Standard 1 : Classify two-dimensional figures and three-dimensional figures based on defining attributes.



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General Information

Number: MA.5.GR.1
Title: Classify two-dimensional figures and three-dimensional figures based on defining attributes.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 5
Strand: Geometric Reasoning

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.5.GR.1.1: Classify triangles or quadrilaterals into different categories based on shared defining attributes. Explain why a triangle or quadrilateral would or would not belong to a category.
Clarifications:
Clarification 1: Triangles include scalene, isosceles, equilateral, acute, obtuse and right; quadrilaterals include parallelograms, rhombi, rectangles, squares and trapezoids.
MA.5.GR.1.2: Identify and classify three-dimensional figures into categories based on their defining attributes. Figures are limited to right pyramids, right prisms, right circular cylinders, right circular cones and spheres.
Clarifications:
Clarification 1: Defining attributes include the number and shape of faces, number and shape of bases, whether or not there is an apex, curved or straight edges and curved or flat faces.


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MA.5.GR.1.AP.1a: Sort triangles into different categories based on the size of their angles. Triangles include acute, obtuse and right.
MA.5.GR.1.AP.1b: Sort quadrilaterals into different categories based on shared defining attributes. Explore why a quadrilateral would or would not belong to a category. Quadrilaterals include parallelograms, rhombi, rectangles, squares and trapezoids.
MA.5.GR.1.AP.2: Identify and sort three-dimensional figures into categories based on their defining attributes. Figures are limited to right rectangular pyramids, right rectangular prisms, right circular cylinders, right circular cones and spheres.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Original Student Tutorials

Name Description
More Quadrilaterals - Part 7:

By the end of this tutorial you should be able to identify examples of quadrilaterals and their defining attributes to classify them using diagrams. We will focus on kites and other quadrilaterals in this tutorial.

This part 7 in a 7-part series. Click below to explore the other tutorials in the series.

Part 1: "Figuring Out" 2D Figures

Part 2: Exploring Relationships with Venn & Euler Diagrams

Part 3: Classifying Triangles by Angles Using Euler Diagrams

Part 4: Classifying Triangles by Sides & Angles Using Venn and Euler Diagrams

Part 5: Quadrilaterals

Trapezoids Part 6:

Explore the defining attributes of trapezoids--a special type of quadrilateral--and classify them using diagrams in this interactive tutorial. You'll also learn how two different definitions for a trapezoid can change affect classifications of quadrilaterals. 

This part 6 in a 6-part series. Click below to explore the other tutorials in the series. 

Part 1: "Figuring Out" 2D Figures

Part 2: Exploring Relationships with Venn & Euler Diagrams

Part 3: Classifying Triangles by Angles Using Euler Diagrams

Part 4: Classifying Triangles by Sides & Angles Using Venn and Euler Diagrams

Part 5: Quadrilaterals

Quadrilaterals - Part 5:

Learn how to classify quadrilaterals--including parallelograms, rectangles, rhombi, and squares--based on their defining attributes using diagrams in this interactive tutorial.

This is part 5 in a 6-part series. Click below to explore the other tutorials in the series.

Exploring Relationships with Venn & Euler Diagrams – Part 2:

Learn how to show relationships represented in Venn & Euler Diagrams as you complete this interactive geometry tutorial.

This is part two of four. Click below to open the other tutorials in the series.

Classifying Triangles by Sides & Angles Using Venn and Euler Diagrams – Part 4:

Learn how triangles can be sorted and classified using side lengths and angle measures in this interactive tutorial.

This is the final tutorial in a four-part series. Click below to open the other tutorials in the series.

Classifying Triangles by Angles using Euler Diagrams – Part 3:

Learn to classify triangles and use Euler diagrams to show relationships, in this interactive tutorial.

This is part-three of four. Click below to open the other tutorials in the series.

"Figuring Out" 2D Figures - Part 1:

Explore 2D (two-dimensional) figures and see how every 2D figure possesses unique attributes in this interactive tutorial.

This is part one of four. Click below to open the other tutorials in the series.

Formative Assessments

Name Description
Classifying Shapes:

Students are asked to classify quadrilaterals and trapezoids by their properties.

Shape Clues:

Using shape attribute clues, the student will determine shapes that fit these clues and describe a category to which they both belong.

Where Do They Belong:

Students are asked to sort shapes using a Venn diagram and to determine the label for each section of the diagram.

Guess My Shape:

Using shape attribute clues, the student is asked to determine two shapes that fit these clues and describe a category to which both belong.

Grouping Triangles:

Students are shown three triangles that fit a rule (each has a right angle) and are asked to determine which of three other triangles also fit the rule.

Classifying Squares:

Students discuss the attributes of squares and rhombuses and consider how these two shapes are related.

Classifying Quadrilaterals:

Students are given a diagram of quadrilaterals that have been sorted and are asked to determine how the shapes were sorted. Then, students are given two additional quadrilaterals and asked to place them into the appropriate region on the diagram.

What Do You Know About Rectangles?:

Students are asked to describe the defining attributes of parallelograms and to consider the relationship between rectangles and parallelograms.

Trapezoids:

Students are asked to consider how the hierarchy of quadrilaterals would change based on the two different definitions of trapezoids.

Sketching Triangles:

Students are asked to use shape descriptions to sketch shapes and explain why some cannot be sketched.

Image/Photograph

Name Description
Clipart: Geometric Shapes:

In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes.

Lesson Plans

Name Description
Polygon Park:

In this lesson students will use standards-based quadrilaterals and triangles to design a roller coaster tower. Students will use the Engineering Design Process to work through the processes in this lesson.

Go TRI a Kite!:

In this lesson, students will identify and classify triangles. In addition, students will demonstrate how to solve problems requiring attention to approximation, selection of appropriate measuring tools, and precision of measurement using triangles.

Where in the Venn are the Quadrilaterals?:

"Where in the Venn are the Quadrilaterals?" is an activity that helps the student to develop a better understanding of classifying two-dimensional figures in a hierarchy based on properties.

A Closer Look at Quadrilaterals - The Parallelogram Connection:

Students work together as a class and in small groups to classify quadrilaterals.

Analyzing Polyhedra:

Students will construct several simple polyhedra, then count the number of faces, edges, and vertices. These data should suggest Euler's formula. 

Quadrilaterals using Unit Origami - Sonobe Cube:

This lesson can be used as an introduction - unit attention grabber- or as a final review on quadrilaterals. As the class forms a Sonobe cube, the different quadrilaterals are formed with each new fold. Included is a Power Point introduction with instructions, a video I made demonstrating how to fold the unit origami design, a video of my introduction lesson  to quadrilaterals and 2 worksheets which accompany the lesson. I enjoy doing this activity each year and am amazed at all the prior knowledge the students have retained as the lesson proceeds.

Triangles are Plane Easy:

The student will be engaged in a paper plane making activity while discovering the attributes of different triangles. The students will learned the similarities and differences of the following triangles: scalene, isosceles, equilateral, right, obtuse, and acute.

Perspectives Video: Teaching Ideas

Name Description
Estimating Angles:

Unlock an effective teaching strategy for teaching students to estimate angle measurements in this Teacher Perspectives video for educators.

Double Bubble Diagram to Compare Math Concepts:

Unlock an effective teaching strategy for helping students make connections in mathematics using the Double Bubble Diagram in this Teacher Perspectives video for educators.

Problem-Solving Tasks

Name Description
Lines of symmetry for triangles:

This activity provides students an opportunity to recognize these distinguishing features of the different types of triangles before the technical language has been introduced. For finding the lines of symmetry, cut-out models of the four triangles would be helpful so that the students can fold them to find the lines.

Lines of symmetry for quadrilaterals:

This task provides students a chance to experiment with reflections of the plane and their impact on specific types of quadrilaterals. It is both interesting and important that these types of quadrilaterals can be distinguished by their lines of symmetry.

Are these right?:

The purpose of this task is for students to measure angles and decide whether the triangles are right or not. Students should already understand concepts of angle measurement  and know how to measure angles using a protractor before working on this task.

Teaching Idea

Name Description
An Introduction To Quadrilaterals:

This lesson is designed to introduce students to quadrilaterals and the terms and properties associated with quadrilaterals. This lesson provides links to discussions and activities related to quadrilaterals as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Tutorials

Name Description
Categorizing Geometric Shapes: Practice Examples:

This Khan Academy tutorial video presents examples and explanations for categorizations of perpendicular sides and right, obtuse, and acute triangles.

Examples of Triangle Categories:

In this Khan Academy tutorial video triangles are categorized by angles or side lengths of a specified size.

Quadrilateral Overview:

This Khan Academy tutorial video introduces quadrilaterals. their categories, and subcategories.

Unit/Lesson Sequence

Name Description
Three Dimensional Shapes:

In this interactive, self-guided unit on 3-dimensional shape, students (and teachers) explore 3-dimensional shapes, determine surface area and volume, derive Euler's formula, and investigate Platonic solids. Interactive quizzes and animations are included throughout, including a 15 question quiz for student completion.



Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Original Student Tutorials

Title Description
More Quadrilaterals - Part 7:

By the end of this tutorial you should be able to identify examples of quadrilaterals and their defining attributes to classify them using diagrams. We will focus on kites and other quadrilaterals in this tutorial.

This part 7 in a 7-part series. Click below to explore the other tutorials in the series.

Part 1: "Figuring Out" 2D Figures

Part 2: Exploring Relationships with Venn & Euler Diagrams

Part 3: Classifying Triangles by Angles Using Euler Diagrams

Part 4: Classifying Triangles by Sides & Angles Using Venn and Euler Diagrams

Part 5: Quadrilaterals

Trapezoids Part 6:

Explore the defining attributes of trapezoids--a special type of quadrilateral--and classify them using diagrams in this interactive tutorial. You'll also learn how two different definitions for a trapezoid can change affect classifications of quadrilaterals. 

This part 6 in a 6-part series. Click below to explore the other tutorials in the series. 

Part 1: "Figuring Out" 2D Figures

Part 2: Exploring Relationships with Venn & Euler Diagrams

Part 3: Classifying Triangles by Angles Using Euler Diagrams

Part 4: Classifying Triangles by Sides & Angles Using Venn and Euler Diagrams

Part 5: Quadrilaterals

Quadrilaterals - Part 5:

Learn how to classify quadrilaterals--including parallelograms, rectangles, rhombi, and squares--based on their defining attributes using diagrams in this interactive tutorial.

This is part 5 in a 6-part series. Click below to explore the other tutorials in the series.

Exploring Relationships with Venn & Euler Diagrams – Part 2:

Learn how to show relationships represented in Venn & Euler Diagrams as you complete this interactive geometry tutorial.

This is part two of four. Click below to open the other tutorials in the series.

Classifying Triangles by Sides & Angles Using Venn and Euler Diagrams – Part 4:

Learn how triangles can be sorted and classified using side lengths and angle measures in this interactive tutorial.

This is the final tutorial in a four-part series. Click below to open the other tutorials in the series.

Classifying Triangles by Angles using Euler Diagrams – Part 3:

Learn to classify triangles and use Euler diagrams to show relationships, in this interactive tutorial.

This is part-three of four. Click below to open the other tutorials in the series.

"Figuring Out" 2D Figures - Part 1:

Explore 2D (two-dimensional) figures and see how every 2D figure possesses unique attributes in this interactive tutorial.

This is part one of four. Click below to open the other tutorials in the series.

Problem-Solving Tasks

Title Description
Lines of symmetry for triangles:

This activity provides students an opportunity to recognize these distinguishing features of the different types of triangles before the technical language has been introduced. For finding the lines of symmetry, cut-out models of the four triangles would be helpful so that the students can fold them to find the lines.

Lines of symmetry for quadrilaterals:

This task provides students a chance to experiment with reflections of the plane and their impact on specific types of quadrilaterals. It is both interesting and important that these types of quadrilaterals can be distinguished by their lines of symmetry.

Are these right?:

The purpose of this task is for students to measure angles and decide whether the triangles are right or not. Students should already understand concepts of angle measurement  and know how to measure angles using a protractor before working on this task.

Tutorials

Title Description
Categorizing Geometric Shapes: Practice Examples:

This Khan Academy tutorial video presents examples and explanations for categorizations of perpendicular sides and right, obtuse, and acute triangles.

Examples of Triangle Categories:

In this Khan Academy tutorial video triangles are categorized by angles or side lengths of a specified size.

Quadrilateral Overview:

This Khan Academy tutorial video introduces quadrilaterals. their categories, and subcategories.



Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Image/Photograph

Title Description
Clipart: Geometric Shapes:

In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes.

Problem-Solving Tasks

Title Description
Lines of symmetry for triangles:

This activity provides students an opportunity to recognize these distinguishing features of the different types of triangles before the technical language has been introduced. For finding the lines of symmetry, cut-out models of the four triangles would be helpful so that the students can fold them to find the lines.

Lines of symmetry for quadrilaterals:

This task provides students a chance to experiment with reflections of the plane and their impact on specific types of quadrilaterals. It is both interesting and important that these types of quadrilaterals can be distinguished by their lines of symmetry.

Are these right?:

The purpose of this task is for students to measure angles and decide whether the triangles are right or not. Students should already understand concepts of angle measurement  and know how to measure angles using a protractor before working on this task.