# Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and ### Cluster

Geometric measurement: understand concepts of angle and measure angles.

Evidence of Learning Statements

 Students with a level 1 understanding of this standard will most likely be able to: Students with a level 2 understanding of this standard will most likely be able to: Students with a level 3 understanding of this standard will most likely be able to: Students with a level 4 understanding of this standard will most likely be able to: Understand there are 360 one-degree angles in a circle. Know that degrees are a unit of measure for angles. Recognize right, acute, and obtuse angles. Recognize that a circle can be decomposed into different angles (e.g., there are four right angles in a circle). Understand the relationship between an angle and a circle. Represent an angle measure n as n/360 and show that it is made up of n one degree angles. Determine the adjacent angle using knowledge of the degrees of a circle when given the measurement of an angle. Find the measurements of unknown angles when given other angle measures within the circle.

Instructional Focus Statements

Level 3:

The instructional focus for this standard should be around helping students understand the connections that exist between angles and circular measurement. Instruction should be integrated with aspects of standard 4.G.A.1 as that is where students develop an understanding of drawing rays, lines, and angles. The overarching concept of connecting circles and angles is typically foreign to students. It is crucial that students are able to conceptually connect these topics as that understanding will be important in subsequent grades and courses.

Students will have to build the understanding that a circle encompasses 360 degrees. They will then connect this and their understanding of fractions to note that each degree is 1/360 of the way around a circle called a "one degree angle". Students will then be able to generalize this information to understand that an angle turning through n representations of this unit fraction would total that many degrees of measure and represent n/360 of a circle.

Students then must develop an understanding of how to measure an angle with reference to a circle.  At this point, instruction should integrate with standard 4.MD.C.6 where students measure angles using a protractor. In measuring angles, students should equally experience measuring angles inscribed in circles and angles not appearing in relationship to a circle.

Level 4:

Students should be challenged to determine unknown angle measures when given one angle measure within the circle based upon their understanding of angles, including straight angles, coupled with the understanding that a circle encompasses 360 degrees.