Download Unit 11 – Geometry Connections Subject/Course: Integrated Algebra

UNIT OF STUDY
Title: Unit 11 – Geometry Connections
Subject/Course: Integrated Algebra A
Length: 2 weeks
Topic:
Grade: 8
Designer: Cox/Nelson
UNIT GOALS AND EXPECTATIONS
IMPORTANT CONCEPTS/UNDERSTANDINGS:
• How to find measures of complementary,
supplementary and vertical angles
• How to identify angles formed when a transversal
intersects two lines
• How to find measures of interior and exterior angles
of convex polygons
• How to transform (translate, reflect and rotate)
figures in a coordinate plane
• How to use distance and midpoint formulas
STUDENT LEARNING EXPECTATIONS:
G.8.8.1 – Form generalizations and validate conclusions
about properties of geometric shapes.
G.9.8.2 – Draw the results of translations and reflections
about the x- and y-axis and rotations of objects about the
origin.
G.9.8.1 – Determine a transformation’s line of symmetry and
compare the properties of the figure and its transformation.
M.12.8.1 – Understand , select and use, with and without
appropriate technology, the appropriate units and tools to
measure angles, perimeter, area, surface area and volume
to solve real world problems.
M.13.8.1 – Draw and apply measurement skills with fluency
to appropriate levels of precision.
G.10.8.1 – Use coordinate geometry to explore the links
between geometric and algebraic representations of
problems (length of segments/distance between points,
slope/perpendicular-parallel lines).
M.13.8.4 – Find the distance between two points on a
coordinate plane using the Pythagorean theorem.
SPECIFIC DECLARATIVE KNOWLEDGE – What I know
• Know where the vertex point, the inner scale and
outer scale are located on a protractor and how
each is used when measuring angles.
• Know the classifications of angles as acute, right,
obtuse and straight based on their measurement in
degrees.
• Recognize vocabulary relevant to angle
relationships: complementary angles,
supplementary angles, vertical angles, transversal,
alternate interior angles, and alternate exterior
angles.
• Identify interior and exterior angles of a polygon.
• Know formula for finding sum of interior angles in a
ESSENTIAL QUESTIONS:
• How is geometry used in the real world?
• What are the relationships that exist between
different types of angles?
• How can spatial relationships be described by
geometric language?
• What is the relationship between a point and its
reflected image in a line?
• How can coordinate geometry be used to
determine the translation of a figure?
• What situations can be analyzed using
transformations and symmetries?
UNIT VOCABULARY:
• Complementary angles
• Supplementary angles
• Vertical angles
• Transversal
• Alternate interior angles
• Alternate exterior angles
• Interior angle of a polygon
• Exterior angle of a polygon
• Transformation
• Pre-image and image
• Translation
• Tessellation
• Reflection
• Line of Reflection
• Symmetry
• Line of symmetry
• Rotation
• Origin
• Clockwise and counterclockwise
• Angle of rotation
• Rotational symmetry
• Midpoint
SPECIFIC PROCEDURAL KNOWLEDGE – What I need to do
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Measure angles of varying degrees with a
protractor and classify as acute, right, obtuse or
straight.
Find an angle measure given the degree of a
complementary or supplementary angle.
Solve problems using supplementary and vertical
angles.
Find corresponding, alternate interior and alternate
exterior angles in architecture.
Find corresponding, alternate interior and alternate
exterior angles measures when given parallel lines,
a transversal and the degrees in one angle.
Find the sum of a polygon’s interior angles.
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polygon (n – 2) 180.
• Find the measure of one interior angle in a regular
Know that the sum of the exterior angles of every
polygon.
polygon is 360 degrees.
• Find the measure of an exterior angle using
• Recognize vocabulary relevant to transformations:
supplementary angles.
translation, reflection, rotation, image, pre-image,
• Find the measure of an exterior angle of a regular
line of reflection, center of rotation, direction of
polygon.
rotation, and angle of rotation.
• Use the sum of the measures of exterior angles to
• Know the difference in the pre-image and the
solve for unknown angle measures.
image in a transformation.
• Describe a translation in words.
• Read and understand a translation in coordinate
• Describe a translation in coordinate notation.
notation.
• Translate a figure on a coordinate plane.
• Know when a translation can form a tessellation.
• Determine if a figure can be translated to create a
• Understand the sign changes in an ordered pair
tessellation.
when a point is reflected in either axis.
• Determine if a transformation is a reflection, and if it
• Recognize vertical, horizontal and diagonal lines of
is identify the line of reflection.
symmetry.
• Describe a reflection in the x- or y-axis using
• Understand clockwise and counterclockwise
coordinate notation.
directions on a grid.
• Reflect a figure in a given axis and draw the image.
• Understand sign changes when a point is rotated
• Find the number of lines of symmetry in a figure.
90 degrees clockwise (switch coordinates and
• Determine if a figure has horizontal, vertical or
multiply the y-coordinate by negative one) or 90
diagonal symmetry.
degrees counterclockwise (switch coordinates and
• Determine if a transformation is a rotation, and if it
multiply the x-coordinate by negative one).
is give the angle and direction of rotation.
• Understand sign changes when a point is rotated
• Rotate an object on a coordinate plane.
180 degrees (multiply each coordinate by negative
• Determine if a figure has rotational symmetry at a
one).
given angle and direction of rotation.
• Understand how to rotate an object by physically
• Calculate the distance between two points on a grid
turning the page and renaming the quadrants to
using the distance formula.
find the new coordinates (tactile/kinesthetic
• Solve problems using the distance formula.
learning).
• Calculate the midpoint between two points using
• Understand that rotational symmetry must be at a
the midpoint formula.
given degree of rotation (rotational symmetry at 90
degrees? at 180 degrees? at 120 degrees?).
• Understand the relationship between the distance
formula and the Pythagorean Theorem.
• Know how to use distance and midpoint formulas.
UNIT ASSESSMENTS
(Include tasks related to Dimensions 3 and 4 and Bloom’s Taxonomy)
Open Response #1 – G.8.8.1 – Teacher-created (application level): 1) Given parallel lines intersected by a transversal and
the measure of one angle find the measure of a second angle. 2) Explain your answer.
Open Response #2 – G.9.8.1 – Triangles on TLI website (application level): 1) Plot a triangle on a grid given the vertices.
2) Plot a congruent triangle 5 units to the right and 3 units down, and list the new coordinates of the new vertices. 3)
Classify the transformation.
Open Response #3 – G.9.8.1 – Symmetric Words on TLI website (application/synthesis): 1) Create two words with three
letters each that have a horizontal line of symmetry (like the word DO). 2) Create two words with three letters each that
have a vertical line of symmetry (like the word AT).
Traditional Assessments:
Other Evidence of Learning:
• Unit 11 Test
• Jump-Start (warm-up activities)
• Unit 11 Vocabulary Quiz
• In-class activities (individual and group)
• Unit 11 Quizzes
• Journal writing
• TLI Assessment
• Homework assignment
• TLI Open Response
• Responses to teacher questioning
• Student questions and comments
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ACTIVITIES AND LEARNING EXPERIENCES
Resources
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Angle Relationships
• APK – Jump-Start: Students will measure angles of varying degrees with a
protractor (as modeled with a virtual protractor on the Smart board) and classify as
acute, right, obtuse or straight.
• Students will find an angle measure given the degree of a complementary or
supplementary angle.
• Students will solve problems using supplementary and vertical angles.
• Students will find corresponding, alternate interior and alternate exterior angles in
pictures of architecture.
• Students will find the measure of corresponding angles, alternate interior angles and
alternate exterior angles when given parallel lines, a transversal and the degrees in
one angle.
• Students will find the sum of a polygon’s interior angles using (n – 2)180.
• Students will find the measure of one interior angle in a regular polygon by finding
the sum of the interior angles and dividing by the number of sides.
• Students will find the measure of an exterior angle using supplementary angles.
• Students will find the measure of an exterior angle of a regular polygon.
• Students will use the sum of the measures of exterior angles to solve for unknown
angle measures.
• Assessment: Students will make a journal entry contrasting complementary and
supplementary angles.
• Assessment: Students will complete Open Response question #1.
Transformations and Symmetry
• APK – Jump-Start: Students will play a reflection game where one student mimics
another’s actions across a line of reflection. Students will also perform clockwise
and counterclockwise rotations for given degrees with their bodies (kinesthetic
learning).
• Students will describe a translation in words.
• Students will describe a translation in coordinate notation.
• Students will translate a figure on a coordinate plane.
• Students will determine if a figure can be translated to create a tessellation
• Students will determine if a transformation is a reflection, and if so will identify the
line of reflection.
• Students will describe a reflection in the x- or y-axis using coordinate notation.
• Students will reflect a figure in a given axis and draw the image.
• Students will find the number of lines of symmetry in a figure.
• Students will determine if a figure has horizontal, vertical or diagonal symmetry.
• Students will determine if a transformation is a rotation, and if so will give the angle
and direction of rotation.
• Students will rotate an object on a coordinate plane.
• Students will determine if a figure has rotational symmetry at a given angle and
direction of rotation.
• Assessment: Students will make a journal entry explaining in words or drawing a
picture to reflect the meanings of transformation, translation, reflection and rotation.
• Assessment: Students will complete Open Response question #2.
Distance and Midpoint Formulas
• APK – Jump-Start: Students will complete problems involving the Pythagorean
Theorem, with and without a grid.
• Students will calculate the distance between two points on a grid using the distance
formula.
• Students will solve problems using the distance formula.
• Students will calculate the midpoint between two points using the midpoint formula.
M/L Text: Sections 13.1 –
13.6 and Section 9.5
• M/L Text, 13.1 –
13.3
• Protractors
• Skill Builder with
angles
• Smart board
• Math journal
• Open Response
question #1
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M/L Text, 13.4 –
13.6
Yard sticks for
reflection game
Smart board
Math journal
Open Response
question #2
M/L Text , 9.5
Smart board
Open Response
question #3
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Assessment: Students will complete Open Response question #3.
Career Connections
Career Link: www.mcdougallittell.com
Sculptor (Claes Oldenburg), furniture designer (Gerrit Rietveld)
Musician, architect, graphic artist
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