Download Course Title: Geometry Grade Level(s): 8th-12th

Course Title: Geometry
Grade Level(s): 8th-12th
Materials:
Objectives: All students will:
 Review and master Algebra concepts previously learned.
 Construct, formulate, and evaluate area, perimeter, and volume of two-dimensional and three-dimensional.
 Explore angle relationships including parallel lines, straight line, angle measurements, and polygon properties.
 Deduce and justify proofs using logic, conjectures, and indirect proofs to establish relationships and solve application problems.
 Demonstrate congruence between polygons specifically triangles.
 Use spatial visualization to construct models, draw diagrams, and solve problems.
 Relate trigonometry to right triangles.
 Demonstrate similarity between polygons and polyhedra; specifically triangles.
 Explore the basic properties, theorems, and measurements of circles
Essential Questions:
Algebra
1. How calculating slope and identifying the y-intercept work together to write and graph an equation?
2. How do we use patterns, tables, systematic lists of data, and diagrams to problem solve?
4. How do you find the length and midpoint of a line segment?
5. How do we solve and graph solutions to single-variable and linear inequalities?
6. How do we simplify radicals?
7. What are the essential components of solving a rational single variable, or Algebraic, fraction to eliminate fractions in an equation prior to
solving?
8. How do we use the law of exponents to solve problems?
9. How do you use the substitution and elimination methods of systems of equations to find the point of intersection?
10. How can we determine the slope of perpendicular, parallel, horizontal, and vertical linear equations?
11. How do we solve quadratic equations using to factoring and the Quadratic Formula?
12. How do we solve factored quadratic equations using to Zero Product Property?
13. How do the solutions of quadratic equations relate graphically?
13. How can we graph non-linear relationships?
14. How to complete arithmetic operations of polynomial expressions and simplification of polynomial expressions.
Area, Perimeter, Volume
1. What ways can we demonstrate how to use visual representation to calculate area and perimeter.
2. What are effective methods for finding perimeter and area of polygons?
3. How do we use patterns, tables, systematic lists of data, and diagrams to problem solve?
4. How would we develop and solve the formulas for Pythagorean Theorem and area and volume of two-dimensional and three-dimensional figures
including polygons.
Angle Relationships
1. How can we identify angle vocabulary and angle relationships to solve problems?
2. How would you recognize angle relationships formed by parallel lines and transversals when you use a diagram?
3. What relationships exist in the sum of the angles of any triangle is 180o and exterior angles of triangles?
4. How do you find the length and midpoint of a line segment?
5. How can angle relationships be used to solve multi-step problems?
Proofs and Logic
1. What are the essential components of constructing logical arguments to justify your solutions to logic games and simple number theory
principles?
2. How can you use observations and patterns to write a conjecture?
3. What information can be extracted from word problems and then apply to draw diagrams?
4. How do we solve previous conjectures using a proof?
5. What are representations of various proof formats?
6. How would you use an indirect proof or proof by contradiction to justify conclusions?
7. What are the essential components of constructing logical arguments to construct a proof?
Congruence
1. How do we transform polygons on a flat surface while preserving their size and shape?
2. What are the most effective ways to discover and use the conditions user which pairs of triangles must be congruent?
3. How would you prove that parts of polygons, specifically triangles and quadrilaterals, are congruent to corresponding parts of other polygons,
specifically triangles and quadrilaterals?
4. How do we determine the limits to the length of the third side of a triangle?
5. How can we determine the slope of perpendicular, parallel, horizontal, and vertical linear equations?
6. How do we solve quadratic equations using to factoring and the Quadratic Formula?
Trigonometry: Triangle Ratios
1. How do we find the lengths of sides in right triangles when you only know two of the six measurements?
2. What strategies can we use to solve trigonometric application problems?
3. How do we find the measures of angles in right triangles when you only know two of the six measurements?
4. What are the essential components of solving a rational single variable fraction to eliminate fractions in an equation prior to solving?
5. How do we simplify radicals?
6. How do we apply the ratios of Special Right Triangles?
Spatial Visualization
3. How do we explore and discuss visualization activities?
4. How do we use cube stacks to draw Isometric representations?
5. How would you recognize relationships among properties, constructions and 2 dimensional drawings of prisms and pyramids?
6. How do I calculate surface areas and volumes of polyhedra?
Similarity
1. How do we use the properties of similarity to determine whether two figures are similar?
2. What strategies can we use to solve application problems?
2
3
3. What are the essential components of r : r : r ?
4. How do we prove triangle and polygonal similarity?
5. What are the basic theorems of similarity?
6. How do the basic theorems of similarity apply to polygons.
Circles
1. What is the essential vocabulary in terms of circles and coordinate geometry?
2. How is the vocabulary used to solve and justify complex problems?
3. How do geometric theorems justify properties of circles?
4. How is the tangent/diameter theorem used to prove and solve problems?
5. How is the diameter/chord theorem used to prove and solve problems?
6. How can we use the concept of similarity to determine arc lengths and areas of sectors of circles?
7. Determine the difference between the description, length, and measurement of arcs including inscribed angles, intercepted arcs, and central angles.
8. What are the essential components used to apply coordinate geometry to formulate simple geometric theorems algebraically?
Standards
Content (What students will know)
Performance (Student will do)
CC.2.3.HS.A.1
Use geometric figures and their properties to
represent transformations in the plane.
Use mirrors and other techniques to transform
polygons.
G.1.3.1.1,
G.1.3.1.2
Explore and discuss visualization activities.
Represent transformation word problems
through spatial visualization and diagrams.
Learn to draw transformation representations
of polygons
CC.2.3.HS.A.2
G.1.3.1.1,
G.1.3.1.2
CC.2.3.HS.A.3
G.1.2.1.1,
G.1.2.1.2,
G.1.2.1.3,
G.1.2.1.4,
G.1.2.1.5, G.1.
3.2.1,
G.2.2.1.1,
G.2.2.1.2,
G.2.2.2.1,
G.2.2.2.2,
G.2.2.2.3,
G.2.2.2.4,
G.2.2.2.5
Transformation of polygons
Apply rigid transformations to determine and
explain congruence.
How to transform polygons and determine
where congruence exists.
Verify and apply geometric theorems as they
relate to geometric figures.
Prove triangle congruence.
Construct models to assess the relationships
between congruent triangles.
Apply geometric theorems as they relate to
geometric figures to solve problems.
2
3
Develop and use the components of r : r : r .
Activities/Assessments
CC.2.3.HS.A.4
CC.2.3.HS.A.5
G.1.3.1.1,
G.1.3.1.2
CC.2.3.HS.A.6
G.1.3.1.1,
G.1.3.1.2,
G.1.3.2.1
Apply the concept of congruence to create
geometric constructions.
Construct proofs and logical argumentation to
prove triangle congruence
properties/theorems.
Develop and prove triangle congruence
properties/theorems.
Create justifications based on transformations
to establish similarity of plane figures.
Explore properties of figures with the same
shape: similarity.
Understand the properties of figures with the
same shape: similarity.
Discover the basic theorems of similarity and
apply them to triangles.
Discover the basic theorems of similarity and
apply them to triangles.
Verify and apply theorems involving similarity
as they relate to plane figures.
Explore properties of plane figures with the
same shape: similarity.
Understand the properties of plane figures
with the same shape: similarity.
Discover the basic theorems of similarity and
apply them to plane figures.
Discover the basic theorems of similarity and
apply them to plane figures.
2
3
Develop and use the components of r : r : r .
CC.2.3.HS.A.7
Apply trigonometric ratios to solve problems
involving right triangles.
Compute the lengths of sides in right triangles
when given exactly two measurements.
G.2.1.1.1,
G.2.1.1.2
Find the lengths of sides in right triangles when
you only know two of the six measurements.
Solve interesting application problems.
How to solve interesting application problems.
Compute the measurements of angles in right
triangles when given exactly two
measurements.
Find the measures of angles in right triangles
when you only know two of the six
measurements.
Solve algebraic fractions.
Review the simplification process for radicals.
How to eliminate fractions in an algebraic
fraction prior to solving equations.
CC.2.3.HS.A.8
G.1.1.1.1,
G.1.1.1.2,
G.1.1.1.3,
G.1.1.1.4,
G.1.3.2.1,
G.2.2.3.1
How to simplify radicals.
Apply geometric theorems to verify properties
of circles.
Compose and explain geometric theorems to
verify properties of circles.
Geometric theorems to justify properties of
circles.
Develop and use the tangent/diameter
theorem and diameter/chord theorem.
CC.2.3.HS.A.9
Extend the concept of similarity to determine
arc lengths and areas of sectors of circles.
G.1.1.1.1,
G.1.1.1.2,
G.1.1.1.3,
G.1.1.1.4,
G.2.2.2.1,
G.2.2.2.2,
G.2.2.2.3,
G.2.2.2.4,
G.2.2.2.5,
G.2.2.3.1
CC.2.3.HS.A.11
How to use the concept of similarity to
determine arc lengths and areas of sectors of
circles.
G.2.1.2.1,
G.2.1.2.2,
G.2.1.2.3
How to apply coordinate geometry to
formulate simple geometric theorems
algebraically.
Justify the concept of similarity to determine
arc lengths and areas of sectors of circles.
Difference between the description, length,
and measurement of arcs including inscribed
angles, intercepted arcs, and central angles.
Apply coordinate geometry to prove simple
geometric theorems algebraically.
Support and defend the application of
coordinate geometry to prove simple
geometric theorems algebraically.
Develop and use the tangent/diameter
theorem and diameter/chord theorem.
CC.2.3.HS.A.12
Explain volume formulas and use them to solve
problems.
Formulate volume formulas of polygons and
use them to solve application problems.
G.2.3.1.1,
G.2.3.1.2,
G.2.3.1.3
Efficient ways to calculate lengths, areas, and
volumes between similar two and three
dimensional figures.
Construct three-dimensional models and
represent them in two-dimensional space.
How to explore and discuss visualization
activities.
Construct and draw Isometric representations
of cube stacks.
Explore and discuss visualization activities.
Learn how to draw Isometric representations
of cube stacks
Understand properties, build and draw
selected polyhedra, specifically prisms and
pyramids, on 2-dimensional surfaces.
How to calculate surface areas and volumes of
polyhedra.
Build polyhedra models, including prisms and
pyramids, to formulate surface area and
volume formulas.
2
3
Develop and use the components of r : r : r .
CC.2.3.HS.A.13
Analyze relationships between two‐
dimensional and three‐dimensional objects.
G.1.1.1.1,
G.1.1.1.2,
G.1.1.1.3,
G.1.1.1.4,
G.1.2.1.1,
G.1.2.1.2,
G.1.2.1.3,
G.1.2.1.4,
G.1.2.1.5,
G.2.3.2.1
Efficient ways to calculate lengths, areas, and
volumes between similar two and three
dimensional figures.
How to explore and discuss visualization
activities.
Learn how to draw Isometric representations
of cube stacks
Compare and assess relationships between
two-dimensional and three-dimensional
objects.
Build models to analyze relationships between
two-dimensional and three-dimensional
objects.
Construct and draw Isometric representations
of cube stacks.
Explore and discuss visualization activities.
Understand properties, build and draw
selected polyhedra, specifically prisms and
pyramids, on 2-dimensional surfaces.
CC.2.3.HS.A.14
G.2.2.4.1,
G.2.3.1.1,
G.2.3.1.2,
G.2.3.1.3
How to calculate surface areas and volumes of
polyhedra.
How to apply geometric concepts to model and Construct models using geometric concepts to
solve real word problems.
solve real word problems.
Create diagrams using geometric concepts to
solve real work problems.
Title: Algebra Concepts
Standards
Content (What students will know)
Performance (Student will do)
CC.2.2.HS.D.1
How to interpret the structure of expressions to
represent a quantity in terms of its context.
Interpret and justify the structure of
expressions to represent a quantity in terms
of its context.
How to write expressions in equivalent forms to
solve problems.
Write expressions in equivalent forms to solve
problems.
Knowledgeable of arithmetic operations and
apply to polynomials.
Demonstrate knowledge of arithmetic
operations and apply to polynomials.
A1.1.1.5.1,
A1.1.1.5.2,
A1.1.1.5.3,
A2.1.2.2.1,
A2.1.2.2.2
CC.2.2.HS.D.2
A1.1.1.5.1,
A1.1.1.5.2,
A1.1.1.5.3,
A2.1.2.1.1,
A2.1.2.1.2,
A2.1.2.1.3,
A2.1.2.1.4,
A2.1.2.2.1,
A2.1.2.2.2
CC.2.2.HS.D.3
A1.1.1.5.1,
A1.1.1.5.2,
A1.1.1.5.3,
A2.1.2.2.1,
A2.1.2.2.2
Activities/Assessments
CC.2.2.HS.D.4
The relationship between zeroes and factors of
polynomials.
A2.1.2.2.1,
A2.1.2.2.2
How to make generalizations about functions
and their graphs
Demonstrate an understanding of the
relationship between zeroes and factors of
polynomials to make generalizations about
functions and their graphs.
Use the concept of factoring and the Zero
Product Property to establish a relationship
between zeroes and factors of polynomials.
CC.2.2.HS.D.5
A1.1.1.5.1,
A1.1.1.5.2,
A1.1.1.5.3,
A2.1.2.2.1,
A2.1.2.2.2,
A2.1.3.1.1,
A2.1.3.1.2,
A2.1.3.1.3,
A2.1.3.1.4
CC.2.2.HS.D.6
A1.1.1.5.1,
A1.1.1.5.2,
A1.1.1.5.3,
A2.1.3.1.1,
A2.1.3.1.2,
A2.1.3.1.3,
A2.1.3.1.4
How to use polynomial identities to solve
problems.
How to extend their knowledge of rational
functions to rewrite in equivalent forms.
Construct and assess quadratic equations
graphically to establish a relationship between
zeroes and factors of polynomials.
Use polynomial identities to solve problems.
Demonstrate an extended knowledge of
rational function to rewrite in equivalent
forms.
CC.2.2.HS.D.7
A1.1.2.1.1,
A1.1.2.1.2,
A1.1.2.1.3,
A1.1.2.2.1,
A1.1.2.2.2,
A1.1.3.1.1,
A1.1.3.1.2,
A1.1.3.1.3,
A1.1.3.2.1,
A1.1.3.2.2,
A2.1.3.1.1,
A2.1.3.1.2,
A2.1.3.1.3,
A2.1.3.1.4,
A2.1.3.2.1,
A2.1.3.2.2,
A2.2.2.1.1,
A2.2.2.1.2,
A2.2.2.1.3,
A2.2.2.1.4
CC.2.2.HS.D.8
A1.1.2.1.1,
A1.1.2.1.2,
A1.1.2.1.3,
A2.1.3.1.1,
A2.1.3.1.2,
A2.1.3.1.3,
A2.1.3.1.4,
A2.1.3.2.1,
A2.1.3.2.2
How to create and graph equations or
inequalities to describe numbers or
relationships.
Create and graphically represent equations or
inequalities to describe numbers or
relationships.
When and how to apply inverse operations to
solve equations or formulas for a given variable.
Apply inverse operations including reciprocal
to solve equations or formulas for a given
variable.
CC.2.2.HS.D.9
A1.1.1.4.1,
A1.1.2.1.1,
A1.1.2.1.2,
A1.1.2.1.3,
A1.1.2.2.1,
A1.1.2.2.2,
A1.1.3.1.1,
A1.1.3.1.2,
A1.1.3.1.3,
A2.1.3.1.1,
A2.1.3.1.2,
A2.1.3.1.3,
A2.1.3.1.4,
A2.1.3.2.1,
A2.1.3.2.2
How to use reasoning to solve equations and
justify the solution method.
Demonstrate the use of reasoning to solve
equations and justify the solution method.
CC.2.2.HS.D.10
A1.1.2.1.1,
A1.1.2.1.2,
A1.1.2.1.3,
A1.1.2.2.1,
A1.1.2.2.2,
A1.1.3.1.1,
A1.1.3.1.2,
A1.1.3.1.3,
A1.1.3.2.1,
A1.1.3.2.2,
A2.1.3.1.1,
A2.1.3.1.2,
A2.1.3.1.3,
A2.1.3.1.4
How to explore relationships between points on
a straight line, leading to an understanding of
and ability to use slope and the y-intercept to
graph linear equations.
Explore relationships between points on a
straight line, leading to an understanding of
and ability to use slope and the y-intercept to
graph linear equations.
Develop the problem solving skills of looking for
patterns, making tables, and systematic lists of
data, and drawing diagrams to create
equations/inequalities.
Find the length and midpoint of a line
segment.
How to graph solutions to linear inequalities,
equations, and system of equations.
How to distinguish between linear, quadratic,
and non-linear functions algebraically and
graphically.
How to solve and graph single variable
inequalities.
Use problem solving skills of looking for
patterns, making tables, and systematic lists
of data, and drawing diagrams to create
equations/inequalities.
Graph solutions to linear inequalities,
equations, and system of equations.
Distinguish between linear, quadratic, and
non-linear functions algebraically and
graphically.
How to solve factored quadratic equations using Demonstrate how to solve and graph single
variable inequalities.
to Zero Product Property.
How to extend graphing to non-linear
relationships; parabolas.
Solve factored quadratic equations using to
Zero Product Property.
Extend graphing to non-linear relationships;
parabolas.
Title: Number and Quantity
Standards
Content (What students will know)
Performance (Student will do)
CC.2.1.HS.F.1
How to apply and extend the properties of
exponents to solve problems with rational
exponents.
Apply and extend the properties of exponents
to solve problems with rational exponents.
How to apply properties of rational and
irrational numbers to solve real world or
mathematical problems.
Apply properties of rational and irrational
numbers to solve real world or mathematical
problems.
How to apply quantitative reasoning to choose
and interpret units and scales in formulas,
graphs, and data displays.
Apply quantitative reasoning to choose and
interpret units and scales in formulas, graphs,
and data displays.
A1.1.1.1.1,
A1.1.1.1.2,
A1.1.1.3.1,
A2.1.2.1.1,
A2.1.2.1.2,
A2.1.2.1.3,
A2.1.2.1.4
CC.2.1.HS.F.2
A1.1.1.1.1,
A1.1.1.1.2,
A1.1.1.3.1,
A1.1.1.2.1
CC.2.1.HS.F.3
A1.1.2.1.1,
A1.1.2.1.2,
A1.1.2.1.3,
A1.2.1.2.1,
A1.2.1.2.2,
A2.2.2.1.1,
A2.2.2.1.2,
A2.2.3.1.1,
A2.2.3.1.2
Activities/Assessments
CC.2.1.HS.F.4
A1.1.2.1.1,
A1.1.2.1.2,
A1.1.2.1.3,
A1.2.1.2.1,
A1.2.1.2.2,
A2.2.2.1.1,
A2.2.2.1.2
CC.2.1.HS.F.5
A1.1.2.1.1,
A1.1.2.1.2,
A1.1.2.1.3,
A1.1.2.2.1,
A1.1.2.2.2,
A1.1.3.1.1,
A1.1.3.1.2,
A1.1.3.1.3,
A1.1.3.2.1,
A1.1.3.2.2,
A2.2.3.1.1,
A2.2.3.1.2
CC.2.1.HS.F.6
A2.1.1.1.1,
A2.1.1.1.2,
A2.1.1.2.1,
A2.1.1.2.2
How to use units as a way to understand
Use units as a way to understand problems
problems and to guide the solution of multi‐step and to guide the solution of multi‐step
problems.
problems.
How to choose a level of accuracy appropriate
to limitations on measurement when reporting
quantities.
Demonstrate a how to choose a level of
accuracy appropriate to limitations on
measurement when reporting quantities.
How to extend the knowledge of arithmetic
operations and apply to complex numbers.
Demonstrate how to extend the knowledge of
arithmetic operations and apply to complex
numbers.
CC.2.1.HS.F.7
A2.2.1.1.1,
A2.2.1.1.2,
A2.2.1.1.3,
A2.2.1.1.4
How to apply concepts of complex numbers in
polynomial identities and quadratic equations
to solve problems.
Apply concepts of complex numbers in
polynomial identities and quadratic equations
to solve problems.