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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

3 proportional reasoning similarity%5b1%5d

Documents