Standard 1 : Reason with shapes and their attributes. (Supporting Cluster) (Archived)



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Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

General Information

Number: MAFS.3.G.1
Title: Reason with shapes and their attributes. (Supporting Cluster)
Type: Cluster
Subject: Mathematics - Archived
Grade: 3
Domain-Subdomain: Geometry

Related Standards

This cluster includes the following benchmarks
Code Description
MAFS.3.G.1.1: 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.
MAFS.3.G.1.2: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MAFS.3.G.1.AP.1a: Identify the attributes of quadrilaterals.
MAFS.3.G.1.AP.2a: Partition a rectangle into equal parts with equal area.
MAFS.3.G.1.AP.1b: Identify different examples of quadrilaterals.


Related Resources

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

Original Student Tutorials

Name Description
Rectangular Road Trip:

Learn about the defining attributes of a rectangle to identify and create rectangles as we visit various national parks in this interactive tutorial.

Square Picnic with Comparison to Rectangles:

Help pack for a square picnic while learning about the defining attributes of a square in comparison to rectangles in this interactive tutorial. 

Square Picnic with Comparison to Rhombi:

Learn about the defining attributes of a square and what makes a square different from a rhombus in this interactive tutorial.

Rhombus Dream: Identifying and Drawing Rhombi:

Learning about the attributes of a rhombus and how to create a rhombus using its attributes in this interactive tutorial.

Educational Game

Name Description
Shape & Solid Exploration: In this game, learners use clues to identify mystery shapes. Use everyday objects (like from the pantry) as the shapes. It is important for learners to be able to describe a shape with correct math vocabulary and to be able to visualize a shape in their head.

Formative Assessments

Name Description
Unit Fractions:

Students divide a hexagon into two, three, and six equal parts and write the unit fraction representing each part.

Two Equal Parts:

Students divide figures into two parts, each having the same area, and write the unit fraction representing each part.

Halves of an Irregular Polygon:

Students partition an irregular hexagon into two equal parts and describe each part using a unit fraction.

Four Parts of the Whole:

Students partition a rectangle into four equal parts and describe each part using a fraction.

Identifying Quadrilaterals – 1:

Students are asked to describe attributes shared by three shapes and to identify a larger category into which these shapes can be placed.

Drawing Quadrilaterals:

Students are asked to draw a shape with four sides that is not a rhombus, rectangle, or square.

Identifying Quadrilaterals - 2:

Students are asked to describe attributes shared by three shapes and to identify a larger category into which these shapes can be placed.

Identifying Polygons:

Students are asked to describe attributes shared by three shapes and to identify a larger category into which these shapes can be placed.

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
Shape Up Your Civility:

Students will be able to listen and cooperate with one another in replicating geometric designs without seeing them and relate this to how citizens demonstrate civility and cooperation to accomplish a common goal.

Coding Geometry Challenges #1-7, 14 & 15:

This set of geometry challenges focuses on creating a variety of polygons as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

 

 

 

Artistic Alley:

Students will use their knowledge of how to identify quadrilaterals and how to analyze data to determine a ranking for the best paver designs for a driveway. In this MEA, students will deepen their understanding of the attributes of parallelograms, rectangles, squares, trapezoids and quadrilaterals that do not belong to any of these categories.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Hoops for Quadrilaterals:

This is an interactive lesson that allows students to inquire, learn, and successfully categorize various quadrilaterals. They will love the challenge and have fun working collaboratively in the classroom.

Best Vegetable Garden:

The students will plan a vegetable garden, deciding which kinds of vegetables to plant, how many plants of each kind will fit, and where each plant will be planted in a fixed-area garden design. Then they will revise their design based on new garden dimensions and additional plant options.  Students will explore the concept of area to plan their garden and they will practice solving 1 and 2-step real-world problems using the four operations to develop their ideas.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Mystery Strips - Fractional Parts of the Whole:

This problem-solving lesson has students working together in groups to discover that fractions are made up of equal parts of one-whole. In this lesson, students are exposed to equivalent fractions as well as challenged to work beyond unit fractions to discover the fractional part of one-whole that the "mystery strips" represent. This highly engaging lesson takes into account all levels of learners and will challenge even your most advanced students.

Quadrilateral Quest:

In this lesson, students categorize shapes identifying the attributes of quadrilaterals. 

Pretzel Quadrilaterals:

This lesson helps students to realize that quadrilaterals have identifying attributes that define them. Students should also discover that a quadrilateral can have multiple names based on the attributes of a category.

Discovering Fractions:

In this lesson students will make initial discoveries about fractions. Students will work together to explain and record the discoveries they make while using manipulatives to explore fractions.

Fractions Meet Pattern Blocks:

Students will identify the fractional parts of a whole using pattern blocks. There is a focus on unit fractions.

It's All About the Shapes:

The teacher reads The Greedy Triangle to the class to explore attributes of figures. As the teacher reads, the students create the shapes in the book using geoboards.  Students follow up their exploration with a card sort. The students create Frayer Models in their journals using information they discovered during the lesson.  

Fraction Counting Book:

Students will make a book of fractions by counting by a specified denominator. They will represent the fractions as pictures, in number form, word form, and on a number line.

Fraction Folding - Part 2:

Students will use foldables to create and name fractions. Students will sing a song to learn the terms numerator and denominator. Students will identify how many unit fractions compose a fraction.

Fraction Folding-Part 1:

In this lesson, students will build the understanding of unit fractions. They will differentiate examples and non-examples of fractional parts of squares. They will label unit fractions and describe unit fractions as those that “build” other fractions.

Presentation/Slideshow

Name Description
Fractions:

This is an accessible, easy-to-read book introducing fractions. It can be downloaded in PowerPoint, Impress, and Flash formats. For struggling or non-readers the book can be read aloud in a variety of voices. All of the books on the Tar Heel Reader site can be used with the Intellikeys keyboard with a custom overlay, a touch screen, and/or 1-3 switches. The text and background colors can be modified for students with visual impairments.

Problem-Solving Tasks

Name Description
Representing Half of a Circle:

This task continues "Which pictures represent half of a circle?" moving into more complex shapes where geometric arguments about cutting or work using simple equivalences of fractions is required to analyze the picture. In order for students to be successful with this task, they need to understand that area is additive.

Geometric pictures of one half:

This task presents students with some creative geometric ways to represent the fraction one half. The goal is both to appeal to students' visual intuition while also providing a hands on activity to decide whether or not two areas are equal. In order for students to be successful with this task, they need to understand that area is additive.

Teaching Ideas

Name Description
Quadrilaterals: This interactive Java applet allows users to manipulate a square rectangle into various quadrilaterals. There are four tabs on the site including Learner, Activity, Help, and Instructor tabs. On the Activity tab, users can create various quadrilaterals. An information window provides data about the shape created including side lengths and angles. The Learner and Help tabs provide information about the activity. The Instructor tab has a worksheet on quadrilaterals that contains exploration questions which instructors can use as guiding questions to lead students in comparing/contrasting the similarities and differences between various quadrilaterals. (Users can also explore tessellations made from quadrilaterals on this site. Please note: this is not part of third grade standards.)
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
Introduction to types of quadrilaterals:

In this tutorial video from Khan Academy, discover attributes and features of four-sided shapes, including parallelograms, rhombuses, rectangles, and squares.

Polygon Gallery:

This combination of illustrations and narration defines convex as well as concave polygons and describes the features of various polygons. Examples of polygons shown include triangles and quadrilaterals of various types, including some that are convex and some that are concave, and even one that has a hole in it. Narration or read-along text describes the shapes for the user. Copyright 2005 Eisenhower National Clearinghouse

Virtual Manipulatives

Name Description
Exploring Fractions:

Match shapes and numbers to earn stars in this fractions game.

  • Match fractions using numbers and pictures
  • make the same fractions using different numbers
  • Match fractions in different picture patterns
  • Compare fractions using numbers and patterns
Polygon Sort: This interactive Flash activity asks the user to sort shapes into a 2 by 2 chart, known as a Carroll Diagram, based on their properties. Properties used to sort include "quadrilateral" or "not quadrilateral" and "regular polygon" or "not regular polygon."
Fraction Models:

An interactive tool to represent a fraction circle, rectangle, or set model with numerators and denominators ranging from 1 to 100. The decimal and percent equivalents of the created fraction are also displayed.

Shape Tool:

This virtual manipulative allows you to create, color, enlarge, shrink, rotate, reflect, slice, and glue geometric shapes, such as: squares, triangles, rhombi, trapezoids and hexagons.



Student Resources

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

Original Student Tutorials

Title Description
Rectangular Road Trip:

Learn about the defining attributes of a rectangle to identify and create rectangles as we visit various national parks in this interactive tutorial.

Square Picnic with Comparison to Rectangles:

Help pack for a square picnic while learning about the defining attributes of a square in comparison to rectangles in this interactive tutorial. 

Square Picnic with Comparison to Rhombi:

Learn about the defining attributes of a square and what makes a square different from a rhombus in this interactive tutorial.

Rhombus Dream: Identifying and Drawing Rhombi:

Learning about the attributes of a rhombus and how to create a rhombus using its attributes in this interactive tutorial.

Presentation/Slideshow

Title Description
Fractions:

This is an accessible, easy-to-read book introducing fractions. It can be downloaded in PowerPoint, Impress, and Flash formats. For struggling or non-readers the book can be read aloud in a variety of voices. All of the books on the Tar Heel Reader site can be used with the Intellikeys keyboard with a custom overlay, a touch screen, and/or 1-3 switches. The text and background colors can be modified for students with visual impairments.

Problem-Solving Tasks

Title Description
Representing Half of a Circle:

This task continues "Which pictures represent half of a circle?" moving into more complex shapes where geometric arguments about cutting or work using simple equivalences of fractions is required to analyze the picture. In order for students to be successful with this task, they need to understand that area is additive.

Geometric pictures of one half:

This task presents students with some creative geometric ways to represent the fraction one half. The goal is both to appeal to students' visual intuition while also providing a hands on activity to decide whether or not two areas are equal. In order for students to be successful with this task, they need to understand that area is additive.

Tutorials

Title Description
Introduction to types of quadrilaterals:

In this tutorial video from Khan Academy, discover attributes and features of four-sided shapes, including parallelograms, rhombuses, rectangles, and squares.

Polygon Gallery:

This combination of illustrations and narration defines convex as well as concave polygons and describes the features of various polygons. Examples of polygons shown include triangles and quadrilaterals of various types, including some that are convex and some that are concave, and even one that has a hole in it. Narration or read-along text describes the shapes for the user. Copyright 2005 Eisenhower National Clearinghouse

Virtual Manipulatives

Title Description
Exploring Fractions:

Match shapes and numbers to earn stars in this fractions game.

  • Match fractions using numbers and pictures
  • make the same fractions using different numbers
  • Match fractions in different picture patterns
  • Compare fractions using numbers and patterns
Polygon Sort: This interactive Flash activity asks the user to sort shapes into a 2 by 2 chart, known as a Carroll Diagram, based on their properties. Properties used to sort include "quadrilateral" or "not quadrilateral" and "regular polygon" or "not regular polygon."
Shape Tool:

This virtual manipulative allows you to create, color, enlarge, shrink, rotate, reflect, slice, and glue geometric shapes, such as: squares, triangles, rhombi, trapezoids and hexagons.



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.

Presentation/Slideshow

Title Description
Fractions:

This is an accessible, easy-to-read book introducing fractions. It can be downloaded in PowerPoint, Impress, and Flash formats. For struggling or non-readers the book can be read aloud in a variety of voices. All of the books on the Tar Heel Reader site can be used with the Intellikeys keyboard with a custom overlay, a touch screen, and/or 1-3 switches. The text and background colors can be modified for students with visual impairments.

Problem-Solving Tasks

Title Description
Representing Half of a Circle:

This task continues "Which pictures represent half of a circle?" moving into more complex shapes where geometric arguments about cutting or work using simple equivalences of fractions is required to analyze the picture. In order for students to be successful with this task, they need to understand that area is additive.

Geometric pictures of one half:

This task presents students with some creative geometric ways to represent the fraction one half. The goal is both to appeal to students' visual intuition while also providing a hands on activity to decide whether or not two areas are equal. In order for students to be successful with this task, they need to understand that area is additive.

Tutorial

Title Description
Introduction to types of quadrilaterals:

In this tutorial video from Khan Academy, discover attributes and features of four-sided shapes, including parallelograms, rhombuses, rectangles, and squares.

Virtual Manipulatives

Title Description
Exploring Fractions:

Match shapes and numbers to earn stars in this fractions game.

  • Match fractions using numbers and pictures
  • make the same fractions using different numbers
  • Match fractions in different picture patterns
  • Compare fractions using numbers and patterns
Polygon Sort: This interactive Flash activity asks the user to sort shapes into a 2 by 2 chart, known as a Carroll Diagram, based on their properties. Properties used to sort include "quadrilateral" or "not quadrilateral" and "regular polygon" or "not regular polygon."
Shape Tool:

This virtual manipulative allows you to create, color, enlarge, shrink, rotate, reflect, slice, and glue geometric shapes, such as: squares, triangles, rhombi, trapezoids and hexagons.