Standard 1 : Draw and identify lines and angles, and classify shapes by properties of their lines and angles. (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.4.G.1
Title: Draw and identify lines and angles, and classify shapes by properties of their lines and angles. (Additional Cluster)
Type: Cluster
Subject: Mathematics - Archived
Grade: 4
Domain-Subdomain: Geometry

Related Standards

This cluster includes the following benchmarks
Code Description
MAFS.4.G.1.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
MAFS.4.G.1.2: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
MAFS.4.G.1.3: Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MAFS.4.G.1.AP.1a: Identify a point, line and line segment and rays in two-dimensional figures.
MAFS.4.G.1.AP.1b: Identify perpendicular and parallel lines in a two-dimensional figure.
MAFS.4.G.1.AP.1c: Identify an angle in a two-dimensional figure.
MAFS.4.G.1.AP.2a: Identify and sort objects based on parallelism, perpendicularity, and angle type.
MAFS.4.G.1.AP.3a: Identify figures that have a line of symmetry.


Related Resources

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

Original Student Tutorials

Name Description
The Nightmare of Pouring Polygons: Quadrilateral Classification:

Overcome the nightmare of quadrilateral classification based on the presence of parallel, perpendicular, and congruent sides as you complete this interactive tutorial.

Shape Surfing: Finding Parallel and Perpendicular Lines:

Help a surfing crab learn how to find parallel and perpendicular sides in a variety of polygons as you complete this interactive tutorial!

ROC Star: Angle Classification:

Classify and name angles in two-dimensional shapes to help a robot create a path using angles in this interactive tutorial.

The Symmetry Sisters Save the Day:

Help the Symmetry Sisters save the City of Symmetry Line and the State of Arithmetic from the Radical Rat in this interactive tutorial!

These are the Right Triangles:

Identify right triangles and explain the properties shared by all right triangles in this interactive tutorial.

The Geometry Super Heroes Save Mathopolis:

Identify parallel lines and line segments, as well as perpendicular lines and line segments in two-dimensional figures by joining Parallel Man and Perpendicular Man as they help Mayor Mathematics save Mathopolis in this interactive tutorial.

Formative Assessments

Name Description
Identifying and Explaining Symmetry:

Students are asked to determine if lines drawn on two-dimensional figures are lines of symmetry and to explain their decisions.

All About Angles:

Students are asked to identify right, acute, and obtuse angles in a two-dimensional figure, and explain the differences among these types of angles.

Using Lines of Symmetry:

Students are asked to use a line of symmetry to complete a drawing. Additionally, they consider how to describe a line of symmetry.

Parallel and Perpendicular Sides:

Students are asked to identify parallel and perpendicular sides and explain how they know.

Line Symmetry:

Students are asked to identify line-symmetric figures and then draw the lines of symmetry.

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.

Squares and Lines of Symmetry:

Students are asked to determine how many lines of symmetry a square has by drawing the lines of symmetry. Students then consider whether all quadrilaterals have four lines of symmetry.

Sketching Triangles:

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

Sketching Quadrilaterals:

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

Locating Points, Lines, and Rays:

Students locate points, lines, line segments, and rays in a given diagram.

Lines, Rays, and Line Segments:

Students are asked to draw parallel lines, perpendicular lines, a point, and a line segment. Students also explain how a line segment is different from a ray or line.

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
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.

 

 

 

Lesson #2 - Moon Phase Unit:

This is lesson 2 of 3 in the Moon Phase unit. This lesson will help students design a flowchart model to find the phase of the Moon by making decisions based on certain conditions. This lesson also gives students insight into working with the design model made earlier and an opportunity to upload/draw costumes of different lunar phases in Scratch.

Lesson #1 - Moon Phase Unit :

This is lesson 1 of 3 in the Moon Phase Unit. This lesson introduces students to the eight Moon phases and their names in a counter-clockwise sequential order starting with the New Moon as phase 1. Students will also be introduced to how a flowchart can help make decisions, in this case whether or not the Moon is full.

Angles All Around Us:

This lesson will provide students with the opportunity to see angles all around them. Students will be able to see how and where geometry exist in the real world.  Please note that this lesson focuses on identifying acute, obtuse, right, straight and reflex angles.

Geometry at the County Fair:

In this lesson which focuses primarily on angles, students work in collaborative groups to construct a two-dimensional model of a county fair. 

ABC Symmetry:

Students will explore the concept of line symmetry in this lesson. Students will explore two-dimensional pictures and decide whether or not each image has symmetry. Students will also fold pre-cut capital letters to decide whether or not each letter has symmetry.

Snowflake Geometry: No Two Alike!:

In this lesson students will make snowflakes, promoting creativity and self-expression, and use them to identify geometric terms. It also gives them an opportunity to follow a sequenced set of instructions for a given outcome.

Angles All Around Us:

This is a lesson that introduces right, acute, obtuse, reflex, straight angles in a fun and challenging way.

Which Angle is Which?:

This is a fun, hands-on activity designed to help students identify and measure obtuse, acute, right, straight and reflex angles. Students create a manipulative tool in their math journals to help them gain understanding of this concept.

Points, Lines, and Angles, Oh My!:

In this lesson, students work to identify points, lines, line segments, rays, angles and perpendicular and parallel lines. Students create webs of yarn and analyze the web for geometric properties listed above. A teacher can select which vocabulary terms are appropriate for the class.

Symmetrical Solutions:

Students will use paper cutout and geoboards to find and create lines of symmetry. Students will have the opportunity to work with a partner and independently.

A Closer Look at Quadrilaterals - The Parallelogram Connection:

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

Geometry, USA:

Students will draw a town based on a set of given directions using the geometry terms (parallel, perpendicular, and intersecting lines). This activity is designed to be taught after the students having learned the meanings of the geometry terms and the ability to identify examples of each.

Runway Rotations:

Students will use small paper airplanes to model rotations required to turn onto a runway. Students will rotate planes 45, 90, 180, 270, and 360 degrees. Students will identify and describe the results of rotations using benchmark angles.

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.

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.

Lines of symmetry for circles:

This is an instructional task that gives students a chance to reason about lines of symmetry and discover that a circle has an an infinite number of lines of symmetry. Even though the concept of an infinite number of lines is fairly abstract, students can understand infinity in an informal way.

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 Ideas

Name Description
Where Are They?: This activity asks students to visualize and generate shapes, paying close attention to the definitions of the polygons. Learners are given a sheet of isometric grid paper and asked to find and sketch 12 specific shapes. A recording sheet is attached where students must justify the shape they generated by using the definitions of the polygons. Ideas for implementation, extension, and support are included along with printable grids and a link to a website with shape definitions. It would be beneficial for students to work with partners in order to construct viable arguments and critique the reasoning of others.
Same Shapes: The problem challenges and extends students' spatial awareness with 2D shapes. The students are given three different irregular shapes. The goal is to divide each of them into two parts that are exactly the same shape and size.

The Teacher's Notes page offers rationale, suggestions for implementation with a link to Happy Halving (cataloged separately), discussion questions, and ideas for extension and support.

Teachers can print the "printable page" for students. Students could cut out shapes and fold to find the line of symmetry, use grid paper, and/or use geoboards.
Angle Hunting: In this activity, learners use a hand-made protractor to measure angles they find in playground equipment. Learners will observe that angle measurements do not change with distance, because they are distance invariant, or constant. Note: The "Pocket Protractor" activity should be done ahead as a separate activity (see related resource), but a standard protractor can be used as a substitute.
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.

Parallel and Perpendicular Lines Introduced:

This Khan Academy tutorial video defines and illustrates parallel and perpendicular lines.

Recognizing Acute, Right, and Obtuse Angles:

This Khan Academy tutorial video identifies acute, right, and obtuse angles and justifies each identification. 

Lines, Line segments and Rays:

This video discusses the differences between lines, line segments and rays.

Virtual Manipulative

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.



Student Resources

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

Original Student Tutorials

Title Description
The Nightmare of Pouring Polygons: Quadrilateral Classification:

Overcome the nightmare of quadrilateral classification based on the presence of parallel, perpendicular, and congruent sides as you complete this interactive tutorial.

Shape Surfing: Finding Parallel and Perpendicular Lines:

Help a surfing crab learn how to find parallel and perpendicular sides in a variety of polygons as you complete this interactive tutorial!

ROC Star: Angle Classification:

Classify and name angles in two-dimensional shapes to help a robot create a path using angles in this interactive tutorial.

The Symmetry Sisters Save the Day:

Help the Symmetry Sisters save the City of Symmetry Line and the State of Arithmetic from the Radical Rat in this interactive tutorial!

These are the Right Triangles:

Identify right triangles and explain the properties shared by all right triangles in this interactive tutorial.

The Geometry Super Heroes Save Mathopolis:

Identify parallel lines and line segments, as well as perpendicular lines and line segments in two-dimensional figures by joining Parallel Man and Perpendicular Man as they help Mayor Mathematics save Mathopolis in this interactive tutorial.

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.

Lines of symmetry for circles:

This is an instructional task that gives students a chance to reason about lines of symmetry and discover that a circle has an an infinite number of lines of symmetry. Even though the concept of an infinite number of lines is fairly abstract, students can understand infinity in an informal way.

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.

Parallel and Perpendicular Lines Introduced:

This Khan Academy tutorial video defines and illustrates parallel and perpendicular lines.

Recognizing Acute, Right, and Obtuse Angles:

This Khan Academy tutorial video identifies acute, right, and obtuse angles and justifies each identification. 

Lines, Line segments and Rays:

This video discusses the differences between lines, line segments and rays.

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.



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.

Lines of symmetry for circles:

This is an instructional task that gives students a chance to reason about lines of symmetry and discover that a circle has an an infinite number of lines of symmetry. Even though the concept of an infinite number of lines is fairly abstract, students can understand infinity in an informal way.

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.

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.