HADDONFIELD PUBLIC SCHOOLS Curriculum Map for College Prep Geometry

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1 Curriculum Map for College Prep Geometry Chapter 1: September (2-3 weeks) Targeted NJ Core Curriculum Content Standards: CC.9-12.G.CO.1; CC.9-12.G.GPE.7; CC.9-12.G.MG.1 Enduring Understandings: Geometry can be broken down into three basic figures: points, lines and planes Essential Questions: How do we define terms? Why is there a need for undefined terms? What are the purposes of postulates, and how do they relate to theorems? What is an angle? How do we characterize angles? How are angles measured and what can we assume about their measures? What are polygons? How do we characterize polygons? What is a polygon and how do we distinguish one polygon from another? How do we describe geometric figures? How do we measure geometric figures? What are equality and congruence and how do they compare? How do we find segment lengths? How do you compare segments? How do you find the midpoint and distance for a segment? What is a segment bisector? 1

2 Chapter 1 Essentials of Geometry 1.1. Identify Points, Lines, and Planes Point, line, plane, collinear, coplanar, line segment, ray, opposite rays 1.2. Use Segments and Congruence Distance formula, segment addition postulate, congruent segments 1.3. Use Midpoints and Distance Formulas Midpoint, segment bisector, midpoint formula, distance formula 1.4. Measure and Classify Angles Parts of an angle, classify angles, angle addition postulate, congruent angles, angle bisector 1.5. Describe Angle Pair Relationships Complimentary angles, supplementary angles, linear pair, vertical angles, adjacent angles 1.6. Classify Polygons Naming polygons, convex vs. nonconvex, regular HADDONFIELD PUBLIC SCHOOLS - Use correct terminology and notation of points, segments, lines, rays, planes, angles, and collinear and coplanar points. - Use geometric tools for measurement and for constructions like angle bisectors and midpoints. - Using midpoint and distance formulas to find information on using coordinates. - Define special angle relationships. - Define and classify angles and polygons and their related terms. - Understand and use segment addition and angle addition postulates Quiz Quiz Chapter 1 Test Resources/Technology: Powerpoint, Protractors, Compasses, Rulers, TI 83 Chapter 2: September to October (2-3 weeks) Targeted NJ Core Curriculum Content Standards: SMP 3; CC.9-12.G.CO.9; CC.9-12.A.REI.1 Enduring Understandings: Proofs can be used to argue geometric relationships Essential Questions: What are the types of special angle relationships? How can you understand geometric relationships in diagrams? What are conditional statements? What are the algebraic properties and how can they be used? How do you use a formal proof to prove geometric and algebraic properties? 2

3 HADDONFIELD PUBLIC SCHOOLS Chapter 2 Reasoning and Proof 2.2 Analyze Conditional Statements If-then statements, hypothesis and conclusion, negation, converse, inverse, contrapositive, biconditional 1.4. Use Postulates and Diagrams Point, line, plane postulates, interpreting a diagram Unions and Intersections 1.5. Reason Using Properties from Algebra Algebraic properties of equality, reflexive symmetric, and transitive properties of equality and congruence, algebraic proofs 1.6. Prove Statements about Segment and Angles Segment and Angle Addition proofs 1.7. Prove Angle Pair Relationships - Discover relationships between special pairs of angles. - Write a two-column proof involving algebraic properties. - Write a two-column proof involving segment and angle addition. - Understand conditional statements and their truth values. - Express sets in terms of unions and intersections. - Algebraic Prop in Proofs Activity - Unions and Intersections Activity Quiz Quiz Chapter 2 Test Resources/Technology: Powerpoint, Protractors, Rulers Chapter 3: October (3 weeks) Targeted NJ Core Curriculum Content Standards: CC.9-12.G.CO.1; CC.9-12.G.CO.9; CC.9-12.G.GPE.5 Enduring Understandings: Parallel and perpendicular lines have certain properties that arise when they intersect Essential Questions: What are the properties of parallel and perpendicular lines? What special angle relationships are formed by two parallel lines cut by a transversal? How can you prove relationships using angle measures? How do parallel and perpendicular lines relate to each other, specifically on the coordinate plane? How can you prove parallel lines exist? 3

4 HADDONFIELD PUBLIC SCHOOLS Chapter 3 Parallel and Perpendicular Lines 3.1 Identify Pairs of Lines and Angles Parallel, skew, perpendicular, corresponding, alternate interior, alternate exterior, same side interior, same side exterior angles, transversal 3.2 Use Parallel Lines and Transversals Given parallel lines, prove angle relationships 1.3. Prove Lines are Parallel Given congruent angle pairs, prove lines are parallel 1.4. Find and Use Slopes of Lines Slopes of parallel and perpendicular lines 1.5. Write and Graph Equations of Lines Slope-intercept form, standard form 1.6. Prove Theorems About Perpendicular Lines - Discover relationships between special pairs of angles. - Write a two-column proof involving parallel lines cut by a transversal. - Graph equations of lines and interpret their slopes. - Understand theorems that arise when parallel and perpendicular lines intersect. - Prove lines are parallel. - Use of TI 83 calculator to graph various functions. - Angle Town Project Quiz Angle Pair Mini Quiz Quiz Chapter 3 Test Resources/Technology: Powerpoint, Protractors, Rulers, TI 83 Chapter 4: October to November (3 weeks) Targeted NJ Core Curriculum Content Standards: CC.9-12.G.CO.10; CC.9-12.G.CO.7; CC.9-12.G.CO.6; CC.9-12.G.CO.8; CC.9-12.G.CO.2 Enduring Understandings: In order to prove two triangles are congruent we typically need three pieces of information Essential Questions: How do we classify triangles? What do we know about corresponding parts of congruent figures? What is the difference between congruence and equality? How do we prove figures are congruent? What algebraic properties help us to prove figures are congruent? How do we use a two column proof? What are the properties of special triangles? How do you find the sums of angle measures in a triangle? What are the criteria for isosceles and equilateral triangles? What are transformations and do they 4

5 produce congruent figures? How do we perform congruence transformations? HADDONFIELD PUBLIC SCHOOLS Chapter 4 Congruent Triangles 4.1 Apply Triangle Sum Properties Classify triangles by sides and angles, interior, exterior angles, triangle sum theorem, exterior angle theorem 4.2 Apply Congruence and Triangles Identify congruent parts, write congruence statements, third angle theorem 1.3. Relate Transformations and Congruence Translations, reflections, rotations 1.9. Perform Congruence Transformations On the coordinate plane Prove Triangles Congruent by SSS, SAS, ASA, AAS, HL, SsA 1.7. Use Congruent Triangles CPCTC 4.8 Use Isosceles and Equilateral Triangles - Apply the SSS, SAS, AAS, ASA, HL, SsA congruency theorems and CPCTC. - Discover and explain the sum of the measures of the angles of a triangle. - Discover a relationship between the base angles of an isosceles triangle. - Perform congruence transformations in the coordinate plane. - In class investigations and hands-on exploration of transformations with use of Geometer s Sketchpad - Create triangles with string and straws Quiz Quiz 4.8 Quiz 4.3 and 4.9 Quiz Chapter 4 Test Resources/Technology: Powerpoint, Protractors, Rulers, Geometer s Sketchpad Chapter 5: November to December (3-4 weeks) 5

6 Targeted NJ Core Curriculum Content Standards: CC.9-12.G.GPE.4; CC.9-12.G.CO.9; CC.9-12.G.C.3; CC.9-12.G.CO.10 Enduring Understandings: There are special segments that exists within triangles Essential Questions: What properties exist with special segments in triangles? How can we use triangle inequalities to determine what triangles are possible? What inequalities exist within two triangles? How do these properties help us with a triangle? Chapter 5 Relationships within Triangles 5.1 Midsegment Theorem 5.2 Use Perpendicular Bisectors Perpendicular bisector definition and theorem, equidistant, circumcenter 1.3. Use Angles Bisectors of Triangles Angle bisector theorem, incenter 1.4. Use Medians and Altitudes Median, centroid, 2/3 rule, altitude, orthocenter 1.5. Use Inequalities in a Triangle Triangle inequality theorem 1.6. Inequalities in Two Triangles - Define median, altitude, angle bisector, and perpendicular bisector for a triangle. - Understand how to find and identify the four different points on concurrency in a triangle. - Determine the relative size of angles and sides in a single triangle and within two triangles. - Segments in Triangles Activity - Circumcenter Activity - Median Activitty - Construction of triangle centers with various tools Quiz Quiz Chapter 5 Test Resources/Technology: Powerpoint, Protractors, Rulers, Geometer s Sketchpad, TI 83 Chapter 6: December to January (2-3 weeks) Targeted NJ Core Curriculum Content Standards: CC.9-12.G.SRT.5; CC.9-12.G.SRT.2; CC.9-12.G.SRT.3; CC.9-12.G.SRT.4; CC.9-12.G.CO.2 6

7 Enduring Understandings: Similar figures have congruent angles but proportional side lengths Essential Questions: How do you set up and solve a proportion? What ways can you show two triangles are similar? What transformations produce similar figures? How can we perform these transformations on the coordinate plane? How do similar triangles translate to our real world? Chapter 6 SImilarity 6.1 Use Similar Polygons Ratios and proprtions 6.3 & 6.4 Prove Triangles are Similar by AA~, SSS~, SAS~ 1.5. Use Proportionality Theorems 6.2 Relate Transformations and Similarity Dilations 1.6. Perform Similarity Transformations Dilations on the coordinate plane - Apply the AA~, SSS~, and SAS~ theorems to similar triangles. - Perform similarity transformations in the coordinate plane. - Apply the triangle proportionality theorem as well as its converse. - In class investigations and hands-on exploration of transformations with use of Geometer s Sketchpad - Create triangles with straws and straws Quiz Quiz Chapter 6 Test Resources/Technology: Powerpoint, Protractors, Rulers, Geometer s Sketchpad 7

8 Chapter 7: January to February (2-3 weeks) Targeted NJ Core Curriculum Content Standards: CC.9-12.G.SRT.8; CC.9-12.G.SRT.5; CC.9-12.G.SRT.6 Enduring Understandings: Special relationships exist within right triangles Essential Questions: How can you use Pythagorean Theorem to find missing side lengths in right triangles? What are the ratios between side lengths of a triangle? What are the ratios between side lengths of a triangle? What is sine? What is cosine? What is tangent? How can the trigonometric ratios help us find missing information about triangles? What are the real life applications of the trigonometric ratios? Chapter 7 Right Triangles and Trigonometry 7.1 Apply the Pythagorean Theorem 7.2 Use the Converse of the Pythagorean Theorem 1.3. Use Similar Right Triangles 7.4 Special Right Triangles triangles, triangles 1.5. & 7.6 Apply the Tangent, Sine and Cosine Ratios SOH CAH TOA 7.7 Solve Right Triangles - Review simplifying radicals and rationalization. - Use the Pythagorean Theorem to find missing side lengths of any right triangle. - Use the ratios to find missing side lengths of special right triangles. - Discover sine, cosine, and tangent ratios from our knowledge of similar triangles. - Find missing angles and sides using all of our knowledge of right triangles. - Use trigonometry to solve applied problems Quiz Quiz Chapter 7 Test Resources/Technology: Powerpoint, Protractors, Rulers, TI 83 8

9 Chapter 8: February to March (3 weeks) Targeted NJ Core Curriculum Content Standards: CC.9-12.G.MG.1; CC.9-12.G.CO.11; CC.9-12.G.SRT.5 Enduring Understandings: The interior angle sum of any polygon can be found by breaking the polygon into triangles and using calculations based on 180 Essential Questions: What special properties can be found in polygons? How do we find the interior angle sum of any given polygon? How can we understand the exterior angle sum of any given polygon? How can we apply the interior and exterior angle sums to find one interior or exterior angle in a regular polygon? How do we classify quadrilaterals? What are the properties of parallelograms and special types of parallelograms? What can you use to prove quadrilaterals? Chapter 8 Quadrilaterials 8.1 Find Angle Measures in Polygons Interior and exterior angle sums in polygons 8.2 Use Properties of Parallelograms Prove things given a parallelogram 1.3. Show that a Quadrilateral is a Parallelogram Prove a polygon is a parallelogram 8.4 Properties of Rhombuses, Rectangles, and Squares 8.5 Use Properties of Trapezoids and Kites 8.6 Identify Special Quadrilaterals Proving different quadrilaterals - Discover the sum of the interior and exterior angle measures in a polygon. - Discover the measure of single interior and exterior angles for regular polygons. - Discover properties of kites, trapezoids, parallelograms, rectangles, rhombuses, and squares. - Define and discover properties of midsegments in trapezoids. - Discuss and complete proofs involving different quadrilaterals. - Discovery activity where students will break polygons into triangles to find the interior angle sum and interior angle measures of regular polygons Quiz Quiz Chapter 8 Test Resources/Technology: Powerpoint, Protractors, Rulers 9

10 Chapter 9: March to April (2-3 weeks) Targeted NJ Core Curriculum Content Standards: CC.9-12.G.CO.5; CC.9-12.N.VM.8; CC.9-12.G.CO.5; CC.9-12.CO.3; CC.9-12.G.SRT.1 Enduring Understandings: Different transformations may be performed on a coordinate plane using various methods Essential Questions: What is a reflection? How do reflections relate to congruence? What are congruence transformations? What do reflections preserve? How do we use reflections to prove congruence among figures? What type of congruence transformation can be done using a vector? How do compositions of reflections affect a figure? What are rotations? What symmetry exists with reflections and rotations? What are dilations? How do dilations relate to similarty? Chapter 9 Properties of Transformations 9.1 Translate Figures and Use Vectors Complete vector translations 9.3 Perform Reflections 9.4 Perform Rotations 9.5 Apply Compositions of Transformations 9.7 Identify and Perform Dialtions 9.6 Identify Symmetry Reflection and rotation symmetry - Perform reflections. - Investigate the translation a figure using a vector. - Perform rotations. - Perform the composition of two or more transformations. - Perform a dilation. - Understand the concept of symmetry and the different ways figures can be symmetric. - In class investigations and hands-on exploration of transformations with use of Geometer s Sketchpad 9.1, 9.3 & 9.4 Quiz Quiz Chapter 9 Test Resources/Technology: Powerpoint, Protractors, Rulers, Geometer s Sketchpad 10

11 Chapter 10: April (2-3 weeks) Targeted NJ Core Curriculum Content Standards: CC.9-12.G.CO.1; CC.9-12.G.C.2; CC.9-12.G.C.3; CC.9-12.G.GPE.1 Enduring Understandings: The length and the measure of an arc of a circle, the diameter and the circumference of a circle, and the radius and the area of a circle can be related by setting up a proportion Essential Questions: What are the relationships among chords, arcs, angles, and tangent lines? How do we calculate the length of an arc? How do we find the measure of an arc? How do arc measure and arc length differ? What are central angles? What are inscribed angles? How do you write the equation of a circle? How can you read the center and radius of a circle from its equation? Chapter 10 Properties of Circles 10.1 Use Properties of Tangents Circle, center, chord, radius, diameter, secant, tangent 10.2 Find Arc Measures Central angle, minor arc, major arc, semicircle 10.3 Apply Properties of Chords 10.4 Use Inscribed Angles and Polygons 10.5 Apply Other Angle Relationships in Circles 10.6 Find Segment Length in Circles 10.7 Write and Graph Equations of Circle - Understand basic properties of a circle. - Discover properties of chords and tangents. - Discover relationships between inscribed angles and their intercepted arcs. - Calculate area, circumference, and arc length/measure of a circle. - Interpret equations of a circle. - Graph circles at origin and at points other than the origin Quiz Quiz Chapter 10 Test Resources/Technology: Powerpoint, Protractors, Rulers, Geometer s Sketchpad 11

12 Chapter 11: May (3-4 weeks) Targeted NJ Core Curriculum Content Standards: CC.9-12.G.C.5; CC.9-12.G.SRT.8; SMP 4; CC.9-12.G.GMD.4; CC.9-12.G.GMD.3 Enduring Understandings: The formula for surface area and volume of a given 3D solid can be used to solve for a missing value Essential Questions: What are the formulas for area and circumference of a circle? How do you find area of regular polygons? What are solids and how do they relate to 2D figures? What are the formulas for surface area and volume of 3D figures? What makes solids similar? Chapter 11 Measurement of Figures and Solids 11.1 Circumference and Arc Length 11.2 Areas of Circles and Sectors 11.3 Area of Regular Polygons 11.5 Explore Solids Lateral Area and Surface Area of Prisms and Cylinders Lateral Area and Surface Area of Pyramids and Cones 11.6 Volume of Prisms and Cylinders 11.7 Volume of Pyramids and Cones 11.8 Surface Area and Volume of Spheres 11.9 Explore Similar Solids - Calculate area, circumference, and arc length/measure of a circle. - Use the formulas to find the surface area of the given threedimensional shapes. - Use the formulas to find the volume of the given threedimensional shapes. - Use triangles to find area of regular polygons. - Understand basic area formulas for polygons. - Students will get to hold and feel various 3D solids Quiz 11.6, 11.7, Surface Area Quiz Chapter 11 Test Resources/Technology: Powerpoint, Protractors, Rulers 12

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