Course:  09th Grade Honors/Gifted Geometry

Text: Geometry:  Holt, Rinehart and Winston

Cost: $47.40

Prerequisite: 08th Grade Honors/Gifted Algebra

 

Curricular goals interwoven throughout the mathematics program are that students will:

            learn to communicate mathematically (QCC)

            learn to use mathematics in their daily lives (QCC)

            become proficient with appropriate computational tools and techniques (QCC)

            learn to reason mathematically (QCC)

            become mathematical problem solvers (QCC)

 

These goals will provide the direction for assessment and instruction. Attainment of these goals is facilitated by the students’ demonstration of the following Academic Knowledge and Skills (AKS).

 

Chapter 1 Exploring Geometry (pp. 2-77)                                                                                  

 

Ÿ         apply properties and analyze relationships associated with points, segments, rays, lines, angles, planes and polygons (QCC, SAT I) (MAHG_A2001-2)

Ÿ         create constructions associated with segments, angles, polygons and circles using compass and straightedge, paper folding, mira, and/or computer graphing software (QCC) (MAHG_A2001-4)

Ÿ        write and graph equations of parallel, perpendicular and intersecting lines satisfying given conditions (QCC, SAT I, ACT) (MAHG_B2001-12)

Ÿ         develop and apply formulas for distance, midpoint, slope, circles (QCC, SAT I, ACT) (MAHG_B2001-13)

Ÿ        analyze effects of reflections, rotations, translations, dilations and symmetry of geometric figures in the coordinate plane (QCC, HSGT) (MAHG_B2001-16)

Ÿ         determine the image, pre image or inverse of a given mapping, and the composite of two mappings (QCC) (MAHG_B2003-6)

Ÿ         create composites of transformations (QCC) (MAHG_B2001-19) [ex.  Glide-reflection]

 

Chapter 2 Reasoning in Geometry (pp. 78-135): Chapter 12 A Closer Look at Proof and Logic ( pp. 766-797, 808-811)

                                                                                                                                                      

Ÿ         apply inductive and deductive reasoning process to form conjectures and then prove conjectures using valid reasoning and laws of logic (QCC) (MAHG_A2001-6)

Ÿ         construct direct and indirect proofs in written form such as paragraph, two-column or flow-chart formats (QCC) (MAHG_A2001-10)

Ÿ         determine the equivalence and validity of truth tables including sentences involving conditional statements, conjunctions, disjunctions, and negations (QCC) (MAHG_A2003-3)

Ÿ         determine truth tables for sentences and use Venn Diagrams to illustrate the relationship represented by truth tables (QCC) (MAHG_A2003-4)

 

Chapter 3 Parallels and Polygons (pp. 136-207)                                                                         

Ÿ         apply properties and analyze relationships associated with points, segments, rays, lines, angles, planes and polygons (QCC, SAT I) (MAHG_A2001-2)

Ÿ         create constructions associated with segments, angles, polygons and circles using compass and straightedge, paper folding, mira, and/or computer graphing software (QCC) (MAHG_A2001-4)

Ÿ         apply inductive and deductive reasoning process to form conjectures and then prove conjectures using valid reasoning and laws of logic (QCC) (MAHG_A2001-6)

Ÿ         prove and apply theorems associated with polygons with respect to angles, sides, segments and angle sums (QCC) (MAHG_A2001-7)

Ÿ         construct direct and indirect proofs in written form such as paragraph, two-column or flow-chart formats (QCC) (MAHG_A2001-10)

Ÿ         apply and prove congruence and similarity properties of polygons and solids

(QCC, SAT I) (MAHG_A2001-11)

Ÿ         recognize parallel lines and planes, skew lines, and pairs of angles formed when two lines are cut by a transversal (alternate and same side, interior and exterior, corresponding) (QCC) (MAHG_A2003-1)

Ÿ         use properties of quadrilaterals to establish and test relationships involving diagonals, angles, and lines of symmetry (QCC) (MAHG_A2003-2)

Ÿ         write and graph equations of parallel, perpendicular and intersecting lines satisfying given conditions (QCC, SAT I, ACT) (MAHG_B2001-12)

Ÿ          develop and apply formulas for distance, midpoint, slope, circles (QCC, SAT I, ACT) (MAHG_B2001-13)

Ÿ          write equations for lines satisfying given conditions (QCC, ACT) (MAHG_C2001-20)

 

 

Chapter 4 Triangle Congruence (pp. 208-291)                                                                           

Ÿ         identify, prove and apply theorems and properties related to congruent triangles, right triangles and polygons (QCC, SAT I) (MAHG_A2001-1)

Ÿ         apply properties and analyze relationships associated with points, segments, rays, lines, angles, planes and polygons (QCC, SAT I) (MAHG_A2001-2)

Ÿ         create constructions associated with segments, angles, polygons and circles using compass and straightedge, paper folding, mira, and/or computer graphing software (QCC) (MAHG_A2001-4)

Ÿ         prove and apply theorems associated with polygons with respect to angles, sides, segments and angle sums (QCC) (MAHG_A2001-7)

Ÿ         apply and prove congruence and similarity properties of polygons and solids (QCC, SAT I) (MAHG_A2001-11)

Ÿ         use properties of quadrilaterals to establish and test relationships involving diagonals, angles, and lines of symmetry (QCC) (MAHG_A2003-2)

Ÿ         analyze effects of reflections, rotations, translations, dilations and symmetry of geometric figures in the coordinate plane (QCC, HSGT) (MAHG_B2001-16)  

Ÿ         create composites of transformations (QCC) (MAHG_B2001-19) [supplement textbook]

 

END of FIRST SEMESTER MATERIAL

 

09th Grade Honors/Gifted Geometry (2nd semester)

Text:  Geometry:   Holt, Rinehart and Winston

Cost:  $47.40

 

Curricular goals interwoven throughout the mathematics program are that students will:

            learn to communicate mathematically (QCC)

            learn to use mathematics in their daily lives (QCC)

            become proficient with appropriate computational tools and techniques (QCC)

            learn to reason mathematically (QCC)

            become mathematical problem solvers (QCC)

 

These goals will provide the direction for assessment and instruction. Attainment of these goals is facilitated by the students’ demonstration of the following Academic Knowledge and Skills (AKS).

 

 

Chapter 5 Perimeter and Areas (pp. 292-369)                                                                            

Ÿ          identify, prove and apply theorems and properties related to congruent triangles, right triangles and polygons (QCC, SAT I) (MAHG_A2001-1)

Ÿ         prove and apply theorems associated with polygons with respect to angles, sides, segments and angle sums (QCC) (MAHG_A2001-7)

Ÿ         write and graph equations of parallel, perpendicular and intersecting lines satisfying given conditions (QCC, SAT I, ACT) (MAHG_B2001-12)

Ÿ         develop and apply formulas for distance, midpoint, slope, circles (QCC, SAT I, ACT) (MAHG_B2001-13)

Ÿ         determine perimeter, area, circumference, arc length, area of sectors, and surface area of geometric figures using appropriate units (QCC, SAT I, ACT) (MAHG_B2001-14)

Ÿ         write coordinate proofs (QCC) (MAHG_B2001-15)

Ÿ         investigate , apply and examine proofs of the Pythagorean Theorem and its converse (QCC) (MAHG_B2003-7)

Ÿ         apply the properties of triangle inequalities (QCC) (MAHG_D2003-11)

Ÿ         apply geometric probability (QCC, PSAT, SAT, ACT) (MAHG_D2003-12)

Ÿ          optimize perimeter, area and volumes of geometric figures and solids (QCC) (MAHG_D2003-13)

 

Chapter 6 Shapes in Space (pp. 370-427)                                                                                   

Ÿ         apply properties and analyze relationships associated with points, segments, rays, lines, angles, planes and polygons (QCC, SAT I) (MAHG_A2001-2)

Ÿ         find the coordinates of the point of intersection of two lines (QCC) (MAHG_B2003-9)]

Ÿ         explore and interpret both two and three dimensional geometric figures using such topics as projections, cross sections, and locus problems (QCC) (MAHG_A2001-3) [see perspective drawings using projections]

 

 

Chapter 7 Surface Area and Volume (pp. 428-495)                                                                   

Ÿ         explore and interpret both two and three dimensional geometric figures using such topics as projections, cross sections, and locus problems (QCC) (MAHG_A2001-3)

Ÿ         determine perimeter, area, circumference, arc length, area of sectors, and surface area of geometric figures using appropriate units (QCC, SAT I, ACT) (MAHG_B2001-14)

Ÿ         develop and apply formulas to find lateral area, volume and surface area of solids

(QCC, ACT) (MAHG_B2002-3)

Ÿ         find the exact or approximate volume and surface area of solids composed of prisms, pyramids, cylinders, cones, and/or spheres (QCC, ACT) (MAHG_B2002-4)

Ÿ         optimize perimeter, area and volumes of geometric figures and solids (QCC) (MAHG_D2003-13)

 

 

 

Chapter 8 Similar Shapes (pp. 496-561)                                                                                     

Ÿ         explore and interpret both two and three dimensional geometric figures using such topics as projections, cross sections, and locus problems (QCC) (MAHG_A2001-3)

Ÿ         apply and prove congruence and similarity properties of polygons and solids

(QCC, SAT I) (MAHG_A2001-11)

Ÿ         compare and apply properties associated with similar figures (QCC) (MAHG_A2002-1)

Ÿ         recognize and apply similar polygons using ratio and proportion (QCC) (MAHG_A2003-5)

Ÿ         write coordinate proofs (QCC) (MAHG_B2001-15)

Ÿ         analyze effects of reflections, rotations, translations, dilations and symmetry of geometric figures in the coordinate plane (QCC, HSGT) (MAHG_B2001-16)

Ÿ         investigate and apply transformation vectors and scale changes to find the image of figures on the coordinate plane (QCC) (MAHG_B2001-17)

Ÿ         create composites of transformations (QCC) (MAHG_B2001-19)

Ÿ         apply indirect measurement and similarity theorems to solve problems involving similar polygons (QCC, ACT) (MAHG_B2002-2)

Ÿ         determine the image, pre image or inverse of a given mapping, and the composite of two mappings (QCC) (MAHG_B2003-6)

Ÿ         compare the areas of similar polygons and the volume of similar solids to solve problems and justify the reasonableness of results (QCC) (MAHG_B2003-8)

 

 

Chapter 9 Circles (pp. 562-627)                                                                                                  

Ÿ         apply properties and analyze relationships with respect to circles and segments, lines, and arcs and angles associated with circles (QCC) (MAHG_A2001-8)

Ÿ         develop and apply formulas for distance, midpoint, slope, and circles (QCC, SAT I, ACT) (MAHG_B2001-13)

Ÿ        determine perimeter, area, circumference, arc length, area of sectors, and surface area of geometric figures using appropriate units (QCC, SAT I, ACT) (MAHG_B2001-14)

 

 

 

Chapter 10 Trigonometry (pp. 628-653)                                                                                     

Ÿ         apply special right triangle relationships (QCC, SAT I, ACT) (MAHG_D2001-25)

Ÿ         explore sine, cosine and tangent functions in right triangles (QCC, SAT I, ACT) (MAHG_D2001-26)

Ÿ         use tangent, sine and cosine ratios to solve application problems (QCC)

(MAHG_D2003-10)

        

 

As time allows:

 

Chapter 10 Trigonometry

         Sections 10.3 – 10.7 (pp. 647-695)

 

Chapter 11 Taxicabs, Fractals and More (pp. 696-765)