Download Geometry Unit 1 Description

LMU|CMAST
Geometry Unit Descriptions
Geometry Unit Descriptions
Mathematical reasoning skills developed in previous courses provide a solid foundation for understanding proof and logic in Geometry. A
study of analytical geometry is weaved throughout this course, highlighted by a study of transformations in the plane. The concept of area is
also weaved throughout, with a discussion of the areas of many different geometric objects. Previous knowledge of angles and angle pairs is
used to prove important results about the congruence of angles. A construction of the angle bisector is explored. Triangles, quadrilaterals,
and polygons are classified and important results are proven. The triangle congruence theorems are explored in depth and used to prove two
triangles congruent. The concepts of ratio and proportion are applied in the study of similar polygons. This leads to a discussion of special
right triangles, and the Pythagorean theorem. Different proofs of the Pythagorean theorem are explored. The concept of a ratio is necessary
for the study of the trigonometric ratios and their relationship to right triangles. Connections among shapes and their properties are made in
the study of circles, including an exploration of how polygons, lines, and circles interact. Finally, the concept of shape is expanded to three
dimensions, with special focus on the study of prisms, pyramids, and cylinders. The concept of function is revisited in the study of the
formulas for volume and surface area.
Unit Organization:
Unit 1: Logic and Reasoning
Unit 2: Angle and Angle Relationships
Unit 3: Triangles and Triangle Congruence
Unit 4: Quadrilaterals
Unit 5: Polygons
Unit 6: Similar Polygons
Unit 7: Right Triangle Trigonometry
Unit 8: Circles
Unit 9: Solid Geometry
Unit 10: CST Review
Textbook: Geometry: Applying, Reasoning, Measuring (2004). McDougal Littell. Houghton Mifflin College Division. Ron
Larson, Laurie Boswell, Lee Stiff.
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LMU|CMAST
Geometry Unit Descriptions
Unit 1: Logic and Reasoning
This unit lays the foundation for proving geometric relationships by developing the effective thinking needed to construct mathematically
accurate logical arguments and proofs. Inductive reasoning is introduced as the type of thinking needed to analyze patterns and create
conjectures. Counterexamples are used to prove some conjectures false. Different forms of logical statements are explored, including the
converse, inverse, contrapositive, and biconditional statements. Counterexamples are used again to show that a logical statement is false.
Logical statements are then used in defining basic geometric objects (i.e. points, lines, and planes), postulates (i.e. addition, etc), and
properties (i.e. reflexive, symmetric, transitive). The understanding of segments is explored with constructions (i.e. copying of segments) and
deductive reasoning is used to prove basic geometric statements, including those about segments. Two column proofs are introduced and a
connection is made between this type of proof, and written justification of steps used in an algebra problem. Multiple types of proofs are used
to prove statements about segment congruence, including two-column proofs and paragraph proofs. As an introduction to coordinate
geometry, the distance formula and the midpoint are derived and organized as proofs. The definition of equidistant is given and illustrated in
the coordinate plane using the distance formula.
#
1A
1B
1C
1D
Learning Targets
Write a conjecture from a given set of information and explain how this is
inductive reasoning.
Show that a statement is false by providing a counterexample.
Explain what it means for a statement to be in “if-then” form, and explain the
relationship between the hypothesis and conclusion.
Write a negation, converse, inverse, contrapositive, and biconditional statement in
words and in symbolic notation.
1E
Judge the validity of conditional statements, including the biconditional.
1F
1G
Explain the role of proof in mathematics.
Use deductive reasoning and the laws of logic to determine whether a
Standard
Textbook
1.0
Pg. 6-9
# 12-33, 42-51, 68-71
3.0
3.0
3.0
3.0
2.0
3.0
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Active Practice
Gallery Walk
Pg. 8
# 34-41; Pg. 75 #1417; Pg. 83 #24-27
Pg. 75-76
#9-13, 22-28
Matching
Pg. 76-77
# 18-24, 44-52; Pg.
91-92 #8-20
Pg. 75-76
# 14-17, 29-39; Pg.
82-83 # 13-23, 28-43
Cube
Pg. 92 #23-35
Puzzle Pieces
T/F Strips
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LMU|CMAST
Geometry Unit Descriptions
1H
1I
statement is valid.
Explain the difference between inductive and deductive reasoning.
State the definition of a point, line, and plane.
1J
Use a compass and protractor to construct a copy of a segment.
1.0
1.0
16.0
1K
1L
Describe the properties of segment congruence.
State the reflexive, symmetric, and transitive properties and use them to
judge the validity of a logical statement.
1M State the addition, subtraction, multiplication, division and substitution
properties, and use them to judge the validity of a logical statement.
1N Develop two column proofs or paragraph proofs involving segment
congruence.
1O Use the distance formula and midpoint formula in the coordinate plane.
1P Explain the concept of equidistant, and provide examples in the coordinate plane.
4.0
3.0
3.0
4.0
17.0
17.0
Pg. 92 # 21-22
Pg. 13-15 # 9-51, 6167
Pg. 38
#14-16;
Pg. 105
#12-15
Pg. 105-106
#6-11, 16-18
Pg. 105 #6-11
Construction
Mini White
Boards
Find the Mistake
Pg. 100 # 16-23; Pg.
101 #32
Find the Mistake
Pg. 105 #6-11
Puzzle Pieces /
Gallery Walk
Post-It Notes
Envelop Activity
Pg. 38-39 #4-9, 17-30
Pg. 38-39 #4-9, 17-30
Essential Standards (CA):
1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and
deductive reasoning.
2.0 Students write geometric proofs, including proofs by contradiction.
3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.
4.0 Students prove basic theorems involving congruence and similarity.
17.0 Students prove theorems by using coordinate geometry, including the midpoints of a line segment, the distance formula, and various
forms of equations of lines and circles.
Supporting Standards (CA):
16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line
parallel to a given line through a point off the line.
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