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

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.2.G.1
Title: Reason with shapes and their attributes. (Additional Cluster)
Type: Cluster
Subject: Mathematics - Archived
Grade: 2
Domain-Subdomain: Geometry

Related Standards

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MAFS.2.G.1.AP.1a
Identify two-dimensional shapes, such as rhombuses, pentagons, hexagons, octagons, and ovals, as well as equilateral, isosceles, and scalene triangles.
MAFS.2.G.1.AP.1b
Distinguish two- or three-dimensional shapes based upon their attributes (i.e., number of sides, equal or different lengths of sides, number of faces, and number of corners).
MAFS.2.G.1.AP.1c
Draw two-dimensional shapes with specific attributes.
MAFS.2.G.1.AP.3a
Partition circles and rectangles into two, three, and four equal parts.
MAFS.2.G.1.AP.3b

Label a partitioned shape (e.g., one whole rectangle was separated into two halves; one whole circle was separated into three thirds.)


MAFS.2.G.1.AP.2a
Count the squares that fill a rectangle drawn on graph paper.

Related Resources

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

Educational Games

Match the 2D Shape:

Play the concentration game. Match the 2D shape to the correct name.

Type: Educational Game

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.

Type: Educational Game

Formative Assessments

Which of These are Cubes?:

Students are shown a set of three-dimensional figures and are asked to identify the cubes. In addition, they are asked to explain why the other figures are not cubes.

Type: Formative Assessment

Different Halves:

Students consider if two different shaped halves of the same rectangle represent equal shares.

Type: Formative Assessment

Four Sided Figures:

Students are shown a quadrilateral and asked to identify it. Then students are asked to draw another example of a quadrilateral that is different from the one that they were shown.

Type: Formative Assessment

Complete the Rectangle:

Students are given a rectangle with one column and one row of unit squares (same size squares) drawn. Students are asked to complete and then find the total number of same size squares in the partition.

Type: Formative Assessment

Three Sided Figures:

Students are asked to draw a triangle and justify his or her drawn shape. Then students are shown a figure that is not a triangle, but that has three sides and asked to determine if the figure on the worksheet is a triangle.

Type: Formative Assessment

Figures With Five Sides:

Students are asked to draw a five-sided figure and name the figure.

Type: Formative Assessment

How Many Units?:

Students are given a rectangle with some columns and rows partially constructed. Students are asked to find how many same-size squares are in the rectangle.

Type: Formative Assessment

Construct Rows and Columns:

Students are given a rectangle with tick marks drawn horizontally on one side of the rectangle and vertically on the bottom of the rectangle. Students are asked to partition the rectangle into columns and rows and then determine how many unit squares (same-size squares) are in the rectangle.

Type: Formative Assessment

Partition the Rectangle Into Unit Squares:

Students are given a rectangle with one unit square (same size square) drawn in the corner of the rectangle. Students are asked to draw the remaining unit squares and then find the total number of unit squares in the rectangle.

Type: Formative Assessment

Different Fourths:

Students consider if two different shaped fourths of the same rectangle represent equal shares.

Type: Formative Assessment

How Many Fourths Are in a Whole?:

Students partition a rectangle into four equal parts and consider what fraction represents the whole.

Type: Formative Assessment

Halves, Thirds, and Fourths:

Students partition three different circles into two, three, and four equal parts and consider what fraction each part represents.

Type: Formative Assessment

Lesson Plans

Partition the Flag:

In this Math and Social Studies Civics lesson plan, students will use their mathematical knowledge of fractions as equal groups, and knowledge of wholes, and fourths. Additionally, students will use two interrelated symbols representing Florida, to design a new Florida State Flag into four equal parts. Students will discuss and reason why Marjory Stoneman Douglas and the Florida Everglades were chosen as symbols of Florida, and brainstorm other possible symbols that could be used based on their personal experiences. As students design their flag, they will determine the best way to partition the rectangular shape into fourths, so that the four areas are equal-sized parts.

Type: Lesson Plan

Let's "Face" it!:

Triangles, Quadrilaterals, Pentagons, and Hexagons! Oh My! Students will get into shape after reading "The Greedy Triangle" by Marilyn Burns. They will explore their own classroom and identify the many shapes that can be found! They will also be able to identify the plane shapes on three-dimensional figures as the faces of the figures. The lesson includes some printable solid figures that the students can construct themselves!

Type: Lesson Plan

Discovering Attributes of Shapes:

The students will use real world items in the classroom and manipulatives to identify, discuss and compare the attributes of triangles, quadrilaterals, pentagons, hexagons, and cubes. Students will fold and make a cube as they practice identifying shapes.

Type: Lesson Plan

Chocolate Pieces:

Students will learn how to partition a rectangle while actively engaged. Students will be working with post-it notes and a Chocolate Bar worksheet. By the end of this lesson, students will be able to identify and explain the difference between a row and a column. They will also be able to count the total number of squares that make up the rectangle.

Type: Lesson Plan

Rectangles Rule! (Lesson 1 of 2):

In this lesson students will use rulers to measure the side lengths of rectangles and use 1-inch square tiles to cover the rectangles. Students will count the total number of square units to find the area and explore relationships between the lengths of the sides and the total number of tiles.  In # 66132 Rectangles Rule! Team Challenge (Lesson 2 of 2), students will expand their understanding of tiling to find area to connect area to a multiplication formula.

Type: Lesson Plan

Rectangles Rule! Team Challenge (Lesson 2 of 2):

This guided inquiry lesson is designed to follow another CPALMS published lesson #63297 Rectangles Rule! In that first lesson, students used a ruler to measure the side lengths of rectangles and used 1-inch square tiles to find the area of the rectangle. In this lesson, students will use the inquiry process to problem-solve a team challenge: Partition a rectangle into same-size squares using a ruler and determine a formula for finding area (area = length x width). Students will brainstorm, investigate, and share their solutions on how their team worked together to find a solution to the challenge. 

Type: Lesson Plan

Animal Sanctuary Engineering Design Challenge:

This Engineering Design Challenge is a hands-on investigation in both math and science. Students will be able to use prior knowledge and problem solving skills to solve non-routine problems and real-world situations, using mathematical and scientific models. It is a great way to introduce your students to real-world problem solving. Students will be engaged in hands-on learning by designing and creating an enclosure for zoo animals. Both math and science standards have been incorporated for an integrated lesson.

Type: Lesson Plan

Which Rectangle is Bigger?:

Students will learn how to partition rectangles into equal parts and write equations to represent the parts. They will gain a basic understanding of area from the book Bigger, Better, BEST! by Stuart J. Murphy.

Type: Lesson Plan

Equal Shares: I Care:

Students will understand the concept of halves, thirds and fourths through the exploration of circles, squares and rectangles. Students will recognize that a half of a circle may not look like a half of a square or a rectangle. Also, students will demonstrate that halves, thirds and fourths of different sizes of circles, squares and rectangles will not look the same.

Type: Lesson Plan

The Greedy Shapes:

The lesson Greedy Shapes will give opportunities for students to use their knowledge of attributes of shapes (number of sides, sides of equal length, number of vertices, shapes that are closed or not, curved or straight edges) to sketch triangles, rectangles, squares, and hexagons. 

Type: Lesson Plan

The Toy Box Company:

The focus of this lesson is to devise a plan, and justify it, in order to select the most appealing toy box.

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.

Type: Lesson Plan

Three Billy Goats Gruff Build a Bridge - An Engineering Design Challenge:

This Engineering Design Challenge is intended to help students apply the concepts of force from SC.2.P.13.1 (investigate the effect of applying various pushes and pulls on different objects) as they build bridges to hold the greatest load. It is also intended to help students apply the concepts of money from MAFS.2.MD.3.8 (Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately) as they strive to construct the most cost effective bridge. It is not intended as an initial introduction to these concepts.

Type: Lesson Plan

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.  

Type: Lesson Plan

Thirds:

In this lesson, students will gain experience partitioning rectangles and circles into equal shares of halves, thirds, and fourths.

Type: Lesson Plan

Lighthouses and Lenses - An Engineering Design Challenge:

This Engineering Design Challenge is intended to help students apply the concepts of force from SC.2.P.13.1 (investigate the effect of applying various pushes and pulls on different objects), the concept of wind from SC.2.E.7.4 (investigate that air is all around us and that moving air is wind), and practice working with money (MAFS.2.MD.3.8 solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately) as they build structures to withstand the force of high-speed winds. The first day's lesson also provides practice in recognizing and drawing shapes (MAFS.2.G.1.1). It is not intended as an initial introduction to these concepts.

Type: Lesson Plan

Attributes of Geometric Shapes:

This resource is a fun and engaging activity that will allow the students to identify and name shapes by their attributes. The students will move around and construct various geometric figures in order to build a solid understanding of the figures.

Type: Lesson Plan

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.

Type: Lesson Plan

Going On a Shape Hunt: Integrating Math and Literacy :

Integrating mathematics and literacy allows students to develop an understanding of the place of mathematics in their world. Students are introduced to the idea of shapes through a read-aloud session with an appropriate book. They then use models to learn the names of shapes, work together and individually to locate shapes in their real-world environment, practice spelling out the names of shapes they locate, and reflect in writing on the process. This lesson provides opportunities to engage students using many different learning modalities.

Type: Lesson Plan

Original Student Tutorials

Partitioning Cakes: Thirds:

It's time for cake! Learn to partition cakes into thirds in this interactive student tutorial. 

Type: Original Student Tutorial

Partitioning Pizzas: Halves:

Learn to partition circular and rectangular pizzas into halves in this interactive tutorial. 

Type: Original Student Tutorial

Partitioning Circular Pies: Fourths:

It's time for pie! Learn to partition circular pies into fourths in this interactive student tutorial. 

Type: Original Student Tutorial

Partitioning Rectangular Pies: Fourths:

It's Thanksgiving and time for pie! Learn to partition rectangular pies into fourths in this interactive student tutorial.

Type: Original Student Tutorial

Chocolate Partitioning!:

Learn to partition a rectangular chocolate bar into equally sized pieces by making rows and columns in this interactive tutorial. 

 

Note: This tutorial extends beyond partitioning a rectangle into 4 equal sized shares and explores partitioning into higher numbers.

Type: Original Student Tutorial

Shapes in Space:

Learn how to recognize and draw triangles, pentagons and hexagons using the shapes' attributes in this space-themed, interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Tasks

Which Pictures Represent One Half?:

The purpose of this task is for students to see different ways of partitioning a figure into two or more equal shares, by which we mean decomposing the figure into "pieces" with equal area.

Type: Problem-Solving Task

Representing Half of a Rectangle:

This task is for assessment purposes, providing a context for indentifying different ways of representing half of an object, a rectangle in this case. The task may also be used for instructional purposes but if so the teacher may wish to introduce some other ways of showing one half of the rectangle, such as dividing along a diagonal (and shading in one piece) or dividing it into four equal pieces, shading in two pieces that only touch at a corner.

Type: Problem-Solving Task

Teaching Idea

Polygons and Shapely Lines:

This activity gives students practice drawing straight lines with a ruler and looking for and categorizing shapes, for example, by the number of sides in polygons. The Teachers' Notes page includes suggestions for implementation, discussion questions and ideas for extension.

Type: Teaching Idea

Tutorial

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

Type: Tutorial

Virtual Manipulatives

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."

Type: Virtual Manipulative

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.

Type: Virtual Manipulative

Shape Cutter:

This virtual manipulative allows students to draw geometric shapes and then decompose and recompose them into other shapes, using slides, turns, and flips to cut and move pieces around.

Type: Virtual Manipulative

Student Resources

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

Original Student Tutorials

Partitioning Cakes: Thirds:

It's time for cake! Learn to partition cakes into thirds in this interactive student tutorial. 

Type: Original Student Tutorial

Partitioning Pizzas: Halves:

Learn to partition circular and rectangular pizzas into halves in this interactive tutorial. 

Type: Original Student Tutorial

Partitioning Circular Pies: Fourths:

It's time for pie! Learn to partition circular pies into fourths in this interactive student tutorial. 

Type: Original Student Tutorial

Partitioning Rectangular Pies: Fourths:

It's Thanksgiving and time for pie! Learn to partition rectangular pies into fourths in this interactive student tutorial.

Type: Original Student Tutorial

Chocolate Partitioning!:

Learn to partition a rectangular chocolate bar into equally sized pieces by making rows and columns in this interactive tutorial. 

 

Note: This tutorial extends beyond partitioning a rectangle into 4 equal sized shares and explores partitioning into higher numbers.

Type: Original Student Tutorial

Shapes in Space:

Learn how to recognize and draw triangles, pentagons and hexagons using the shapes' attributes in this space-themed, interactive tutorial.

Type: Original Student Tutorial

Educational Game

Match the 2D Shape:

Play the concentration game. Match the 2D shape to the correct name.

Type: Educational Game

Problem-Solving Tasks

Which Pictures Represent One Half?:

The purpose of this task is for students to see different ways of partitioning a figure into two or more equal shares, by which we mean decomposing the figure into "pieces" with equal area.

Type: Problem-Solving Task

Representing Half of a Rectangle:

This task is for assessment purposes, providing a context for indentifying different ways of representing half of an object, a rectangle in this case. The task may also be used for instructional purposes but if so the teacher may wish to introduce some other ways of showing one half of the rectangle, such as dividing along a diagonal (and shading in one piece) or dividing it into four equal pieces, shading in two pieces that only touch at a corner.

Type: Problem-Solving Task

Tutorial

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

Type: Tutorial

Virtual Manipulatives

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."

Type: Virtual Manipulative

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.

Type: Virtual Manipulative

Shape Cutter:

This virtual manipulative allows students to draw geometric shapes and then decompose and recompose them into other shapes, using slides, turns, and flips to cut and move pieces around.

Type: Virtual Manipulative

Parent Resources

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

Problem-Solving Tasks

Which Pictures Represent One Half?:

The purpose of this task is for students to see different ways of partitioning a figure into two or more equal shares, by which we mean decomposing the figure into "pieces" with equal area.

Type: Problem-Solving Task

Representing Half of a Rectangle:

This task is for assessment purposes, providing a context for indentifying different ways of representing half of an object, a rectangle in this case. The task may also be used for instructional purposes but if so the teacher may wish to introduce some other ways of showing one half of the rectangle, such as dividing along a diagonal (and shading in one piece) or dividing it into four equal pieces, shading in two pieces that only touch at a corner.

Type: Problem-Solving Task

Virtual Manipulatives

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."

Type: Virtual Manipulative

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.

Type: Virtual Manipulative