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Curriculum Map - Mathematics - Geometry Concepts
Course Resources:
Geometry Concepts - Course Syllabus
Geometry Concepts - Course Syllabus
Description:
This course begins with review and introduction of definitions of the building blocks of geometry. Students develop a strong foundation of working with definitions, postulates, and
axioms. They will explore logic as it relates to mathematics, reasoning, and proofs. Course content helps the learner cultivate a strong sense of working with figures and shapes of
all forms, and expands their ideas into real life problems. Strong spatial reasoning skills are taught as students explore different properties of shapes and figures including
congruence, area, perimeter, volume, surface area, and similarity. These new ideas provide learners a place to continually apply their accumulated Algebra knowledge and skills.
The course concludes with examining the many properties related to circles, and an introduction to Trigonometry.
Textbook: Geometry Concepts – Joseph G. Williams, B.A. / © Excel Education Systems, Inc. 2019
Course objectives:
Throughout the course, you will meet the following goals:
Understand points, lines and planes - the basic building blocks of geometry
Recognize postulates, theorems and properties, and how they are used in geometry
Identify 2-dimensional and 3-dimensional shapes and their related formulas
Comprehend and apply the Pythagorean Theorem to right triangle problems
Understand the geometry of circles and terms used to identify its parts
Learn the basic tools of Trigonometry and how to apply them to angle measurement
Semester A Semester B
1: Foundations of Geometry 6: Volume and Surface Area
2: Logic and Reasoning in Geometry 7: Similarity in Shapes
3: Shapes and Parallel Lines 8: Geometry of Circles
4: Triangle Congruence 9: Introduction to Trigonometry
5: Area and Perimeter
Grading Scale Grade Weighting
A = 90-100% Quizzes.............. 70%
B = 80-89% Final Exam......... 30%
C = 70-79% 100%
D = 60-69%
F = under 59%
Instructional
Unit Benchmarks Essential Questions Learning Objectives Strategies Resources Assessments
Months 1-12
Module 1: 1: MA.9.3.3.6(A) What are the Students will identify and apply direct 1.1: The Building Section
Foundations of Know and apply properties of building blocks of basic definitions of geometry. instruction - Blocks of Geometry Exercise
Geometry congruent and similar figures to solve geometry? Students will identify and apply textbook 1.2: Measuring Problems
problems and logically justify results. How can you postulates. direct Length Unit 1 Quiz
(updated 3/12/21) MA.9.3.4.6(A) describe the Students will understand varying instruction - 1.3: Measuring
Use numeric, graphic and symbolic attributes of a units of measure and why units are interactive Angles
representations of transformations in segment or angle? important. video 1.4: Triangles and
two dimensions, such as reflections, What properties do Students will analyze and apply guided practice Special Points
Page 1 of 5
Curriculum Map - Mathematics - Geometry Concepts
What properties do Students will analyze and apply guided practice Special Points
translations, scale changes and lines and angles angle relationships (e.g., linear independent 1.5 Motion in
rotations about the origin by multiples
of 90, to solve problems involving demonstrate in pairs, vertical, complementary, practice Geometry
figures on a coordinate grid. Geometry? supplementary, corresponding, and 1.6: Motion on the
What types of angles alternate interior angles) in Coordinate Plane
exist in Geometry? real-world or mathematical Unit 1: Definitions,
problems. Postulates, and
Students will identify definitions, Theorems Glossary
axioms, and theorems and
understand their role in Geometry.
Instructional
Unit Benchmarks Essential Questions Learning Objectives Strategies Resources Assessments
Months 1-12
Module 2: MA.9.3.2.1(A) How can you make a Students will learn how theorems, direct 2.1 Introduction to Section
Logic and Understand the roles of axioms, conjecture and prove postulates, and axioms are used in instruction - Proofs Exercise
Reason definitions, undefined terms and that it is true? proofs. textbook 2.2 Introduction to Problems
theorems in logical arguments. How can we use Students will complete two-column direct Logic Unit 2 Quiz
(updated 3/12/21) MA.9.3.2.2(A) postulates, theorems, proofs instruction - 2.3 Defining
Accurately interpret and use words and and axioms to prove Students will explore logic interactive Definitions
phrases such as "if…then," "if and only math concepts? including converse, contrapositive, video 2.4 Two-Column
if," "all," and "not." Recognize the How and why is and negations. guided practice Proofs
logical relationships between an deductive reasoning independent 2.5 Theorems and
"if…then" statement and its inverse,
converse and contrapositive. used in geometric practice Reasoning
MA.9.3.2.3(A) proof? Unit 2: Definitions,
Assess the validity of a logical Postulates, and
argument and give counterexamples Theorems Glossary
to disprove a statement.
MA.9.3.2.4(A)
Construct logical arguments and write
proofs of theorems and other results in
geometry, including proofs by
contradiction. Express proofs in a form
that clearly justifies the reasoning,
such as two-column proofs, paragraph
proofs, flow charts or illustrations.
Instructional
Unit Benchmarks Essential Questions Learning Objectives Strategies Resources Assessments
Months 1-12
Module 3: MA.9.3.3.1(A) How do you prove Students will analyze and apply direct 3.1: Polygons Section
Shapes and Know and apply properties of parallel that two lines are spatial relationships (not using instruction - 3.2: Quadrilaterals Exercise
Parallel Lines and perpendicular lines, including parallel? Cartesian coordinates) among textbook 3.3: Parallel Lines Problems
properties of angles formed by a What is the sum of points, lines, and planes (e.g., direct and Transversals Unit 3 Quiz
(updated 3/12/21) transversal, to solve problems and the measures of the betweenness of points, midpoint, instruction - 3.4: Proving Parallel
logically justify results. angles of a triangle? segment length, collinear, parallel, interactive Lines
MA.9.3.3.2(A) How do you write an perpendicular.) video 3.5: Learning more
Know and apply properties of angles, equation of a line in Students will Identify relationships guided practice about Triangles
including corresponding, exterior, the coordinate plane? between lines independent 3.6: The Angles of
interior, vertical, complementary and
supplementary angles, to solve What algebraic and Identify/use relationships of angle practice Polygons
problems and logically justify results. geometric conditions pairs formed by lines and a 3.7: Midsegments
MA.9.3.3.7(A) are sufficient and transversal 3.8: Analyzing
Use properties of polygons—including necessary to prove Prove & use angle relationships Polygons in the
quadrilaterals and regular lines parallel or involving parallel lines and a Coordinate Plane
polygons—to define them, classify perpendicular? transversal Unit 3: Definitions,
them, solve problems and logically What properties Prove lines are parallel, given Postulates, and
justify results. make a quadrilateral angle relationships Theorems Glossary
different from other Use slopes to identify
geometric figures? parallel/perpendicular lines in the
What are the coordinate plane
properties of Use properties of lines to prove
quadrilaterals? statements
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Curriculum Map - Mathematics - Geometry Concepts
Instructional
Unit Benchmarks Essential Questions Learning Objectives Strategies Resources Assessments
Months 1-12
Module 4: MA.9.3.3.3(A) How do you identify Students will classify triangles by direct 4.1: Congruent Section
Triangle Know and apply properties of corresponding parts their sides and angles. instruction - Polygons Exercise
Congruence equilateral, isosceles and scalene of congruent Students will prove triangles textbook 4.2: Triangle Problems
triangles to solve problems and triangles? congruent using SAS, SSS, ASA, direct Congruence Unit 4 Quiz
(updated 3/12/21) logically justify results. How do you show AAS Theorems instruction - 4.3: Triangle
MA.9.3.3.7(A) that two triangles are Students will be able to name interactive Congruence
Use properties of polygons—including congruent? corresponding parts of congruent video Continued
quadrilaterals and regular How can you tell polygons guided practice 4.4: Using the
polygons—to define them, classify whether a triangle is Students will identify congruent independent Congruence of
them, solve problems and logically
justify results. isosceles or polygons practice Triangles
equilateral? Students will be able to describe 4.5: Quadrilaterals 2
How can we tell the characteristics of quadrilaterals 4.6: Conditions of a
different common (parallelograms, rectangles, Quadrilateral
quadrilateral shapes rhombi, squares, trapezoids). 4.7: Triangle
apart? Inequality Theorem
Unit 4: Definitions,
Postulates, and
Theorems Glossary
Instructional
Unit Benchmarks Essential Questions Learning Objectives Strategies Resources Assessments
Months 1-12
Module 5: Area MA.9.3.1.2(A) How does the Students will apply formulas for direct 5.1: Perimeter and Section
and Perimeter Compose and decompose two- and Pythagorean perimeter and area to real-world instruction - Area Exercise
three-dimensional figures; use Theorem help solve situations. textbook 5.2: Areas of other Problems
(updated 3/16/21) decomposition to determine the real world problems? Students will identify the area of direct Common Shapes Unit 5 Quiz
perimeter, area, surface area and How does one find common shapes. instruction - 5.3: Area and
volume of various figures. the area of a figure? Students will apply definitions and interactive Circumference
MA.9.3.1.3(A) How does the Pythagorean theorem to video 5.4: The
Understand that quantities associated manipulation of a determine area of shapes and to guided practice Pythagorean
with physical measurements must be part of a figure affect solve real-world and mathematical independent Theorem
assigned units; apply such units
correctly in expressions, equations and its area? problems. practice 5.5: Using Triangles
problem solutions that involve Students will apply algebraic in Polygons and
measurements; and convert between concepts, graphing, and the Special Triangles
measurement systems. distance formula in the coordinate 5.6: The Distance
MA.9.3.1.4(A) plane to find perimeter and area of Formula
Understand and apply the fact that the shapes. Unit 5: Definitions,
effect of a scale factor k on length, Postulates, and
area and volume is to multiply each by Theorems Glossary
k, k2 and k3, respectively.
MA.9.3.3.4(A)
Apply the Pythagorean Theorem and
its converse to solve problems and
logically justify results.
MA.9.3.3.5(A)
Know and apply properties of right
triangles, including properties of
45-45-90 and 30-60-90 triangles, to
solve problems and logically justify
results.
MA.9.3.4.4(A)
Use coordinate geometry to represent
and analyze line segments and
polygons, including determining
lengths, midpoints and slopes of line
segments.
MA.9.3.4.7(A)
Use algebra to solve geometric
problems unrelated to coordinate
Page 3 of 5
Curriculum Map - Mathematics - Geometry Concepts
geometry, such as solving for an
unknown length in a figure involving
similar triangles, or using the
Pythagorean Theorem to obtain a
quadratic equation for a length in a
geometric figure.
Instructional
Unit Benchmarks Essential Questions Learning Objectives Strategies Resources Assessments
Months 1-12
Module 6: MA.9.3.1.1(A) How can you find the The student will be able to direct 6.1: Surface Area Section
Volume and Determine the surface area and surface area and calculate the volumes and surface instruction - 6.2: Volume Exercise
Surface Area volume of pyramids, cones and volume of a solid? areas of solid figures including textbook 6.3: Pyramids Problems
spheres. Use measuring devices or How do the surface composite figures. direct 6.4: Cylinders Unit 6 Quiz
(updated 3/12/21) formulas as appropriate. areas and volumes of The student will be able to instruction - 6.5: Cones
MA.9.3.1.2(A) similar solids understand how changing part of interactive 6.6: Spheres
Compose and decompose two- and compare? the shape or figure affects its video Unit 6: Definitions,
three-dimensional figures; use How does changing a surface area and volume. guided practice Postulates, and
decomposition to determine the dimension affect its Students will be able to determine independent Theorems Glossary
perimeter, area, surface area and
volume of various figures. surface area and the surface area and volume of practice
MA.9.3.1.4(A) volume? right rectangular prisms, pyramids,
Understand and apply the fact that the oblique and right cylinders, cones,
effect of a scale factor k on length, and spheres in real-world and
area and volume is to multiply each by mathematical problems.
k, k2 and k3, respectively.
Instructional
Unit Benchmarks Essential Questions Learning Objectives Strategies Resources Assessments
Months 1-12
Module 7: MA.9.3.1.5(A) How do you use Set up ratios and solve proportions direct 7.1: Scale Factors Section
Similarity in Make reasonable estimates and proportions to find for given similar geometric shapes. instruction - and Dilations Exercise
Shapes judgments about the accuracy of side lengths in similar Determine the similarity of textbook 7.2: Similarity 1: Problems
values resulting from calculations polygons? geometric figures by applying direct Polygons Unit 7 Quiz
(updated 3/16/21) involving measurements. How do you show two appropriate similarity theorems. instruction - 7.3: Similarity 2:
MA.9.3.3.6(A) triangles are similar? Apply ratios and proportions to interactive Triangles
Know and apply properties of How do you identify solve problems using the video 7.4: The
congruent and similar figures to solve corresponding parts properties of similar figures. guided practice Side-Spitting
problems and logically justify results. of similar triangles? independent Theorem
MA.9.3.4.1(A) practice 7.5: Indirect
Understand how the properties of
similar right triangles allow the Measurement
trigonometric ratios to be defined, and Unit 7: Definitions,
determine the sine, cosine and Postulates, and
tangent of an acute angle in a right Theorems Glossary
triangle.
MA.9.3.4.4(A)
Use coordinate geometry to represent
and analyze line segments and
polygons, including determining
lengths, midpoints and slopes of line
segments.
MA.9.3.4.6(A)
Use numeric, graphic and symbolic
representations of transformations in
two dimensions, such as reflections,
translations, scale changes and
rotations about the origin by multiples
of 90, to solve problems involving
figures on a coordinate grid.
MA.9.3.4.7(A)
Use algebra to solve geometric
problems unrelated to coordinate
geometry, such as solving for an
unknown length in a figure involving
similar triangles, or using the
Pythagorean Theorem to obtain a
quadratic equation for a length in a
Page 4 of 5
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