# Shapes and Their Perimeter

Students explore concepts of perimeter and geometry, specifically measuring perimeter. They start by exploring the specific attribute of perimeter, and then come to differentiate between perimeter and area as different measurements.

## Unit Summary

In Unit 5, students explore concepts of perimeter and geometry. Students have gradually built their understanding of geometric concepts since Kindergarten, when students learn to name shapes regardless of size and orientation. They also learn to distinguish between flat and solid shapes. In Grade 1, students’ understanding grows more nuanced, as they learn to distinguish between defining and non-defining attributes, as well as compose and decompose both flat and solid shapes. In Grade 2, students draw and identify shapes with specific attributes. All of this understanding gets them ready for Grade 3, in which students begin their journey of measuring those attributes, including area (addressed in Unit 4), and perimeter (explored here), as well as classification of shapes based on attributes into one or more categories.

Students begin the unit by defining perimeter as the boundary of a two-dimensional shape and measure it by finding its length. For a polygon, the length of the perimeter is the sum of the lengths of the sides. They develop their understanding of perimeter by measuring it with a ruler, finding it when all side lengths are labeled, and then finding it when some information about the length of a shape’s side lengths needs to be deduced, such as when a rectangle only has its length and width labeled. Students then solve real-world and mathematical problems, both given a figure and without one, involving perimeters of polygons (3.MD.8). With this understanding of perimeter, they are able to compare the measurement of area and perimeter of a rectangle, seeing that a rectangle with a certain area can have a variety of perimeters and, conversely, a rectangle with a certain perimeter can have a variety of areas, connecting the additional cluster content of perimeter to the major cluster content of area. Students then solve various problems involving area and perimeter. The last topic of the unit explores geometry. Students build on Grade 2 ideas about polygons and their properties, specifically developing and expanding their knowledge of quadrilaterals. They explore the attributes of quadrilaterals and classify examples into various categories (3.G.1), then explore attributes of polygons and classify examples into various categories, now including quadrilaterals. Students also draw polygons based on their attributes. Students next use tetrominoes and tangrams to compose and decompose shapes.

In this unit, students reason abstractly and quantitatively, translating back and forth between figures and equations in the context of perimeter problems (MP.2). Students will also construct viable arguments and critique the reasoning of others as they develop a nuanced understanding of the difference between area and perimeter, as well as when they classify shapes according to their attributes and justify their rationale (MP.3). Lastly, students will use appropriate tools strategically by using rulers to measure the side lengths of polygons to find their perimeter, as well as use rulers and right angle templates to find attributes of shapes to determine their classification (MP.5).

Students will further deepen their understanding of these ideas in future grade levels. In Grade 4, students solve more complex word problems involving area and perimeter (4.MD.3), as well as classify shapes based on the presence of parallel and perpendicular shapes (4.G.2), which is very connected to their study of angles (4.MD.5—7). The beginning work on categorization in Grade 3 culminates in Grade 5, where students have a complete picture of the hierarchical nature of classifying shapes (5.G.3). In the middle grades and high school, increasingly complex problems rely on students’ deep understanding of attributes of shapes and how to measure them, threaded throughout this unit.

Pacing: 17 instructional days (15 lessons, 1 flex day, 1 assessment day)

For guidance on adjusting the pacing for the 2021-2022 school year, see our 3rd Grade Scope and Sequence Recommended Adjustments. • Expanded Assessment Package
• Problem Sets for Each Lesson
• Student Handout Editor
• Vocabulary Package

## Assessment

This assessment accompanies Unit 5 and should be given on the suggested assessment day or after completing the unit.

## Unit Prep

### Intellectual Prep

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#### Intellectual Prep for All Units

• Read and annotate “Unit Summary” and “Essential Understandings” portion of the unit plan.
• Do all the Target Tasks and annotate them with the “Unit Summary” and “Essential Understandings” in mind.
• Take the Post-Unit Assessment.

### Essential Understandings

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• “A perimeter is the boundary of a two-dimensional shape. For a polygon, the length of the perimeter is the sum of the lengths of the sides” (GM Progression, p. 16).
• Rectangles with the same perimeter do not necessarily have the same area. Rectangles with the same area do not necessarily have the same perimeter.
• Shapes in different categories may share attributes that define a larger, superordinate category of shapes. For example, the category of shapes called quadrilaterals includes categories such as squares, rectangles, rhombuses, parallelograms, and trapezoids, since they are all closed shapes with four sides.

### Materials

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• Optional: Paper plate (1 per student) — See Lesson 1 Anchor Task 1 Notes for more information.
• Optional: Rectangular object (1 per student) — See Lesson 1 Anchor Task 1 Notes for more information.
• Crayons or markers (2 per student) — Students could use a pen and a pencil instead
• String or pipe cleaners (about 2 feet worth per student)
• Quadrilaterals Template (1 per student or small group)
• Right-angle template (1 per student) — This can be any tool used to verify right angle measures, e.g., the corner of a piece of paper.
• Polygons Template (1 per student or small group)
• Game Cards (1 per pair of students)
• Tetrominoes Template (1 5-page copy per group of 4 students)
• Blank paper (1 sheet per student)
• Rulers (1 per student) — These need to have both inch and centimeter measures.
• Optional: Square-inch tiles (Maximum of 24 per student or small group) — Students might not need these depending on their reliance on concrete materials. You can provide students with the Square Inch Grid Template cut into individual units if you don't have enough square inch tiles.

### Vocabulary

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right angle

polygon

perimeter

parallel

attribute

parallelogram

To see all the vocabulary for this course, view our 3rd Grade Vocabulary Glossary. #### Unit Practice

With Fishtank Plus you can access our Daily Word Problem Practice and our content-aligned Fluency Activities created to help students strengthen their application and fluency skills.

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# 1

3.MD.D.8

Understand perimeter to be the boundary around a two-dimensional shape. Compare perimeters of various shapes.

# 2

3.MD.D.8

Find perimeter by measuring side lengths in whole number units.

# 3

3.MD.D.8

Find perimeter of shapes with all side lengths labeled.

# 4

3.MD.D.8

Find perimeter of polygons with sides of equal length and of rectangles when some side lengths are missing.

# 5

3.MD.D.8

Solve word problems involving finding perimeter given the side lengths.

# 6

3.MD.D.8

Find side lengths of polygons with sides of equal length and of rectangles when given perimeter and other side lengths.

# 7

3.MD.D.8

Solve more complex word problems involving perimeter, such as finding a missing side length given perimeter and other side lengths.

# 8

3.MD.D.8

Find rectangles with the same area and different perimeters.

# 9

3.MD.D.8

Find rectangles with the same perimeter and different areas.

# 10

3.MD.D.8

Solve a variety of word problems involving area and perimeter.

3.G.A.1

# 12

3.G.A.1

Compare and classify other polygons.

# 13

3.G.A.1

Draw shapes with specified attributes.

# 14

3.G.A.1

Reason about composing and decomposing polygons using tetrominoes.

# 15

3.G.A.1

Reason about composing and decomposing polygons using tangrams.

## Common Core Standards

Key: Major Cluster Supporting Cluster Additional Cluster

### Core Standards

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##### Geometry
• 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.

##### Measurement and Data
• 3.MD.D.8 — Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

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• 2.G.A.1

• 2.MD.A.1

• 3.MD.C.5

• 3.MD.C.6

• 3.MD.C.7

• 3.OA.D.8

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• 4.G.A.1

• 5.G.B.3

• 4.MD.A.3

### Standards for Mathematical Practice

• CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

• CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

• CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

• CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

• CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

• CCSS.MATH.PRACTICE.MP6 — Attend to precision.

• CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

• CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.