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Geometry Honors CURRICULUM ROAD MAP Core Questions How is logic used in geometry? How can algebra be applied to geometry? How can geometry be used to solve real-world problems? What relationships hold for figures composed of lines, line segments, or planes? FIRST QUARTER UNIT 1 BLOCK: 9 periods How does your point of view affect what you see? TRADITIONAL: 13 periods KEY CONCEPT FOCUS CONTENT BENCHMARKS 1. Points, lines, and planes are the Key Concept 1 MA.912.G.1.1 building blocks of geometry. Points, lines, segments, rays, planes, and angles MA.912.G.2.1 Ruler Postulate, Segment Addition Postulate MA.912.G.7.1 Congruent segments Distinguishing between MA.912.G.8.6 sketching, drawing, and constructing geometric figures LA.1112.1.6.1 Constructing congruent segments using a straightedge and compass LA.1112.1.6.2 or a drawing program Characterization in Flatland LA.1112.1.6.5 2. If you know the coordinates of Key Concept 2 the endpoints of a segment, you Midpoint formula can find its length and the Distance formula coordinates of its midpoint. 3. There are important Key Concept 3 relationships between some Protractor Postulate and Angle pairs of angles. Addition Postulate Constructing congruent angles and angle bisectors using a straightedge and compass or a drawing program Complementary, supplementary, and vertical angles CORE RESOURCE(S): Pearson Geometry Florida Edition Chapter 1 UNIT PERFORMANCE ASSESSMENT: Students will work in groups to design a tri-fold brochure about a concept studied in the unit, and then they will present their brochures to the class. Geometry Honors ROADMAP UNIT 2 BLOCK: 12 periods What does it mean to say, “I proved it”? TRADITIONAL: 18 periods KEY CONCEPT FOCUS CONTENT BENCHMARKS 1. Some versions of a conditional Key Concept 1 MA.912.D.6.1 statement are equivalent to each Conditional statements other and some are not. Converse, inverse, and MA.912.D.6.2 contrapositive of conditional statements MA.912.D.6.3 Equivalent statements Biconditionals MA.912.G.8.1 2. Conjectures are often based on Key Concept 2 MA.912.G.1.2 inductive reasoning, can be Inductive reasoning and disproved with one counterexamples MA.912.G.1.3 counterexample, and can be Deductive reasoning proved with deductive reasoning. Proving statements about MA.912.G.2.2 segments and angles MA.912.G.8.5 3. Special pairs of angles are formed Key Concept 3 when a transversal intersects Parallel and perpendicular lines LA.1112.1.6.1 coplanar lines. Special pairs of angles formed by coplanar lines and transversals LA.1112.1.6.5 Using postulates and theorems about the pairs of angles formed by parallel lines and transversals Distinguishing between postulates and theorems Constructing parallel and perpendicular lines (including perpendicular bisectors) using a straightedge and compass or a drawing program Explaining and justifying the process used to construct parallel lines CORE RESOURCE(S): Pearson Geometry Florida Edition Chapters 2 and 3 UNIT PERFORMANCE ASSESSMENT: Students will use logical reasoning and knowledge of parallel lines to investigate a series of school vandalism incidents. 2 MANATEE CORE CURRICULUM SECOND QUARTER UNIT 3 BLOCK: 7 periods What does it mean for two objects or ideas to be congruent? TRADITIONAL: 10 periods KEY CONCEPT FOCUS CONTENT BENCHMARKS 1. You can classify and describe Key Concept 1 MA.912.G.2.3 triangles in several different Classifying triangles ways. Proving and applying the Triangle MA.912.G.4.1 Sum Theorem Triangle Exterior Angle Theorem MA.912.G.4.4 MA.912.G.4.6 2. You can use SSS and SAS to prove Key Concept 2 two triangles are congruent. Corresponding parts of LA.1112.1.6.1 congruent triangles SSS and SAS Congruency LA.1112.1.6.5 Postulates Real-world problems involving triangle congruency Constructing triangles Explaining and justifying constructions 3. You can use ASA, AAS, and HL to Key Concept 3 prove that two triangles are ASA, AAS, and HL Congruency congruent. Theorems Properties of isosceles and equilateral triangles CORE RESOURCE(S): Pearson Geometry Florida Edition Chapters 4 UNIT PERFORMANCE ASSESSMENT: Students will use postulates and theorems about triangles and triangle congruence to solve problems related to creating bridges to cross waters in Manatee County. Geometry Honors ROADMAP 3 UNIT 4 BLOCK:7 periods What are the relationships within triangles? TRADITIONAL: 10 periods KEY CONCEPT FOCUS CONTENT BENCHMARKS 1. Most triangles have more than Key Concept 1 MA.912.D.6.4 one center. Perpendicular bisectors and circumcenters MA.912.G.4.2 Angle bisectors and incenters Medians and centroids MA.912.G.4.5 Altitudes and orthocenters 2. You can use theorems about MA.912.G.4.7 inequalities in triangles to solve Key Concept 2 problems. Inequalities in one triangle LA.1112.1.6.1 Triangle Inequality Theorem Hinge Theorem and its converse LA.1112.1.6.5 Indirect proof CORE RESOURCE(S): Pearson Geometry Florida Edition Chapters 5 UNIT PERFORMANCE ASSESSMENT: Students will make a mobile out of balanced triangles and then answer questions about their mobiles using theorems about triangle inequalities. 4 MANATEE CORE CURRICULUM UNIT 5 BLOCK:8 periods What does it mean to belong to the family of quadrilaterals? TRADITIONAL: 12 periods KEY CONCEPT FOCUS CONTENT BENCHMARKS 1. Quadrilaterals are named, Key Concept 1 MA.912.G.3.1 described, and classified based on Defining and classifying the relative lengths of their sides quadrilaterals MA.912.G.3.2 and the measures of their angles. Exploring the hierarchy of Quadrilaterals MA.912.G.3.3 MA.912.G.3.4 2. You can use ordinary proofs and Key Concept 2 coordinate geometry proofs to Examining the properties of MA.912.G.4.8 prove properties of parallelograms parallelograms. Proving quadrilaterals are LA.1112.1.6.1 parallelograms Using coordinate geometry to LA.1112.1.6.5 prove properties of congruent, regular, and similar quadrilaterals 3. You can use ordinary proofs and Key Concept 3 coordinate geometry proofs to Examining the properties of prove properties of rhombi, rhombi, rectangles, squares, rectangles, squares, trapezoids, trapezoids, and kites and kites. Comparing and contrasting special quadrilaterals on the basis of their properties Using coordinate geometry to prove properties of congruent, regular, and similar quadrilaterals CORE RESOURCE(S): Pearson Geometry Florida Edition Chapter 6 UNIT PERFORMANCE ASSESSMENT: Students will draw from several resources in order to compile a collection of images of quadrilaterals in the real world. Students will use these images to illustrate and prove the properties of quadrilaterals. Unit 5 will continue into the Third Quarter Geometry Honors ROADMAP 5 THIRD QUARTER UNIT 6 BLOCK:5 periods How can polygons, transformations, and tessellations be used to produce works of art? TRADITIONAL: 8 periods KEY CONCEPT FOCUS CONTENT BENCHMARKS 1. The sum of the measures of the Key Concept 1 MA.912.D.9.3 interior angles of a polygon Convex, concave, regular, and depends on its number of sides, irregular polygons MA.912.G.2.4 but the sum of the measures of Measures of the interior angles its exterior angles does not. of regular and irregular polygons MA.912.G.2.6 Sums of the measures of the exterior angles of polygons LA.1112.1.6.1 Applications of properties of congruent polygons to solve LA.1112.1.6.5 mathematical or real-world problems Tessellations 2. The image of a shape created by Key Concept 2 a translation, reflection, or Translations rotation is congruent to the Reflections original shape. Rotations Applications of translations, reflections, and rotations to polygons to determine congruence 3. Line symmetry, rotational Key Concept 3 symmetry, and tessellations are Line symmetry used in works of art. Rotational symmetry CORE RESOURCE(S): Pearson Geometry Florida Edition Chapter 9 (9-1, 9-2, 9-3, 9-4, 9-6, 9-7) UNIT PERFORMANCE ASSESSMENT: Students will use regular polygons, transformations, and tessellations to create marketing products. 6 MANATEE CORE CURRICULUM UNIT 7 BLOCK:6 periods What does it mean for two objects or ideas to be similar? TRADITIONAL: 9 periods KEY CONCEPT FOCUS CONTENT BENCHMARKS 1. You can use AA Similarity Key Concept 1 MA.912.D.11.5 Postulate to prove that two Corresponding parts of similar triangles are similar. polygons MA.912.G.2.3 Scale factors AA Similarity Postulate MA.912.G.2.6 Similar triangles in real-world problems MA.912.G.4.5 2. You can use SSS and SAS Key Concept 2 MA.912.G.5.2 Similarity Theorems to prove SSS and SAS Similarity Theorems that two triangles are similar. Similar triangles in real-world MA.912.G.8.3 problems Midsegment Theorem LA.1112.1.6.1 3. Drawing a line through a triangle Key Concept 3 LA.1112.1.6.5 parallel to one side creates Triangle Proportionality Theorem segments with special and its converse properties. Other theorem involving segments divided proportionally 4. The image of a shape created by Key Concept 4 dilation is similar to the original Dilations shape. Perspective drawings CORE RESOURCE(S): Pearson Geometry Florida Edition Chapters 7 and 9 (9-5). UNIT PERFORMANCE ASSESSMENT: Students will use similarity to verify methods of creating enlargements. They will explore pantographs and use dilations to create billboards and business cards for a client. Geometry Honors ROADMAP 7 UNIT 8 BLOCK: 8 periods How can you find the length of a side of a right triangle? TRADITIONAL: 12 periods KEY CONCEPT FOCUS CONTENT BENCHMARKS 1. In any right triangle, there is an Key Concept 1 MA.912.G.2.3 important relationship, called Applying the Pythagorean the Pythagorean Theorem, Theorem and its converse MA.912.G.5.1 When c < a + b , the triangle is 2 2 2 between the lengths of the legs 2 2 2 and of the length of the acute. When c > a + b , the MA.912.G.5.3 hypotenuse. triangle is obtuse. Expressing the lengths of the MA.912.G.5.4 sides of right triangles in terms of radicals in simplest form and with MA.912.T.2.1 decimal approximations LA.1112.1.6.1 2. There are special relationships Key Concept 2 between the lengths of the sides Relationships that exist when the LA.1112.1.6.5 of 30°–60°–90° and 45°–45°–90° altitude is drawn to the triangles. hypotenuse of a right triangle Use special right triangles to solve real-world problems 3. You can use the basic Key Concept 3 trigonometric functions to solve Defining “sine,” “cosine,” and real-world problems. “tangent,” and using them to solve real-world problems (including problems about finding the height of an object and problems involving an angle of elevation and an angle of depression) 4. You can use the inverse functions Key Concept 4 of the basic trigonometric Defining “inverse sine,” “inverse functions to solve real-world cosine,” and “inverse tangent” problems. Using the basic trigonometric functions and their inverses to solve real-world problems (including problems about finding an angle of elevation or an angle of depression) 5. Vectors need a magnitude and a Key Concept 5 direction. Vectors CORE RESOURCE(S): Pearson Geometry Florida Edition Chapters 7 (7-4) and 8. UNIT PERFORMANCE ASSESSMENT: Students will use special right triangles and trigonometric functions to solve problems related to structures. 8 MANATEE CORE CURRICULUM FOURTH QUARTER UNIT 9 BLOCK:8 periods What happens to the perimeter and area of a polygon when you enlarge it? TRADITIONAL: 12 periods KEY CONCEPT FOCUS CONTENT BENCHMARKS 1. You can use formulas for the Key Concept 1 MA.912.G.2.5 area of a rectangle and a Areas of rectangles and squares parallelogram to develop Areas of parallelograms and MA.912.G.2.7 formulas for the areas of other triangles polygons, circles, and sectors of Areas of trapezoids and MA.912.G.6.2 circles. rhombuses Areas of regular polygons MA.912.G.6.4 Using properties of congruent and similar triangles to solve MA.912.G.6.5 problems involving areas Meaning of circle, radius, LA.1112.1.6.1 diameter, circumference Finding the circumference of a LA.1112.1.6.5 circle Finding the area of a circle and sectors of a circle 2. The ratio of the perimeters of Key Concept 2 similar polygons is equal to the Perimeters of rectangles, scale factor (similarity ratio) of squares, and other polygons the polygons and the ratio of Using properties of congruent their areas is a2:b2, where a:b is and similar triangles to solve the scale factor. problems involving lengths and areas Relationship of the perimeters of similar figures Relationship of the areas of similar figures Determining how changes in dimensions affect the perimeter and area of rectangles when one dimension is scaled up but the other one is not CORE RESOURCE(S): Pearson Geometry Florida Edition Chapter 10. UNIT PERFORMANCE ASSESSMENT: Students will find the amount of baseboard and the amount of carpeting needed for rooms of various shapes and find the cost for those materials. Students will use a scale factor to find the perimeter and area of a room that is an enlargement of one of the original rooms. Geometry Honors ROADMAP 9 UNIT 10 BLOCK:8 periods What are the relationships between two-dimensional and three dimensional figures? TRADITIONAL: 12 periods KEY CONCEPT FOCUS CONTENT BENCHMARKS 1. You can describe polyhedra in Key Concept 1 MA.912.G.7.2 terms of their faces, vertices and Cutting out the net for various edges. polyhedra, cones, and cylinders; MA.912.G.7.3 then folding, and taping to model the polyhedron MA.912.G.7.5 Sketching the net for a given polyhedron and vice versa MA.912.G.7.6 Describing and making regular, non-regular, and oblique MA.912.G.7.7 polyhedra The relationship between the LA.1112.1.6.1 number of faces, edges, and vertices of polyhedra (Euler’s LA.1112.1.6.5 formula) 2. Most formulas for the volume of Key Concept 2 a three-dimensional solid are Spheres; chords, tangents, radii, based on the formula V = Bh, and great circles of spheres where B is the base of the solid Volume of prisms, cylinders, and h is its height. pyramids, cones, and spheres Identifying and using properties of congruent three-dimensional solids 3. The formulas for the surface Key Concept 3 areas and lateral areas of prisms, Surface area of prisms, cylinders, cylinders, pyramids, and cones pyramids, cones, and spheres are based on the formulas for Lateral area of prisms, pyramids, the area of polygons and circles. cylinders, and cones. Key Concept 4 4. The ratio of the surface areas of Determining how changes in similar solids is a2:b2, and the dimensions affect the surface ratio of their volumes is a3:b3, area and volume of common where a:b is the scale factor three-dimensional geometric (similarity ratio) of the solids. solids Relationship of the surface areas of similar three-dimensional solids Relationship of the volumes of similar three-dimensional solids CORE RESOURCE(S): Pearson Geometry Florida Edition Chapter 11. UNIT PERFORMANCE ASSESSMENT: Students will make and describe several polyhedra representing real-world objects and make and check predictions about the surface area and volume of the polyhedra. 10 MANATEE CORE CURRICULUM UNIT 11 BLOCK:5 periods How can you describe circles and the angles created by chords, secants, and tangents? TRADITIONAL: 8 periods KEY CONCEPT FOCUS CONTENT BENCHMARKS 1. Angles drawn through or Key Concept 1 MA.912.G.6.1 alongside circles divide them in Meaning of arc, arc length, chord, different ways. secant, tangent, concentric MA.912.G.6.3 circles Finding arc length MA.912.G.6.6 Using the definition of the measure of an arc in terms of the MA.912.G.6.7 measure of its central angle Using the relationship between LA.1112.1.6.1 the measure of an inscribed angle and the arc it intercepts LA.1112.1.6.5 Using the relationships between the measures of angles created by intersections of tangents and secants and the arcs they intercept Key Concept 2 2. You can use the Pythagorean Given the center and the radius Theorem to find the equation of of a circle, sketch the graph of any circle. the circle Given the equation of a circle in center-radius form, sketch the graph of the circle Given the center and the radius, find the equation of a circle in the coordinate plane Given the equation of a circle in center-radius form, state the center and the radius of the circle Finding the locus CORE RESOURCE(S): Pearson Geometry Florida Edition Chapter 12. UNIT PERFORMANCE ASSESSMENT: Students will complete a project about the geometry in the world around them by drawing on what they have learned throughout the course. Geometry Honors ROADMAP 11

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