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.
Measurement Topic
This standard is reported on the report card in these quarters as follows:
4th Grade Students Learning 4th Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic:Demonstrates understanding of measurement and geometry.
3rd Grade Students Learning 4th Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic:Demonstrates understanding of measurement, data and geometry.
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 dictionaryLinks to an external site.) 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.
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)
These tasks can be used with small group or whole group instruction.
Using the circle side of the Geoboard and two AngLegs attached together, students will investigate how an angle is measured in reference to a circle with its center at the common endpoint of the rays. Begin with the two AngLegs together with the common endpoint in the center of the circle. Tell students that when we measure an angle, we are measuring how many degrees it revolves in a circle and that we measure the whole rotation as 360 degrees. Students can rotate one of the AngLegs all the way around the circle and explain that is has traveled 360 degrees. With the AngLegs back together, rotate one of the AngLegs halfway around the circle. Attach the points with a rubber band and ask students to predict the measurement of this angle. Students might say that it is half of 360 degrees and then need to compute to find an accurate answer. Continue creating angles with rubber bands and AngLegs for angles that are 90 and 45 degrees.
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.
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.
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.