Grade 4 Measurement and Data

4.MD.5

About the Math

Full Standard

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

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.
An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Learning Targets

Describe an angle.
Describe an angle's relationship to a circle.
Explain how to measure an angle.

About the Math

An angle is the union of two rays with a common endpoint. The common endpoint is called a vertex. Angles are measured in degrees from 0 to 360. One complete rotation is 360 degrees. Angles have special names based on their degree measures. An acute angle is less than 90 degrees. An obtuse angle is more than 90 degrees. An angle that measures exactly 90 degrees is called a right angle and it looks like a square corner. The measurement of an angle depends upon the fraction of the circle cut off by the rays. The degree measure of an angle can be estimated by comparing it to 90 degrees as more or less than 90 degrees. To find the exact measurement, students need to use a protractor. Essential vocabulary for this standard includes: angle, ray, endpoint, vertex, degree, acute, obtuse, right, and straight. Visit the (online dictionary) for vocabulary support.

Progression of Standard within Grade 4

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1	Quarter 2	Quarter 3	Quarter 4
			Describe what an angle. Describe an angle's relationship to a circle. Explain how to measure an angle.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map. Information is not the complete standard.

Progression Across Grades
Grade 3	Grade 7
This concept is not taught prior to grade 4.	Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (7.G.B.5)

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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

Show an obtuse and an acute angle. What are the possible measurements of the two angles?
How many angles can you find in our classroom? Estimate the size of at least three of the angles that you found.
Tara is thinking of an obtuse angle that is less than 115 degrees. What angle could she be thinking of?
What types of angles can you see in this roller coaster?
Plans for a new roller coaster include a drop of 86 degrees (with 90 degrees being straight down, perpendicular to the ground). However, due to safety regulations, the drop needs to be reduced. What could the angle of the changed drop be?

SLIDE-BASED TASKS

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 14 • Geometry and Angles

Understand and Describe Angles and Their Relationship to a Circle:

Additional Tasks

These links provide instructional ideas connected to this standard.

Cover It Up (Lesson Seed)
The Shape of Things (Lesson Seed)
Angle Hunters (Lesson Seed)
Measuring Angles Activities (Lesson Seeds)
Piece It Together (Inside Mathematics, Problem)
My Name Is Worth (Lesson Seed)
Baseball (Utah Core Academy Lesson)
Guess My Angle! (Georgia Department of Education, pg. 161-167)

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

Print Resources
Book Title	Grade	Pages
Teaching Student-Centered Mathematics	3-5	A Unit Angle, Activity 9.12, Page 272
Brain-Compatible Activities for Mathematics	4-5	82-86
Math In Practice Teaching Fourth-Grade Math	4	Module 14

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

Letters and Angles (HCPSS-adapted print resource)
Dividing Circles into Angles (HCPSS-adapted print resource)

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

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Assessment

Learning Targets

Describe an angle.
Describe an angle's relationship to a circle.
Explain how to measure an angle.

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading.

Rubric for Tasks (pdf)

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