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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.

Standard 3 : Geometric measurement: understand concepts of angle and measure angles. (Additional Cluster)Archived
Cluster Standards

This cluster includes the following benchmarks.

Visit the specific benchmark webpage to find related instructional resources.

  • MAFS.4.MD.3.5 : Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
    1. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
    2. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
  • MAFS.4.MD.3.6 : Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
  • MAFS.4.MD.3.7 :

    Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.


Cluster Information
Number:
MAFS.4.MD.3
Title:
Geometric measurement: understand concepts of angle and measure angles. (Additional Cluster)
Type:
Cluster
Subject:
Mathematics - Archived
Grade:
4
Domain-Subdomain
Measurement and Data
Cluster Access Points

This cluster includes the following Access Points.

Cluster Resources

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

Original Student Tutorials
  • Additive Angles: Wondrous Windows: Decompose and compose various angles while exploring clocks and windows in this interactive tutorial.

    Note: this tutorial exceeds clarification limits and is meant as enrichment for students to improve their problem-solving skills.

  • Additive Angles: Tessellating Tiles: Are you up for a challenge? You will use tile designs to explore how angles can be decomposed into smaller angles and how those parts can be shown as addends in equations in this interactive tutorial.

    Note: this tutorial exceeds clarification limits and is meant as enrichment for students who met the standards to increase problem-solving skills.

  • Map the ROC: Angle Measure: Learn how to measure angles with a protractor to help get a robot through an obstacle course in this interactive tutorial.

  • Dash or Bash: Discovering Angles: Discover what an angle is by helping to program a robot through an obstacle course in this interactive tutorial.

Formative Assessments
  • Understanding Angles: Students are asked to recognize the additive nature of angles to determine an unknown angle measure.

  • Drawing and Measuring Angles: Students are asked to draw and measure acute and obtuse angles whose vertices are at the center of a circle.

  • Using Known Angles: Students are asked to determine adjacent angle measurements using the additive structure of angle measurement and known angle measurements.

  • Using a Protractor to Draw Angles: Students use a protractor to draw angles with a specified measure.

  • Turns on a Skateboard: Students are asked to determine an unknown angle measure that is one component of a larger known angle when given the other component.

  • Measuring Angles With a Protractor: Students are asked to use a protractor to determine the measure of four angles.

  • What Is the Measure of the Angle?: Students are asked to determine an unknown angle measure that is one component of a larger known angle when given the other components.

  • Town of Happyville: Students are asked to draw specified angles within a circle in the context of a real world problem.

  • This Angle: Students are given two angles with the same angle measure but with sides of different lengths and asked to explain which component of an angle determines its measure.

  • Lawn Sprinkler: Students are asked determine angle measures based on how many one-degree turns are made.

  • Determining An Angle’s Measure: Students are asked to analyze two angles and explain how their measures are determined.

  • 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
  • Angles (Clipart ETC): This large collection of clipart contains images of angles that can be freely used in lesson plans, worksheets, and presentations.
Lesson Plans
  • Coding Geometry Challenge # 12 & 13: This set of geometry challenges focuses on creating circles and calculating area/circumference 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

  • 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.

  • 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.

  • 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.

  • Edible Angles: Decomposing Angles Into Parts of a Whole: This lesson is designed to review help students apply their understanding that when an angle is decomposed into parts, the measure of the parts is equal to the whole measure of the original angle. 

  • 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.

  • What's Your Angle? Measuring and Drawing Angles With Protractors: In this lesson, students will be able to measure various angle sizes using a protractor. Students will also learn how to use a protractor to draw angles when given a specific degree of measure. Students will also know how to compare and contrast angles of different sizes using math terminology.

  • 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.

  • Protractor Power: How to measure and create angles using a protractor: Students will learn how to use a protractor to measure and create angles of different sizes. Students will work cooperatively to explore this skill.

  • 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.

  • Angles for $500: This lesson engages students in measuring angles using a protractor.

  • 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.

  • What’s Your Angle?: In this lesson, students will use addition or subtraction to find the measure of two adjacent angles and determine the measure of an unknown angle.

Problem-Solving Task
  • 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.

Teaching Idea
  • 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.
Tutorials