Why do I measure?
Why do I need standardized units of measurement?
How does what I measure influence how I measure?
What types of problems are solved with measurement?
What are tools of measurement and how are they used?
How do units within a system relate to each other?
When is an estimate more appropriate than an actual measurement?
What strategies help estimate measurements?
When will I use angle measurement in real-life problem solving?
Lesson Plan C.5-7: Measuring Angles
Lesson Seed C.5-6: Using a Unit Angle to Measure
Lesson Seed C.5-6: Length of the Ray vs. Angle Measure
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Content Emphasis By Clusters in Grade 4
Progressions from Common Core State Standards in Mathematics
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In this unit, students learn that an angle is made up of two rays with a common endpoint or vertex. They explore a totally different type of measurement, that of angles. Unlike length, area, or volume, this measures an angle by the ’turning’ distance between two rays in increments of 1/360 of a circle with the vertex of the angle being at the center of the circle.
One acute angle might be that made by turning 45/360 or 45°. A right angle would be made by one ray moving 90/360 away from the other, or 90°. A straight angle would be made by one ray moving 180/360 away from the other, or 180°.
Students will need many experiences with angles in a variety of positions. For example, the angle in the graphic above is NOT lined up so that one of the rays in a horizontal position. To measure this angle, a student would need to align the protractor or circle protractor to one of the rays of the angle in order to determine its size in degrees.
During this unit, students will measure angles, decompose and compose angles to model complementary and supplementary angles, and solve real world and mathematical problems to find the measurement of unknown angles.
At the completion of the unit on Arithmetic with multi-digit numbers, the student will understand that:
Focus Standards (Listed as Examples of Opportunities for In-Depth Focus in the PARCC Content Framework document):
Possible Student Outcomes:
Evidence of Student Learning:
The Partnership for Assessment of Readiness for College and Careers (PARCC) has awarded the Dana Center a grant to develop the information for this component. This information will be provided at a later date. The Dana Center, located at the University of Texas in Austin, encourages high academic standards in mathematics by working in partnership with local, state, and national education entities. Educators at the Center collaborate with their partners to help school systems nurture students' intellectual passions. The Center advocates for every student leaving school prepared for success in postsecondary education and in the contemporary workplace.
Fluency Expectations and Examples of Culminating Standards:
* A right angle is an angle that point to the right.
* Two right angles represented with different orientations are not equal in measure.
* In order to correctly use a protractor, one ray must be horizontal, like a base.
* No angle can be larger than 180°.
* a right angle and left angle
* Students associate the word ‘right’ with directional language.
Sample Assessment Items:
Interventions/Enrichments/PD: (Standard-specific modules that focus on student interventions/enrichments and on professional development for teachers will be included later, as available from the vendor(s) producing the modules.)
Vocabulary/Terminology/Concepts: This section of the Unit Plan is divided into two parts. Part I contains vocabulary and terminology from standards that comprise the cluster, which is the focus of this unit plan. Part II contains vocabulary and terminology from standards outside of the focus cluster. These “outside standards” provide important instructional connections to the focus cluster.
Part I – Focus Cluster
ray: a subset of a line that has one endpoint and extends infinitely in one direction.
angle: a figure formed by two rays that have the same endpoint. Types of angles include acute, right, obtuse, and reflex angles. Angles are measured in degrees.
right angle: an angle that has a measurement of 90°.
acute angle: an angle that has a measurement of less than 90°.
obtuse angle: an angle that has a measurement greater than 90° but less that 180°.
Part II – Instructional Connections outside the Focus Cluster
point: a position in space
line: a set of points that extend infinitely in two opposite directions.
line segment: a subset of a line bounded by two endpoints.
perpendicular lines: two lines that intersect to form right angles.
parallel lines: two lines on a plane that do not intersect.
two-dimensional figures: a geometric figure that lies entirely in one plane. (Also called plane figures.)
Math Related Literature: