Download Measuring Angles and Using Angles to Solve Problems

Grade 4 Unit 4.2
Measuring Angles and
Using Angles to Solve Problems
Vocabulary to Know:
Key Content from This Unit:
Students understand that an angle is formed when two
rays share a common endpoint. They recognize that angles
can be measured using tools and can refer to the turn
around the center of a circle. The focus is for students to
conceptually understand that angles are measured in
degrees and a degree consists of a turn. It takes 360 turns
to complete a circle. Students recognize that angles are
additive. For example, 45 one-degree angles are equal to
a 45-degree angle. In addition, students decompose (or
divide) an angle into parts that add up to the measure of
\
the original angle. They measure angles using a
protractor and sketch angles of specified measures.
Given a geometrical drawing like the one
below, students will learn to use what they
know to solve for an unknown angle measure.
Solve for < TRU.
< QRS is a straight angle.
What came before this:
In grade 2, students recognized, drew,
and analyzed shapes having specified
attributes. They also partitioned circles
into two, three, or four equal shares. In
grade 3, students compared and classified
shapes by their sides and the number of
angles.
What comes after this:
In grade 5, students will understand that
attributes of two-dimensional figures also
belong to all subcategories. For example, all
rectangles have four right angles and
squares are rectangles, so all squares have
four right angles.
Angle: union of two different rays sharing a
common vertex
Acute Angle: angle with a measure of less
than 90 degrees
Obtuse angle: angle with a measure greater
than 90 degrees but less than 180 degrees
Parallel: two lines in a plane that do not
intersect
Perpendicular: Two lines are perpendicular
if they intersect, and any of the angles
formed between the lines is a 90° angle
Right angle: angle formed by perpendicular
lines, measuring 90 degrees
Straight angle : angle that measures 180
degrees
Triangle: A triangle consists of three noncollinear points and the three line segments
between them.
Vertex : a point, often used to refer to the
point where two lines meet, such as in an
angle or the corner of a triangle
Common Core Focus:
Understand that an angle is formed wherever
two rays share a common endpoint.
Understand that a circle has 360 one-degree
turns and each degree represents 1/360 of the
arc of a circle.
Use a protractor to measure and sketch angles
in whole-number degrees.
Recognize that an angle is made up of nonoverlapping parts and angle measures are
additive.
Recognize that as an angle turns n units, it
measures n degrees
4. MD.5, 4. MD.6, 4. MD.7
Unit 4.4.2, Created Fall 2014
Spotlight on the Math Practices
Reason Abstractly and Quantitatively
Mathematically proficient students will recognize angle
measure as additive in relation to the reference to a circle.
In this unit, students will reason abstractly and
quantitatively when they:
Represent a problem with symbols
Explain their thinking
Use numbers flexibly by applying properties of
operations and place value
Examine the reasonableness of their
answers/calculations
How Can You Help?

Continue to review vocabulary in this
unit as there are many new terms.

Practice adding to make 90, 180, 270
and 360, as well as subtracting from those
numbers. This will be useful when students
are solving problems.
KEY MATHEMATICAL MODELS of the COMMON CORE
Pattern Blocks
Some Resources to Help at Home



http://www.shodor.org/interactivate/activities/Angles/ - angle measurement game
http://www.xpmath.com/forums/arcade.php?do=play&gameid=75#.Ug4vHVPodJN - play Space Angle to find
the angle measurement
https://learnzillion.com/lessons/2633-measure-full-and-half-rotations - learn how to form rays by looking at
real-world situations
Unit 4.4.2, Created Fall 2014