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Grade 4, Module 4, Topic A
4th Grade Math
Focus Area – Topic A
Math Parent Letter
Words to Know:
Lines and Angles
Module 4: Angle Measure and Plane Figures
This document is created to give parents and students a better
understanding of the math concepts found in Eureka Math (© 2013
Common Core, Inc.) that is also posted as the Engage New York
material which is taught in the classroom. Module 4 of Eureka Math
(Engage New York) covers angle measures and plane figures.
Focus Area – Topic A Lines and Angles
Words to Know:
Point -precise location in the plane
Line - straight path with no thickness that extends in both
directions without end
Line segment – part of a line connecting two endpoints
Ray - a part of a line which starts at a point and goes off
in a particular direction to infinity.
 Always name a ray by starting with its endpoint
OBJECTIVES OF TOPIC A
 Identify and draw points, lines, line segments, rays, and angles and
recognize them in various contexts and familiar figures.
 Use right angles to determine whether angles are equal to, greater
than, or less than right angles. Draw right, obtuse, and acute angles.
 Identify, define, and draw perpendicular and parallel lines.
Arc -connected portion of a circle
Angle - union of two different rays sharing a vertex
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
Obtuse angle - angle with a measure greater than 90
degrees but less than 180 degrees
Acute angle - angle with a measure of less than 90
degrees
Module 4: Angle Measure and Plane Figures
In topic A students use their understanding of angles to
explore relationships between pairs of lines, defining and
recognizing intersecting, perpendicular, and parallel lines.
Their knowledge of right angles leads them to identify and
define as well as construct perpendicular lines. Students
learn how lines that never intersect also have a special
relationship and are called parallel. They explore these
concepts by finding parallel and perpendicular lines in
common shapes and objects.
Example Problem and Answer
Label points on the figure and then use those points to
label and name representations of each of the following in
the table below: ray, line, line segment, and angle.
Words to Know:
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.
Intersecting lines - lines that contain at least one point in
common
Trace at least one pair of lines that are perpendicular.
Trace at least one pair of lines that appear to be parallel.
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 4, Module 4, Topic B
4th Grade Math
Focus Area – Topic B
Angle Measurement
Module 4: Topic B: Angle Measurement
Math Parent Letter
This document is created to give parents and students a better
understanding of the math concepts found in Eureka Math (©
2013 Common Core, Inc.) that is also posted as the Engage New
York material which is taught in the classroom. Module 4 of
Eureka Math (Engage New York) covers angle measures and
plane figures.
Example Problem and Answer
Students are asked to identify the measures of angles.
Protractor Types
Students will use two different types of protractors in class.
The Standard Protractor or Half Protractor
In this example, they will place the center point of the
protractor over point L. Then match the 0° line of
the protractor along line segment LJ. They can then
read where line segment LK crosses the edge of the
protractor to find the angle measurement.
The Circular Protractor
The measure of this angle is 40°.
The students will write angle KLJ is 40° or
OBJECTIVES OF TOPIC B
Use protractors to measure and draw angles.
Sketch given angle measures and verify with a protractor.
Identify and measure angles as turns and recognize them in
various contexts.
.
Using a Protractor to Draw Angles
Students are asked to draw angles that match a certain degree measure. These are steps for drawing a 70° angle.
Step 4 - Use the straight edge of the protractor to draw
the next ray beginning at point A and continuing to the
mark you made above the 70°.
Step 1 - Draw a ray and label the endpoint A.
.
Step 2 - Line up the protractor, placing the center over
endpoint A making sure the ray lines up with the 0° line.
Step 3 - Find 70° on the protractor and draw a small
point right above it.
Step 5 - Use the protractor to verify the angle is 70°.
Angles as Turns
Students further explore angle measure as an amount of turning. They reason that a ¼ turn is a right angle and measures 90°, a
½ turn measures 180°, and a ¾ turn measures 270°. They go on to identify these angles in their environment.
Example Question and Answer
Joe stood in the middle of the yard and faced the house. Joe turned 90° to the right. To what was Joe now facing?
Answer: Joe would be facing the park.
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 4, Module 4, Topic C
4th Grade Math
Module 4: Topic C:
Problem Solving with the Addition of Angle Measures
Math Parent Letter
This document is created to give parents and students a
better understanding of the math concepts found in
Eureka Math (© 2013 Common Core, Inc.) that is also
posted as the Engage New York material which is taught
in the classroom. Module 4 of Eureka Math ( Engage
New York) covers angle measures and plane figures.
Focus Area– Topic C
Addition of Angle Measures
Example Problem and Answer
In class, students will use concrete examples to discover the
additive nature of angle measure. Working with pattern blocks,
they see that the measures of all of the angles at a point, with no
overlaps or gaps, add up to 360 degrees, and they use this fact to
find the measure of the pattern blocks’ angles.
Words to Know:
Degree -measure of an angle Subdivide the length around
a circle into 360 arcs of equal length. A central angle for
any of these arcs is called a one-degree angle and is said to
have angle measure of 1°.
Adjacent angle - two angles are adjacent if they have a
common side and a common vertex (corner point) and
don't overlap. Consider the example below.
Complementary angles - two angles with a sum of 90 °.
.
The students will write addition and subtraction equations to
solve unknown angle problems.
Write an equation and solve for the measure of
In this example, angle A measures 40° and angle B
measures 50°. Together they form a 90° angle. They are
complementary.
OBJECTIVES OF TOPIC B
Decompose angles using pattern blocks.
Use the addition of adjacent angle measures to solve
problems using a symbol for the unknown angle measure.
.
The student should see angle BDA is
a 90° angle or a right angle. Since
angle CDA has a measure of 20°,
they can subtract the angle they
know to find the unknown angle
90° = 20° + X °
or 90° - 20° = X °
X = 70°
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 4, Module 4, Topic D
4th Grade Math
Module 4: Topic D: Two-Dimensional Figures and Symmetry
Math Parent Letter
This document is created to give parents and students a
better understanding of the math concepts found in
Eureka Math (© 2013 Common Core, Inc.) that is also
posted as the Engage New York material which is taught
in the classroom. Module 4 of Eureka Math (Engage
New York) covers angle measures and plane figures.
Line of Symmetry - line through a figure such that when
the figure is folded along the line two halves are created
that match up exactly
Consider figures A, B,
and C. Only one of
them shows a line of
symmetry. Students will
need to see that figure
A can be folded along
the dotted line making
the halves line up
exactly. Therefore,
figure A has the line of
symmetry.
Focus Area – Topic D
Two-Dimensional Figures and Symmetry
Words to Know:
Triangle - A triangle consists of three points and the
three line segments between them. The three segments
are called the sides of the triangle and the three points
are called the vertices.
Obtuse triangle - triangle
with an interior obtuse angle
Right triangle- triangle that
contains one 90° degree angle
Scalene triangle - triangle with
no sides or angles equal
Isosceles triangle - triangle
with at least two equal sides
Example Problem and Answer
Students are asked to decide if a given triangles can be
described as right triangle and an isosceles triangle.
Consider this example.
OBJECTIVES OF TOPIC B
Recognize lines of symmetry for given two-dimensional
figures; identify line-symmetric figures and draw lines of
symmetry.
Analyze and classify triangles based on side length, angle
measure, or both.
Define and construct triangles from given criteria. Explore
symmetry in triangles.
Classify quadrilaterals based on parallel and perpendicular
lines and the presence or absence of angles of a specified
size.
Reason about attributes to construct quadrilaterals on
square or triangular grid paper.
Can
be described
as a right triangle and an
isosceles triangle?
Answer: Yes because it has a right angle and two equal
sides.
Module 4: Topic D:
Two-Dimensional Figures and Symmetry
Two-Dimensional Figures and Symmetry
Words to Know:
Attribute - a characteristic that describes an object
Polygon - closed two-dimensional figure with straight
sides
Quadrilateral - polygon with four sides
Example Problem and Answer
Follow the directions below to draw a figure.
Rectangle - quadrilateral
with four right angles
Square - rectangle with all
sides of equal length
Rhombus - quadrilateral
with all sides of equal
length
Parallelogram quadrilateral with two pairs
of parallel sides
Trapezoid - quadrilateral
with at least one pair of
parallel sides
Example Problem and Answer
Explain the attribute that makes a square a special
rectangle.
Which figure did you draw? What attributes does it have?
A rectangle has 4 sides and 4 right angles. A square has 4
sides and 4 right angles as well so a square is a rectangle.
We say it is a special rectangle because it has 4 equal sides.
I drew triangle JKL or
. It has 3 sides. It is a
scalene triangle because it has no sides or angles that are
equal.
This information was generously shared by LPSS, Lafayette, LA