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Mathematics Department Geometry Honors Curriculum Map Volusia County Schools 1206320/ISC Revision 6-27-12

Volusia County Mathematics Curriculum Map

Geometry Honors Course Number 1206320/ISC

Mathematics Department ii Geometry Honors Curriculum Map Volusia County Schools 1206320/ISC Revision 6-6-12

KEY TERMINOLOGY OF THE CURRICULUM MAP

Unit/Organizing Principle: the overarching organizational structure used to group content and concepts within the curriculum map Pacing: the recommended time period within the year for instruction related to the essential questions to occur Essential Questions: the overarching question(s) that will serve to guide instruction and push students to higher levels of thinking; essential questions should guide students to the heart of the content Measurement Topics: a list of the major underlying concepts covered in the development of the essential questions Learning Targets/Skills: the content knowledge, processes and enabling skills that will ensure successful mastery of the essential questions Benchmarks: the Next Generation Sunshine State Standards Academic Language: the content vocabulary and other key terms and phrases with which students should be familiar and that support mastery of the learning targets, skills and essential questions Activities and Resources: a listing of available, high quality and appropriate materials, strategies, lessons, textbooks, videos and other media sources that are aligned with the learning targets, skills and essential questions; developed to save teachers time when planning for instruction Assessment: a list of required formative assessments as well as suggested assessments that are available to use as formative or summative assessments

Mathematics Department iii Geometry Honors Curriculum Map Volusia County Schools 1206320/ISC Revision 6-6-12

UNIT/ORGANIZING PRINCIPLE: Lengths and Midpoints – Segments (G.1.1) PACING: 1st Quarter 8.5 days

ESSENTIAL QUESTIONS:

Can the student understand the relationships between points, lines, and planes?

MEASUREMENT TOPIC

T01: Lengths and Midpoints – Segments

LEARNING TARGETS/SKILLS

The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE

(Bold Assessed on EOC)

Pearson Screening Test www.pearsonsuccessnet.com Teacher Resources – Progress Monitoring Assessments Skills Review (pgs. 852, 858, 860, 861)

review prerequisite vocabulary 2 MA.912.G.1.1

Point Line Plane Dimension Collinear Coplanar Ray Line Segment Midpoint of a line Distance formula Coordinate Plane Congruent Segments

1.2 Points, Lines, Planes

understand that point, lines and planes have NO definitions 0.5 MA.912.G.8.1


demonstrate understanding of a line, line segment, and ray 1 MA.912.G.1.1


name 3 points that are collinear or coplanar 0.5 MA.912.G.1.1

1.2 Points, Lines, Planes draw 4 points that are coplanar but not collinear 0.5 MA.912.G.1.1


use postulates to justify relationships between points, lines and planes

2 MA.912.G.1.1

1.3 Measuring Segments 1.7 Midpoint & Distance in Coordinate Plane

given two points, find the distance between them and the coordinates of the midpoint

2 MA.912.G.1.1

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision. Look for and make use of structure.

Look for and express regularity in repeated reasoning.

MACC.K12.MP.1 MACC.K12.MP.2 MACC.K12.MP.3 MACC.K12.MP.4 MACC.K12.MP.5 MACC.K12.MP.6 MACC.K12.MP.7 MACC.K12.MP.8

http://www.pearsonsuccessnet.com/

Mathematics Department 1 Geometry Honors Curriculum Map Volusia County Schools 1206320/ISC Revision 6-6-12

ESSENTIAL QUESTIONS: Can the student understand the relationships between points, lines, and planes?

Activities and Resources Assessment

Suggested Resources Big Ideas:

CPALMS: http://www.floridastandards.org

TI Activity Exchange & APPS:

TI-Nspire Geometry Activity: Points, Lines, Angles – Determining Angle Measures

http://www.ti-mathnspired.com/geometry/points-lines-and-angles/determining-angle-measures/

Internet Resources

http://www.mathmeasures.org

http://www.interactmath.com/

http://www.math.com/homeworkhelp/Geometry.html

http://www.pearsonsuccessnet.com

http://fcat.fldoe.org/eoc/itemspecs.asp (EOC info, sample items)

Required Assessment State Assessments

State Mandated (DA) Assessments o #1: Beginning of First Semester (TBA) o #2: End of First Semester (TBA)

Tied to essential questions Defined Testing Window Data collected through Scantron

EOC Exam for Geometry – Defined Testing Window (TBA)

District Interim Assessments

Tied to benchmarks

Focus items imported into Scantron

Data available through Scantron and Performance Matters

Suggested Assessments/Internet Resources

teacher made tests/quizzes

chapter tests/quizzes from PearsonSuccessNet.com or using ExamViewPro

http://www.floridastandards.org/

http://www.mathnspired.com/



http://www.mathmeasures.org/




http://fcat.fldoe.org/eoc/itemspecs.asp


UNIT/ORGANIZING PRINCIPLE: Parallel lines and Special Angle Relationships (G.1.3)

PACING: 1st Quarter 12 days


Can the student use the appropriate vocabulary to identify and use the relationships of the angles formed by intersecting lines and parallel lines cut by a transversal?

MEASUREMENT TOPIC

T02: Parallel Lines/ Angle Relationships


The student will:

PACING (Days)

BENCHMARK ACADEMIC LANGUAGE


Skills Review (pg.852) use a protractor to draw various types of angles 0.5 MA.912.G.1.3 Conditional statement Hypothesis Conclusion Converse Postulate Axiom Theorem Angles – Right, Obtuse, Acute Sides of an angle

Protractor Linear Pairs Vertical Angles Adjacent Angles Complementary Angles Supplementary Angles Parallel lines Perpendicular lines Transversal

Corresponding angles Alternate interior/exterior angles Consecutive (same side) int. angles Angle Bisectors Perpendicular Bisectors Slope

Equations of Lines

1.4 Measuring Angles identify vertical angles, linear pairs, complementary and

supplementary angles 2 MA.912.A.3.1

Skills Review (pg.862) 1.5 Exploring Angle Pairs 2.6 Proving Angles Congruent (theorems only,

postpone formal proofs)

find the measure of these angles when given algebraic expressions to represent the angles

3.5 MA.912.G.1.3

2.2 Conditional

Statements 3.1-3.4 Perpendicular

and Parallel Lines

identify and use the relationships between special pairs of angles (corresponding, alternate interior, alternate exterior, and consecutive/same-side interior angles) formed by intersecting lines, parallel lines, transversals

6 MA.912.G.1.3

1.6 Basic Constructions

construct (using straight edge and compass and/or drawing programs) congruent segments and angles, and angle bisectors

* MA.912.G.1.2 (Not assessed moved to 4

th quarter)

1.6 Basic Constructions distinguish between sketching, constructing, and drawing

basic constructions *

MA.912.G.8.6 (Not assessed moved to 4

th quarter)

3.7 Equations of Lines in the Coordinate Plane 3.8 Slopes of Parallel and Perpendicular Lines

identify and determine if lines are parallel or perpendicular lines in the coordinate plane


th quarter)


explain if two lines are parallel, perpendicular, or neither given coordinates of points determine the equation of the line


th quarter)










ESSENTIAL QUESTIONS: Can the student use the appropriate vocabulary to identify and use the relationships of the angles formed by intersecting lines and parallel lines cut by a transversal?


Suggested Resources Big Ideas: CPALMS: http://www.floridastandards.org


TI-Nspire Geometry Activity: Points, Lines, and Angles –Alternate Interior Angles

http://www.ti-mathnspired.com/geometry/points-lines-and-angles/alternate-interior-angles/

TI-Nspire Geometry Activity: Points, Lines, and Angles – Parallel Lines and Transversals

http://www.ti-mathnspired.com/geometry/points-lines-and-angles/creating-parallel-lines-and-transversals/

Internet Resources






http://www.ies.co.jp/math/products/geo1/menu.html






Tied to benchmarks




















UNIT/ORGANIZING PRINCIPLE: Triangle Inequality Theorems and Properties of Triangles (G.4.7)

PACING: 1st Quarter 6.5 days


Can the student express and construct the classification of triangles and their components?

MEASUREMENT TOPIC

T03: Triangle Theorems and Properties


The student will:

PACING (Days)



Skills Review (pg.853)

classify triangles as obtuse, acute, or right angles 0.5 MA.912.G.4.1 Equilateral Isosceles Scalene Acute, Right, Obtuse Straight Angle Triangle Midsegment Compass Straight edge Altitude Perpendicular Bisector Angle Bisector Median Concurrent Equidistant Incenter Circumcenter Centroid Orthocenter Hinge Theorem Indirect Proof Inequalities in a triangle

3.5 Parallel Lines and Triangles

calculate each interior and exterior angle of a triangle 1 MA.912.G.2.2

5.6 Inequalities in One Triangle 5.7 Inequalities in Two Triangles

understand and apply the inequality theorems: o triangle inequality theorem o inequality in one triangle o Hinge Theorem

3 MA.912.G.4.7

5.1-5.4 Relationships within Triangles

define and identify altitudes, medians, triangle midsegments, angle bisectors and perpendicular bisectors

2 MA.912.G.4.2


explain the difference between sketching, constructing and drawing geometric figures


th quarter)


define, identify and construct altitudes, medians, triangle midsegments, angle bisectors, perpendicular bisectors and points of concurrency: orthocenter, incenter, circumcenter, centroid


th quarter)










ESSENTIAL QUESTIONS: Can the student express and construct the classification of triangles and their components?




TI-Nspire Geometry Activity: Triangles –Triangle Inequality Theorem

http://www.ti-mathnspired.com/geometry/triangles/triangle-inequality-theorem/

Internet Resources






http://oneweb.utc.edu/~Christopher-Mawata/geom/geom2.htm






Tied to benchmarks

















UNIT/ORGANIZING PRINCIPLE: Logic Part One: Conjectures and Justification (G.8.4)



Can the student identify a logical argument following the laws of inductive and deductive reasoning?

MEASUREMENT TOPIC

T04: Logic Part One


The student will:

PACING (Days)



2.2 Conditional Statements 2.5 Reasoning in Algebra & Geometry 2.6 Proving Angles Congruent

determine if a solution is reasonable based on the given situation

0.5 MA.912.G.8.3

Conditional statement If-then form Hypothesis Conclusion Converse Postulates Axiom Theorems Diagramming Conjecture Formal Proof Direct Proof Deductive Reasoning


make conjectures and justify and support the conjectures with geometric concepts and proofs

1 MA.912.G.8.4


write geometric and algebraic proofs 3 MA.912.G.8.5










ESSENTIAL QUESTIONS: Can the student identify a logical argument following the laws of inductive and deductive reasoning?




TI-Nspire Geometry Activity (from TI Activity Exchange) –Conditional Statements

http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=8744

Internet Resources











Tied to benchmarks















UNIT/ORGANIZING PRINCIPLE: Logic Part Two: Inverse, Converse, and Contrapositive (D.6.2)



Can the student identify a logical argument following the laws of inductive and deductive reasoning?

MEASUREMENT TOPIC

T05: Logic Part Two


The student will:

PACING (Days)



2.3 Biconditional Statements 2.4 Deductive Reasoning

find the converse, inverse and contrapositive of a statement 2 MA.912.D.6.2

Conditional statement If-then form Hypothesis Conclusion Postulate Axiom Theorem Converse Contrapositive Inverse Diagramming Conjecture Direct Proof Deductive Reasoning Law of Syllogism Law of Detachment


determine whether two propositions are logically equivalent 0.5 MA.912.D.6.3


determine whether a given short proof is logically valid using methods of direct proofs

0.5 MA.912.D.6.4


demonstrate and use a variety of problem solving strategies to include diagramming, charting, equation writing and solving, trial and error

0.5 MA.912.G.8.2










ESSENTIAL QUESTIONS: Can the student identify a logical argument following the laws of inductive and deductive reasoning?




TI-Nspire Geometry Activity (from TI Activity Exchange) –Conditional Statements


Internet Resources











Tied to benchmarks















UNIT/ORGANIZING PRINCIPLE: Prove Triangles (and Other Polygons) Congruent (G.2.3A and G.4.6A)

PACING: 15 days 1st Quarter 7 days 2nd Quarter 8 days


Can the student make the appropriate conclusions based on triangles and their congruency?

MEASUREMENT TOPIC

T06: Congruence


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


4.1-4.6 Congruent Triangles

use properties of congruent polygons to solve real-world problems

2 MA.912.G.2.3

Congruency Corresponding Parts SSS SAS ASA AAS CPCTC HL Isosceles Triangle Base Base Angles Right Triangle Equilateral Triangle Leg Hypotenuse Two-column proof Flow-chart proof Paragraph Proof Congruent Triangles Segment lengths


use properties and theorems to prove triangles are congruent using a variety of methods such as flow charts, two-column and paragraph proofs

5 MA.912.G.8.5


use the concept of corresponding parts of congruent triangles are congruent (CPCTC) prove more triangles parts congruent

2 MA.912.G.4.6


use properties of congruent triangles to solve problems involving side length

2 MA.912.G.4.4


use properties of special triangles (isosceles, right and equilateral) to solve problems involving angle measures and side lengths

3 MA.912.G.4.1


use coordinate geometry to prove triangles are congruent 1 MA.912.G.8.5


using congruent triangles find the measure of interior angles * MA.912.G.2.6 (Not assessed moved to 4

th quarter)










ESSENTIAL QUESTIONS: Can the student make the appropriate conclusions based on triangles and their congruency?




TI-Nspire Geometry Activity: Triangles – Corresponding Parts of Congruent Triangles

http://www.ti-mathnspired.com/geometry/triangles/corresponding-parts-of-congruent-triangles/

TI-Nspire Geometry Activity: Triangles –Congruent Triangles

http://www.ti-mathnspired.com/geometry/triangles/congruent-triangles/

Internet Resources











Tied to benchmarks

















UNIT/ORGANIZING PRINCIPLE: Prove Triangles (and Other Polygons) Similar (G.2.3B and G.4.6B)

PACING: 2nd Quarter 10 days


Can the student prove and apply the properties of similar triangles with a variety of methods?

MEASUREMENT TOPIC

T07: Similarity


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


7.1 Ratios and Proportions

do ratio and proportion practice 0.5 MA.912.G.2.4 Conversions Customary units Metric units Standard units Non-standard units Similarity Ratio

Means Extremes Proportions

Golden Ratio Fibonacci Sequence Coordinate Geometry Similar Triangles Similar Polygons

AA Δ Similarity Postulate SAS Δ Similarity Theorem SSS Δ Similarity Theorem Included Angles Included Side Direct Measurement Indirect Measurement Scale Drawing Scale Factor Rationalize Geometric Mean Dilations Reductions Enlargements

7.5 Proportions in Triangles

use ratios and proportions from patterns in sequences and series found in nature like the Fibonacci sequence and the golden ratio

0.5 MA.912.G.4.5

7.2 – 7.5 Similarity use properties of similar polygons to solve real-world

problems 0.5 MA.912.G.2.3

7.3 – 7.5 Similarity prove that triangles are similar 2 MA.912.G.4.6

7.3 Proving Triangles Similar

use properties of similar triangles to solve problems involving side length

1 MA.912.G.4.4

7.4 Similarity in Right Triangles

use coordinate geometry to prove that two triangles are similar using properties, postulates, and theorems

2 MA.912.G.8.5

7.4 Similarity in Right Triangle

use similar triangles to describe the relationship of the triangles formed when the altitude is drawn to the hypotenuse of a right triangle

1.5 MA.912.G.5.2

7.4 Similarity in Right Triangle

use geometric mean to apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle

1 MA.912.G.5.2

9.5 Dilations identify and apply dilations 0.5 MA.912.G.2.4

7.5 Proportions in Triangles apply theorems where segments are divided proportionally 0.5 MA.912.G.4.5










ESSENTIAL QUESTIONS: Can the student prove and apply the properties of similar triangles with a variety of methods?






TI-Nspire Geometry Activity: Triangles – Congruent Triangles http://www.ti-mathnspired.com/geometry/triangles/congruent-triangles/

Internet Resources











Tied to benchmarks

















UNIT/ORGANIZING PRINCIPLE: Polygon Angle Measures (G.2.2) PACING: 2nd Quarter 3.25 days


Can the student use a variety of methods to find measures of interior and exterior angles? Can the student identify characteristics of a variety of types of polygons to solve real-world problems?

MEASUREMENT TOPIC

T08: Polygon Angles


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


6.1 – Polygon Angle Sum Theorems identify and describe concave and convex polygons 0.25 MA.912.G.2.1

Polygons (2-D figures) Side Dimension Closed Figure Vertex Diagonal Equilateral Polygon Equiangular Polygon Regular Polygons Convex polygons Concave polygons Exterior Angle Interior Angle Adjacent angles Linear pair Angle-Sum Theorem

6.1 – Polygon Angle Sum Theorems

identify the polygon by the number of sides 0.25 MA.912.G.2.1


identify a regular polygon 0.25 MA.912.G.2.1


calculate the sum of the interior and exterior angles of any polygon including when angles are represented by algebraic expressions

1 MA.912.G.2.2


given an exterior angle numerically or as an algebraic expression, calculate an interior angle

0.5 MA.912.G.2.2


determine missing angle measures of polygons 0.5 MA.912.G.2.2


calculate each interior and exterior angle of a regular polygon 0.5 MA.912.G.2.2










ESSENTIAL QUESTIONS: Can the student use a variety of methods to find measures of interior and exterior angles? Can the student identify characteristics of a variety of types of polygons to solve real-world problems?




TI-Nspire Geometry Activity: Triangle –Triangle Sum Theorem

http://www.ti-mathnspired.com/geometry/triangles/triangle-sum-theorem/

TI-Nspire Geometry Activity: Quadrilaterals and Polygons – Interior Angles of a Polygon

http://www.ti-mathnspired.com/geometry/quadrilaterals-and-polygons/interior-angles-of-regular-polygons/

Internet Resources











Tied to benchmarks








http://www.ti-mathnspired.com/geometry/triangles/triangle-sum-theorem/










UNIT/ORGANIZING PRINCIPLE: Quadrilaterals – Properties and Proofs (G.3.4) PACING: 2nd Quarter 4.25 days


Can the student use precise language to identify quadrilaterals?

MEASUREMENT TOPIC

T09: Quadrilateral Proofs


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


6.2 – 6.7 Quadrilaterals

know that a parallelogram has both pairs of opposite sides congruent; both pairs of opposite sides are parallel; and diagonals bisect each other

0.25 MA.912.G.3.1

Quadrilateral Parallelogram Square Rectangle Rhombus Trapezoid Isosceles Trapezoid Kite Diagonals Perpendicular Parallel Consecutive Sides Opposite Sides Opposite Angles Venn Diagram Trapezoid Midsegment


understand that a rectangle is a parallelogram with four right angles and congruent diagonals

0.25 MA.912.G.3.1


understand that a rhombus is a parallelogram with four congruent sides and perpendicular diagonals

0.25 MA.912.G.3.1


understand that a square is a parallelogram with four congruent sides and four right angles

0.25 MA.912.G.3.1


know that a trapezoid has both pairs of opposite sides parallel

0.25 MA.912.G.3.1


find the midsegment (median) of a trapezoid 0.5 MA.912.G.3.1


explain the special properties of the right and the isosceles trapezoids

0.25 MA.912.G.3.1


know that a kite is a quadrilateral with two pairs of consecutive sides congruent; diagonals perpendicular; one diagonal bisected; one pair of opposite angles bisected

0.25 MA.912.G.3.1


use Venn diagrams to associate all types of quadrilaterals 1 MA.912.G.3.2


use two-column proofs to prove the theorems involving quadrilaterals

1 MA.912.G.3.4










ESSENTIAL QUESTIONS: Can the student use precise language to identify quadrilaterals?




TI-Nspire Geometry Activity: Quadrilaterals and Polygons – Diagonals of Quadrilaterals

http://www.ti-mathnspired.com/geometry/quadrilaterals-and-polygons/diagonals-of-quadrilaterals/

TI-Nspire Geometry Activity: Quadrilaterals and Polygons – Rhombi, Kites, and Trapezoids

http://www.ti-mathnspired.com/geometry/quadrilaterals-and-polygons/rhombi-kites-and-trapezoids/

Internet Resources











Tied to benchmarks

















UNIT/ORGANIZING PRINCIPLE: Quadrilaterals in the Coordinate Plane (G.3.3) PACING: 2nd Quarter 4 days


Can the student prove the properties of various quadrilaterals?

MEASUREMENT TOPIC

T10: Quadrilaterals in Coordinate Plane


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


6.7 – 6.9 Polygons in the Coordinate Plane

use coordinate geometry to prove properties of congruent, regular, and similar quadrilaterals

1.5 MA.912.G.3.3

Midpoint Slope Distance Formula Perpendicular Parallel Diagonals Consecutive Sides Opposite Sides Opposite Angles Quadrilateral Parallelogram Square Rectangle Rhombus Trapezoid Kite

6.7 – 6.9 Polygons in the Coordinate Plane

use coordinate geometry to give the most specific name of a quadrilateral in the coordinate plane

2.5 MA.912.G.3.3

6.8, 6.9, 7.3 Polygons in the Coordinate Plane

use coordinate geometry to prove properties of congruent, regular and similar triangles

* MA.912.G.4.8


















Internet Resources











Tied to benchmarks

















UNIT/ORGANIZING PRINCIPLE: Solving Triangles – Real World (G.5.4) PACING: 2nd Quarter 5.5 days


Can the student understand the Pythagorean Theorem? Can the student use right triangle relationships to solve application problems?

MEASUREMENT TOPIC

T11: Triangles – Real World


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


8.1 Pythagorean Theorem and Its Converse

prove and apply the Pythagorean Theorem and its converse to find missing sides of a right triangle

1 MA.912.G.5.1

Hypotenuse Leg Pythagorean Theorem Pythagorean Triple Converse of Pythagorean Theorem Solving Right Triangles Right Triangle Geometry Elevation

45-45-90 triangle

30-60-90 triangle

8.2 Special Right Triangles

use the formulas to find missing side lengths of 45-45-90

or 30-60-90 special right triangles 2.5

MA.912.G.5.3

8.1 – 8.2 Right Triangles

use a variety of methods to solve real-world problems involving right triangles

2 MA.912.G.5.4










ESSENTIAL QUESTIONS: Can the student understand the Pythagorean Theorem? Can the student use right triangle relationships to solve application problems?




TI-Nspire Geometry Activity: Right Triangles and Trig – Pythagorean Relationships

http://www.ti-mathnspired.com/geometry/right-triangles-trig/pythagorean-relationships/

TI-Nspire Geometry Activity: Right Triangles and Trig – Special Right Triangles

http://www.ti-mathnspired.com/geometry/right-triangles-trig/special-right-triangles/

Internet Resources











Tied to benchmarks


















UNIT/ORGANIZING PRINCIPLE: Trigonometric Ratios (T.2.1) PACING: 3rd Quarter 12 days


Can the student solve right triangles using trigonometric ratios?

MEASUREMENT TOPIC

T12: Trigonometric Ratios


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


8.3 Trigonometry define and use the trigonometric ratios (sine, cosine, tangent)

in terms of angles of right triangles 5 MA.912.T.2.1

Hypotenuse Adjacent Leg Opposite Leg Pythagorean Theorem Trigonometric Ratios Reference Angle Elevation Sine Cosine Tangent Angle of Elevation Angle of Depression

Vectors Initial Point Terminal Point Magnitude Direction Law of Sines Law of Cosines Included Angle Non-included Angle

8.4 Angles of Elevation and Depression

use angles of elevation and depression to solve real-world problems

2 MA.912.G.5.4

8.1 – 8.4 Right Triangles

determine whether a solution is reasonable in the context of the original situation

1 MA.912.G.8.3

8-5 Vectors Describe vectors. Recognize that vectors are represented

geometrically and algebraically. 0.5 MA.912.G.9.2

8-5 Vectors Use vectors to model and solve application problems. 1 MA.912.G.9.3

8-5 Vectors Solve problems involving vector addition. 0.5 MA.912.G.9.3

Concept Byte pg. 522 Law of Sines and Law of Cosines

Apply the laws of sines and cosines to solve real-world problems using technology.

2 MA.912.T.2.3










ESSENTIAL QUESTIONS: Can the student solve right triangles using trigonometric ratios?




TI-Nspire Geometry Activity: Right Triangles and Trig –Pythagorean Relationships


Internet Resources











Tied to benchmarks
















UNIT/ORGANIZING PRINCIPLE: Perimeter and Area of Polygons (G.2.5) PACING: 3rd Quarter 3 days


Can the student find area and perimeter?

MEASUREMENT TOPIC

T13: Perimeter and Area Polygons


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


1.8 Perimeter, Circumference, Area

solve real-world problems using measures of circumference and areas of circles

1 MA.912.G.6.5

Length Width Base Height Circumference Altitude Area Perimeter Regular Polygon Irregular Polygon Apothem Radius of Regular Polygon Area of Regular Polygon Perimeter of Regular Polygon Trigonometric Ratios

10.1 – 10.2 Areas of Triangles and Quadrilaterals

explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, etc.)

1 MA.912.G.2.5

10.3 Areas of Regular Polygons

find the area and perimeter of regular polygons, including trigonometric ratios

1 MA.912.T.2.1














TI-Nspire Geometry Activity: Perimeter and Area – Areas of Irregular Polygons

http://www.ti-mathnspired.com/geometry/perimeter-area-volume/areas-of-irregular-polygons/

TI-Nspire Geometry Activity: Perimeter and Area – Exploring Diameter and Circumference

http://www.ti-mathnspired.com/geometry/perimeter-area-volume/exploring-diameter-and-circumference/

Internet Resources











Tied to benchmarks

















UNIT/ORGANIZING PRINCIPLE: Transformations of Polygons (G.2.4) PACING: 3rd Quarter 3 days


Can the student identify the types of transformation?

MEASUREMENT TOPIC

T14: Polygon Transformations


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


9.1 – 9.4, 9.7 Transformations and Tessellations

identify if a figure has been reflected, rotated, or translated 1 MA.912.G.2.4

Image Pre-image Transformation Isometry Symmetry Reflections – Flip Line of reflection Line of symmetry Rotation – Turn Center of rotation Angle of rotation Rotational symmetry Translations – Slide Tessellations

9.1 – 9.4, 9.7 Transformations and Tessellations

use the coordinate plane to draw transformations and show that the image and the pre-image are the same

2 MA.912.G.2.4










ESSENTIAL QUESTIONS: Can the student identify the types of transformation?




TI-Nspire Geometry Activity: Transformational Geometry – Exploring Transformations: Translations and Rotations

http://www.ti-mathnspired.com/geometry/transformational-geometry/exploring-transformations-translations-rotations/

TI-Nspire Geometry Activity: Transformational Geometry –Tessellations

http://www.ti-mathnspired.com/geometry/transformational-geometry/tessellations-with-regular-polygons/

Internet Resources






http://www.mathsnet.net/transform/index.html

Enrichment Tessellation Project (Prentice Hall Section 9.7)






Tied to benchmarks
















http://www.mathsnet.net/transform/index.html


UNIT/ORGANIZING PRINCIPLE: Describe and Sketch Polyhedrons (G.7.1) PACING: 3rd Quarter 2 days


Can the student describe and identify the properties of polyhedra and spheres and use them to find the perimeter and areas of cross sections?

MEASUREMENT TOPIC

T15: Polyhedrons


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


1.1 Nets and Drawings for Visualizing Geometry 11.1 Space Figures and Cross Sections

identify the types of polyhedrons and sketch the net for a given polyhedron

0.5 MA.912.G.7.1

Solid Figures (3-D), Nets Polyhedron Prisms / Right Prisms Pyramids / Right Pyramids Cone / Right Circular Cone Cylinder Sphere Right Polyhedron Oblique polyhedron Non-regular polyhedron Hexahedron Regular polyhedron Platonic solids Cube – Regular Hexahedron Tetrahedron Octahedron Dodecahedron Icosahedron Faces (side) / Edges / Bases Vertices of polyhedron Cross section of polyhedron

1.1 Nets and Drawings for Visualizing Geometry 11.1 Space Figures and Cross Sections

determine the number of faces, edges and vertices of a polyhedron

1 MA.912.G.7.2

11.1 Space Figures and Cross Sections

identify the cross section of a solid and find the perimeter and area

0.5 MA.912.G.7.2










ESSENTIAL QUESTIONS: Can the student describe and identify the properties of polyhedra and spheres and use them to find the perimeter and areas of cross sections?




TI-Nspire Geometry Activity (from TI Activity Exchange) – The Painted Cube


Internet Resources











Tied to benchmarks















UNIT/ORGANIZING PRINCIPLE: Surface/Lateral Area & Volume of Solids (G.7.5)

PACING: 3rd Quarter 7 days


Can the student describe and identify the properties of polyhedra and spheres and use them to find the perimeter and areas of cross sections? Can students apply the formulas for finding surface area and volume of a given solid?

MEASUREMENT TOPIC

T16: SA and V of Solids


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


11.2 – 11.6 Surface Area and Volume

explain and use the formulas for lateral area, surface area, and volume of various solids

6 MA.912.G.7.5

Prism, Rectangular Prisms Cross Section Pyramid, Square Pyramid Dimension Cone, Right Circular Cone Cylinder Sphere Faces, Lateral Faces Bases, Edges, Vertices Height, Slant Height Radii Great circle LA-SA Prisms / Cylinders LA-SA Pyramids / Cones Mass, Weight Volume of Prisms / Cylinders Volume of Pyramids / Cones Capacity of Solid Similar solids ratio

11.6 Surface Area and Volume of Spheres

identify chords, tangents, radii, and great circles of spheres 1 MA.912.G.7.4










ESSENTIAL QUESTIONS: Can the student describe and identify the properties of polyhedra and spheres and use them to find the perimeter and areas of cross sections? Can students apply the formulas for finding surface area and volume of a given solid?




TI-Nspire Geometry Activity (from TI Activity Exchange) –Volume


Internet Resources











Tied to benchmarks















UNIT/ORGANIZING PRINCIPLE: Effect of Changing Dimensions on Polygons and Polyhedrons (G.7.7)

PACING: 3rd Quarter 5.5 days


Can the student describe and identify the properties of polyhedra and spheres and use them to find the perimeter and areas of cross sections? Can students apply the formulas for finding surface area and volume of a given solid?

MEASUREMENT TOPIC

T17: Changes in Dimensions


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


10.4 Perimeters and Areas of Similar Figures

solve mathematical or real-world problems using the properties and theorems of congruent and similar polygons

0.5 MA.912.G.2.3

Prism, Pyramid, Cylinder, Cone, Sphere Dimension Length Width Bases, Edges Altitude Height, Slant Height Radii Circumference Great circle Perimeter Area Lateral Area Surface Area Volume Capacity of Solid Similar solids ratio

10.4 Perimeters and Areas of Similar Figures

determine how changing the parameters of the dimensions of various geometric figures affect the perimeter and area of the figure

2 MA.912.G.2.7

11.7 Areas and Volumes of Similar Solids

identify and use the properties of congruent and similar solids in real-world problems

0.5 MA.912.G.7.6

11.2 – 11.7 Areas and Volumes of Similar Solids

determine the effect of changing parameter of the dimensions on the surface area and volume of a given solid

2 MA.912.G.7.7

11.7 Areas and Volumes of Similar Solids

find and use the scale factor of similar solids 0.5 MA.912.G.2.7










ESSENTIAL QUESTIONS: Can the student describe and identify the properties of polyhedra and spheres and use them to find the perimeter and areas of cross sections? Can students apply the formulas for finding surface area and volume of a given solid?




Internet Resources











Tied to benchmarks













UNIT/ORGANIZING PRINCIPLE: Circles – Real World (G.6.5) PACING: 3rd Quarter 7 days


Can the student use the appropriate vocabulary to identify and define the components of a circle? Can the student use angles, segments, and arc measures formed by chords, secants, and tangents to solve problems?

MEASUREMENT TOPIC

T18: Real World Circles


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


12.1, 12.2, 12.4 - Circles

define the vocabulary associated with circles including circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles

0.5 MA.912.G.6.2

Circle Center of a Circle Chord Secant Tangent to a Circle Point of Tangency Arc – Major/Minor Intercepted Arc Semicircle Central Angles Inscribed Angles Circumference Arc Length Concentric Circles Inscribed Circumscribed Radius Diameter Internal/External Tangents Area Sector of a Circle Segment of a Circle

12.1, 12.2, 12.4 - Circles identify the components of a circle 0.5 MA.912.G.6.2

12.1, 12.2, 12.4 - Circles identify tangents to a circle and point of tangency 0.5 MA.912.G.6.2

12.3, 12.4 - Circles

determine and use measures of arcs and related angles (central, inscribed and intersections of secants and tangents) and use theorems and formulas to find missing segment lengths

2 MA.912.G.6.4

12.3, 12.4 - Circles solve real-world problems using measures of circumference,

arc length, and areas of circles and sectors 2.5 MA.912.G.6.5

11.7 – Areas and Volumes of Similar Solids

determine how changes in dimension affect changes in perimeter and area of common geometric figures

1 MA.912.G.2.7

12.1 – Tangent Lines draw circles circumscribed and inscribed using triangles and

regular polygons *

(Not assessed moved to 4

th quarter)

12.3 – Inscribed Angles

identify and use the characteristics of quadrilateral inscribed in a circle

* (Not assessed moved to 4

th quarter)















TI-Nspire Geometry Activity: Circles – Angles and Arcs http://www.ti-mathnspired.com/geometry/circles/angles-and-arcs/

TI-Nspire Geometry Activity: Circles – Intersecting Lines and Segment Measures

http://www.ti-mathnspired.com/geometry/circles/intersecting-lines-and-segment-measures/

Internet Resources











Tied to benchmarks







http://www.ti-mathnspired.com/geometry/circles/angles-and-arcs/









UNIT/ORGANIZING PRINCIPLE: Equations of Circles (G.6.6) PACING: 3rd Quarter 3 days


Can the student use the equation of circle and use its graph to solve problems?

MEASUREMENT TOPIC

T19: Circle Equations


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


12.5 Circles in the Coordinate Plane

given the equation of a circle, identify the center and the radius

0.5 MA.912.G.6.6

Coordinate Plane Standard Equation of Circle Distance Formula Center of a Circle Radius Interior of Circle Exterior of Circle Locus Arc Intersection Perpendicular Bisector Angle Bisector Circle Solids


write the equation of a circle given the radius and the center 0.5 MA.912.G.6.6


in the coordinate plane, identify the center and radius and write the equation of the circle

1 MA.912.G.6.6


graph the equation of a circle on the coordinate plane given the equation or the radius and center of the circle

0.5 MA.912.G.6.7

Determine whether a solution is reasonable in the context of

the original situation. 0.5 MA.912.G.8.3


write the equation of circle, given the coordinates of the center and a point on the circle

* (Not assessed moved to 4

th quarter)

identify if a given point is on the circle or on the

exterior/interior of a circle *

(Not assessed moved to 4

th quarter)















TI-Nspire Geometry Activity: Circles – Equation of a Circle http://www.ti-mathnspired.com/geometry/circles/equation-of-a-circle/

Internet Resources











Tied to benchmarks







http://www.ti-mathnspired.com/geometry/circles/equation-of-a-circle/







UNIT/ORGANIZING PRINCIPLE: Parallel lines and Special Angle Relationships (G.1.3)

PACING: 4th Quarter 12 days


Can the student use the appropriate vocabulary to identify and use the relationships of the angles formed by intersecting lines and parallel lines cut by a transversal?

MEASUREMENT TOPIC

T20: Parallel Lines/ Angle Relationships


The student will:

PACING (Days)



1.6 Basic Constructions

construct (using straight edge and compass and/or drawing programs) congruent segments and angles, and angle bisectors

* MA.912.G.1.2

Conditional statement Hypothesis Conclusion Converse Postulate Axiom Theorem Angles – Right, Obtuse, Acute Sides of an angle

Protractor Linear Pairs Vertical Angles Adjacent Angles Complementary Angles Supplementary Angles Parallel lines Perpendicular lines Transversal

Corresponding angles Alternate interior/exterior angles Consecutive (same side) int. angles Angle Bisectors Perpendicular Bisectors Slope

Equations of Lines

1.6 Basic Constructions distinguish between sketching, constructing, and drawing

basic constructions *

MA.912.G.8.6


identify and determine if lines are parallel or perpendicular lines in the coordinate plane

* MA.912.G.1.4


explain if two lines are parallel, perpendicular, or neither given coordinates of points determine the equation of the line

* MA.912.G.1.4










ESSENTIAL QUESTIONS: Can the student use the appropriate vocabulary to identify and use the relationships of the angles formed by intersecting lines and parallel lines cut by a transversal?




TI-Nspire Geometry Activity: Points, Lines, and Angles –Alternate Interior Angles


TI-Nspire Geometry Activity: Points, Lines, and Angles – Parallel Lines and Transversals


Internet Resources












Tied to benchmarks




















UNIT/ORGANIZING PRINCIPLE: Triangle Inequality Theorems and Properties of Triangles (G.4.7)

PACING: 4th Quarter 6.5 days


Can the student express and construct the classification of triangles and their components?

MEASUREMENT TOPIC

T21: Triangle Theorems and Properties


The student will:

PACING (Days)




explain the difference between sketching, constructing and drawing geometric figures

* MA.912.G.8.6

Equilateral Isosceles Scalene Acute, Right, Obtuse Straight Angle Triangle Midsegment Compass Straight edge Altitude Perpendicular Bisector Angle Bisector Median Concurrent Equidistant Incenter Circumcenter Centroid Orthocenter Hinge Theorem Indirect Proof Inequalities in a triangle


define, identify and construct altitudes, medians, triangle midsegments, angle bisectors, perpendicular bisectors and points of concurrency: orthocenter, incenter, circumcenter, centroid

* MA.912.G.4.2










ESSENTIAL QUESTIONS: Can the student express and construct the classification of triangles and their components?




TI-Nspire Geometry Activity: Triangles –Triangle Inequality Theorem


Internet Resources












Tied to benchmarks

















UNIT/ORGANIZING PRINCIPLE: Prove Triangles (and Other Polygons) Congruent (G.2.3A and G.4.6A)

PACING: 15 days 4th Quarter 7 days


Can the student make the appropriate conclusions based on triangles and their congruency?

MEASUREMENT TOPIC

T22: Congruence


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE



using congruent triangles find the measure of interior angles * MA.912.G.2.6

Congruency Corresponding Parts SSS SAS ASA AAS CPCTC HL Isosceles Triangle Base Base Angles Right Triangle Equilateral Triangle Leg Hypotenuse Two-column proof Flow-chart proof Paragraph Proof Congruent Triangles Segment lengths










ESSENTIAL QUESTIONS: Can the student make the appropriate conclusions based on triangles and their congruency?






TI-Nspire Geometry Activity: Triangles –Congruent Triangles


Internet Resources











Tied to benchmarks

















UNIT/ORGANIZING PRINCIPLE: Quadrilaterals in the Coordinate Plane (G.3.3) PACING: 4th Quarter 4 days


Can the student prove the properties of various quadrilaterals?

MEASUREMENT TOPIC

T23: Quadrilaterals in Coordinate Plane


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


6.8, 6.9, 7.3 Polygons in the Coordinate Plane

use coordinate geometry to prove properties of congruent, regular and similar triangles

* MA.912.G.4.8

Midpoint Slope Distance Formula Perpendicular Parallel Diagonals Consecutive Sides Opposite Sides Opposite Angles Quadrilateral Parallelogram Square Rectangle Rhombus Trapezoid Kite


















Internet Resources











Tied to benchmarks

















UNIT/ORGANIZING PRINCIPLE: Circles – Real World (G.6.5) PACING: 4th Quarter 7 days



MEASUREMENT TOPIC

T18: Real World Circles


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE


12.1 – Tangent Lines draw circles circumscribed and inscribed using triangles and

regular polygons *

Circle Center of a Circle Chord Secant Tangent to a Circle Point of Tangency Arc – Major/Minor Intercepted Arc Semicircle Central Angles Inscribed Angles Circumference Arc Length Concentric Circles Inscribed Circumscribed Radius Diameter Internal/External Tangents Area Sector of a Circle Segment of a Circle

12.3 – Inscribed Angles

identify and use the characteristics of quadrilateral inscribed in a circle

*










UNIT/ORGANIZING PRINCIPLE: Equations of Circles (G.6.6) PACING: 4th Quarter 3 days


Can the student use the equation of circle and use its graph to solve problems?

MEASUREMENT TOPIC

T19: Circle Equations


The student will:

PACING (Days)

BENCHMARK

ACADEMIC LANGUAGE



write the equation of circle, given the coordinates of the center and a point on the circle

*

Coordinate Plane Standard Equation of Circle Distance Formula Center of a Circle Radius Interior of Circle Exterior of Circle Locus Arc Intersection Perpendicular Bisector Angle Bisector Circle Solids

identify if a given point is on the circle or on the

exterior/interior of a circle *















TI-Nspire Geometry Activity: Circles – Equation of a Circle http://www.ti-mathnspired.com/geometry/circles/equation-of-a-circle/

Internet Resources











Tied to benchmarks







http://www.ti-mathnspired.com/geometry/circles/equation-of-a-circle/






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