Curriculum  /  Math  /  3rd Grade  /  Unit 5: Shapes and Their Perimeter  /  Lesson 4

Shapes and Their Perimeter

Lesson 4

Math

Unit 5

3rd Grade

Lesson 4 of 16

Objective

Reason about composing and decomposing polygons using tangrams.

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.

Criteria for Success

  1. Decompose a square into various polygons to create a tangram set.
  2. Use tangrams to compose a shape with specified attributes or using specific pieces, such as a rectangle that does not have all equal sides or making a parallelogram from the two small triangles.
  3. Use tangrams to compose a shape given its outline.

Tips for Teachers

  • “More advanced paper-folding (origami) tasks afford the same mathematical practices of seeing and using structure (MP.7), conjecturing (MP.1), and justifying conjectures (MP.3). Paper folding can also illustrate many geometric concepts. For example, folding a piece of paper creates a line segment. Folding a square of paper twice, horizontal edge to horizontal edge, then vertical edge to vertical edge, creates a right angle, which can be unfolded to show four right angles. Students can be challenged to find ways to fold paper into rectangles or squares and to explain why the shapes belong in those categories” (G Progression, p. 13).

Lesson Materials

  • Blank Paper (1 sheet per student)
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Anchor Tasks

25-30 minutes

Problem 1

Create a tangram set by following the directions below:

  1. Fold a piece of paper so that a shorter side lies along a longer side. Cut off the extra strip of paper.
  2. Unfold the remaining paper. Cut along the diagonal line formed by the fold you just did. Draw these two shapes and label them.
  3. Fold one of your triangles in half to make two equal sides. Unfold the triangle and cut along the fold. Draw these two new shapes and label them.
  4. Take the remaining big triangle you made in #1. Fold it in half to make two triangles similar to the ones you made in #2. Unfold the paper and fold the tip of the triangle that has a crease in it down to meet the bottom side of the triangle at the crease. Draw these two new shapes and label them.
  5. Take the trapezoid you made in #3. Fold it in half and cut it on the fold. Draw these two new shapes and label them.
  6. Take one of the trapezoids you made in #4 and fold along the longest side so that the corners of that side meet. Cut along the fold. Draw these two new shapes and label them.
  7. Take the other trapezoid you made in #4 and put the side with no right angles on the bottom. Fold the corner at the top to meet the corner of the side on the bottom that is directly underneath it. Cut along the fold. Draw these two new shapes and label them.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 3 Mathematics > Module 7 > Topic B > Lesson 8 — Concept Development

Grade 3 Mathematics > Module 7 > Topic B > Lesson 8 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

Using your tangram set, compose the following shapes:

a.   The original square you started with in Anchor Task #1.

b.   A rectangle that does not have all equal sides.

c.   A hexagon.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 3 Mathematics > Module 7 > Topic B > Lesson 9 — Concept Development

Grade 3 Mathematics > Module 7 > Topic B > Lesson 9 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 3

Use your tangram pieces to create the shape below. You may not use all of your pieces.

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • Which shape was the most challenging for you to make in #1? Why?
  • Could you make the same shapes you made in #2 with the large triangles? Why or why not?
  • Compare the attributes of the shape you created in #3 with a partner’s. What is similar? What is different?
  • Share answers to #4. Was something easy for you but challenging for others? Likewise, was something easy for others but challenging for you? Why?

Target Task

5-10 minutes

Use at least two tangram pieces to make a rectangle. Sketch the rectangle below, drawing lines to show how the tangram pieces fit together.

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

Understand perimeter to be the boundary around a two-dimensional shape. Compare perimeters of various polygons using concrete non-standard units.

Lesson 5
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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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