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Unit Map 2012-2013Oa k l a n d Sc h o o l s
Co l l a b o r a t i o n / M a t h 7 * ( C C) / Gr a d e 7 ( Co m m o n Co r e )
Friday, July 27, 2012, 12:47PM
Unit: 3 - Proportional Reasoning & Similarity (Week 1, 1 Week)
Common Core Initiative
Overarching Questions and Enduring Understandings
What does proportionality look like in geometric contexts (similar figures) and what does itmean for two geometric figures to be mathematically similar and how can these ideas help you
solve real-world problems?
Graphic Organizer
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Unit Abstract
In this unit, students come to deepen their understanding of proportional relationships by and through thedevelopment of similarity. The study of similarity includes an exploration of the following proportionally
based relationships present in similar figures:
- corresponding angles are equal,
- the ratios of the lengths of corresponding sides are equal,
- the perimeter increases or decreases by the same factor (scale factor) as side lengths, and
- the areas increase or decrease by the square of that scale factor for side lengths.
Students come to see that similarity is an instance of proportionality, as the ratios of corresponding sidesin similar figures are equal. This unit develops this understanding through multiple experiences of creating
similar figures, such as using rubber band stretchers, coordinate systems and algebraic rules, and tiling of
congruent shapes. The idea of similar figures is explored in the context of interesting and everydayproblems in life.
The unit connects to specific grade 7 CCSS standards and cluster headings, and also specifically addresses
statements in the introduction of the Grade 7 CCSS:
"Students solve problems about scale drawings by relating corresponding lengths between the
objects or by using the fact that relationships of lengths within an object art preserved in similar
objects." and "...they reason about relationships among two-dimensional figures using scale drawing andinformal geometric constructions."
Unit Template 6.26.12 (PDF)
Unit Template 6.26.12 (Word)
Content Expectations/Standards
CCSS: Mathematics, CCSS: Grade 7, Ratios &
Proportional Relationships7.RP Analyze proportional relationships and use
them to solve real-world and mathematical
problems.
7.RP.1. Compute unit rates associated withratios of fractions, including ratios of lengths,
areas and other quantities measured in like ordifferent units.
7.RP.2. Recognize and represent proportionalrelationships between quantities.
7.RP.2a. Decide whether two quantities arein a proportional relationship, e.g., by testing
for equivalent ratios in a table or graphing ona coordinate plane and observing whether the
Unit Level Standards
Not applicable.
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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 relationshipsby equations.
7.RP.3. Use proportional relationships tosolve multistep ratio and percent problems.
CCSS: Mathematics, CCSS: Grade 7, Geometry7.G Draw construct, and describe geometrical figures
and describe the relationships between them.
7.G.1. Solve problems involving scaledrawings of geometric figures, including
computing actual lengths and areas from ascale drawing and reproducing a scale
drawing at a different scale.
7.G Solve real-life and mathematical problems
involving angle measure, area, surface area, andvolume.
7.G.4. Know the formulas for the area andcircumference of a circle and use them to
solve problems; give an informal derivation ofthe relationship between the circumference
and area of a circle.
CCSS: Mathematics, CCSS: Grade 8, Geometry8.G Understand congruence and similarity using
physical models, transparencies, or geometry
software.
8.G.4. Understand that a two-dimensionalfigure is similar to another if the second canbe obtained from the first by a sequence of
rotations, reflections, translations, anddilations; given two similar two-dimensional
figures, describe a sequence that exhibits thesimilarity between them.
Essential/Focus Questions
1. How can one apply ideas aboutproportionality in geometric shapes in theeveryday world?
2. How are ideas about similarity used in theeveryday world?
3. When two figures are similar, what is thesame? What is different?
4. When two figures are similar, what is therelationship between the areas? The
perimeters?
5. How do the ratios of similar figures relate?
Key Concepts
proportional relationships in geometry
enlarging and shrinking plane figures
similarity
congruency
corresponding parts of similar figures
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6. How does one use scale factor to determinemap distances?
transformations of plane figures
scale
scale factor
Assessment Tasks
Formative Assessment Template 6_27_12Handout - Similar Triangles Assessment
Handout - One of these things is not like theothers! Rectangles
Handout - One of these things is not like the
others! Recording Sheet
Artifact - Sample Student Work: Reengagement of
Similar Rectangles Assessment
Artifact Accommodated Resource for the
Assessment: Using Easier Measurements to Make
Ratio Connect
Intellectual Processes
Standards of Mathematical Practice
Look for and make use of structure: Usetables to find the constant of proportionalityfor real-world problem situations.
Reason abstractly and quantitatively Look for and express regularity in
repeated reasoning
Lesson Sequence
Lesson Template
7.3 Worksheet for Proportional Reasoning and
Similarity Lesson
7-3 Answer key for Lesson Free Trip - Down Underin DC
Handout - Subway Map of DC Metro
Handout - Google Map of Washington DC Area
Handout - Google Map II of Washington DC Area
Resources
Unit Resources