Standard #: MA.4.GR.1.1


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Informally explore angles as an attribute of two-dimensional figures. Identify and classify angles as acute, right, obtuse, straight or reflex.


Clarifications


Clarification 1: Instruction includes classifying angles using benchmark angles of 90° and 180° in two-dimensional figures.

Clarification 2: When identifying angles, the expectation includes two-dimensional figures and real-world pictures.



General Information

Subject Area: Mathematics (B.E.S.T.)
Grade: 4
Strand: Geometric Reasoning
Standard: Draw, classify and measure angles.
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Acute Angle 
  • Angle 
  • Obtuse Angle 
  • Reflex Angle 
  • Right Angle 
  • Straight Angle

 

Vertical Alignment

Previous Benchmarks

 

Next Benchmarks

 

Purpose and Instructional Strategies

The purpose of this benchmark is to begin the understanding of angles and how they can be identified in lines and shapes. Understanding angles will be used to define shapes by their attributes. This builds on the work students completed in grade 3 to identify perpendicular lines in shapes in mathematical and real-world situations (MA.3.GR.1.1). 
  • During instruction, students should gain experience using benchmark angles of 90° and 180° (MTR.6.1). For right angles (90°) students can use the corner of a piece of paper. By lining the edge of the corner of the paper on one ray to the vertex of the angle, students can determine that angles that are smaller than the corner are acute and angles that are larger than the corner are obtuse. Similarly, students can use the side of a piece of paper to determine if the angles are greater than 180°. Students believe a wide angle with short sides may seem smaller than a narrow angle with long sides. Students can compare two angles by tracing one and placing it over the other. Students will then realize that the length of the sides does not determine whether one angle is larger or smaller than another angle. The measure of the angle does not change.
Benchmark angles

 

Common Misconceptions or Errors

  • Students believe a wide angle with short sides may seem smaller than a narrow angle with long sides. Students can compare two angles by tracing one and placing it over the other. Students will then realize that the length of the sides does not determine whether one angle is larger or smaller than another angle. The measure of the angle does not change.

 

Strategies to Support Tiered Instruction

  • Instruction includes providing a graphic organizer and several examples of each type of angle (acute, right, obtuse, straight and reflex). The graphic organizer will have angles labeled on them for the students to use to help them classify the figures provided. 
    • For example, the teacher provides a graphic organizer similar to the one shown below. Along with the graphic organizer, the teacher provides examples of various angles to classify. 
a graphic organizer
  • Instruction includes providing a right angle and a straight angle printed on a clear transparency or sheet protector. Students lay the angles over angle examples provided by the teacher to help them classify the angles as less than 90 degrees (acute angle), greater than 90 degrees (obtuse angle), exactly 90 degrees (right angle), exactly 180 degrees (straight angle), or greater than 180 degrees (reflex angle). Students trace one angle and place it over the other to compare them. 
    • For example, the teacher may provide the student with a clear transparency with a right angle printed on it. The teacher provides sample angles and asks students to place the transparency over the angles. The students sort the angles into greater than 90 degrees, less than 90 degrees, and equal to 90 degrees. The teacher will then provide a straight angle printed on a transparency and have students use that to classify the angles that were sorted as greater than 90 degrees into an additional grouping. Students will determine if the angles are equal to 180 degrees or greater than 180 degrees.

 

Instructional Tasks

Instructional Task 1 (MTR.4.1) 

Part A: Draw and label an example of 3 objects that have a right angle. 
Part B: Draw and label and example of 3 objects that have an acute angle. 
Part C: Draw and label an example of 3 objects that have an obtuse angle. 
Part D: Is it possible to find an object with a reflex angle? Why or why not?

 

Instructional Items

Instructional Item 1 

Which statement correctly describes the figure? 

figures and statements

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.



Related Courses

Course Number1111 Course Title222
5012060: Grade Four Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))


Related Access Points

Access Point Number Access Point Title
MA.4.GR.1.AP.1 Informally explore angles as an attribute of two-dimensional figures. Limit angles to acute, obtuse and right.


Related Resources

Formative Assessments

Name Description
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.

Circle the Angles

Students are asked to circle figures that show angles from a set of figures and then describe the defining attributes of angles.

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
Using Machine Learning and Computational Thinking to Train an AI Model

Students will explore Artificial Intelligence (AI) and use computational thinking and Machine Learning (ML) to pretrain a model to recognize and identify objects, including geometric shapes and aircraft. They will used unplugged activities to mimic sorting and classification of the objects using their prior knowledge and then make connections to human learning and Machine Learning. Students will then problem solve and propose solutions using computational thinking to improve the ML model to better recognize the objects. This lesson is an integrated Computer Science, Science and Math lesson designed for students in grades 3-5 to apply math and science content knowledge while exploring and using computational thinking as they think like Computer Engineers and reflect on potential career paths.

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. 

Waterpark Angles

Your students have been hired as a team to build an amazing new slide for the brand new Water World theme park! Their teams will work to build multiple water slides and will decide which angle degree best helps the marble shoot farthest. Throughout the lesson they will be working with identifying and measuring angles while relating angle types and their measurements. Students will also be working with the idea of kinetic and potential energy.

Angles, angles, everywhere!

This is an introductory lesson that allows students to explore complementary and supplementary angles and their relationships. Students will measure the degrees for sets of angles. They will then use their knowledge of straight, right, obtuse, and acute angles to make connections to complementary, supplementary, adjacent, and vertical angles. This lesson provides opportunities for kinesthetic, auditory, and visual learning.

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.

Angle Your Way Around

In this lesson students will be introduced to the protractor and benchmark angles, practice reading angles properly, make estimates on angle degrees, measure angles precisely, and participate in a small group activity using their new skills.

Kissing “V”s

This lesson uses a paper-cutting activity to teach vertical angles. The lesson provides examples in which students must solve equations to find missing measures.

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.

Original Student Tutorials

Name Description
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.

These are the Right Triangles

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

Perspectives Video: Expert

Name Description
B.E.S.T. Journey

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. mathematics benchmarks in this Expert Perspectives video.

Perspectives Video: Teaching Ideas

Name Description
Classifying Squares and Rectangles

Unlock an effective teaching strategy for classifying squares and rectangles in this Teacher Perspectives video for educators.

Discovering Math Vocabulary in Context

Unlock an effective teaching strategy for vocabulary instruction in this Teacher Perspectives video for educators.

Finding Angles on Clocks

Unlock an effective teaching strategy for identifying angles in this Teacher Perspectives video for educators.

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 Task

Name Description
Finding an unknown angle

The purpose of this task is to give students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90° and that angle measure is additive.

Tutorials

Name Description
Recognizing Acute, Right, and Obtuse Angles

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

Angle Measurements and Circle Arcs

This Khan Academy tutorial video demonstrates the relationship between the measurement of an angle and the arc of a circle.

Angle Basics

This Khan Academy tutorial video presents how an angle is formed and labeled.

Student Resources

Original Student Tutorials

Name Description
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.

These are the Right Triangles:

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

Problem-Solving Task

Name Description
Finding an unknown angle:

The purpose of this task is to give students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90° and that angle measure is additive.

Tutorials

Name Description
Recognizing Acute, Right, and Obtuse Angles:

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

Angle Measurements and Circle Arcs:

This Khan Academy tutorial video demonstrates the relationship between the measurement of an angle and the arc of a circle.

Angle Basics:

This Khan Academy tutorial video presents how an angle is formed and labeled.



Parent Resources

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.

Problem-Solving Task

Name Description
Finding an unknown angle:

The purpose of this task is to give students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90° and that angle measure is additive.



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