Download Madras High School Unit Plan Subject: Geometry Grades: 9

Madras High School
Unit Plan
Subject: Geometry
Grades: 9-12
Semesters: 1
Unit of Study: Basics of Geometry
Pacing-Teaching: 6 lessons – approximately 12 days of teaching
Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the
unit & 1 near the end of the unit
Summative Assessment – 1 comprehensive test (1 day) at the end of the unit
Essential Questions:
1. How can you visualize geometric concepts?
2. How can you measure and construct a line segment?
3. How can you find the midpoint and length of a line segment in a coordinate plane?
4. How can you measure and classify an angle?
5. How can you describe angle pair relationships and use these descriptions to find
angle measures?
CCSS Math Standards
G.CO.A.1, G.CO.D.12, G.GPE.B.7, G.MG.A.1
Common Core Writing Standards:

ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence
clearly, concisely, and logically such that listeners can follow the line of reasoning
and the organization, development, substance, and style are appropriate to purpose,
audience, and task.
Concepts (Need to Know)
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Skills
Name points, lines, planes, segments, and rays
Find segment lengths using the Ruler Postulate, the
Segment Addition Postulate, midpoints, segment
bisectors, and the Distance Formula
Classify polygons and angles
Find perimeters and areas of polygons in the coordinate
plane
Construct congruent segments and angles, and bisect
segments and angles
*Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create
Blooms
Level
*Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3
Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create.
Assessments:
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Unit 1, Quiz #1
Unit 1, Quiz #2
Unit 1, Comprehensive Test
Madras High School
Unit Plan
Subject: Geometry
Grades: 9-12
Semesters: 1
Unit of Study: Reasoning and Proof
Pacing-Teaching: 6 lessons – approximately 12 days of teaching
Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the
unit & 1 near the end of the unit
Summative Assessment – 1 comprehensive test (1 day) at the end of the unit
Essential Questions:
1. When is a conditional statement true or false?
2. How can you use reasoning to solve problems?
3. In a diagram, what can be assumed and what needs to be labeled?
4. How can algebraic properties help you solve an equation?
5. How can you prove a mathematical statement?
6. How can you use a flowchart to prove a mathematical statement?
CCSS Math Standards
G.CO.C.9, G.CO.C.10, G.CO.C.11, G.SRT.B.4
Common Core Writing Standards:

ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence
clearly, concisely, and logically such that listeners can follow the line of reasoning
and the organization, development, substance, and style are appropriate to purpose,
audience, and task.
Concepts (Need to Know)
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Skills
Write conditional and biconditional statements
Use inductive and deductive reasoning
Use properties of equality to justify the steps in solving
equations and to find segment lengths and angle measures
Write two-column proofs, flowchart proofs, and
paragraph proofs
*Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create
Blooms
Level
*Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3
Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create.
Assessments:
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Unit 2, Quiz #1
Unit 2, Quiz #2
Unit 2, Comprehensive Test
Madras High School
Unit Plan
Subject: Geometry
Grades: 9-12
Semesters: 1
Unit of Study: Parallel and Perpendicular Lines
Pacing-Teaching: 5 lessons – approximately 12 days of teaching
Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the
unit & 1 near the end of the unit
Summative Assessment – 1 comprehensive test (1 day) at the end of the unit
Essential Questions:
1. What does it mean when two lines are parallel, intersecting, coincident, or skew?
2. When two parallel lines are cut by a transversal, which of the resulting pairs of
angles are congruent?
3. For which of the theorems involving parallel lines and transversals is the converse
true?
4. What conjectures can you make about perpendicular lines?
5. How can you write an equation of a line that is parallel or perpendicular to a given
line and passes through a given point?
CCSS Math Standards
G.CO.A.1, G.CO.C.9, G.CO.D.12, G.GPE.B.5, G.GPE.B.6
Common Core Writing Standards:

ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence
clearly, concisely, and logically such that listeners can follow the line of reasoning
and the organization, development, substance, and style are appropriate to purpose,
audience, and task.
Concepts (Need to Know)
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Identify planes, pairs of angles formed by transversals,
parallel lines, and perpendicular lines
Use properties and theorems of parallel lines
Prove theorems about parallel lines and about perpendicular
lines
Write equations of parallel lines and perpendicular lines
Find the distance from a point to a line
Skills
Blooms
Level
*Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create
*Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3
Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create.
Assessments:
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Unit 3, Quiz #1
Unit 3, Quiz #2
Unit 3, Comprehensive Test
Madras High School
Unit Plan
Subject: Geometry
Grades: 9-12
Semesters: 1
Unit of Study: Transformations
Pacing-Teaching: 6 lessons, approximately 12 days of lessons
Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the
unit & 1 near the end of the unit
Summative Assessment – 1 comprehensive test (1 day) at the end of the unit
Essential Questions:
1. How can you translate a figure in a coordinate plane?
2. How can you reflect a figure in a coordinate plane?
3. How can you rotate a figure in a coordinate plane?
4. What conjectures can you make about a figure reflected in two lines?
5. What does it mean to dilate a figure?
6. When a figure is translated, reflected, rotated or dilated in the plane, is the image
similar to the original figure?
CCSS Math Standards
G.CO.A.2, G.CO.A.3, G.CO.A.4, G.CO.A.5, G.CO.B.6, G.MG.A.3, G.SRT.A.1a, G.SRT.A.1b, G.SRT.A.2
Common Core Writing Standards:
 ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly,
concisely, and logically such that listeners can follow the line of reasoning and the
organization, development, substance, and style are appropriate to purpose, audience, and
task
Concepts (Need to Know)
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Skills
Perform translations, reflections, rotations, dilations, and
compositions of transformations
Solve real-life problems involving transformations
Identify lines of symmetry and rotational symmetry
Describe and perform congruence transformations and
similarity transformations
*Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create
Blooms
Level
*Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3
Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create.
Assessments:
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Unit 4, Quiz #1
Unit 4, Quiz #2
Unit 4, Comprehensive Test
Madras High School
Unit Plan
Subject: Geometry
Grades: 9-12
Semesters: 1
Unit of Study: Congruent Triangles
Pacing-Teaching: 8 lessons, approximately 15 teaching days
Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the
unit & 1 near the end of the unit
Summative Assessment – 1 comprehensive test (1 day) at the end of the unit
Essential Questions:
1. How are the angle measures of a triangle related?
2. Given two congruent triangles, how can you use rigid motions to map one triangle to
the other triangle?
3. What can you conclude about two triangles when you know that two pairs of
corresponding sides and the corresponding included angles are congruent?
4. What conjectures can you make about the side lengths and angle measures of an
isosceles triangle?
5. What can you conclude about two triangles when you know the corresponding sides
are congruent?
6. What information is sufficient to determine whether two triangles are congruent?
7. How can you use congruent triangles to make an indirect measurement?
8. How can you use a coordinate plane to write a proof?
CCSS Math Standards
G.CO.C.10, G.MG.A.1, G.CO.B.7, G.CO.B.8, G.CO.D.13, G.MG.A.3, G.SRT.B.5, G.GPE.B.4.
Common Core Writing Standards:

ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence
clearly, concisely, and logically such that listeners can follow the line of reasoning
and the organization, development, substance, and style are appropriate to purpose,
audience, and task.
Concepts (Need to Know)
Skills
Blooms
Level
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Identify and use corresponding parts
Use theorems about the angles of a triangle
Use SAS, SSS, HL, ASA, and AAS to prove two triangles
congruent
Prove constructions
Write coordinate proofs
*Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create
*Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3
Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and 1to create.
Assessments:
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Unit 5, Quiz #1
Unit 5, Quiz #2
Unit 5, Comprehensive Test
Madras High School
Unit Plan
Subject: Geometry
Grades: 9-12
Semesters: 1
Unit of Study: Relationships within Triangles
Pacing-Teaching: 6 lessons, approximately 13 days of teaching
Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the
unit & 1 near the end of the unit
Summative Assessment – 1 comprehensive test (1 day) at the end of the unit
Essential Questions:
1. What conjectures can you make about a point on the perpendicular bisector of a
segment and a point on the bisector of an angle?
2. What conjectures can you make about the perpendicular bisectors and the angle
bisectors of a triangle?
3. What conjectures can you make about the medians and altitudes of a triangle?
4. How are midsegments of a triangle related to the sides of triangle?
5. How are the sides related to the angles of a triangle? How are any two sides of a
triangle related to the third side?
6. If two sides of one triangle are congruent to two sides of another triangle, what can
you say about the third sides of the triangles?
CCSS Math Standards
G.CO.C.9, G.MG.A.1, G.CO.D.12, G.C.A.3, G.MG.A.3, G.CO.C.10
Common Core Writing Standards:

ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence
clearly, concisely, and logically such that listeners can follow the line of reasoning
and the organization, development, substance, and style are appropriate to purpose,
audience, and task.
Concepts (Need to Know)
Skills
Blooms
Level
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Understand and use angle bisectors and perpendicular
bisectors to find measures
Find and use the circumcenter, incenter, centroid, and
orthocenter of a triangle
Use the Triangle Midsegment Theorem and the Triangle
Inequality Theorem
Write indirect proofs
*Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create
*Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3
Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create.
Assessments:
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Unit 6, Quiz #1
Unit 6, Quiz #2
Unit 6, Comprehensive Test
Madras High School
Unit Plan
Subject: Geometry
Grades: 9-12
Semesters: 2
Unit of Study: Quadrilaterals and Other Polygons
Pacing-Teaching: 5 lessons, approximately 12 days of teaching
Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the
unit & 1 near the end of the unit
Summative Assessment – 1 comprehensive test (1 day) at the end of the unit
Essential Questions:
1. What is the sum of the measures of the interior angles of a polygon?
2. What are the properties of parallelograms?
3. How can you prove that a quadrilateral is a parallelogram?
4. What are the properties of the diagonals of rectangles, rhombuses, and squares?
5. What are some properties of trapezoids and kites?
CCSS Math Standards
G.CO.C.11, G.SRT.B.5, G.MG.A.1, G.MG.A.3
Common Core Writing Standards:

ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence
clearly, concisely, and logically such that listeners can follow the line of reasoning
and the organization, development, substance, and style are appropriate to purpose,
audience, and task.
Concepts (Need to Know)
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Skills
Find and use the interior and exterior angle measures of
polygons
Use properties of parallelograms and special parallelograms
Prove that a quadrilateral is a parallelogram
Identify and use properties of trapezoids and kites
*Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create
Blooms
Level
*Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3
Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create.
Assessments:
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Unit 7, Quiz #1
Unit 7, Quiz #2
Unit 7, Comprehensive Test
Madras High School
Unit Plan
Subject: Geometry
Grades: 9-12
Semesters: 2
Unit of Study: Similarity
Pacing-Teaching: 4 lessons, approximately 10 days of teaching
Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the
unit & 1 near the end of the unit
Summative Assessment – 1 comprehensive test (1 day) at the end of the unit
Essential Questions:
1. How are similar polygons related?
2. What can you conclude about two triangles when you know that two pairs of
corresponding angles are congruent?
3. What are two ways to use corresponding sides of two triangles to determine that
the triangles are similar?
4. What proportionality relationships exist in a triangle intersected by an angle bisector
or by a line parallel to one of the sides?
CCSS Math Standards
G.SRT.A.2, G.MG.A.3, G.SRT.A.3, G.SRT.B.5, G.SRT.B.4, G.GPE.B.5, G.MG.A.1, G.GPE.B.6
Common Core Writing Standards:
 ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly,
concisely, and logically such that listeners can follow the line of reasoning and the
organization, development, substance, and style are appropriate to purpose, audience, and
task
Concepts (Need to Know)
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Skills
Use the AA, SSS, and SAS similarity Theorems to prove
triangles are similar
Decide whether polygons are similar
Use similarity criteria to solve problems about lengths,
perimeters, and areas
Prove the slope criteria using similar triangles
Use the Triangle Proportionality Theorem and other
proportionality theorems
*Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create
Blooms
Level
*Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3
Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create.
Assessments:
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Unit 8, Quiz #1
Unit 8, Quiz #2
Unit 8, Comprehensive Test
Madras High School
Unit Plan
Subject: Geometry
Grades: 9-12
Semesters: 2
Unit of Study: Right Triangles and Trigonometry
Pacing-Teaching: 7 lessons, approximately 15 days of teaching
Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the
unit & 1 near the end of the unit
Summative Assessment – 1 comprehensive test (1 day) at the end of the unit
Essential Questions:
1. How can you prove the Pythagorean Theorem?
2. What is the relationship among the side lengths of 45°-45°-90° triangles and 30°-60°90° triangles?
3. How are altitudes and geometric means of right triangles related?
4. How is a right triangle used to find the tangent of an acute angle? Is there a unique
right triangle that must be used?
5. How is a right triangle used to find the sine and cosine of an acute angle? Is there a
unique right triangle that must be used?
6. When you know the lengths of the sides of a right triangle, how can you find the
measures of the two acute angles?
7. What are the Law of Sines and the Law of Cosines?
CCSS Math Standards
G.SRT.B.4, G.SRT.C.8, G.MG.A.1, G.SRT.B.5, G.SRT.C.6, G.SRT.C.7, G.MG.A.3, G.SRT.D.9, G.SRT.D.10,
G.SRT.D.11
Common Core Writing Standards:
 ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly,
concisely, and logically such that listeners can follow the line of reasoning and the
organization, development, substance, and style are appropriate to purpose, audience, and
task
Concepts (Need to Know)
Skills
Blooms
Level
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Use the Pythagorean Theorem and the Converse of the
Pythagorean Theorem
Use geometric means
Find side lengths and solve real-life problems involving
special right triangles
Find the tangent, sine, and cosine ratios and use them to
solve real-life problems
Use the Law of Sines and Law of Cosines to solve triangles
*Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create
*Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3
Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create.
Assessments:
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Unit 9, Quiz #1
Unit 9, Quiz #2
Unit 9, Comprehensive Test
Madras High School
Unit Plan
Subject: Geometry
Grades: 9-12
Semesters: 2
Unit of Study: Circles
Pacing-Teaching: 7 lessons, approximately 16 days of teaching
Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the
unit & 1 near the end of the unit
Summative Assessment – 1 comprehensive test (1 day) at the end of the unit
Essential Questions:
1. What are the definitions of the lines and segments that intersect a circle?
2. How are circular arcs measured?
3. What are two ways to determine when a chord is a diameter of a circle?
4. How are inscribed angles related to their intercepted arcs? How are the angles of an
inscribed quadrilateral related to each other?
5. When a chord intersects a tangent line or another chord, what relationships exist
among angles and arcs formed?
6. What relationships exist among the segments formed by two intersecting chords or
among segments of two secants that intersect outside a circle?
7. What is the equation of a circle with center (h, k) and radius r in the coordinate
plane?
CCSS Math Standards
G.CO.A.1, G.C.A.2, G.C.A.4, G.C.A.1, G.MG.A.3, G.CO.D.13, G.MG.A.1, G.GPE.A.1, G.GPE.B.4
Common Core Writing Standards:
 ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly,
concisely, and logically such that listeners can follow the line of reasoning and the
organization, development, substance, and style are appropriate to purpose, audience, and
task
Concepts (Need to Know)
Skills
Blooms
Level
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Identify chords, diameters, radii, secants, and tangents of
circles
Find angle and arc measures
Use inscribed angles and polygons and circumscribed angles
Use properties of chords, tangents, and secants to solve
problems
Write and graph equations of circles
*Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create
*Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3
Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create.
Assessments:
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Unit 10, Quiz #1
Unit 10, Quiz #2
Unit 10, Comprehensive Test
Madras High School
Unit Plan
Subject: Geometry
Grades: 9-12
Semesters: 2
Unit of Study: Circumference, Area, and Volume
Pacing-Teaching: 8 lessons, approximately 17 teaching days
Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the
unit & 1 near the end of the unit
Summative Assessment – 1 comprehensive test (1 day) at the end of the unit
Essential Questions:
1. How can you find the length of a circular arc?
2. How can you find the area of a sector of a circle?
3. How can you find the area of a regular polygon?
4. What is the relationship between the numbers of vertices V, edges E, and faces F of
a polyhedron?
5. How can you find the volume of a prism or cylinder that is not a right prism or right
cylinder?
6. How can you find the volume of a pyramid?
7. How can you find the surface area and the volume of a cone?
8. How can you find the surface area and the volume of a sphere?
CCSS Math Standards
G.GMD.A.1, G.C.B.5, G.CO.A.1, G.MG.A.2, G.GMD.A.3, G.GMD.B.4, G.GMD.A.2, G.MG.A.1, G.MG.A.3,
Common Core Writing Standards:
 ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly,
concisely, and logically such that listeners can follow the line of reasoning and the
organization, development, substance, and style are appropriate to purpose, audience, and
task
Concepts (Need to Know)
Skills
Blooms
Level
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Measure angles in radians
Find arc lengths and areas of sectors of circles
Find areas of rhombuses, kites, and regular polygons
Find and use volumes of prisms, cylinders, pyramids, cones,
and spheres
Describe cross-sections and solids of revolutions
*Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create
*Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3
Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create.
Assessments:
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Unit 11, Quiz #1
Unit 11, Quiz #2
Unit 11, Comprehensive Test
Madras High School
Unit Plan
Subject: Geometry
Grades: 9-12
Semesters: 2
Unit of Study: Probability
Pacing-Teaching: 6 lessons, approximately 14 days of teaching
Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the
unit & 1 near the end of the unit
Summative Assessment – 1 comprehensive test (1 day) at the end of the unit
Essential Questions:
1. How can you list the possible outcomes in the sample space of an experiment?
2. How can you determine whether two events are independent or not?
3. How can you construct and interpret a two-way table?
4. How can you find probabilities of disjoint and overlapping events?
5. How can a tree diagram help you visualize the number of ways in which two or more
events can occur?
6. How can you determine the frequency of each outcome of an event?
CCSS Math Standards
S.CP.A.1, S.CP.A.2, S.CP.A.3, S.CP.A.4, S.CP.A.5, S.CP.B.6, S.CP.B.7, S.CP.B.8, S.CP.B.9, A.APR.C.5
Common Core Writing Standards:

ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence
clearly, concisely, and logically such that listeners can follow the line of reasoning
and the organization, development, substance, and style are appropriate to purpose,
audience, and task.
Concepts (Need to Know)
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Skills
Find probabilities of independent and dependent events
Use conditional relative frequencies to find conditional
probabilities
Use the formulas for the number of permutations and the
number of combinations
Construct and interpret probability distributions and
binomial distributions
*Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create
Blooms
Level
*Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3
Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create.
Assessments:
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Unit 12, Quiz #1
Unit 12, Quiz #2
Unit 12, Comprehensive Test