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Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Maryland College and Career-Ready Standards
In this unit, students will build their understanding of geometry by making constructions, identifying attributes within geometric figures, such
as perpendicular and parallel lines, obtuse, right, and acute angles, and classify figures based on those attributes.
Students will also understand angles as the space between intersecting rays or line segments. They will see angles as parts of a circle and
will be able to measure angles in degrees using information about the angle in relation to a circle or a protractor.
Students will recognize patterns within a group of shapes and be able to make a conjecture based on the pattern. Patterns will also be
found when studying symmetry of shapes. Students will look at repeating shape patterns and make algebraic conjectures by studying the
terms in the pattern and noticing patterns in the multiples matched with each term.
Research
Students, by 4th grade, should be ready to make conjectures about relationships they notice within geometry. This helps student learn to
analyze and interpret the world around them and gives students tools for solving problems.
Geometry instruction should focus on the relationship among geometric figures and the properties of those figures, not just naming shapes
or figures. Geometric thinking extends students mathematical thinking within other concepts.
Helping Children Learn Mathematics Reys, 2004
“As students sort, build, draw, model, trace, measure, and construct, their capacity to visualize geometric relationships will develop” (p.
165) Students can learn to be special and visual thinkers, they need rich experiences provided for them to develop this skill.
Navigations through Geometry NCTM, 2000
As students learn geometric concepts, they pass through five sequential levels of development, called the Van Hiele levels. The levels are not based
on age/grade, instead they describe how we think and what types of geometric ideas we think about. A student is likely to be at different levels at any
one time. Geometric experience is the greatest single factor influencing advancement through the levels. It is important to be aware of these levels, so
that instruction can be designed to help students move through this hierarchy or thinking. “When instruction or language is at a level higher than that of
the students, there will be a lack of communication. Students required to wrestle with objects of thought that have not been constructed at the earlier
level may be forced into rote learning and achieve only temporary and superficial success.” (p208)
The first three levels (0-2) of thinking will most likely be developed during elementary school and are briefly described below. See TSCM pages 206-210
for more detailed information.
Level 0: Visualization: Students identify shapes/figures only on the bases of appearance. Instruction needs to include examples of a variety of each
type of shape shown in various orientations. This encourages students to make generalizations about common features.
Level 1: Analysis: Students begin to analyze shapes and figures based on properties and attributes. Students make generalizations about how different
shapes relate to one another by spending time comparing and classifying properties of shapes.
Level 2: Informal Deduction: Students can generalize relationships between various shapes.
Students are able to justify their generalizations (“if-then” reasoning) by providing examples and non-examples. (not full proofs)
Level 3: Formal Deduction: This is the level of the traditional high school geometry course.
Level 4: Rigor: This is the level of college mathematics.
Teaching Student Centered Mathematics Van de Walle, 2006
1
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
The chart below highlights the key understandings of Unit 7 along with important questions that teachers should pose to
promote these understandings. The chart also includes key vocabulary that should be modeled by teachers and used by
students to show precision of language when communicating mathematically.
Enduring Understandings
Two-dimensional figures can be
analyzed and classified by their
properties.
Parallel sides, perpendicular sides,
angle measures, and symmetry can
be used to classify geometric
figures.
Some two-dimensional figures have
one or more lines of symmetry.
Angles are measured in degrees
using protractors.
An angle can be decomposed into
two or more smaller angles. The
original angle measure is equal to
the sum of the smaller angle
measures.
Essential Questions
How can two-dimensional figures
be classified?
How can parallelism,
perpendicularity, and angle
measure be used to analyze
quadrilaterals and triangles?
How are quadrilaterals similar and
different?
How are triangles alike and
different?
How do I know when a figure is
symmetrical?
How do you measure an angle?
How do you construct an angle of
a given measure?
How can an angle be divided?
Key Vocabulary
acute angle/triangle
angle
circle
decompose
degree
endpoint
figure
geometric shape
intersect
line
line segment
parallel
perpendicular
point
protractor
obtuse angle/triangle
one-degree angle
ray
right angle/triangle
straight
unknown
vertex
equilateral triangle
isosceles triangle
scalene triangle
line of symmetry
Background Reading
Focus in Grade 4:
Teaching with
Curriculum Focal Points
Teaching StudentCentered Mathematics
– Grades 3-5
Putting the Practices
into Action:
Implementing the
Common Core
Standards for
Mathematical Practice
K-8
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Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Throughout this unit, students will develop their use of the 8 Mathematical Practices while learning the instructional standards. The
mathematical practices in the shaded boxes should be emphasized during instruction this unit due the how well they connect with the
content standards in this unit.
Standards for Mathematical
Practice
1. Make sense of problems and
persevere in solving them
2. Reason abstractly and
quantitatively
3. Construct viable arguments and
critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
Connections to this Cluster
Solve problems in which the solution is not immediately evident.
To determine and articulate what the problem is asking:

Ask students to restate the problem in their own words.

Have students turn to a partner to state the problem.

Discuss familiar problems (When have we seen something like this before? What did we do?)
To self-monitor progress and change directions when necessary:

Have students talk or write about how they got “stuck” and then “unstuck” when solving a problem.

Think aloud to show students how to change course when needed.
To demonstrate perseverance in problem-solving and identify different ways to solve a problem:

Make a classroom list of possible strategies.

Acknowledge those who modify their thinking and persevere to get to the solution and have students show
and talk about how they solved problems.

Encourage students to show at least two ways to solve a problem.
Write an equation for a situation and be able to explain how the equation relates to the situation presented. Solve
the equation outside of the context of the problem, and then connect the solution back to the situation presented.
 Represent how to find unknown angle measures using understanding of complementary and
supplementary angles.
To make sense of quantities and their relationships in problem situations:

Represent a given problem situation with an equation using a variable for the unknown.

Write a situation problem that matches a specific equation.
Justify conclusions, communicate them to others, and respond to the arguments of others. Ask useful questions to
clarify or improve the arguments.

Examine the steps taken that produce an incorrect solution and provide a viable argument as to why the
process produced an incorrect response.

Discuss strategies for categorizing two-dimensional figures, finding lines of symmetry, finding unknown angle
measures.
-Ask students to restate and try peer methods for solving problems.
-Help students make mathematical connections between different representations/solution methods.
-Evaluate the efficiency of the strategies based on the probability of an error occurring.
Identify models that are most efficient for solving specific problems or representing specific geometry ideas.
 Construct visual models using concrete or virtual geometric manipulatives, pictures, or equations to justify
thinking and display the solution.
 Represent real-world geometry situations.
Use tools effectively when classifying, measuring, and constructing geometric figures.

Tiles, ruler, straight edges for constructing two-dimensional figures and drawing lines of symmetry
3
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days



6. Attend to precision
Index cards or corners of paper for right angles
Protractors for measuring and constructing angles
Graphic organizers for classifying two-dimensional shapes
Create accurate drawings and representations of mathematical situations.
Use specific math vocabulary to communicate mathematical ideas.

Develop and display anchor charts with precise math vocabulary, such as parallel, perpendicular, etc.

Orally rephrase student explanations using appropriate vocabulary.

Label geometric components and angles accurately.
7. Look for and make use of structure Look closely to discover a pattern or structure.
8. Look for and express regularity in
repeated reasoning

Analyze properties of geometric figures and classify two-dimensional figures based on properties.

Model the composing and decomposing of angles to build understanding of the additive quality of angles.
Notice repetitive actions in mathematics and try to make sense of it. Make generalizations about rules and “shortcuts” to get to answers more quickly.
4
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Draw and identify lines and angles, and classify shapes by properties of
their lines and angles.
Maryland College and CareerReady Standards
4.G.A.1
Draw points, lines, line
segments, rays, angles
(right, acute, obtuse), and
perpendicular and parallel
lines. Identify these in twodimensional figures.
SMP
1. Make sense of problems
and persevere in solving them
3. Construct viable arguments
and critique the reasoning of
others
5. Use appropriate tools
strategically
6. Attend to precision
7. Look for and make use of
structure
Instructional Strategies and Resource Support
This standard asks students to identify and construct foundational
geometric figures including points, lines, line segments, rays, and angles.
They build on this understanding in this standard and throughout the unit as
they:
 describe, compare and classify two-dimensional shapes by their
properties
 relate parallelism and perpendicularity
 measure and classify angles and triangles
It is vital that students construct figures throughout the unit. Drawing shapes
and their geometric components help to deepen students’ understanding
of two-dimensional figures and help them make meaning of abstract
concepts. These drawings provide a basis for a student to connect visual
images with vocabulary and enable him to analyze and communicate
precisely.
Geoboards, grid paper (square and triangle grids), popsicle sticks, and
straws are useful tools to have available as students explore twodimensional figures.
Provide criteria for students to use to construct figures:
 Draw a polygon with at least 2 pairs of parallel sides.
 Construct a trapezoid with 2 right angles.
 Sketch a triangle with an obtuse angle.
Additionally, have students identify properties of given shapes:
 What types of angles does this figure have?
 Are there parallel sides? Perpendicular sides?
Study Jams PPT – Types of Lines
http://studyjams.scholastic.com/studyjams/jams/math/geometry/types-oflines.htm
Formative Assessments
FA.4.G.A.1.a
Seth uses a ruler to construct a twodimensional figure on his paper. He
follows these steps:


Draw a line segment on your paper
with point A and point B as
endpoints.
Draw another line segment that is
perpendicular to the first and shares
endpoint A. Label the other
endpoint C.
FA.4.G.A.1.b
Adam, Brian, and Charlie all live
in the same neighborhood. The
points below show the location of
their homes. Each point matches
the first letter in each boy’s name.
A
B
C
FA.4.G.A.1.c
Look at each of the figures below.
Use a highlighter to trace one pair
of perpendicular sides in each
figure.
Use a highlighter to trace one pair
of parallel sides in each figure.
5
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Draw and identify lines and angles, and classify shapes by
properties of their lines and angles.
Maryland College and CareerReady Standards
4.G.A.1
Draw points, lines, line
segments, rays, angles
(right, acute, obtuse),
and perpendicular and
parallel lines. Identify
these in twodimensional figures.
Instructional Strategies and Resource Support
Geometric Term
point
line
This is just a visual.
A point actually
lacks dimension.
Definition
a location in space
a straight path that continues
in both directions with an
infinite number of points but no
endpoints
part of a line with 2 endpoints
line segment
ray
SMP
1. Make sense of problems
and persevere in solving
them
3. Construct viable
arguments and critique
the reasoning of others
5. Use appropriate tools
strategically
6. Attend to precision
7. Look for and make use
of structure
Figure
angle
acute angle
right angle
obtuse angle
straight angle
parallel
perpendicular
Formative Assessments
part of a line with 1 endpoint
and extends forever in one
direction
the amount of space
between 2 intersecting lines,
line segments, or rays
FA.4.G.A.1.d
On each object, trace one pair
of lines that are parallel using a
blue colored pencil.
How do you know if lines are
parallel?
an angle that measures less
than 90°
a 90° angle
an angle that measures 91° 179°
An angle that forms a straight
line - 180°
lines that are always the same
distance apart
intersecting lines that form
right angles
6
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Draw and identify lines and angles, and classify shapes by properties
of their lines and angles.
Maryland College and
Career-Ready Standards
4.G.A.2
Classify twodimensional figures
based on the
presence
or absence of
parallel or
perpendicular lines,
or the presence or
absence of angles of
a specified size.
Recognize right
triangles as a
category, and
identify right
triangles.
SMP
1. Make sense of
problems and
persevere in solving
them
3. Construct viable
arguments and
critique the reasoning
of others
5. Use appropriate
tools strategically
6. Attend to precision
7. Look for and make
use of structure
Instructional Strategies and Resource Support
Two-dimensional shapes are classified based on relationships of sides and angles. Multiple
opportunities in comparing and contrasting shapes allow students to gain a deeper
understanding about shapes and their properties.
http://www.illustrativemathematics.org/illustrations/1275
Formative Assessments
FA.4.G.A.2.a
Use the Geoboards and a
ruler to draw each twodimensional figure.
Quadrilaterals: A quadrilateral is a 4-sided polygon. In 3rd grade, students learn to identify
quadrilaterals and recognized parallel lines within them. In 4th grade, you can build on that
by exploring quadrilaterals in-depth. Students can determine if the sides are parallel or
perpendicular, analyze angles and classify accordingly. Characteristics of rectangles
(including squares) can be used to strengthen the concept of parallel and perpendicular
lines.
Quadrilateral
Figure
.
rectangle
square
rhombus
parallelogram
trapezoid
kite
Properties
4 right angles (perpendicular sides)
2 sets of parallel sides
Opposite sides are congruent
4 right angles (perpendicular sides)
4 congruent sides
2 sets of parallel sides
FA.4.G.A.2.b
Julia sorted the figures into
a Venn diagram as shown.
4 congruent sides
2 sets of parallel sides
2 sets of parallel sides
Opposite sides are congruent
At least 1 set of parallel sides
2 pairs of congruent sides
adjacent (next to each other)
FA.4.G.A.2.c
Jeff classified triangles into
the following groups:
Students can try to write the shortest definition of a quadrilateral. For a parallelogram do
you need to say 2 sets of parallel sides and opposite sides are equal? Why or why not?
7
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Draw and identify lines and angles, and classify shapes by properties of
their lines and angles.
Maryland College and CareerReady Standards
4.G.A.2
Classify twodimensional figures
based on the presence
or absence of parallel
or perpendicular lines,
or the presence or
absence of angles of a
specified size.
Recognize right
triangles as a category,
and identify right
triangles.
Instructional Strategies and Resource Support
Informal understanding of the characteristics of triangles is developed
through angle measures and side length relationships. Triangles are
named according to their angle measures (right, acute or obtuse) and
side lengths (scalene, isosceles or equilateral).
Triangles Classified by Angles:
Name
Figure
Properties
.
right
1 right angle (measures 90º)
3 angles that are acute
(measure less than 90º)
acute
1 angle that is obtuse
(measures greater than
90º)
obtuse
SMP
1. Make sense of problems
and persevere in solving
them
3. Construct viable
arguments and critique
the reasoning of others
5. Use appropriate tools
strategically
6. Attend to precision
7. Look for and make use
of structure
Formative Assessments
Triangles Classified by Side Length:
Name
equilateral
isosceles
scalene
Figure
Properties
.
3 equal sides
2 equal sides
no sides equal
8
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Draw and identify lines and angles, and classify shapes by properties
of their lines and angles.
Maryland College and CareerReady Standards
4.G.A.2
Classify two-dimensional
figures based on the
presence or absence of
parallel or perpendicular
lines, or the presence or
absence of angles of a
specified size. Recognize
right triangles as a
category, and identify
right triangles.
SMP
1. Make sense of problems
and persevere in solving
them
3. Construct viable
arguments and critique the
reasoning of others
5. Use appropriate tools
strategically
6. Attend to precision
7. Look for and make use of
structure
Instructional Strategies and Resource Support
Formative Assessments
Students can also explore parallelism, perpendicularity, and angle size when
analyzing qualities of other polygons including pentagons, hexagons,
octagons in addition to irregular polygons (polygons that do not have all
sides equal and all angles equal). Students can create and analyze sorts
based on properties.
Example:
At least 1 set of
parallel sides
At least 1 obtuse
angle
Additionally, students should have opportunities to prove/disprove
conjectures (with counter-examples). Pose statements such as the
ones below for students to test validity:
 A parallelogram can have exactly one right angle.
 A trapezoid can have 2 right angles.
 A right triangle can be isosceles.
 Draw and name a figure that has 2 right angles and has 1 pair
of parallel sides.
 A quadrilateral must be a parallelogram.
Geoboards, dot paper, virtual geoboards, wiki sticks, and pipe
cleaners are useful tools to create 2-dimensional figures.
9
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Draw and identify lines and angles, and classify shapes by properties
of their lines and angles.
Maryland College and CareerReady Standards
4.G.A.3
Recognize a line of
symmetry for a twodimensional figure as a
line across the figure
such that the figure can
be folded along the line
into matching parts.
Identify line-symmetric
figures and draw lines of
symmetry.
SMP
1. Make sense of problems
and persevere in solving
them
3. Construct viable
arguments and critique
the reasoning of others
5. Use appropriate tools
strategically
6. Attend to precision
7. Look for and make use
of structure
Instructional Strategies and Resource Support
In this standard, students explore symmetry in relation to two-dimensional
figures. A line of symmetry divides a figure into 2 congruent halves. It can
be considered a “folding line” so that if the figure is folded along the line,
the 2 parts match.
Students need opportunities to work with symmetrical figures and nonsymmetrical figures including regular and irregular polygons. Through work
with paper cut-outs, students can identify a shape’s line(s) of symmetry
and begin to investigate symmetry patterns with questions such as:
 Do all triangles have 3 lines of symmetry?
 How many lines of symmetry does a circle have?
 Is the number of lines of symmetry related to the number of
angles/sides of a regular polygon?
Students need to be able to apply their understanding of symmetry to
drawings of two-dimensional figures as well. On dot paper, have students
draw polygons based on given characteristics and identify lines of
symmetry. Example: Draw a regular hexagon and draw all lines of
symmetry. What do you notice? What about a regular pentagon?
Formative Assessments
FA.4.G.A.3.a
Draw all of the lines of symmetry
for each of shapes below:
Rectangle A has ____ lines of
symmetry.
Rectangle B has ____ lines of
symmetry.
FA.4.G.A.3.b
A square has 4 lines of symmetry.
Draw all of the lines of symmetry for
each of the quadrilaterals below. Write
the number of lines on the blank under
each figure.
FA.4.G.A.3.c
Half of each figure is shown. The dotted
line represents the line of symmetry.
Use this to draw the other half of the
figure.
Additionally, provide one-half of a figure and the line of symmetry.
Students should draw the other half of the shape.
FA.4.G.A.3.d
http://illuminations.nctm.org/lesson.aspx?id=1800
Draw all of the lines of symmetry
for each of the polygons. Write the
number of lines on each blank.
10
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Maryland College and CareerReady Standards
Geometric measurement: understand concepts of angle and
measure angles.
4.MD.C.5
Recognize angles as
geometric shapes that are
formed wherever two rays
share a common endpoint,
and understand concepts of
angle measurement:
4.MD.C.5.a
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.
4.MD.C.5.b
An angle that turns
through n one-degree
angles is said to have an
angle measure of n
degrees.
Instructional Strategies and Resource Support
This standard connects angles and circular measurement (360 degrees). An
angle is the union of two rays with a shared endpoint called the vertex. The
rays can be called the sides of the angles.
The rays can rotate one from the other about the vertex. This rotation
determines the size of the angle between the rays.
Angles are measured in reference to a circle with its center at the vertex of
the rays. An angle that turns through 1/360 of a circle is called a “onedegree angle,” and degrees are the unit used to measure angles. A
complete rotation is 360º. Real world connections can be seen in the
movement of hands on a clock, a rotating water sprinkler, or the opening of
a door (the hinge is the vertex), or degrees of a compass.
Formative Assessments
FA.4.MD.C.5.a.a
Harry is standing on the court
with a basketball in his hands.
He pivots to find a teammate
so that he can pass the ball.
Harry turns 60°with each
pivot. How many times will
Harry pivot by the time he
makes a complete circle?
FA.4.MD.C.5.a.b
Scott is hiking through the
woods. He is holding a
compass to help him with
direction.
FA.4.MD.C.5.c
Jason’s farm uses a large
sprinkler that rotates in a
circle. The sprinkler
rotates 23 degrees in 10
seconds. How far will it
rotate in 30 seconds?
Show your thinking:
11
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Maryland College and CareerReady Standards
Geometric measurement: understand concepts of angle and
measure angles.
4.MD.C.5
Recognize angles as
geometric shapes that are
formed wherever two rays
share a common endpoint,
and understand concepts of
angle measurement:
Instructional Strategies and Resource Support
Formative Assessments
Students should use their understanding of the degrees in a circle to
explore questions such as:

If each circle was divided into equal parts, what is the measure of
each angle?
4.MD.C.5.a
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 “onedegree angle,” and can be
used to measure angles.
4.MD.C.5.b
(360º ÷ 4 = 90º)
(360º ÷ 3 = 120º)
(360º ÷ 6 = 60º)
Students should also explore the concept that an angle
measurement is not related to the area between 2 rays. For
example, the visual below shows that while the area between the 2
rays is different in each of the circles; the angle measure is the
same.
An angle that turns
through n one-degree angles
is said to have an angle
measure of n degrees.
12
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Geometric measurement: understand concepts of angle and
measure angles.
Maryland College and CareerReady Standards
4.MD.C.6
Measure angles in wholenumber degrees using a
protractor. Sketch angles
of specified measure.
SMP
1. Make sense of problems
and persevere in solving
them
3. Construct viable
arguments and critique the
reasoning of others
5. Use appropriate tools
strategically
6. Attend to precision
7. Look for and make use of
structure
Instructional Strategies and Resource Support
Prior to using a protractor, students need to have a strong understanding of
benchmark angles. Through their earlier work in the unit, they have explored
a circle as having 360º, a straight angle (line) measuring 180º, a right angle as
90º, an acute angle as less than 90º and an obtuse angle measuring from 91º
to 179º.
Formative Assessments
FA.4.MD.C.6.a
Classify (acute, obtuse, right)
and measure each angle.
Students need to be able to both measure and draw angles of a given value
using a protractor.
Measuring an angle:
 Place the vertex at the center point of the protractor.
 Align one ray along the horizontal edge of the protractor.
 The angle is measured by finding where the second ray intersects the
arc of the protractor.
Drawing an angle:
 Draw a ray and place the center of the protractor on the endpoint of
the ray. This will become the vertex.
 Place a point on the paper that aligns with the angle measure on the
protractor.
 Use the straightedge of the protractor to connect point to the vertex.
To avoid misconceptions in measuring or drawing angles, students should:
 Classify the type of angle to determine an appropriate estimate of
the angle measure.
 Have experience with many different angles (not just those that are in
a standard position with one ray that is horizontal).
 Identify angle measures within figures.
Use your protractor and ruler
to draw the following angles.
Identify each as acute, obtuse,
right, or straight.
45º
135º
90º
60º
FA.4.MD.C.6.b
Use your protractor to
measure the angles. Label the
degrees in each angle.
13
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Geometric measurement: understand concepts of angle and measure
angles.
Maryland College and CareerReady Standards
4.MD.C.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.
SMP
1. Make sense of problems
and persevere in solving
them
3. Construct viable
arguments and critique the
reasoning of others
5. Use appropriate tools
strategically
6. Attend to precision
7. Look for and make use of
structure
Instructional Strategies and Resource Support
Angle measure is additive. An angle can be divided into two
smaller angles. The combined measures of the two smaller angles
equal the original angle.
B
BAC =
BAD +
DAC
D
A
C
If a right angle is decomposed (broken apart) into two adjacent
angles, the sum is 90º, thus they are complementary. Two adjacent
angles that compose a “straight angle” of 180º are supplementary.
You can find an unknown angle measure, if you know the measure
of the original angle and one of the smaller angles.
Formative Assessments
FA.4.MD.C.7.a
Stacey’s bedroom door is opened
32 degrees. Her mom wants it to
be opened the full 90 degrees.
How many degrees does Stacey
need to open her door?
________________
Draw an angle sketch to show
what Stacey’s door looked like at
32 degrees.
FA.4.MD.C.7.b
Vikki was ice skating and
attempted to complete a 180
degree turn. She turned some
and then tripped. She needed
to turn 42 degrees more to
complete her turn.
How many degrees did Vikki
turn before she tripped?
FA.4.MD.C.7.c
Find the missing angle
measurements:
(Progressions for the CCSSM, Geometric Measurement, CCSS Writing Team, June 2012, page
23)
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Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Geometric measurement: understand concepts of angle and measure
angles.
Maryland College and CareerReady Standards
4.MD.C.7
Recognize angle
measure as additive.
When an angle is
decomposed into nonoverlapping 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.
SMP
1. Make sense of problems
and persevere in solving
them
3. Construct viable
arguments and critique the
reasoning of others
5. Use appropriate tools
strategically
6. Attend to precision
7. Look for and make use of
structure
Instructional Strategies and Resource Support
Formative Assessments
Students apply the additive quality of angles in order to find unknown angles.
Examples:
1. A revolving door rotates 65º, pauses, and then rotates 45º more.
 What is the total angle measure of the door so far? (110º)
 How many more degrees will the door need to turn to make a full 360º
rotation? (360º - 110º = 250º)
45º
65º
2. There are 360º in a complete circle. If the hands of a clock are exactly on
12 and 1, the angle created measures 30º. What is the angle measure if
the hands are exactly on 12 and 4? (120º); 8 and 11? (90º); 1 and 7?
(180º)
3. If the 2 rays are perpendicular, what is the value of n?
n = 90º - (30º + 35º)
30º
n = 90º - 65º = 25º
35º
n
15
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Maryland College and CareerReady Standards
Generate and analyze patterns.
4.OA.C.5
Generate a number or
shape pattern that follows
a given rule. Identify
apparent features of the
pattern that were not
explicit in the rule itself.
Instructional Strategies and Resource Support
In unit 1, students understood this standard in terms of generating,
identifying, and extending number patterns. In this unit, students will
make conjectures and explore patterns using two-dimensional
figures, or properties of two-dimensional figures.
Symmetry Patterns
Students make and test conjectures about the number of lines of
symmetry in regular polygons (polygons having equal sides and
equal angles).
Identify and record the number of sides and the number of lines of
symmetry in each figure.
SMP
1. Make sense of problems
and persevere in solving
them
3. Construct viable
arguments and critique the
reasoning of others
5. Use appropriate tools
strategically
6. Attend to precision
7. Look for and make use of
structure
Number of Sides
3
4
5
6
Number of Lines of
Symmetry
3
4
5
?


Formative Assessments
FA.4.OA.C.5.a
A new high school is under
construction, and the materials
for the tile floor are being ordered.
The design of the main hallway
floor is shown below:
The school needs to order a total
of 224 shape tiles for the hallway
design. How many square tiles
should the school order? Show
your thinking.
How many lines of symmetry will a hexagon have? An
octagon?
What pattern is created by where the lines of symmetry are
located for an even number of sides versus an odd number
of sides?
16
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Maryland College and CareerReady Standards
Generate and analyze patterns.
4.OA.C.5
Generate a number or
shape pattern that follows
a given rule. Identify
apparent features of the
pattern that were not
explicit in the rule itself.
Instructional Strategies and Resource Support
Students can solve real world pattern problems related to angle
measurement and properties of polygons. They can use a table to find a
rule, extend elements of a pattern, and answer questions based on the
pattern.
Angle Measure Example
At the carnival, the Ferris wheel has 12 seats, evenly spaced. At the
beginning of the ride, the people get on the ride as follows:
Seat Number
Number of
Passengers
Number of
Degrees Wheel
Moved

SMP
1. Make sense of problems
and persevere in solving
them
3. Construct viable
arguments and critique the
reasoning of others
5. Use appropriate tools
strategically
6. Attend to precision
7. Look for and make use of
structure
Formative Assessments

1
2
3
2
4
6
30º
60º
90º
4
5
6
How many passengers will be on the Ferris wheel when the wheel has
rotated 240º?
When 20 people are on the ride, how many degrees has the wheel
rotated?
Polygon Example
David is designing a toothpick bridge. He makes a drawing of the bridge
before constructing it. Each line segment is 1 toothpick.
?
1 section




2 sections
3 sections
4 sections
?
5 sections
Draw how 4 sections and 5 sections of the bridge would look.
Create a table to record the number of toothpicks used for each section size.
Extend your table to find the number of toothpicks needed for 10 sections.
How many toothpicks are needed for 20 sections? 100 sections? What rule connects the
number of sections to the number of toothpicks needed?
17
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
Triangle Sort
Cut out the triangles. Sort the triangles into categories. (Each triangle MUST fit into one of the categories). Describe
your sort. Then, mix the triangles and create a new sort. How did your groups change?
A
B
C
D
E
F
G
H
I
J
K
L
18
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 7: Geometry and Patterns – 26 Days
19