Unit Overview
Content Area: Math
Unit Title: Geometry/Geometric Measurement
Unit: 6
Target Course/Grade Level: Fourth Grade
Timeline: 3-4 weeks
Unit Summary: Students will use appropriate terminology to describe angles and rays. Student will
recognize angles are formed when two rays share a common endpoint and measure angles in wholenumbers degrees using a protractor. They will identify, classify and describe two-dimensional figures.
Primary interdisciplinary connections: Visual Arts, Technology, Science, Language Arts
NJ Standard 9.1: 21st – Century Life & Career Skills
Standard 9.1: All students will demonstrate the creative, critical thinking, collaboration, and problem
solving skills needed to function successfully as both global citizens and workers in diverse ethnic and
organizational cultures.
Strand:
A. Critical Thinking and Problem Solving
B. Creativity and Innovation
C. Collaboration, Teamwork and Leadership
D. Cross-Cultural Understanding and Interpersonal Communication
Content Statement:
9.1.4.A: The ability to recognize a problem and apply critical thinking and problem-solving
skills to solve the problem is a lifelong skill that develops over time.
9.1.4.B: Brainstorming activities enhance creative and innovative thinking in individual and
group goal setting and problem solving.
9.1.4.C: Practice collaborative skills in groups, and explain how these skills assist in
completing tasks in different settings such as home, play or school.
9.1.4.D: Effective communication skills convey intended meaning to others and assist in
preventing misunderstandings.
21st century themes and skills: Critical Thinking and Problem Solving, Communication and
Collaboration, Teamwork and Leadership, Creativity and Innovation
Mathematical Practices:
4.MP.1 Make sense of problems and persevere in solving them.
4.MP.2 Reason abstractly and quantitatively.
4.MP.4 Model with mathematics.
4.MP.5 Use appropriate tools strategically.
4.MP.6 Attend to precision.
4.MP.7 Look for and make use of structure.
4.MP.8 Look for and express regularity in repeated reasoning.
Learning Targets
Domain: Measurement and Data/Geometry
Cluster: Geometric measurement: understand concepts of angle and measure angles. Draw and
identify lines and angles, and classify shapes by properties of their lines and angles.
Standard #
Standards
4.MD.5
Recognize angles as geometric shapes that are formed wherever two rays share a common
endpoint, and understand concepts of angle measurement.
Educator’s Notes:
The diagram below will help students understand that an angle measurement is not
related to an area since the area between the 2 rays is different for both circles yet the
angle measure is the same.
4.MD.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 a 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.5.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.
Educator’s Notes:
Before students begin measuring angles with protractors, they need to have some
experiences with benchmark angles. They transfer their understanding that a 360º rotation
about a point makes a complete circle to recognize and sketch angles that measure
approximately 90º and 180º. They extend this understanding and recognize and sketch
angles that measure approximately 45º and 30º. They use appropriate terminology (acute,
right, and obtuse) to describe angles and rays (perpendicular).
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, eg. by using an equation with a symbol for the unknown angle
measure.
Educator’s Notes:
If the two rays are perpendicular, what is the value of m?

Joey knows that when a clock’s hands are exactly on 12 and 1, the angle formed
by the clock’s hands measures 30º. What is the measure of the angle formed
when a clock’s hands are exactly on the 12 and 4?

The five shapes in the diagram are the exact same size. Write an equation that will
help you find the measure of the indicated angle. Find the angle measurement.
4.G.1
Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and
parallel lines. Identify these in two-dimensional figures.
Educator’s Notes:
Right angle
Acute angle
Examples of points, line segments, lines, angles,
parallelism, and perpendicularity can be seen
daily. Students do not easily identify lines and rays
because they are more abstract.
Obtuse angle
Straight angle
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.
Educator’s Notes:
Two-dimensional figures may be classified using different characteristics such as, parallel
or perpendicular lines or by angle measurement.
Parallel or Perpendicular Lines:
Students should become familiar with the concept of parallel and perpendicular lines. Two
lines are parallel if they never intersect and are always equidistant. Two lines are
perpendicular if they intersect in right angles (90º).
Students may use transparencies with lines to arrange two lines in different ways to
determine that the 2 lines might intersect in one point or may never intersect. Further
investigations may be initiated using geometry software. These types of explorations may
lead to a discussion on angles.
Parallel and perpendicular lines are shown below:
Example:
 Identify which of these shapes have perpendicular or parallel sides and justify your
selection.
A possible justification that students might give is:
The square has perpendicular lines because the sides meet at a corner, forming right
angles.
Angle Measurement:
This expectation is closely connected to 4.MD.5, 4.MD.6, and 4.G.1. Students’
experiences with drawing and identifying right, acute, and obtuse angles support them in
classifying two-dimensional figures based on specified angle measurements. They use the
benchmark angles of 90°, 180°, and 360° to approximate the measurement of angles.
Right triangles can be a category for classification. A right triangle has one right angle.
There are different types of right triangles. An isosceles right triangle has two or more
congruent sides and a scalene right triangle has no congruent sides.
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.
Educator’s Notes:
Students need experiences with figures which are symmetrical and non-symmetrical.
Figures include both regular and non-regular polygons. Folding cut-out figures will help
students determine whether a figure has one or more lines of symmetry.
CPI#
Cumulative Progress Indicator (CPI)
9.1.4.A.1
Recognize a problem and brainstorm ways to solve the problem individually or
collaboratively.
9.1.4.A.2
Evaluate available resources that can assist in solving problems.
9.1.4.A.3
Determine when the use of technology is appropriate to solve problems.
9.1.4.A.5
Apply critical thinking and problem-solving skills in classroom and family
settings.
9.1.4.B.1
Participate in brainstorming sessions to seek information, ideas, and strategies that foster
creative thinking.
9.1.4.C.1
Practice collaborative skills in groups, and explain how these skills assist in completing
tasks in different settings (at home, in school, and during play).
9.1.4.D.1
Use effective oral and written communication in face-to-face and online interactions and
when presenting to an audience.
Unit Essential Questions
 What strategies can be used to verify symmetry
and congruency?
 What is an angle and how is it measured?
 What strategies can be used to compose and
decompose angle measurements?
Unit Enduring Understandings
 Triangles can be identified using two categories –
angles and sides: acute, obtuse and right and/or
equilateral, isosceles and scalene.
 Symmetry is a line that divides a two dimensional
figure into congruent parts.
 Certain two dimensional figures have more than
one line of symmetry.
 A right angle is 90 degrees, an obtuse angle is
greater than 90 degrees and less than 180 degrees
and an acute angle is less than 90 degrees and
greater than 0 degrees.
 An angle is measured in relationship to a circle
which is 360 degrees.
 A protractor is a tool which can be used to measure
various angles.
 Known measurements of smaller angles can be
added together to get the unknown measurement of
a larger angle.
 Known measurement of smaller angles can be
subtracted from the know measurement of a larger
angle to get the unknown angle measurement.
Unit Learning Targets
Students will ...
 Draw points, lines, line segments, and rays and identify these in two-dimensional figures.
 Draw parallel, intersecting, and perpendicular lines and identify these in two-dimensional figures.
 Understand concepts of angles and angle measurement.
 Use concepts of angle measurement to classify angles.
 Use a protractor to measure angles to the nearest degree.
 Use a protractor to draw angles of a specified measure.
 Solve addition and subtraction problems to find unknown angles on a diagram in real-world and
mathematical situations.
 Classify triangles based on angle measures and describe triangles using their attributes.
 Classify quadrilaterals using their attributes.
 Identify figures with line symmetry and draw lines of symmetry.
 Solving problems by making a model.
Evidence of Learning
Summative Assessment
 Give an angle; identify it as acute, obtuse or right angle.
 Using a protractor, measure a given angle.
 Given a degree, draw the angle using a protractor.
 Without the use of a protractor, determine the measurement of the unknown angle in a diagram by using
the known angle measurement/s.
 Write an equation using a variable to find an unknown angle measurement, i.e. 90* - n = 60*, therefore n
=30*.
 Identify a point, line, line segment, and ray, parallel and perpendicular lines in a given diagram.
 Determine whether a figure has lines of symmetry. If so, draw the line(s) of symmetry for the given
figure.
 Given a specific triangle, classify it based on its angles and sides.
 Identify quadrilaterals according to its attributes.
Equipment needed: protractors, geometric software, rulers, paper quadrilaterals, graph paper
Teacher Instructional Resources: Scott Foresman and Addison Wesley
Formative Assessments




Skill sheets
Quizzes
Student workbook
Math games



Homework
Teacher observation
Student participation
Integration of Technology:
 SmartBoard to play online games and utilize online.
 https://www.pearsonsuccessnet.com/snpapp/login/login.jsp - Scott Foresman Online Text/Activities
 http://illuminations.nctm.org/ActivitySearch.aspx - Interactive examples and activities
 http://www.factmonster.com/
 http://www.gamequarium.com/
 http://www.mathisfun.com/
 http://www.mathleague.com/help/help.htm
 http://www.softschools.com/math/
 http://www.teachersdomain.org/
 http://www.aaamath.com/
 http://www.funbrain.com
 http://www.aplusmath.com/
 http://www.sharpbrains.com/teasers/brain-games-and-teasers-top-50/
 http://cemc2.math.uwaterloo.ca/mathfrog/main.shtml
 http://www.cut-the-knot.org/Curriculum/index.shtml
Technology Resources:
Click the links below to access additional resources used to design this unit:

http://www.corestandards.org/the-standards/mathematics -NJ DOE Common Core Standards

http://www.azed.gov/standards-practices/mathematics-standards/ -Arizona DOE Common Core Standards
Opportunities for Differentiation:
 Utilize leveled worksheet pages – Reteach, Practice, Problem Solving, Enrichment
 Problem based learning activities




Use virtual manipulatives during instruction
Utilize manipulatives or act out activities for each lesson
Flexible partners/grouping
Learning Centers – Use of classroom computers for practice
Teacher Notes: The standards for Fourth Grade are based only on the study of plane figures – students
are not responsible for information on solid figures. Also, the study of circles is confined to angles and
measurement of angles.