Primary Standard:
MAFS.4.MD.3.5: Recognize angles as geometric shapes that are formed when 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
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.
MAFS.4.G.1.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Content Knowledge:
In prior grades, students have worked with angles/vertices within geometric shapes, mostly counting the number of vertices, and sometimes recognizing right angles as “square” angles. In 4th grade, students will be introduced to the understanding of measuring angles, and the unit of measurement in degrees.
In this Unit, students will relate angles to circles, and measuring angles as a rotation. They use the benchmark measurements of 90○ to estimate the measurement of other angles. To find the exact measurement, students are taught to use a protractor (both full circle and semi-circle). Through investigations, observations, and discussions students learn that angle measure is additive which includes finding the sum of two angles when the measure of one angle is missing. Using degree measures, students are also able to identify and label types of angles as right, acute, obtuse, and straight. This understanding will be used in the following Geometry Unit where students will identify angles within geometric shapes, and use these angles to classify triangles, quadrilaterals and other polygon shapes.
GCG 1 – Learning Goal: As a mathematician, I can Identify and classify angles based on a comparison to right angles
- Step 1: Identify points, lines, line segments, and rays
- Step 2: Recognize an angle is formed where two rays meet, use letters to name an angle
- Step 3: Recognize a right angle is a “square corner,” use a right angle to identify acute and obtuse angles (without measuring in degrees)
GCG 2 – Learning Goal: As a mathematician, I can Estimate angles and use a protractor to measure and draw angles
- Step 1: Identify angles are measured using degrees and unit degrees are 1/360 of a circle
- Step 2: Use prior knowledge of angles to estimate a measure as acute or obtuse
- Step 3: Measure angles using a protractor within 180 degrees or 360 degrees with a circular protractor
- Step 4: Sketch angles of given degree measures
GCG 3 – Learning Goal: As a mathematician, I can Solve problems involving addition and subtraction to find unknown angle measures