MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
Unit Description
Big Idea(s)
What enduring
understandings are
essential for application
to new situations within or
beyond this content?
Essential Question(s)
What questions will
provoke and sustain
student engagement
while focusing learning?
Standards
Curriculum and Instruction
Unit 8
Geometry and Angle Measurement
Suggested Length: 6 weeks
Enduring Understanding
Describe, Analyze, Compare, and Classify Geometric Shapes
Enduring Skills Rubric measures competency of the following skills:
 Can identify all types of angles.
 Can recognize both parallel and perpendicular lines.
 Consistently generate a pattern (number or shape) following a given
rule.
 Consistently apply the area and perimeter formulas to solve
mathematical or real world problems.
 Can measure and draw angles accurately.
 Solves addition and subtraction problems to find unknown angles
accurately.
 Can draw points, lines, line segments, rays, angles, perpendicular or
parallel lines accurately.
 Can recognize and draw a line of symmetry accurately.
 How are two-dimensional objects different from one another?
 How can shapes be classified by their angles and sides?
 How can I determine the lines of symmetry in a figure?
 How are the units used to measure perimeter different from the units used
to measure area?
 How is perimeter different from area?
 What is the relationship between an angle and a circle?
 How can I construct an angle of a given measure?
 What are benchmark angles and how can they be useful in estimating
angle measures?
 How can I decompose/compose angles to solve geometric problems?
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them. Students make
sense of problems and persevere in solving them by exploring and
investigating properties of geometric figures and lines of symmetry.
Students solve problems involving measurement and the conversion of
measurements from a larger unit to a smaller unit.
2. Reason abstractly and quantitatively. Students reason abstractly and
quantitatively by comparing, contrasting, and classifying two-dimensional
shapes and determining their lines of symmetry. Students recognize angle
measure as additive in relation to the reference to a circle.
3. Construct viable arguments and critique the reasoning of others. Students
construct viable arguments and critique reasoning when determining the
properties of geometric shapes and determining their lines of symmetry.
Students construct and critique arguments regarding the relative size of
measurement units and relating them to everyday objects.
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
4. Model with mathematics. Students model with mathematics by drawing,
folding, tracing, and constructing lines of symmetry and categorizing twodimensional shapes based on their properties. Students use line plots to
display data of measurements in fractions of a unit.
5. Use appropriate tools strategically. Students use appropriate tools such as
geometric shapes, corners of paper, tiles, rulers, protractors, and/or
graphic organizers to determine angles, classify two-dimensional shapes,
and draw lines of symmetry. Students select and use tools such as a ruler,
balance, graduated cylinder, angle ruler, and protractor to measure.
6. Attend to precision. Students attend to precision when observing and
determining the attributes of sides and degree of angles within geometric
shapes. Students carefully specify unit measure and state the meaning of
the symbols they choose.
7. Look for and make use of structure. Students look for and make sense of
structure when exploring properties of geometric shapes and determining
how to fold them to show lines of symmetry. Students use the structure of a
two-column table to generate a conversion table for measurement
equivalence.
8. Look for and express regularity in repeated reasoning. Students look for
and express regularity in repeated reasoning while exploring the geometric
properties of two-dimensional shapes by comparing, contrasting,
classifying, and identifying lines of symmetry. Students notice repetitive
actions in computations to make generalizations about conversion of
measurements from a larger unit to a smaller unit.
Standards for Mathematical Content
 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse),
and perpendicular and parallel lines. Identify these in two-dimensional
figures.
 4.G.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.
 4.G.3 Recognize a line of symmetry for a two-dimensional 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.
 4.MD.3 Apply the area and perimeter formulas for rectangles in real world
and mathematical problems. For example, find the width of a
rectangular room given the area of the flooring and the length, by
viewing the area formula as a multiplication equation with an unknown
factor.
 4.MD.5 Recognize angles as geometric shapes that are formed wherever
two rays share a common endpoint, and understand concepts of angle
measurement:
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
Curriculum and Instruction
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
Supporting
Standard(s)
Which related standards
will be incorporated to
support and enhance
the enduring standards?
Instructional
Outcomes
What must students learn
and be able to do by the
end of the unit to
demonstrate mastery?
Curriculum and Instruction
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.
b. An angle that turns through n one-degree angles is said to have
an angle measure of n degrees.
 4.MD.6 Measure angles in whole-number degrees using a protractor.
Sketch angles of specified measure.
 4.MD.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.
 4.OA.3 Solve multistep word problems posed with whole numbers and
having whole-number answers using the four operations, including
problems in which remainders must be interpreted. Represent these
problems using equations with a letter standing for the unknown quantity.
Assess the reasonableness of answers using mental computation and
estimation strategies including rounding.
 4.MD.2 Use the four operations to solve word problems involving
distances, intervals of time, liquid volumes, masses of objects, and money,
including problems involving simple fractions or decimals, and problems
that require expressing measurements given in a larger unit in terms of a
smaller unit. Represent measurement quantities using diagrams such as
number line diagrams that feature a measurement scale.
I am learning to….
4.G.1
1. classify angles as acute, right, obtuse
2. analyze two-dimensional figures to identify points, lines, line
segments, rays, angles (right, acute, obtuse), and perpendicular and
parallel lines
3. construct examples of a point, ray, line segment, line, ray, angle
(right, acute, obtuse), perpendicular lines, and parallel lines
4.G.2
1. classify triangles as “right triangles” or “not right triangles”
2. recognize a right triangle in any setting no matter its position
3. classify two-dimensional figures based on the size of the angles
4. classify two-dimensional figures based on parallel or perpendicular
lines
4.G.3
1. recognize a line of symmetry as a line across a figure that when
folded on the line it creates matching parts
2. identify line-symmetric figures
3. distinguish between symmetrical and asymmetrical figures
4. draw lines of symmetry in two-dimensional figures
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
Vocabulary
What vocabulary must
students know to
understand and
communicate effectively
about this content?
Resources/Activities
What resources could we
use to best teach this
unit?
Curriculum and Instruction
4.MD.3
1. determine the area of a rectangle using a formula
2. determine the perimeter of a rectangle using a formula
3. determine the length or width of a rectangle using an area formula
4. solve area and perimeter problems in which there is an unknown
factor (n)
5. apply area and perimeter formulas to real world and mathematical
problems
4.MD.5
1. recognize angles as geometric shapes that are formed by two rays
with a common endpoint
2. recognize a circle as a geometric figure that has 360 degrees
3. recognize that an angle is a fraction of a 360 degree circle
4. explain the angle measurement in terms of degrees
5. calculate angle measurement using the 360 degrees of a circle
6. compare angles to circles with the angles pointing at the center of
the circle to determine the measure of the angle
4.MD.6
1. determine which scale on the protractor to use, based on the
direction the angle is open
2. use a protractor to measure angles to the nearest whole-number
degree
3. construct an angle with a given measurement
4.MD.7
1. decompose an angle into smaller parts
2. determine the sum of an angle by adding the degree of its parts
3. use addition and/or subtraction to find unknown angle
measurements on a diagram
Essential Vocabulary
acute
endpoint
perimeter
additive
formula
perpendicular
plane figures
angle
fractions
point
arc
length
protractor
area
line
ray
circle
line of symmetry
right angle
compose
line plot
right triangle
line segment
congruent
scale
obtuse
data
two-dimensional
parallel
decompose
width
degrees
Stepping Stones (www.origoeducation.com)
4.MD.3
o Module 9: Lessons 1-4
4.MD.5
o Module 5: Lessons 9,10
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
4.MD.6
o Module 5: Lessons 10-12
4.MD.7
o Module 5: Lesson 12
4.G.1
o Module 5: Lessons 10,11
o Module 10: Lessons 9,10
4.G.2
o Module 5: Lesson 11
o Module 10: Lesson 10
4.G.3
o Module 10: Lessons 11,12
Engage NY (https://www.engageny.org/resource/grade-4-mathematics)
o Module 8, all Topics
From Howard County website
 https://grade4commoncoremath.wikispaces.hcpss.org/Assessing+4.MD
.5
 https://grade4commoncoremath.wikispaces.hcpss.org/Assessing+4.MD
.6
 https://grade4commoncoremath.wikispaces.hcpss.org/Assessing+4.MD
.7
 https://grade4commoncoremath.wikispaces.hcpss.org/Assessing+4.G.1
 https://grade4commoncoremath.wikispaces.hcpss.org/Assessing+4.G.2
 https://grade4commoncoremath.wikispaces.hcpss.org/Assessing+4.G.3
From K-5 Math Teaching Resources
4.MD.3
o http://www.k-5mathteachingresources.com/support-files/howmany-tables.pdf
o http://www.k-5mathteachingresources.com/support-files/fencing-agarden.pdf
o http://www.k-5mathteachingresources.com/support-files/designinga-zoo-enclosure.pdf
4.MD.5
o http://www.k-5mathteachingresources.com/supportfiles/estimating-angle-measures.pdf.pdf
o http://www.k-5mathteachingresources.com/support-files/angles-incircles.pdf
4.MD.6
o http://www.k-5mathteachingresources.com/supportfiles/predicting-and-measuring-angles.pdf
o http://www.k-5mathteachingresources.com/support-files/anglebarrier-game.pdf
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
http://www.k-5mathteachingresources.com/support-files/howmany-degrees.pdf
o http://www.k-5mathteachingresources.com/supportfiles/anglesintriangles.pdf
o http://www.k-5mathteachingresources.com/supportfiles/anglesinquadrilaterals.pdf
o http://www.k-5mathteachingresources.com/support-files/angles-ina-right-triangle.pdf
4.MD.7
o http://www.k-5mathteachingresources.com/support-files/additiveangles.pdf
o http://www.k-5mathteachingresources.com/support-files/unknownangle-word-problems.pdf
o http://www.k-5mathteachingresources.com/support-files/patternblock-angles.pdf
4.G.1
o http://www.k-5mathteachingresources.com/support-files/alphabetlines.pdf
o http://www.k-5mathteachingresources.com/supportfiles/geoboard-line-segments.pdf
o http://www.k-5mathteachingresources.com/support-files/angleson-the-geoboard.pdf
o http://www.k-5mathteachingresources.com/support-files/anglebarrier-game.pdf
4.G.2
o http://www.k-5mathteachingresources.com/supportfiles/classifying-2d-figures.pdf
o http://www.k-5mathteachingresources.com/support-files/righttriangles-on-the-geoboard.pdf
o http://www.k-5mathteachingresources.com/support-files/isoscelestriangles-on-the-geoboard.pdf
o http://www.k-5mathteachingresources.com/supportfiles/constructing-quadrilaterals.pdf
o http://www.k-5mathteachingresources.com/supportfiles/quadrilateral-criteria.pdf
o http://www.k-5mathteachingresources.com/support-files/triangleson-the-geoboard.pdf
o http://www.k-5mathteachingresources.com/supportfiles/classifying-triangles-v1.pdf
o http://www.k-5mathteachingresources.com/supportfiles/classifying-triangles-v2.pdf
4.G.3
o http://www.k-5mathteachingresources.com/support-files/symmetryon-the-geoboard.pdf
o http://www.k-5mathteachingresources.com/support-files/symmetryo
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
o
in-regular-polygons.pdf
http://www.k-5mathteachingresources.com/supportfiles/symmetrical-coin-design.pdf
Illustrative Mathematics
4.MD.3
o https://www.illustrativemathematics.org/contentstandards/4/MD/A/3/tasks/876
4.MD.6
o https://www.illustrativemathematics.org/contentstandards/4/MD/C/6/tasks/909
4.MD.7
o https://www.illustrativemathematics.org/contentstandards/4/MD/C/7/tasks/1168
o https://www.illustrativemathematics.org/contentstandards/4/MD/C/7/tasks/909
4.G.1
o https://www.illustrativemathematics.org/contentstandards/4/G/A/1/tasks/1263
o https://www.illustrativemathematics.org/contentstandards/4/G/A/1/tasks/1272
o https://www.illustrativemathematics.org/contentstandards/4/G/A/1/tasks/909
4.G.2
o https://www.illustrativemathematics.org/contentstandards/4/G/A/2/tasks/1273
o https://www.illustrativemathematics.org/contentstandards/4/G/A/2/tasks/1275
o https://www.illustrativemathematics.org/contentstandards/4/G/A/2/tasks/1504
o https://www.illustrativemathematics.org/contentstandards/4/G/A/2/tasks/1274
o https://www.illustrativemathematics.org/contentstandards/4/G/A/2/tasks/1168
4.G.3
o https://www.illustrativemathematics.org/contentstandards/4/G/A/3/tasks/676
o https://www.illustrativemathematics.org/contentstandards/4/G/A/3/tasks/1060
o https://www.illustrativemathematics.org/contentstandards/4/G/A/3/tasks/1058
o https://www.illustrativemathematics.org/contentstandards/4/G/A/3/tasks/1059
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
Illuminations
o http://illuminations.nctm.org/Search.aspx?view=search&cc=1973_2
005
o http://illuminations.nctm.org/Search.aspx?view=search&cc=1973_2
010
Making Math Magic (http://www.makingmathmagic.net/files/101948420.pdf)
Remember there are other sources in your school that may not be listed on
this common resources list due to variation in each individual school.
Examples of other great resources your school may have access to
include: Everyday Math Games, Investigations, Everyday Partner Games,
AVMR file folders, Ongoing Assessment Project, etc. The Kentucky
Numeracy Project is also a great resource that can be searched by AVMR
strand, CCSS, and grade level. Find this resource at
http://knp.kentuckymathematics.org/#!/page_knphome. Kentucky teachers
can use it for free. Just put in your school email address and the username
“bluegrass”, and password is “math”.
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Curriculum and Instruction
2015-2016
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