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Chapter 1 - Essentials of GeometryStart Date – 8/19/14End Date – 08/29/14 Section Number

and TopicStandards Learning Target Instructional

Time FrameAdditional Resources

Introduction/Syllabus 1 Day

1.1 Identifying Points, Lines, and Planes

MAFS.912.G.CO.1 Name and sketch geometric figures.Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circle arc.

1 Day Parallel, Intersecting, and Skew Lines

1.2 Use Segments and Congruence

MAFS.912.G.CO.1 Will use segment postulates to identify congruent segments.Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circle arc.

1 Day Constructing Congruent Segments and Angles

1.3 Use Distance and Midpoint Formulas

MAFS. 912.G.GPE.7

Will find lengths of segments in the coordinate plane.Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

1 Day Distance Formula - Activity A

1.4 Measure and Classify Angles

MAFS.912.G.CO.1 Will name, measure, and classify angles.Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circle arc.


1.5 Describe Angle Pair Relationship

MAFS.912.G.CO.1 Will use special angle relationships to find angle measures.Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and

1 Day Investigating Angle Theorems - Activity B

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distance around a circle arc. 1.6 Classify Polygons

MAFS.912.G.MG.1 Will classify polygons. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder.)

1 Day Polygon Angle Sum

Classifying Triangles

Classifying Quadrilaterals - Activity B

Chapter Test 1 Day

Total 8 Days






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Chapter 2 - Reasoning and ProofStart Date – XX/XX/14 End Date – XX/XX/14

Section Number and

Topic

Standards Learning Target Instructional Time Frame

Additional Resources

2.1 Use Inductive Reasoning

SMP3 Will describe patterns and use inductive reasoning.Construct viable arguments and critique the reasoning of others.

1 Day

2.2 Analyze Conditional Statements

SMP3 Will write definitions as conditional statements.Construct viable arguments and critique the reasoning of others.

2 Days Conditional Statements

2.3 Apply Deductive Reasoning

SMP3 Will use deductive reasoning to form a logical argument.Construct viable arguments and critique the reasoning of others.

2 Days

2.4 Use Postulates and Diagrams

MAFS.912.G.CO.9 Will use postulates involving points, lines, and planes. Prove theorems about lines and angles.

1 Day

Quiz 1 Day

2.5 Reason Using Properties from Algebra

MAFS.912.G.REI.1 Will use algebraic properties in logical arguments too. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

2 Days

2.6 Prove Statements about Segments and Angles

MAFS.912.G.CO.9 Will write proofs using geometric theorems. Prove theorems about lines and angles.

1.5 Days

2.7 Prove Angle Pair Relationships

MAFS.912.G.CO.9 Will use properties of special pairs of angles.Prove theorems about lines and angles.

2 Days Investigating Angle Theorems - Activity B

Test 1 Day






Chapter 3 - Parallel and Perpendicular LinesStart Date – XX/XX/14 End Date – XX/XX/14 Section Number and

TopicStandards Learning Target Instructional


3.1 Identify Pairs of Lines and Angles

MAFS.912.G.CO.1 Will identify angle pairs formed by three intersecting lines. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circle arc.


3.2 Use Parallel Lines and Transversals

MAFS.912.G.CO.9 Will use angles formed by parallel lines and transversals.Prove theorems about lines and angles.

2 Days Parallel, Intersecting, and Skew Lines

3.3 Prove Lines Parallel MAFS.912.G.CO.9 Will use angle relationships to prove that lines are parallel. Prove theorems about lines and angles.

2 DaysConstructing Parallel and Perpendicular Lines

Quiz 1 Day

3.4 Find and Use Slopes of Lines

MAFS.912.G.GPE.5

Will find and compare slopes of lines.Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

2 Days Slope - Activity B

3.5 Write and Graph Equations of Lines

MAFS.912.G.GPE.5

Will find equations of lines.Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

2 Days

3.6 Prove Theorems about Perpendicular Lines

MAFS.912.G.CO.9 Will find the distance between a point and a line. Prove theorems about lines and angles.

2 Days

Test 1 Day








Chapter 4 - Congruent TrianglesStart Date – XX/XX/14End Date – XX/XX/14 Section Number and Topic Standards Learning Target Instructional


4.1 Apply Triangle Sum Properties

MAFS.912.CO.10 Will classify triangles and find measures of their angles. Prove theorems about triangles.

1 Day Classifying Triangles

4.2 Apply Congruence and Triangles

MAFS.912.CO.7 Will identify congruent figures.Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

2 Days Proving Triangles Congruent

4.3 Relate Transformations and Congruence

MAFS.912.CO.6 Will use transformations to show congruence.Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

1 Day Reflections

Rotations, Reflections and Translations

Translations

4.4 Prove Triangles Congruent by SSS

MAFS.912.CO.8 Will use the side lengths to prove triangles are congruent.Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

1.5 Days Proving Triangles Congruent

Quiz 1Day

4.5 Prove Triangles Congruent by SAS and HL

MAFS.912.CO.8 Will use sides and angles to prove congruence.Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

1.5 Days Proving Triangles Congruent

4.6 Prove Triangles Congruent by ASA and AAS

MAFS.912.CO.8 Will use two more methods to prove congruences.

1.5 Days Proving Triangles



















Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Congruent

4.7 Use Congruent Triangles

MAFS.912.CO.10 Will use congruent triangles to prove corresponding parts congruent.Prove theorems about triangles.

2 Days

4.8 Use Isosceles and Equilateral Triangles

MAFS.912.CO.10 Will use theorems about isosceles and equilateral triangles. Prove theorems about triangles.

2 Days

4.9 Perform Congruence Transformations

MAFS.912.CO.2 Will create an image congruent to a given triangle,Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

1.5 Days Dilations

Reflections


Translations

Test 1 Day








Chapter 5 - Relationships within TrianglesStart Date – XX/XX/14End Date – XX/XX/14

Section Number and Topic



5.1 Midsegment Theorem and Coordinate Proof

MAFS.912.G.GPE.4 Will use properties of midsegments and write coordinate proofs. Use coordinates to prove simple geometric theorems algebraically.

2 Days

5.2 Use Perpendicular Bisectors

MAFS.912.G.CO.4 Will use perpendicular bisectors to solve problems.Prove theorems about lines and angles.

2 Days Concurrent Lines, Medians, and Altitudes

5.3 Use Angle Bisectors of Triangles

MAFS.912.G..C.3 Will use angle bisectors to find distance relationships.Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

2 Days Concurrent Lines, Medians, and Altitudes

5.4 Use Medians and Altitudes

MAFS.912.G.CO.10 Will use medians and altitudes of triangles.Prove theorems about triangles.

1.5 Day

Review 0.5 Day

Quiz 1 Day

5.5 Use Inequalities in a Triangle

MAFS.912.G.CO.10 Will find possible side lengths of a triangle.Prove theorems about triangles.

1 Day Triangle Inequalities

5.6 Inequalities in Two Triangles

MAFS.912.G.CO.10 Will use inequalities to make comparisons in two triangles. Prove theorems about triangles.

1 Day

Test 1 Day









Chapter 6 - Similarity Start Date – End Date –




6.1 Use Similar Polygons MAFS.912.G.SRT.5 Will use proportions to identify similar polygons.

2 Days

6.2 Relate Transformations and Similarity

MAFS.912.G.SRT.2 Will identify similarity transformations called dilations.Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

2 Days

6.3 Prove Triangles Similar by AA

MAFS.912.G.SRT.3 Will use the AA Similarity PostulateUse the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

1 Day Proving Triangles Congruent

6.4 Prove Triangles Similar by SSS and SAS

MAFS.912.G.SRT.4 Will use the SSS and SAS Similarity Theorems. Prove theorems about triangles.

1. Day Proving Triangles Congruent

Quiz 1 Day

6.5 Use Proportionality Theorems

MAFS.912.G.SRT.4 Will use proportions with a triangle or parallel lines.Prove theorems about triangles.

1 Day

6.6 Perform Similarity Transformations

MAFS.912.G.CO.2 Will perform dilations.Represent transformations in the plane using e.g., transparencies and geometry software; describe transformations as functions that take

1 Day Dilations








points in the plane as inputs and give other point as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

Review 1 Day

Test 1 Day

Midterm exam 1 Day

Chapter 7 - Right Triangles and TrigonometryStart Date – End Date –




7.1 Apply the Pythagorean Theorem

MAFS.912.G.SRT.8 Will find side lengths in right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

.5 Day Pythagorean Theorem - Activity B

Distance Formula - Activity A

7.2 Use the Converse of the Pythagorean Theorem

MAFS.912.G.SRT.8 Will use its converse to determine if a triangle is a right triangle. Use trigonometric ratios and the Pythagorean Theorem in applied problems.

.5 Day Pythagorean Theorem - Activity B

7.3 Use Similar Right Triangles

MAFS.912.G.SRT.5 Will use properties of the altitude of a right triangle.Use congruence and similarity criteria for triangles to solve problems and prove relationship in geometric figures.

1 Day Similarity in Right Triangles

7.4 Special Right Triangles MAFS.912.G.SRT.6 Will use the relationships among the sides in special right triangles.Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

1.5 Days

7.5 Apply the Tangent Ratio

MAFS.912.G.SRT.8 Will use the tangent ratio for indirect measurement.Use trigonometric ratios and the Pythagorean Theorem to solve right

1.5 DaysTangent Ratio















triangles in applied problems.

7.6 Apply the Sine and Cosine Ratios

MAFS.912.G.SRT.8 Will use the sine and cosine ratios.Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

1.5 Days Sine, Cosine, and Tangent Ratios

7.7 Solve Right Triangles MAFS.912.G.SRT.8 Will use inverse tangent, sine, and cosine ratios. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

1.5 Day Distance Formula - Activity A

Pythagorean Theorem - Activity B

Pythagorean Theorem with a Geoboard

Sine and Cosine Ratios - Activity A

Tangent Ratio


















Chapter 8 - QuadrilateralsStart Date – End Date –




8.1 Find Angles Measure in Polygons

MAFS.912.G.MG.1 Will find angle measures in polygons.Use geometric shapes, their measure, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

1 Day

8.2. Use Properties of Parallelograms

MAFS.912.G.CO.11 Will find angle and side measures in parallelograms. Prove theorems about parallelograms.

1 Day Parallelogram Conditions

Special Parallelograms

8.3 Show that a Quadrilateral is a Parallelogram

MAFS.912.G.CO.11 Will use properties to identify parallelograms.Prove theorems about parallelograms.

1 Day Parallelogram Conditions

8.4 Properties of Rhombuses, Rectangles, and Squares

MAFS.912.G.CO.11 Will use properties of rhombuses, rectangles, and squares. Prove theorems about parallelograms.

1 Day Special Parallelograms

8.5 Use Properties of Trapezoids and Kites

MAFS.912.G.SRT.5 Will use properties of trapezoids and kites.Use congruence and similarity criteria for triangles to solve problems and prove relationship in geometric figures.

1 Day Special Parallelograms

8.6 Identify Special Quadrilaterals

MAFS.912.G.CO.11 Will identify special quadrilaterals. Prove theorems about parallelograms.

1 Day






Chapter 9 - Properties of TransformationsStart Date – End Date –




9.1 Translate Figures and Use Vectors

MAFS.912.G.CO.5 Will use a vector to translate a figure. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

1 Day Reflections


Translations

9.2 Use Properties of Matrices

MAFS.912.N.VM.8(+) Will perform translations using matrix operations.Add, subtract, and multiply matrices of appropriate dimensions.

1.5 Days Dilations

Translations

9.3 Perform Reflections MAFS.912.G.CO.5 Will reflect a figure in any given line.Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

1.5 Days Reflections


9.4 Perform Rotations MAFS.912.G.CO.5 Will rotate figures about a point. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

1.5 Days Rotations, Reflections and Translations















9.5 Apply Compositions of Transformations

MAFS.912.G.CO.5 Will perform combinations of two or more transformations. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

1.5 Days

9.6 Identify Symmetry MAFS.912.G.CO.3 Will identify line and rotational symmetries of a figure. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

1 Day

9.7 Identify and Perform Dilations

MAFS.912.G.SRT.1 Will use drawing tools and matrices to draw dilations. Verify experimentally the properties of dilations given by a center and a scale factor; a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

1 Day Dilations


Chapter 10 - Properties of CirclesStart Date – End Date –




10.1 Use Properties of Tangents

MAFS.912.G.CO.1 Will use properties of a tangent to a circle. Know precise definition of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

1.5 Days

10.2 Find Arc Measures MAFS.912.G.CO.1 Will use angle measures to find arc measures. Know precise definition of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

1 Day Chords and Arcs

10.3 Apply Properties of Chords

MAFS.912.G.C.2 Will use relationships of arcs and chords in a circle. Identify and describe relationships among inscribed angles, radii, and chords.

1.5 Days Chords and Arcs

10.4 Use Inscribed Angles and Polygons

MAFS.912.G.C.3 Will use inscribed angles of circles.Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

1.5 Days Inscribed Angles

10.5 Apply Other Angles Relationships in Circles

MAFS.912.G.C.2 Will find the measures of angles inside or outside a circle. Identify and describe relationships among inscribed angles, radii, and chords.

1.5 Day

10.6 Find Segment Lengths MAFS.912.G.C.2 Will find segment lengths in 1 5 Days







in Circles circles.Identify and describe relationships among inscribed angles, radii, and chords.

10.7 Write and Graph Equations of Circles

MAFS.912.G.GPE.1

Will write equations of circles in the coordinate plane.Derive the equation of a circle of given center and radius using the Pythagorean theorem; complete the square to find the center and radius of a circle given by an equation.

1 Day Circles


Chapter 11 - Measurements of Figures and SolidsStart Date – End Date –




11.1 Circumference and Arc

MAFS.912.G.C.5 Will find arc lengths and other measures. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

1 Day Circles: Circumference and Area

11.2 Areas of Circles and Sectors

MAFS.912.G.C.5 Will find the areas of circles and sectors.Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

1 Day Circles: Circumference and Area

11.3 Areas of Regular Polygons

MAFS.912.G.SRT.8 Will find areas of regular polygons inscribed in circles.Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

1 Day

11.4 Use Geometric Probability

SMP 4 Will use lengths and areas to find geometric probabilities. Model with mathematics

1 Day Geometric Probability - Activity A

11.5 Explore Solids MAFS.912.G.GMD.4 Will identify solids. Identify the shapes of two-dimensional cross-sections of three-dimensional

1 Day










objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

11.6 Volume of Prisms and Cylinders

MAFS.912.G.GMD.3 Will find volumes of prisms and cylinders. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

1 Day Prisms and Cylinders - Activity A

11.7 Volume of Pyramids and Cones

MAFS.912.G.GMD.3 Will find volumes of pyramids and cones. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

1 Day Pyramids and Cones - Activity B

11.8 Surface Area and Volume of Spheres

MAFS.912.G.GMD.3 Will find surface areas and volumes of spheres. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

1 Day

11.9 Exploring Similar Solids

MAFS.912.G.GMD.3 Will use properties of similar solids. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

1 Day





Chapter 12 - ProbabilityStart Date – End Date –




12.1 Find Probability and Odds

MAFS.912.G.CP.1 Will find sample spaces and probabilities. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

1 Day

12.2 Find Probability Using Permutations

MAFS.912.G.CP.9 Will use the formula for the number of permutations. Use permutations and combinations of compound events and solve problems.

2 Days Permutations and Combinations

12.3 Find Probability Using Combinations

MAFS.912.G.CP.9 Will use combinations to count possibilities. Use permutations and combinations of compound events and solve problems.

1 Day Permutations and Combinations

12.4 Find Probabilities of Disjoint and Overlapping Events

MAFS.912.G.CP.7 Will find probabilities of compound eventsApply the Addition Rule, P(A or B)=P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.

1 Day

12.5 Find Probabilities of Independent and Dependent Events

MAFS.912.G.CP.8 Will examine independent and dependent events. Apply the Addition Rule, P(A or B)=P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.

2 Days Compound Independent Events

Compound Independent and Dependent Events










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