, then the two quantities
are non-proportional. Two quantities are
proportional if they have a constant ratio.
 In a scale drawing or scale model, the dimensions
of the object being represented are reduced or
enlarged. The scale is the ratio that compares the
measurements of the drawing or model to the
measurement of the real object.
 In similar figures, corresponding angles are
congruent and corresponding sides are
proportional. The ratio of the perimeters of two
similar figures is equal to the ratio of the
corresponding sides. The ratio of the areas of the
areas of two similar figures is equal to the square
of the ratio of the corresponding sides.
 When two variable quantities have a constant ratio,
their relationship is called a direct variation. When
two variable quantities have a constant product
their relations is called an inverse variation.
 Similar solids are three-dimensional figures that
have the same shape and whose corresponding
linear measures are proportional.
Unit Learning Targets
Students will ...
 Model proportions using bar diagrams.
 Determine unit rate
 Identify proportional and non-proportional relationships.
 Use proportions to solve problems
 Use proportions to estimate populations.
 Solve problems by drawing a diagram.
 Solve problems involving scale drawings.
 Solve problems involving similar figures.
 Find the relationship between perimeters and areas of similar figures.
 Solve problems by using a graph.
 Compare and contrast proportional and non-proportional linear functions
 Use dire variation to solve problems.
 Solve problems making a model.
 Will determine how changes in dimensions affect area and volume.
 Solve problems involving similar solids.
Evidence of Learning
Summative Assessment
 Distinguish between situations that are proportional or not proportional.
 Use proportions to solve problems.
 Apply proportionality to measure in multiple contexts, including scale drawings and constant speed.
 Solve problems involving similar figures.
 Determine how changes in dimensions affect the perimeter, area, and volume of common geometric
figures.
 Distinguish direct variation from other relationships including inverse variation.
 Determine how changes in dimensions affect surface area and volume.
Equipment needed: Smart Board, white boards, calculators, Elmo
Teacher Instructional Resources: Textbook (To be determined)
Study Island
Khan Academy Videos
Formative Assessments
 Skill sheets
 Quizzes/Tests
 Student workbook
 Homework
 Math games
 Study Island
Integration of Technology:
 Smart Board to play online games, utilize online resources, generate models with Smart Software.
 Kahn Academy Videos
 Elmo – for demonstration
 Study Island
Technology Resources:
http://www.purplemath.com
http://www.khanacademy.org – Interactive 2.0 instructional and practice site. Students can view
instructional videos and complete practice modules for additional practice/remediation.
http://www.studyisland.com/ - Web-based instruction, practice, assessment and reporting built from NJ
standards.
http://www.ixl.com/math/grade-7 - IXL 7th grade online interactive activities for the students to
complete
http://www.aaamath.com/grade7.html - AAA math 7th grade – online interactive activities and
problems for the student to complete.
http://www.adaptedmind.com/Math-Worksheets.html?type=hstb – Grade level material for practice,
lessons, games, etc.
Opportunities for Differentiation:
Decelerate:
Have students model a unit rate using counters as the numerator and denominator and a pencil as the
fraction bar.
Accelerated:
Have students find a map of the United States in an atlas or online. Ask what is the scale factor? Then
have them use the scale factor to calculate how many miles are represented by an inch on the map.
Teacher Notes: