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

Related Standards

This cluster includes the following benchmarks
Code Description
MAFS.1.G.1.1: Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
MAFS.1.G.1.2: Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
MAFS.1.G.1.3: Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MAFS.1.G.1.AP.1a: Distinguish two-dimensional shapes based upon their defining attributes (i.e., size, corners, and points).
MAFS.1.G.1.AP.2a: Draw or build two- and three-dimensional shapes.
MAFS.1.G.1.AP.3a: Partition circles and rectangles into two and four equal parts.


Related Resources

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

Original Student Tutorials

Name Description
Shape Sleuths: Trapezoids:

Learn about the defining attributes of trapezoids in this interactive tutorial series about shapes.

Click below to learn about other shapes.

Note: This tutorial uses the definition of trapezoid that includes exactly one pair of parallel sides.

Shape Sleuths: Rectangles and Squares:

Help find clues to identify rectangles and squares and their defining attributes in this interactive tutorial.

Circus Fun: The Search for Circles:

Learn the attributes, or characteristics, of a circle in this interactive tutorial.

Shape Sleuths: Hexagons:

Learn about the defining attributes of hexagons in this interactive tutorial series about shapes.

Click below to learn about other shapes.

Shape Sleuths: Triangles:

Learn about the defining attributes of triangles in this interactive tutorial series about shapes.

Click below to learn about other shapes.

Equal Shares Heroes Find Fourths:

Be a hero and partition circles and rectangles into four equal shares. Describe equal shares using the words "fourths" and "quarters" in this interactive tutorial.

Equal Shares Heroes:

Help the heroes separate circles and rectangles into equal shares and describe the equal shares as "halves" or "half of" as you complete 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
Partition A Rectangle:

Students partition a rectangle into two equal parts and then describe the parts.

Which Is Less?:

Students are asked to share a rectangular cake between two people and then among four people and decide which results in smaller pieces.

Turning a Square:

Students are shown a square in various orientations and asked if it is still a square.

Partition the Pizza:

Students fold a picture of a circular pizza into four equal parts and then are asked to describe each part.

Is it Still a Rectangle?:

Students discuss the defining and non-defining attributes of rectangles.

Draw Triangles:

Students draw two triangles and are prompted to describe the triangles in terms of defining attributes.

Half of a Rectangle:

Students are asked to partition a rectangle into halves.

Fill in the Missing Part:

Students view a composite shape with a missing piece and identify shapes that can fill in the space.

Composing a Trapezoid:

Students use triangles to compose a trapezoid.

Compose Shapes with Triangles and a Trapezoid:

Students compose new shapes from equilateral triangles and a trapezoid.

Compose Shapes With Triangles:

Students join right triangles together to compose a rectangle and then use the rectangle to compose a new shape. Students describe this new shape made from the composite shape.

Attributes of a Hexagon:

Students draw two hexagons and are asked to justify their drawings.

Building With Three Dimensional Shapes:

Students use different three dimensional shapes to compose a composite shape.

 

Note: This task includes the use of triangular prisms.

Lesson Plans

Name Description
Build a New Shape:

Build a New Shape is a lesson for building composite shapes from triangle(s), square(s) and trapezoid(s). This lesson uses a story and certain pattern block manipulative to help students to gain this skill.

It's a Piece of Cake...and Pizza:

This lesson focuses only on partitioning circles and rectangles into two equal shares, describing the shares with the word half/halves and half of. Students will be partitioning paper pizzas and cakes to learn the concepts and then building pizzas through a game.

Equal Shares at the Zoo? Who Knew!:

In this lesson, students will be partitioning shapes into halves and fourths. The class will get a letter from a zoo requesting their help in solving some problems with designing the layout of animal enclosures.

Must or Might: Exploring Defining Attributes of 3-D Figures:

The purpose of this lesson is for students to examine defining and non-defining attributes of 3-dimensional figures. Students compare and contrast various representations of 3-dimensional figures (including real-world objects) to determine what the solid must have, compared to what it might have. This exploration is also supported by sorting 3-dimensional figures.

Puzzled by Pattern Blocks!:

In this lesson, the students will use two-dimensional pattern blocks to compose new shapes and fill in composite outlines of shapes.

Shape Identifying and Sketching:

In this lesson students will describe attributes of triangles, rectangles, squares, and hexagons and identify these shapes by their attributes. Given the name of one of these shapes, students will use their knowledge of the shape's attributes to represent the shape with a sketch.

Halves and Quarters of Circles:

In this lesson, students will learn how to partition circles into halves and quarters/fourths and examine how partitioning a circle into more equal shares creates smaller shares.

Life Jackets:

In this MEA the students are to decide what criteria is the most important for a company to consider when choosing life jackets. Students will use data tables of qualitative information to solve the problem.

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.

Pizza Anyone? Exploring Halves and Fourths/Quarters:

This lesson practices the partitioning a whole to equal shares for halves, fourths, and quarters through pizza and candy bar manipulatives. Students are then challenged to demonstrate how many different ways they can fold a square sticky note into fourths!

Halves, Quarters and Fourths:

In this lesson, the students will partition circles and rectangles into halves and fourths in order to gain a solid foundation for fractions.

Halves and Fourths:

In this lesson, students will gain experience partitioning rectangle and circles into equal shares of halves and fourths and naming the parts appropriately.

Fair Share Picnic:

In this introductory lesson on halves, pairs of students will rotate through math stations to prepare for a picnic. They will use paper materials to represent wholes and partition each whole into halves, using applicable mathematics vocabulary.

Who gets the bigger share?:

Use this interactive lesson to help your students learn about fractions by partitioning circles and rectangles into two, three, or equal-sized parts and by using a real life scenario.

Being Shapely!:

In this lesson, students will work collaboratively to identify and sketch shapes with defining and non-defining attributes.

Fun with Shapes:

In this lesson students explore the composing of new shapes from other two-dimensional shapes. The students will utilize math benchmarks as they analyze math solutions and explain their solutions. Since the lesson uses composing, it is also a good lesson to use to show decomposing (taking a shape apart).

Quilt Squares:

Students will use pattern blocks to create a quilt square for the Quick Quilters Society. They will have to consider information on a data chart to help them create their squares. They will have to add up the cost to make their square, too.

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.

Halves and Fourths:

This lesson uses a discovery approach to exploring the meaning of halves and fourths. The students will utilize math benchmarks as they analyze math solutions and explain their solutions. This lesson also teaches students that they can decompose larger sized parts to make smaller sized parts.

Halves and Wholes:

In this lesson, students will gain a foundation for fractions by partitioning circles and rectangles into two equal-sized shares.

Composite Creature:

The students will use pattern blocks to build and draw new composite geometric shapes, ultimately using composite shapes to form a creature.

I'll Share With You:

This lesson focuses on the beginning understanding of fractions through fair-sharing. Students will partition circles and rectangles into 2 and 4 equal-sized parts and be able to describe these parts using appropriate language such as halves and fourths.

A Fourth of That?:

Students will partition circles and rectangles into four equal-sized parts. This is a foundational building block of fractions. Students should also develop an understanding of the idea of the whole. This is part of a series of lessons dealing with the foundation for fractions. The other two lessons are Resource ID 46582 and 46846. Throughout the three lessons the students are creating a Fraction Book.

Half of This, A Fourth of That, A Whole Lot of Fun!:

Students will partition circles and rectangles into two and four equal-sized parts. They will also explore and discuss the concept that decomposing into more equal shares creates smaller shares. This is a foundational building block of fractions. Students should also develop an understanding of the idea of the whole. This is part of a series of lessons dealing with the foundation for fractions. The other two lessons are Resource IDs 46582 and 46764. Throughout the three lessons the students are creating a Fraction Book.

Half of This?:

Students will partition circles and rectangles into two equal-sized parts. This is a foundational building block of fractions. Students should also develop an understanding of the idea of the whole. This is part of a series of lessons dealing with the foundation for fractions. The other two lessons are Resource ID 46764 and 46846. Throughout the three lessons the students are creating a Fraction Book.

Shape Detectives:

In this hands-on lesson, students will become Shape Detectives as they identify the two-dimensional shapes, such as triangles, squares and rectangles, needed to build three-dimensional figures including rectangular prisms, square pyramids and cubes. The students will gain an understanding of how two-dimensional shapes are joined together to form three-dimensional figures as well as creating an edible example!

Problem-Solving Tasks

Name Description
Overlapping Rectangles:

The purpose of this task is to give students an opportunity to compose and decompose polygons to make rectangles. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment.

Make Your Own Puzzle:

The purpose of this task is to give students a hands-on experience with composing and decomposing geometric figures and is meant as an instructional task.

Counting Squares:

The purpose of this task is to give students an opportunity to compose and decompose squares. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment. However, if presented as a brainteaser it can be useful for giving the students practice in recognizing squares and stimulate interest as students compete to try to find the most squares.

Teaching Ideas

Name Description
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.
Shape Hunt:

To give students opportunities to recognize, describe, build, and explore shapes in many different contexts.

Virtual Manipulatives

Name Description
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.

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.



Student Resources

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

Original Student Tutorials

Title Description
Shape Sleuths: Trapezoids:

Learn about the defining attributes of trapezoids in this interactive tutorial series about shapes.

Click below to learn about other shapes.

Note: This tutorial uses the definition of trapezoid that includes exactly one pair of parallel sides.

Shape Sleuths: Rectangles and Squares:

Help find clues to identify rectangles and squares and their defining attributes in this interactive tutorial.

Circus Fun: The Search for Circles:

Learn the attributes, or characteristics, of a circle in this interactive tutorial.

Shape Sleuths: Hexagons:

Learn about the defining attributes of hexagons in this interactive tutorial series about shapes.

Click below to learn about other shapes.

Shape Sleuths: Triangles:

Learn about the defining attributes of triangles in this interactive tutorial series about shapes.

Click below to learn about other shapes.

Equal Shares Heroes Find Fourths:

Be a hero and partition circles and rectangles into four equal shares. Describe equal shares using the words "fourths" and "quarters" in this interactive tutorial.

Equal Shares Heroes:

Help the heroes separate circles and rectangles into equal shares and describe the equal shares as "halves" or "half of" as you complete this interactive tutorial. 

Problem-Solving Tasks

Title Description
Overlapping Rectangles:

The purpose of this task is to give students an opportunity to compose and decompose polygons to make rectangles. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment.

Counting Squares:

The purpose of this task is to give students an opportunity to compose and decompose squares. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment. However, if presented as a brainteaser it can be useful for giving the students practice in recognizing squares and stimulate interest as students compete to try to find the most squares.

Virtual Manipulatives

Title Description
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.

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.



Parent Resources

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

Problem-Solving Tasks

Title Description
Overlapping Rectangles:

The purpose of this task is to give students an opportunity to compose and decompose polygons to make rectangles. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment.

Make Your Own Puzzle:

The purpose of this task is to give students a hands-on experience with composing and decomposing geometric figures and is meant as an instructional task.

Counting Squares:

The purpose of this task is to give students an opportunity to compose and decompose squares. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment. However, if presented as a brainteaser it can be useful for giving the students practice in recognizing squares and stimulate interest as students compete to try to find the most squares.

Virtual Manipulative

Title Description
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.