# Shapes and Their Perimeter

Students explore concepts of perimeter and geometry, specifically measuring perimeter. They start by exploring attributes of shapes in different categories, then learn to measure at least one of these attributes, their perimeter. Finally they come to differentiate between perimeter and area as different measurements.

Math

Unit 5

## Unit Summary

In Unit 5, students explore concepts of geometry and perimeter. Students have gradually built their understanding of geometric concepts since Kindergarten, when students learned to name shapes regardless of size and orientation and to distinguish between flat and solid shapes. In Grade 1, students’ understanding grew more nuanced, as they learned to distinguish between defining and non-defining attributes, as well as composed and decomposed both flat and solid shapes. In Grade 2, students drew and identified 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 into one or more categories based on attributes.

Students begin the unit by building on Grade 2 ideas about polygons and their properties, specifically developing and expanding their knowledge of quadrilaterals. They explore the attributes of polygons and classify examples into various categories, then explore attributes of quadrilaterals and classify examples into various categories (3.G.1). Students also draw polygons based on their attributes. Students next use tangrams to compose and decompose shapes.  In Topic B, students shift to measuring an attribute of these polygons, namely perimeter. They define perimeter as the boundary of a two-dimensional shape and compare the perimeters of various shapes using concrete units. Next, they find the perimeter of polygons whose sides are marked with unit length marks, then labeled with numerals. Then, after finding the perimeter by measuring the length of each side, they find the perimeter when some information about the length of a shape’s side lengths needs to be deduced, such as when a rectangle only has one length and one 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 in Topic C, 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.

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 using rulers and right-angle tools to determine what attributes shapes have 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)

Fishtank Plus for Math

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress. ## Assessment

The following assessments accompany Unit 5.

### Pre-Unit

Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.

### Mid-Unit

Have students complete the Mid-Unit Assessment after lesson 9.

### Post-Unit

Use the resources below to assess student mastery of the unit content and action plan for future units.

Expanded Assessment Package

Use student data to drive your planning with an expanded suite of unit assessments to help gauge students’ facility with foundational skills and concepts, as well as their progress with unit content.

## Unit Prep

### Intellectual Prep

Unit Launch

Prepare to teach this unit by immersing yourself in the standards, big ideas, and connections to prior and future content. Unit Launches include a series of short videos, targeted readings, and opportunities for action planning. #### 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

• 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.
• “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.

### Materials

• Rulers (1 per student) — These need to have both inch and centimeter measures.
• Right-angle tool (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)
• Quadrilaterals Template (1 per student or small group)
• Game Cards (1 per pair of students)
• 1-inch paper clips (Maximum of 25 per student or small group)
• Crayons or markers (2 per student) — Students could use a pen and a pencil instead
• Dot Paper Template (at least one copy per student)
• About 3" by 3" square piece of paper (1 per student)
• Optional: Square-inch tiles (Maximum of 25 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.
• Optional: Colored paper (1 sheet of each of 4 colors per group of 4 students)
• Tetrominoes Template (1 5-page copy per group of 4 students)

### Vocabulary

attribute

parallelogram

parallel

perimeter

polygon

rhombus

right angle

To see all the vocabulary for Unit 5, view our 3rd Grade Vocabulary Glossary.

## Unit Practice

Word Problems and Fluency Activities

Access daily word problem practice and our content-aligned fluency activities created to help students strengthen their application and fluency skills. ## Lesson Map

Topic A: Attributes of Two-Dimensional Shapes

Topic B: Understanding Perimeter

Topic C: Distinguishing Between Area and Perimeter

## Common Core Standards

Key

Major Cluster

Supporting Cluster

### Core Standards

#### 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.

• 2.G.A.1

• 2.MD.A.1
• 3.MD.C.5
• 3.MD.C.6
• 3.MD.C.7

• 3.OA.D.8

• 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.

Unit 4

Area

Unit 6

Fractions