Curriculum  /  Math  /  3rd Grade  /  Unit 5: Shapes and Their Perimeter  /  Lesson 2

Shapes and Their Perimeter

Lesson 2

Math

Unit 5

3rd Grade

Lesson 2 of 16

Objective

Compare and classify quadrilaterals.

Common Core Standards

Core Standards

  • 3.G.A.1 — Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Foundational Standards

  • 2.G.A.1

Criteria for Success

  1. Classify quadrilaterals according to their attributes, like presence of parallel sides, presence of right angles, and side length; and justify those classifications (MP.2, MP.3, MP.5).
  2. Understand that two sides are parallel if they go in the same direction and would never cross, even if they were extended forever.
  3. Understand that a trapezoid is a quadrilateral with at least one pair of parallel sides. (See Notes/Tips for Teachers section.)
  4. Understand that a parallelogram is a quadrilateral with exactly two pairs of parallel sides.
  5. Understand that a rectangle is a quadrilateral with four right angles.
  6. Understand that a rhombus is a quadrilateral with four sides of equal length.
  7. Understand that a square is a quadrilateral with four right angles and four sides of equal length.
  8. Recognize rhombuses, rectangles, squares, and trapezoids as examples of quadrilaterals.
  9. Understand that there exist quadrilaterals that do not belong into any of the subcategories mentioned above.

Tips for Teachers

  • Students have learned much of the vocabulary used in today’s lesson in prior grade levels, but not all. New vocabulary includes parallel, parallelogram, and rhombus. 
  • Quadrilateral is a particularly important term at this grade level, since it provides “the raw material for thinking about the relationships between classes. For example, students can form larger, superordinate, categories, such as the class of all shapes with four sides, or quadrilaterals, and recognize that it includes other categories, such as squares, rectangles, rhombuses, parallelograms, and trapezoids. They also recognize that there are quadrilaterals that are not in any of those subcategories” (Geometry Progression, p. 13). 
  • “In the U.S., that the term ‘trapezoid’ may have two different meanings. In their study The Classification of Quadrilaterals (Information Age Publishing, 2008), Usiskin et al. call these the exclusive and inclusive definitions:
    • T(E): a trapezoid is a quadrilateral with exactly one pair of parallel sides
    • T(I): a trapezoid is a quadrilateral with at least one pair of parallel sides.

These different meanings result in different classifications at the analytic level. According to T(E), a parallelogram is not a trapezoid; according to T(I), a parallelogram is a trapezoid. Both definitions are legitimate. However, Usiskin et al. conclude, ‘The preponderance of advantages to the inclusive definition of trapezoid has caused all the articles we could find on the subject, and most college-bound geometry books, to favor the inclusive definition.’” (Geometry Progression, p. 3). Thus, the inclusive definition is used below and throughout the curriculum. 

Lesson Materials

  • Quadrilaterals Template (1 per student or small group) — See Anchor Task 1 to see how to prepare this material before the lesson.
  • Right-angle tool (1 per student) — This can be any tool used to verify right angle measures, e.g., a protractor, the corner of a piece of paper, etc.
  • Ruler (1 per student) — These need to have both inch and centimeter measures.
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Anchor Tasks

25-30 minutes

Problem 1

Sort these shapes (cut out from Quadrilaterals Template) into groups. You may sort them any way you want and into as many groups as you want. Be prepared to explain how you sorted the shapes.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 3 Mathematics > Module 7 > Topic B > Lesson 4 — Concept Development

Grade 3 Mathematics > Module 7 > Topic B > Lesson 4 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Play a round of Mystery Quadrilateral with a partner.

  • Partner A: Choose a shape from the group of quadrilaterals (cut out from Quadrilaterals Template). Look at it without your partner seeing it.
  • Partner B: Ask up to 5 “yes” or “no” questions to identify the quadrilateral. Then guess which quadrilateral is the mystery quadrilateral.
  • Partner A: Show your partner the mystery quadrilateral.
  • Switch roles and play again.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 3 Unit 7 Lesson 3 Activity 2

Grade 3 Unit 7 Lesson 3 Activity 2, accessed on Nov. 14, 2022, 2:09 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes

Discussion of Problem Set

  • What answer did you choose in #2? How do you know that that shape also belongs in the same group? What vocabulary term can you use to describe this group of shapes?
  • What vocabulary term did you use to describe the shape you drew in #3? What other words can you use to describe it?
  • I drew a rectangle for #3. Is that correct? Why or why not? What about a rhombus? A square?
  • What other shape categories could you have listed in #4? Which shapes belong to each of those categories?
  • Why did the first shape and the third shape have the same categories checked even though we might use two different terms to describe them?
  • How did Sally sort her shapes in #6? What shapes did you draw to go in each group?

Target Task

5-10 minutes

Problem 1

Select the two statements that are true.

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Student Response

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Problem 2

List all the attributes you can that describe the shape below.

Student Response

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Draw shapes with specified attributes.

Lesson 3
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Attributes of Two-Dimensional Shapes

Topic B: Understanding Perimeter

Topic C: Distinguishing Between Area and Perimeter

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