Word (.docx)
Acrobat (.pdf)
Clarifications
Clarification 1: Instruction includes measuring given angles and drawing angles using protractors.
Clarification 2: Instruction includes estimating angle measures using benchmark angles (30°, 45°, 60°, 90° and 180°).
Clarification 3: Instruction focuses on the understanding that angles can be decomposed into non-overlapping angles whose measures sum to the measure of the original angle.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Acute Angle
- Angle
- Obtuse Angle
- Right Angle
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is to build understanding that angles can be measured. Students have experience identifying acute, obtuse, and right angles (MA.4.GR.1.1). Through instruction in this benchmark, students will attach precise measurements to their informal understanding of the angles they have explored.- Students will also estimate angle measures based on their growing familiarity of the size of angles according to the benchmark angles 30°, 45°, 60°, 90° and 180°.
- Instruction should allow students to draw angles of all sizes, including situations where they must make angles that are larger than their protractor or their piece of paper. This will ensure that students have an understanding that the angle measure does not change even if the length of the rays do.
- Instruction should use explicit and direct instruction to show students how to use a protractor (standard or circle) to measure and draw angles. Using circle protractors helps students explore reflex angles.
- Instructional time should also be spent breaking apart angles into smaller angles so that students build understanding that angle measures are additive.
Common Misconceptions or Errors
- Students that have difficulty using a protractor to measure. Assist students with this misconception as they may:
- use the centimeter ruler or inch ruler instead of the baseline when measuring the angles.
- measure the length of each ray and find the sum of the lengths.
- not correctly line up the angle to be measured on the protractor.
Strategies to Support Tiered Instruction
- Instruction includes using a right angle, 90 degrees measure, as a benchmark to estimate angle measures prior to measuring with a protractor. The teacher provides students with a right angle to overlap with the angles they are measuring as a way to compare their size.
- For example, when given an angle, students will determine if the angle is 90 degrees, greater than 90 degrees, or less than 90 degrees. Students then measure the angle using a protractor and determine if their measurement makes sense based on their estimate.
- The teacher provides angles that have a baseline ray labeled so that students know which ray to line up with the baseline on the protractor and begin their measurement from. Students explain how they will use the protractor to measure the angle (which set of numbers they will use to measure and how they know where to stop measuring).
- For example, the teacher provides an angle similar to the one shown below. Students line up the baseline of the protractor with the ray on the angle that is labeled as the baseline. Students will start measuring with the set of numbers that begins with 0 at the end of the ray and follow the measurements around to the point where the other ray intersects with the protractor.
Instructional Tasks
Instructional Task 1
- Use a protractor to find the measure of each indicated angle.
Instructional Items
Instructional Item 1
- Which angles when added together make a right angle?
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Image/Photograph
Lesson Plans
Original Student Tutorials
Perspectives Video: Teaching Ideas
Tutorial
MFAS Formative Assessments
Students are asked to analyze two angles and explain how their measures are determined.
Students are asked to draw and measure acute and obtuse angles whose vertices are at the center of a circle.
Students are asked determine angle measures based on how many one-degree turns are made.
Students are asked to use a protractor to determine the measure of four angles.
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.
Students are asked to draw specified angles within a circle in the context of a real world problem.
Students use a protractor to draw angles with a specified measure.
Students are asked to determine an unknown angle measure that is one component of a larger known angle when given the other components.
Original Student Tutorials Mathematics - Grades K-5
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.
Discover what an angle is by helping to program a robot through an obstacle course in this interactive tutorial.
Learn how to measure angles with a protractor to help get a robot through an obstacle course in this interactive tutorial.
Student Resources
Original Student Tutorials
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.
Type: Original Student Tutorial
Learn how to measure angles with a protractor to help get a robot through an obstacle course in this interactive tutorial.
Type: Original Student Tutorial
Discover what an angle is by helping to program a robot through an obstacle course in this interactive tutorial.
Type: Original Student Tutorial
Tutorial
This Khan Academy tutorial video presents the strategy for finding the measure of one of two adjacent angles, when the sum of both and measure of one are known.
Type: Tutorial
Parent Resources
Image/Photograph
In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes.
Type: Image/Photograph
