Unit Overview. Learning Targets. Guiding Questions

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1 Content Area: Geometry Unit Title: Preparing for Geometry Target Course/Grade Level Geometry Duration 10 days Unit Overview Description : In this unit, students will review a number of topics and skills previously obtained through other courses, such as converting units of measure (customary and metric), simple probability, solving linear equations, solving and graphing linear inequalities, and simplifying square roots and rational expressions. Students are evaluated by a unit test, quizzes, notebook, homework, and class participation along with other alternative assessments throughout the unit. Concepts Units of measure Simple probability Algebraic expressions Linear equations Linear inequalities Ordered pairs Systems of linear equations Square roots and simplifying radicals Concepts & Understandings Understandings Finding probability of simple events Graphing linear equations and inequalities Solving systems of linear equations Simplifying radical expressions CPI Codes Learning Targets A- SSE.HS.04 F-BF.HS.02 CO.HS.01 CO.HS.09 CO.HS.12 GPE.HS st Century Themes and Skills See Addendum Guiding Questions Name some of the different types of units of measurement you are already familiar with (i.e. foot, inches, meters, etc.)

2 What pneumatic device can you create to help remember how to convert between units of measure in the metric system? What is theoretical probability? What is experimental probability? Name the order of operations? How do we graph a linear inequality? Determine the signs of the coordinates in each of the four quadrants of the coordinate plane? What is the product property? What is the quotient property/ What steps need to be taken to rationalize the denominator? Students will... Unit Results Convert units of measure within the customary and metric systems. Find the probability of simple events. Use the order of operations to evaluate algebraic expressions. Use algebra to solve linear equations. Use algebra to solve linear inequalities. Name and graph points in the coordinate plane. Use graphing, substitution, and elimination to solve systems of linear equations. Evaluate square roots and simplify radical expressions. Suggested Activities The following activities can be incorporated into the daily lessons: Convert units of length, mass, and capacity. Convert between customary and metric units. Find theoretical and experimental probability of a given event. Solve multi-step algebraic expressions. Solve and graph linear inequalities Play battleship using the coordinate plane. Solve and graph systems of equations. Simplify radicals Simplify radical expressions using the conjugate. Content Area: Geometry Unit Title: Tools of Geometry Target Course/Grade Level Geometry Duration: 3 Weeks Unit Overview Description : In this unit students will be introduced to several key geometry terms and concepts. Angles are classifies as acute, right, obtuse, or straight. Vertical angles, linear pairs, complementary angles and supplementary angles are identified. The midpoint formula is used to find the coordinates of the midpoint of a segment. The distance formula is use to find the distance between two points on a number line as well as two points within a plane. The area, perimeter, surface area, and volume of two and three dimensional figures will be addressed. Students are evaluated by a unit test, quizzes, notebook, homework, and class participation along with other alternative assessments throughout the unit. Concepts & Understandings

3 Concepts Points, lines, and planes Linear Measure Distance and Midpoints Angle Measures Angle Relationships Two-Dimensional figures Three-Dimensional figures CPI Codes Learning Targets Understandings Find distances between points and midpoints of line segments. Identify angle relationships. Find perimeters, area, surface area, and volumes. CO.HS.01 CO.HS.12 GMD.HS.0 3 GPE.HS.07 SRT.HS st Century Themes and Skills See Addendum Guiding Questions What do the terms collinear and coplanar mean? What is the intersection of two planes? What is a line segment? Name the distance formulas. How do you to find distance in coordinate geometry? How do you find midpoint in coordinate geometry? How do we use a protractor to measure the degree of an angle? Describe the angle measures of an acute, obtuse, and a right angle? What is the difference between adjacent and vertical angles? What is a linear pair? How can you determine if two lines are perpendicular? What is the difference between equilateral, equiangular, and regular polygons? What is the formula to find the area of a triangle? What is the formula to find the surface area of a cylinder? Students will... Unit Results Identify and model points, lines, and planes.

4 Identify intersecting lines and planes. Measure segments. Calculate with measures. Find the distance between lines and points. Find the midpoint of a segment. Measure and classify angles. Identify and use congruent angles and the bisector of an angle. Identify and use special pairs of angles. Identify perpendicular lines. Identify and name polygons. Find perimeter, circumference, and area of two dimensional figures. Identify and name three-dimensional figures. Find surface area and volume of three-dimensional figures. Suggested Activities The following activities can be incorporated into the daily lessons: Interpret geometric drawings in order to determine the different types of planes found within a figure. Use a ruler to find the measure of a line segment in metric and customary units. Construct a copy of a line segment. Use the distance formula to find the distance of the hypotenuse of a triangle plotted in the coordinate plane. Use the terms acute, right, obtuse, and straight to classify the different types of angles. Identify adjacent, vertical, complementary and supplementary angles. Construct perpendicular lines. Determine whether a set of given shapes are or are not polygons. Find the area and perimeter of a triangle. Find the perimeter and circumference of a circle. Find the surface area and volume of a cone. Content Area: Geometry Unit Title: Reasoning and Proof Target Course/Grade Level: Geometry Duration: 3 Weeks Unit Overview Description: The goals of this chapter include recognizing, analyzing, and writing conditional statements as well as writing postulates using conditional statements. Students recognize and use definitions and biconditional statements. They use symbolic notation to represent logical statements and use laws of logic to draw conclusions from arguments. Students use properties from algebra and geometry to measure and justify segment and angle relationships and congruence. Students also prove statements about segments and angles using congruence. Students are evaluated by a unit test, quizzes, notebook, homework, and class participation along with other alternative assessments throughout the unit. Concepts Inductive reasoning and conjecture Logic Conditional statements Deductive reasoning Concepts & Understandings Understandings Make conjectures and find counterexamples for statements. Use deductive reasoning to reach valid conclusions. Write proofs involving segment and angle

5 CPI Codes Postulates and paragraph proofs Algebraic proof Proving segment relationships Proving angle relationships CO.HS.09 CO.HS.10 CO.HS.11 CO.HS.12 MG.HS.03 Learning Targets theorems. 21 st Century Themes and Skills See Addendum Guiding Questions What is a conjecture? What is the purpose of creating a counterexample? How can we tell the difference between of conjunction and a disjunction? Is the negation of a statement always false? What is the Hypothesis and conclusion? What does it mean for two statements to be logically equivalent? What is the key word for biconditional statement? Given certain statements tell whether there is enough information to evaluate deductive reasoning? Given various congruent line segments, will you be able to tell all the valid statements about the given information? What is the difference between a postulate and an axiom? Given various congruent lines, will you be able to solve for the variable to find the missing length of the line segment? Given two or more angles will you be able to prove properties of angle congruence? Students will... Unit Results Make conjectures based on inductive reasoning. Find counterexamples. Determine truth values of negations, conjunctions, and disjunctions, and represent them using Venn diagrams. Find counterexamples. Analyze statements in if-then form. Write the converse, inverse, and contra-positive of if-them statements.

6 Use the Law of Detachment. Use the Law of Syllogism. Identify and use basic postulates about points, lines, and planes. Write paragraph proofs. Use algebra to write two-column proofs. Use properties of equality to write geometric proofs. Write proofs involving segment addition. Write proofs involving segment congruence. Write proofs involving supplementary and complementary angles. Write proofs involving congruent and right angles. Suggested Activities The following activities can be incorporated into the daily lessons: Make conjectures from a set of data. Find counterexamples. Determine truth values of conjunctions and disjunctions, negations, and true statements. Construct truth tables. Create a Venn diagram. Write conditional statements in if-then form. Construct a truth table for conditional statements. Analyze statements using postulates. Justify each step when solving equations using the properties of real numbers. Use the segment addition postulate. Prove complementary and supplementary angles. Content Area: Geometry Unit Title: Perpendicular and Parallel Lines Target Course/Grade Level: Geometry Duration: 3 Weeks Unit Overview Description: In this chapter, Students investigate the relationships between lines and angles on a plane and in space. They will study the angles formed when two lines are cut by a transversal. They will learn how to write flow proofs and use these proofs along with two-column and paragraph proofs and use these proofs along with two-column and paragraph proofs to prove theorems about perpendicular and parallel lines. Students will apply properties of parallel lines to solve real-life problems. They will also use a straightedge and a compass to construct parallel lines. Students will find the slopes of lines and use slope to identify parallel and perpendicular lines in a coordinate plane. They will write equations of parallel and perpendicular lines in a coordinate plane. The student will get evaluation by quizzes and by tests after completion of sections and the chapter. Concepts Parallel lines Transversals Angles Parallel lines Slopes of lines Concepts & Understandings Understandings Investigate the relationships between lines and angles on a plane and in space. Study the angles formed when two lines are cut by a transversal. learn how to write flow proofs and use these

7 CPI Codes Equations of lines Proving lines parallel Perpendiculars and distance Learning Targets proofs along with two-column and paragraph proofs and use these proofs along with two-column and paragraph proofs to prove theorems about perpendicular and parallel lines. Apply properties of parallel lines to solve real-life problems. Find the slopes of lines and use slope to identify parallel and perpendicular lines in a coordinate plane. Write equations of parallel and perpendicular lines in a coordinate plane. CO.HS.01 CO.HS.09 CO.HS.12 GPE.HS.05 MG.HS st Century Themes and Skills See Addendum Guiding Questions How can you identify the relationships between lines and angles? How can you write and prove results about perpendicular lines? What is a transversal? How can you use properties of parallel lines to solve real-life problems? How can you prove lines are parallel? How can you use Properties of Parallel Lines? How to Finding slopes of lines and use slope to identify parallel lines in a coordinate plane? How to Use slope to identify perpendicular lines in a coordinate plane? Students will... Unit Results Identify the relationship between two lines or two planes. Name angle pairs formed by parallel lines and transversals. Use theorems to determine the relationships between specific pairs of angles. Use algebra to find angle measurements. Find slopes of lines.

8 Use slope to identify parallel and perpendicular lines. Write an equation of a line given information about the graph. Solve problems by writing equations. Recognize angle pairs that occur with parallel lines. Prove that two lines are parallel. Find the distance between a point and a line. Find the distance between parallel lines. Suggested Activities The following activities can be incorporated into the daily lessons: Identify parallel and skew lines. Explore angles which are formed by parallel lines and transversals. Use the corresponding angles postulate. Prove the alternate interior angle theorem. Investigate slope and its relationship between real-world quantities. Classify the different types of slope. Find the equations of lines using the slope-intercept and point-slope form. Prove two lines are parallel. Use angle relationships like the alternate exterior angle and consecutive interior angle theorem to find the value of x. Construct a perpendicular line. Find the distance from a point on a line to a point in the plane. Content Area: Geometry Unit Title: Basic of Geometry Target Course/Grade Level: Geometry Duration: 3 Weeks Unit Overview Description : This chapter introduces students to proving triangles congruent and using congruent triangles in real-life problems. Students first classify triangles and find angle measures. They identify congruent figures and corresponding parts of figures, and learn to correctly name angles and triangles. Students prove triangles are congruent using SSS, SAS, ASA, and AAS. They use congruence postulates to solve real-life problems. They use congruent triangles to plan and write proofs and to prove the validity of constructions. They use properties of isosceles, equilateral, and right triangles. Finally they learn how to place geometric figures in a coordinate plane to prove statements about the figures. The student will get evaluation by quizzes and by tests after completion of sections and the chapter. Concepts Classifying triangles Angles of triangles Congruent triangles SSS and SAS congruence ASA and AAS congruence Isosceles and Equilateral Triangles Congruence transformations Triangles and Coordinate Proofs Concepts & Understandings Understandings Apply special relationships about the interior and exterior angles of a triangle. Identify congruent figures and corresponding parts. Prove that two triangles are congruent are congruent. Use congruence postulates in real-life problems Use congruence postulates and theorem to prove triangles congruent. Use properties of right triangles.

9 Special properties of isosceles and equilateral triangles. CPI Codes Learning Targets CO.HS.06 CO.HS.07 CO.HS.10 CO.HS.12 GPE.HS.04 SRT.HS st Century Themes and Skills See Addendum Guiding Questions How can we go about classifying different types of triangles? What are the different classifications for a triangle based on their angle and side length measures? What role do auxiliary lines play in proving the Triangle Angle-Sum Theorem? What is a congruent polygon? What is the angle addition postulate? How do the theorems and postulates of triangle congruence apply to right triangles? How can we prove that two triangles are congruent? Can you use the lengths of the hypotenuse and leg to show that two right triangles are congruent? Which two angles in an isosceles triangle are equal? Name three words that can be used to describe the why a figure it moved. What does the word isometry mean? What information does it give about the congruence of the preimage and the image? What is a coordinate proof? How can we use a coordinate proof to find the missing coordinates of a triangle found in the coordinate plane? Students will... Unit Results

10 Identify and classify triangles by angle measures. Identify and classify triangles by side measures. Apply the triangle angle sum theorem. Supply the exterior angle theorem. Name and use corresponding parts of congruent polygons. Prove triangles congruent using the definition of congruence. Use the SSS postulate to test for triangle congruence. Use the SAS postulate to test for triangle congruence. Use the ASA postulate to test for triangle congruence. Use the AAS theorem to test for congruence. Use properties of isosceles triangles. Use properties of equilateral triangles. Identify reflections, translations, and rotations. Verify congruence after a congruence transformation. Position and label triangles for use in coordinate proofs. Write coordinate proofs. Suggested Activities The following activities can be incorporated into the daily lessons: Make formal geometric constructions with a variety of tools and methods. Classify triangles based on their angles measure. Classify triangles based on the measure of their sides. Complete geometry lab to find special relationships among the angles of triangles. Prove triangle angle-sum theorem. Define and determine the meaning of congruent polygons. Identify corresponding congruent parts. Prove that two triangles are congruent. Use SSS to prove triangle congruence. Use SAS to prove triangle congruence. Construct congruent triangles. Use ASA to prove triangle congruence. Use AAS to prove triangle congruence. Apply triangle congruence theorems to right triangles. Identify congruent segments and angles. Find the missing values in two congruent triangles. Apply triangle congruence to real-world situations. Content Area: Geometry Unit Title: Properties of Triangles Target Course/Grade Level: Geometry Duration: 3 Weeks Unit Overview Description : This chapter covers various properties of triangles. Students begin by studying perpendicular bisectors and angle bisectors in general and then they relate these to specific triangles. Students learn that the perpendicular bisectors of a triangle are concurrent. Students then study medians and altitudes and learn that these three segments associated with a triangle are also concurrent. Students study the Midsegment Theorem and learn about various triangle inequalities. The chapter concludes with a lesson indirect proof. The student will get evaluation by quizzes and by tests after completion of sections and the chapter.

11 Concepts Bisectors of Triangles Medians and Altitudes of Triangles Inequalities in one triangle Indirect proof Triangle inequality Inequalities in two triangles CPI Codes CO.HS.07 CO.HS.10 MG.HS.03 SRT.HS.04 Concepts & Understandings Learning Targets 21 st Century Themes and Skills Understandings Studying perpendicular bisectors and angle bisectors in general and then they relate these to specific triangles. Learn that the perpendicular bisectors of a triangle are concurrent. Study medians and altitudes and learn that these three segments associated with a triangle are also concurrent. Study the Midsegment Theorem and learn about various triangle inequalities. Relationships between the sides and angles of triangles. Writing indirect proofs. See Addendum Guiding Questions What is true about any point on the perpendicular bisector of a segment? What is true about any point on the bisector of the angle? What happens when perpendicular bisectors of a triangle intersect, where do they intersect? What is a circumcenter of the triangle? What is the in center of the triangle? If you want to balance a triangular model on the tip of a pencil, where would you place the pencil? What is a centroid? What is the orthocenter of the triangle? What is a midsegment of a triangle? What is special about the midsegment of a triangle? What angles in a triangle are used in the exterior angle inequality? If given the sides and the measures of the interior angles of a triangle, can you state what you know using the triangle inequality theorem?

12 What is the first step of writing an indirect proof? Students will... Unit Results Identify and use perpendicular bisectors in triangles. Identify and use angles bisectors in triangles. Identify and use the medians in triangles. Identify and use altitudes in triangles. Recognize and apply properties of inequalities to the measures of the angles of a triangle. Recognize and apply properties of inequalities to the relationships between the angles and sides of a triangle. Write indirect algebraic proofs. Write indirect geometric proofs. Use the triangle inequality theorem to identify possible triangles. Prove triangle relationships using the triangle inequality theorem. Apply the hinge theorem or its converse to make comparisons in two triangles. Prove triangle relationships using the Hinge theorem or its converse. Suggested Activities The following activities can be incorporated into the daily lessons: Construct a perpendicular bisector of the side of a triangle. Use the perpendicular bisector theorem. Finding the circumcenter of a triangle. Using the incenter of a triangle. Constructing medians and altitudes. Using the centriod of the triangle to find the missing lengths. Finding the othrocenter. Proving the exterior angle inequality theorem. Ordering the sides of a triangle from smallest to largest or largest to smallest. Ordering the measure of a triangle from smallest to largest or largest to smallest. Writing indirect algebraic and geometric proofs. Proving triangle equalities in one triangle and two triangles. Content Area: Geometry Unit Title: Quadrilaterals Target Course/Grade Level: Geometry Duration: 3 Weeks Unit Overview Description: The students will learn how to classify special quadrilaterals and how to use their properties. They will write proofs about special quadrilaterals. They will learn how to find areas of triangles and quadrilaterals. Students are evaluated by a unit test, quizzes, notebook, homework, and class participation along with other alternative assessments throughout the unit. Concepts Angles of polygons Parallelograms Tests for parallelograms Rectangles Concepts & Understandings Understandings Find and use the sum of the measures of the interior and exterior angles of a polygon. Use properties of parallelograms. Recognize and apply properties of quadrilaterals.

13 CPI Codes Rhombi and squares Trapezoids and kites Learning Targets Compare quadrilaterals. Find areas of triangles and quadrilaterals. Write proofs about special quadrilaterals. CO.HS.11 GPE.HS.04 MG.HS.01 MG.HS.03 GPE.HS st Century Themes and Skills See Addendum Guiding Questions How many sides are there in the following figure? What's the name of the polygon if the figure has 5 angles? Which two angles are the same in a parallelogram? What did you learn about consecutive angles in a parallelogram? Describe the properties of parallelogram. What is the sum of the interior angles of a parallelogram? Which sides are congruent in a kite? Describe the properties of a trapezoid. Describe the properties of a kite. Describe the properties of a rhombus. What classifies a trapezoid as isosceles? What s the area of a square? What's the area of a quadrilateral? Which angles are congruent in a kite? Students will... Unit Results Find and use the sum of the measures of the interior angles of a polygon. Find and use the sum of the measures of the exterior angles of a polygon. Recognize and apply properties of the sides and angles of parallelograms. Recognize and apply properties of the diagonals of parallelograms. Recognize the conditions that ensure quadrilateral is a parallelogram. Prove that a set of points forms a parallelogram in the coordinate plane.

14 Recognize and apply properties of rectangles. Determine whether parallelograms are rectangles. Recognize and apply the properties of rhombi and squares. Determine whether quadrilaterals are rectangles, rhombi, or squares. Apply properties of trapezoids. Apply properties of kites. Suggested Activities The following activities can be incorporated into the daily lessons: Content Area: Geometry Unit Title: Similarity Target Course/Grade Level: Geometry Duration: 2.5 Weeks Unit Overview Description: In this chapter, students explore the concept of similarity. Students will first simplify ratios; solve proportions using the cross product property, and use properties of proportions to solve real-life problems. Similar polygons are then introduced and their properties are used to solve real-life problems. Next, similar triangles are explored in greater depth. Students will learn to prove that two triangles are similar using the AA Similarity Postulate, the SSS Similarity Theorem, and the SAS Similarity Theorem. Similar triangles are used to solve indirect measurement problems. Proportionality theorems involving parallel lines, angle bisectors, and transversals are examined and used to calculate segment lengths. Finally students identify dilations and use properties of dilations in real-life applications. The student will get evaluation by quizzes and by tests after completion of sections and the chapter. Concepts Ratios and proportions Similar polygons Similar triangles Parallel lines and perpendicular parts Parts of similar triangles Similarity Transformations Scale drawings and models Concepts & Understandings Understandings Identify similar polygons and use ratios and proportions to solve problems. Identify and apply similarity transformations. Use scale models and drawings to solve problems. Identify types of polygons Identify similar polygons Use corresponding parts of similar figures. CPI Codes Learning Targets GPE.HS.05 MG.HS.03 SRT.HS.01

15 SRT.HS.02 SRT.HS.03 SRT.HS.04 SRT.HS st Century Themes and Skills See Addendum Guiding Questions What's the second way to write the Ratio? For any Ratio can denominator be zero? What is the cross product property? Is it possible to switch the denominator on both sides? When can you say two triangles are similar? How many conditions do you need to show to prove two triangles similar? How do you show the triangles are similar, when you are given compound figures? When can you say that two triangles are similar? What is the SSS similarity theorem? What is dilation? How can we determine the dilation of a given figure? Students will... Unit Results Write ratios. Write and solve proportions. Use proportions to identify similar polygons. Solve problems using the properties of similar polygons. Identify similar triangles using the AA Similarity postulate and the SSS and SAS Similarity Theorems. Use the similar triangles to solve problems. Use proportional parts within triangles. Use proportional parts with parallel lines. Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of similar triangles. Use the triangle bisector theorem. Identify similarity transformations. Verify similarity transformations. Interpret scale models. Use scale factors to solve problems. Suggested Activities The following activities can be incorporated into the daily lessons: Writing and simplifying ratios. Use extended ratios. Using cross products to solve proportions.

16 Create similarity statements. Identifying similar polygons. Using similar figures to find missing measurements. Proving the AA similarity postulate. Identifying parts of similar triangles. Finding the midsegment of a triangle. Using special segments to prove similar triangles. Identifying dilations. Using a scale drawing. Content Area: Geometry Unit Title: Right Triangles and Trigonometry Target Course/Grade Level: Geometry Duration: 3 Weeks Unit Overview Description: The goals of this chapter include solving problems involving similar right triangles using the geometric mean and indirect measurement Students prove the Pythagorean Theorem and use it and its converse to solve problems. Students find the lengths of sides of special right triangles and use them to solve real-life problems. They find the sine, cosine, and tangent ratios and use them to solve real-life problems. Finally, students find the magnitude and direction of vectors and add vectors. The student will get evaluation by quizzes and by tests after completion of sections and the chapter. Concepts Geometric mean The Pythagorean Theorem and its converse Special right triangles Trigonometry Angles of elevations and depression Laws of sines Laws of cosines Vectors Concepts & Understandings Understandings Use the Pythagorean Theorem. Use properties of special right triangles. Use trigonometry to find missing of triangles. Identify four ways to prove triangles are similar. Give information about their sides and angles. Identify how to use similar polygons to solve real life problems. CPI Codes Learning Targets GPE.HS.06 MG.HS.03

17 SRT.HS.04 SRT.HS.05 SRT.HS.06 SRT.HS.07 SRT.HS.08 SRT.HS.09 SRT.HS st Century Themes and Skills See Addendum Guiding Questions What is the geometric mean of the numbers 14 and 86? Given the altitude of a right triangle can you find the similar triangles? Define the Pythagorean triple and give an example. Find the length of the second leg of a right triangle with a given the values of a leg and the hypotenuse. Describe how to classify a triangle with side lengths 6,9,10. Describe how to use the converse of the Pythagorean Theorem. How can we use the Pythagorean Theorem to classify different kinds of triangles? Find the ratio of the lengths of the sides of a 30, 60, 90 triangle and a 45, 45, 90 triangle. Can the side lengths of a 45, 45, 90 triangle form a Pythagorean triple?

18 What does the term SOHCAHTOA mean? What is the component form of a vector? What kind of operations can we perform using vectors? How do we add vectors? How do we find the magnitude and direction of a given vector? Students will... Unit Results Find the geometric mean between two numbers. Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse. Use the Pythagorean Theorem. Use the converse of the Pythagorean Theorem. Use the properties of triangles. Use the properties of triangles. Find trigonometric ratios using right triangles. Use trigonometric ratios to find angle measures in right triangles. Solve problems involving angles of elevation and depression. Use angles of elevation and depression to find the distance between two objects. Use the Laws of Sines to solve triangles. Use the Law of Cosines to solve triangles. Perform vector operations geometrically. Perform vector operations on the coordinate plane. Suggested Activities The following activities can be incorporated into the daily lessons: Finding geometric mean. Students will be able to solve problems involving similar right triangles formed by altitude drawn to the hypotenuse of a right triangle. Identifying similar right triangles. Determine whether or not a triangle is a right triangle using the Pythagorean Theorem. Use the converse of the Pythagorean Theorem to classify the different kinds of triangles. Finding the length of the hypotenuse in a triangle. Finding the length of the hypotenuse in a triangle. Finding sine, cosine, and tangent ratios. Use special right triangles to find trigonometric ratios. Finding angle measures using inverse Trigonometric Ratios. Solving a right triangle. Finding the angle of elevation and the angle of depression. Using the laws of sines and cosines. Represent vectors geometrically. Find the resultant vector of two vectors. Writing vectors in component form. Finding the magnitude and direction of a vector.

19 Completing operations with vectors. Content Area: Geometry Unit Title: Transformations Target Course/Grade Level: Geometry Duration: 3 Weeks Unit Overview Description: In this chapter, student will identify reflections, rotations, translations, and the characteristics of an isometric. They will solve problems involving rigid transformations in the coordinate plane and will prove theorems about reflections, rotations, and translations. They will also use software to investigate double reflections in the coordinate plane Students will describe translations using vectors and will identify vector components. Students will also learn how two or more translations produce a composition and they will identify glide reflections in a plane. In the final lesson, they will use transformations to classify, identify, and draw frieze patterns. Then they will examine how to use frieze patterns to create decorative borders for real-life objects. Throughout the chapter, students will apply what they learn to real-life applications such as stenciling designs, carpentry, surveying, molecular chemistry, log design, navigation, and land architecture. The student will get evaluation by quizzes and by tests after completion of sections and the chapter. Concepts Reflections Translations Rotations Compositions of Transformations Symmetry Dilations CPI Codes Concepts & Understandings Learning Targets Understandings Identifying types of rigid transformations. Using properties of reflections. Relating reflections and line symmetry. Relating rotations and rational systems. Name and draw figures that have been reflected, translated, rotated, or dilated. Recognize and draw compositions of transformations. Identify symmetry in two- and three- dimensional figures. Using properties of translations. Using the properties of glide reflections. Classifying frieze patterns. CO.HS.01 CO.HS.02 CO.HS.03

20 CO.HS.04 CO.HS.05 CO.HS.06 CO.HS.07 SRT.HS st Century Themes and Skills See Addendum Guiding Questions What is a transformation? What is the image? What is the preimage? What is a reflection? How can we graph a reflection in a coordinate plane? What is a line of reflection? What is a rotation? Where is the fixed point of rotation? What is the angle of rotation? How to identify and use translations in the plane? How to use vectors in real-life situations? How to identify and use reflections, translations, rotations, and freeze patterns? How to use the transformations in real-life? What is symmetry? What is rotational symmetry? What is a dilation? Describe how to create a dilation of a given figure with a scale factor of ½. Students will... Unit Results Draw reflections. Draw reflections in the coordinate plane. Draw translations. Draw translations in the coordinate plane. Draw rotations. Draw rotations in the coordinate plane. Draw glides reflections and other compositions of isometries in the coordinate plane. Draw compositions of reflections in parallel and intersecting lines. Identify line and rotational symmetries in two-dimensional figures. Identify plane and axis symmetries in three-dimensional figures. Draw dilations. Draw dilations in the coordinate plane.

21 Suggested Activities The following activities can be incorporated into the daily lessons: Naming transformations Identifying Isometrics. Reflecting a figure in a line. Drawing translations in the coordinate plane. Drawing rotations. Graphing a glide reflection. Reflecting a given figure in two lines. Identifying lines of symmetry. Identifying rotational symmetry. Determining symmetry in a three-dimensional figure. Drawing a dilation. Finding the scale factor of a dilation. Creating dilations in the coordinate plane. Preserving length and angle measures. Identify and use reflection in a plane Identify relationships between Identify rotations in a plane Rotations in a coordinate plane. Use properties of Translations Finding the image of a composition Describe a composition Content Area: Geometry Unit Title: Circles Target Course/Grade Level: Geometry Duration: 3 Weeks Unit Overview Description The goals of this chapter include identifying segments and lines related to circles, using properties of a tangent to a circle, using properties of arcs and chords of circles, using inscribed angles and properties of inscribed polygons to solve problems related to circles, and finding angles and arc measures related to circles. Students find the lengths of the segments of chords, tangents, and secants They find the equation of a circle and use it to graph and solve problems. Finally, students draw loci that satisfy given conditions. The student will get evaluation by quizzes and by tests after completion of sections and the chapter. Concepts Circles and Circumference Measuring angles and arcs Arcs and chords Inscribed angles Tangents Secants, Tangents, and Angle Measures Special Segments in a Circle Equations of Circles. Concepts & Understandings Understandings Use properties of circle. Write the equation of a circle. Use properties of inscribed polygons. Use the relationships between central angles, arcs, and inscribed angles in a circle. Define and use secants and tangents. Use an equation to identify or describe a circle.

22 CPI Codes CO.HS.01 CO.HS.12 Learning Targets GPE.HS.01 GPE.HS.06 MG.HS.03 GC.HS.01 GC.HS.02 GC.HS.03 GC.HS.04 GC.HS st Century Themes and Skills See Addendum Guiding Questions Name the different parts of a circle (i.e. radius, diameter, and chords). What is chord? How do we find the circumference of a circle? How can we go about finding the central angle of a circle? Which is the longest chord in a circle? What is an arc? Can you name any two properties of a circle? What is an inscribed angle? How can we find the length of a segment tangent to a circle? What is the point of tangency? What is a secant line? How can we find the measure of the angle created by two secant line segments? Students will... Unit Results

23 Identify and use parts of circles. Solve problems involving the circumference of a circle. Identify the central angles, major arcs, minor arcs, and semicircles, and find their measures. Find arc lengths. Recognize and use relationships between arcs and chords. Recognize and use relationships between arcs, chords, and diameters. Find measure of inscribed angles. Find measures of angles of inscribed polygons. Use properties of tangents. Solve problems involving circumscribed polygons. Find measures of angles formed by lines intersecting on or inside a circle. Find measures of angles formed by lines intersecting outside the circle. Find measures of segments that intersect in the interior of a circle. Find the measure of segments that intersect in the exterior of a circle. Write the equation of a circle. Graph a circle on the coordinate plane. Suggested Activities The following activities can be incorporated into the daily lessons: Identify segments in a circle. Find ratios and diameter. Find measures in intersecting circles. Finding measures of central angles. Classifying arcs and find arc measures. Using arc addition to find measures of arcs. Use congruent chords to find arc measure. Use congruent arcs to find chord lengths. Using inscribed angles to find measures. Using inscribed angles in proofs. Identifying common tangents. Using tangents to find missing values. Using congruent tangents to find missing measurements. Using intersecting chords or secants. Using tangent sand secants that intersect outside a circle. Using the intersection of two chords. Identify segments and lines, & tell whether the line or segment is best described as a chord, secant, a tangent, a diameter, or a radius of a given circle. Recognize relationships between arcs and central angles of circles, and chords and diameters of circles Solve problems or find variable values using the measures of inscribed angles and intercepted arcs. Create simple proofs involving the measures of inscribed angles. Content Area: Geometry Unit Title: Area of Polygons and Circles Target Course/Grade Level: Geometry Duration: 2 Weeks Unit Overview Description : Explores many topics which relate to the area of polygons and circles. The chapter begins by finding the measures of the

24 interior and exterior angles of polygons. These angle measures are then used to find the area of an equilateral triangle and other polygons. Perimeters and areas of similar figures are investigated. Next, students are introduced to the circumference of a circle and the length of a circular arc. This leads to finding the area of a circle and the area of a sector of a circle. Finally geometric probability is introduced. Throughout the chapter, real-life problems involving area, perimeter, circumference, arc length, and geometric probability are solved. The student will get evaluation by quizzes and by tests after completion of sections and the chapter. Concepts Concepts & Understandings Understandings Areas of Parallelograms and Triangles Areas of Trapezoids, Rhombi, and Kites Areas of Circles and Sectors Areas of Regular Polygon and Composite Figures Areas of Similar Figures Finding areas of polygons Solve problems involving areas and sectors of circles Find scale factors using similar figures To understand the properties of special parallelograms and find the area of polygons and circles. CPI Codes GMD.HS.0 1 GPE.HS.07 MG.HS.01 MG.HS.03 GC.HS.05b Learning Targets 21 st Century Themes and Skills See Addendum Guiding Questions State the types of polygons. Apply the theorem 11.2 to the given question. What is a regular polygon? What is an equilateral and equiangular polygon? When can you say the figures are similar? What is scale factor? Can a circle be a polygon? What is circumference? Describe the difference between circumference and perimeter. How do you find the area of two concentric circles? How do you find the area and perimeter of a triangle?

25 Describe the steps that need to be taken in order to find the area of a composite figure. How do you find the area of a sector of a circle? What is a regular polygon? Students will... Unit Results Find perimeters and areas of parallelograms. Find perimeters and areas of triangles. Find areas of trapezoids. Find areas of rhombi and kites. Find areas of circles. Find areas of sectors of a circle. Find areas of regular polygons. Find areas of composite figures. Find areas of similar figures by using scale factors. Find scale factors or missing measures given the areas of similar figures. Suggested Activities The following activities can be incorporated into the daily lessons: Finding the perimeter and area of a parallelogram. Prove the area congruence postulate. Finding the perimeter and area of a triangle. Using area to find missing measures. Finding the area of a trapezoid. Finding the area of a Rhombus and Kite. Finding the area of a circle. Using the area of a circle to find the missing measurement. Finding the area of a sector. Identify segments and angles in regular polygons. Finding the area of a regular polygon. Using the formulas for the area of regular polygons. Find the area of a composite figure by adding and subtracting. Finding areas of similar figures. Using areas of similar figures. Content Area: Geometry Unit Title: Surface Area and Volume Target Course/Grade Level: Geometry Duration: 2 Weeks Description: Unit Overview In this chapter students will investigate the surface area and volume of solids. First, they will learn to distinguish polyhedra from other solids and to classify polyhedra. They will identify the Platonic solids and use Euler's Theorem. Students will use nets to help them explore the surface area of prisms and cylinders. They will use the Pythagorean theorem to identify the surface area of pyramids, and use proportions involving circles to identify the surface area of cones. They will then develop methods for finding the volume of prisms and cylinders, including using Cavalieri's

26 Principle. Students will find the volume of pyramids and cones. After learning to find the surface area and volume of spheres, students will investigate similar solids, including scale factors and how surface area and volume relate to the dimensions of similar solids. The student will get evaluation by quizzes and by tests after completion of sections and the chapter. Concepts Concepts & Understandings Understandings Representations of Three-Dimensional Figures Surface Areas of Prisms and Cylinders Surface Areas of Pyramids and Cones Volumes of Prisms and Cylinders Volumes of Pyramids and Cones Surface Area and Volume of Spheres Spherical Geometry Congruent and Similar Solids Find lateral areas, surface areas, and volumes of various solid figures Investigate Euclidean and spherical geometries Use properties of similar solid figures. CPI Codes Learning Targets CO.HS.13 GMD.HS.0 1 GMD.HS.0 2 GMD.HS.0 3 GMD.HS.0 4 GPE.HS st Century Themes and Skills See Addendum Guiding Questions What is a three-dimensional figure? What is lateral area? What three things do you need to know in order to find the surface area of a pyramid? What formula is needed to find the lateral area of a cylinder?

27 What is the volume of a sphere whose radius is 22 ft? Describe Euclidean geometry. Describe spherical geometry. Compare and contrast Euclidean and spherical geometries. What information do you need to know in order to determine whether or not two solids are congruent? What information do you need to know in order to determine whether or not two solids are similar? Students will... Unit Results Draw isometric views of three-dimensional figures. Investigate cross sections of three-dimensional figures. Find lateral areas and surface areas of prisms. Find lateral areas and surface areas of cylinders. Find lateral areas and surface areas of pyramids. Find lateral areas and surface areas of cones. Find volumes of prisms. Find volumes of cylinders. Find volumes of pyramids. Find volumes of cones. Find surface areas of spheres. Find volumes of spheres. Describe sets of points on a sphere. Compare and contrast Euclidean and spherical geometries. Identify congruent of similar solids. Use properties of similar solids. Suggested Activities The following activities can be incorporated into the daily lessons: Use dimensions of a solid to sketch a solid. Finding the lateral area of a prism. Finding the surface area of a prism. Finding the lateral area and surface area of a cylinder. Find the lateral area of a regular prism. Find the surface area of a square pyramid. Finding the surface area of a cone. Find the volume of a prism and a cylinder. Comparing volumes of solids. Finding real world volumes. Use great circles to find surface area. Find surface area of a sphere. Describe sets of points on a sphere. Compare plane Euclidean and spherical geometries. Identify lines in spherical geometry. Identify similar and congruent solids.