FLORIDA GEOMETRY EOC TOOLKIT CORRELATION Correlated to the Geometry End-of-Course Benchmarks For more information, go to etacuisenaire.com\florida 78228IS ISBN 978-0-7406-9565-0
MA.912.D.6.2 Find the converse, inverse, and contrapositive of a statement. (Also assesses MA.912.D.6.3.) MA.912.D.6.3 Determine whether two propositions are logically equivalent. (Assessed with MA.912.D.6.2.) MA.912.D.6.4 Use methods of direct and indirect proof and determine whether a short proof is logically valid. (Assessed with MA.912.G.3.4 and MA.912.G.4.6.) Daily Warm-Up 28 Conditional Statements (AngLegs) Daily Warm-Up 28 Conditional Statements (AngLegs) Daily Warm-Up 19 Statement and Reasoning Proof 1 Daily Warm-Up 20 Statement and Reasoning Proof 2 Daily Warm-Up 24 Formal Proof Daily Warm-Up 29 Indirect Proof Activity 1:24 If-Then Statements (converse only) Activity 1:24 If-Then Statements (converse only) Book 1 pages 12 13 Converse, Inverse, and Contrapositive Book 1 page 15 Conditionals and Logical Equivalents Book 1 pages 16 17 Laws of Logic and Indirect Proof Daily Warm-Up 40 Corresponding Parts of Congruent Triangles MA.912.G.1.1 Find the lengths and midpoints of line segments in twodimensional coordinate systems. Daily Warm-Up 8 Midpoint of a Line Segment Book 4 page 2 Halfway There Book 4 page 3 The End Is in Sight MA.912.G.1.2 Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straightedge and compass or a drawing program, explaining and justifying the process used. (Not assessed.) Activity 1:22 Angles and Transversals (AngLegs) Activity 1:23 Parallel Lines and Transversals (AngLegs) Activity 3:1 Polygons and Lines of Symmetry (Double Sided Geoboards) Daily Warm-Up 13 Complementary Angles and Complements (AngLegs) MA.912.G.1.3 Identify and use the relationships between special pairs of angles formed by parallel lines and transversals. Daily Warm-Up 14 Supplementary Angles and Supplements (AngLegs) Daily Warm-Up 15 Vertical Angles (AngLegs) Daily Warm-Up 25 Transversals, Interior Angles, and Exterior Angles Daily Warm-Up 26 Corresponding Angles Activity 1:23 Parallel Lines and Transversals (AngLegs) Activity 3:12 The Bigger Quadrilateral Puzzle Book 1 pages 4 5 Aren t These Angle Pairs Special? Book 1 pages 6 7 Using Algebra with Parallel and Perpendicular Lines Book 1 page 8 All About Angles Book 1 page 9 Angle Pairs Daily Warm-Up 27 Alternate Interior and Alternate Exterior Angles MA.912.G.2.1 Identify and describe convex, concave, regular, and irregular polygons. (Assessed with MA.912.G.2.3.) Daily Warm-Up 32 Convex and Concave Polygons Daily Warm-Up 35 Regular and Irregular Polygons Activity 2:3 Concave and Convex Polygons (Tangrams) 2
MA.912.G.2.2 Determine the measures of interior and exterior angles of polygons, justifying the method used. MA.912.G.2.3 Use properties of congruent and similar polygons to solve mathematical or real- world problems. (Also assesses MA.912.G.2.1, MA.912.G.4.1, MA.912.G.4.2, MA.912.G.4.4, MA.912.G.4.5.) MA.912.G.2.4 Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent to the original shape. Create and verify tessellations of the plane using polygons. MA.912.G.2.5 Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons, etc.). (Also assesses MA.912.G.2.7.) MA.912.G.2.7 Determine how changes in dimensions affect the perimeter and area of common geometric figures. (Assessed with MA.912.G.2.5 and MA.912.G.7.7.) MA.912.G.3.1 Describe, classify, and compare relationships among quadrilaterals including the square, rectangle, rhombus, parallelogram, trapezoid, and kite. (Assessed with MA.912.G.3.4.) Daily Warm-Up 34 Sum of Interior Angles of a Polygon Daily Warm-Up 51 Trapezoids Daily Warm-Up 76 Measure of an Interior Angle of a Regular Polygon Daily Warm-Up 52 Similar Polygons Daily Warm-Up 53 Congruent Polygons Daily Warm-Up 54 Corresponding Vertices Daily Warm-Up 55 Corresponding Sides Daily Warm-Up 129 Transformations: Translations Daily Warm-Up 130 Transformations: Reflections (XY Coordinate Pegboard) Daily Warm-Up 131 Glide Reflections (XY Coordinate Pegboard) Daily Warm-Up 132 Transformations: Rotations Daily Warm-Up 171 Area of a Rectangle Daily Warm-Up 172 Area of a Parallelogram Daily Warm-Up 173 Perimeter of a Quadrilateral Daily Warm-Up 174 Area of a Rhombus Daily Warm-Up 47 Rectangles Daily Warm-Up 48 Squares Daily Warm-Up 49 Rhombuses Activity 3:5 Finding the Sum of the Interior Angles of a Polygon Activity 3:20 The Big Quadrilateral Puzzle Activity 3:23 The Basics of Transformations (XY Coordinate Pegboard) Activity 6:2 Finding Perimeter - Fencing a Yard Activity 6:4 Finding Area - Tiling a Floor Activity 6:5 Finding Area - Fertilizing a Lawn Activity 6:6 Comparing Areas Activity 6:12 Creating Problems and Applying Formulas (Advanced) Activity 2:15 Sorting Activity 2:16 Charts and Activity 3:18 Classifying Lessons for instruction on this specific standard can be found on illumations.nctm.org. Also, this skill can be embedded into the instruction of MA.912.G.2.5 and MA.912.G.7.7. Book 2 page 19 Angles in Polygons Book 2 pages 20 21 Congruent and Similar Polygons Book 4 page 21 Quadrilateral Query Book 4 pages 22 23 Polygon Plot Book 1 pages 10 11 Moving Around Book 4 page 14 Translations Book 4 page 15 Reflections Book 4 pages 16 17 Rotations Book 4 pages 18 19 Dilations Book 4 page 20 Double Transformations Book 2 pages 22 23 Area and Perimeter Formulas Book 4 pages 10 11 Around the Edge Book 4 pages 12 13 Areas of Rectangles and Triangles Book 2 page 24 Those Changing Dimensions 3
MA.912.G.3.2 Compare and contrast special quadrilaterals on the basis of their properties. (Assessed with MA.912.G.3.4.) MA.912.G.3.3 Use coordinate geometry to prove properties of congruent, regular, and similar quadrilaterals. MA.912.G.3.4 Prove theorems involving quadrilaterals. (Also assesses MA.912.D.6.4, MA.912.G.3.1, MA.912.G.3.2, and MA.912.G.8.5.) MA.912.G.4.1 Classify, construct, and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular. (Assessed with MA.912.G.2.3.) MA.912.G.4.2 Define, identify, and construct altitudes, medians, angle bisectors, perpendicular bisectors, orthocenter, centroid, incenter, and circumcenter. (Assessed with MA.912.G.2.3.) MA.912.G.4.3 Construct triangles congruent to given triangles. (Not assessed.) MA.912.G.4.4 Use properties of congruent and similar triangles to solve problems involving lengths and areas. (Assessed with MA.912.G.2.3.) MA.912.G.4.5 Apply theorems involving segments divided proportionally. (Assessed with MA.912.G.2.3.) Activity 3:17 Attributes of Activity 3:22 Identifying Attributes of Daily Warm-Up 30 Classifying Triangles by Sides Daily Warm-Up 31 Classifying Triangles by Angles Daily Warm-Up 12 Bisector of an Angle Daily Warm-Up 44 Isosceles Triangles: Median and Altitude Daily Warm-Up 36 The SSS Method Daily Warm-Up 37 The SAS Method Daily Warm-Up 38 The ASA Method Daily Warm-Up 39 The AAS Method Daily Warm-Up 56 Proving Triangles Similar Daily Warm-Up 61 Segments Divided Proportionally: Lines Daily Warm-Up 62 Segments Divided Proportionally: Triangles Daily Warm-Up 63 Segments Divided Proportionally: Parallel Lines and Transversals Activity 3:19 Diagonals of Activity 3:20 The Big Quadrilateral Puzzle Activity 3:21 The Bigger Quadrilateral Puzzle Activity 2:7 Try your Hand at Drawing Triangles Activity 3:9 Attributes of Triangles Activity 3:7 Medians of Triangles Activity 3:13 Identifying What is Needed to Prove Triangles are Congruent Activity 3:14 Proving Triangles Similar Lessons for instruction on this specific standard can be found on illumations.nctm.org. Not assessed independently, but lessons for this skill can be found on illumations.nctm.org. Book 1 page 24 Special Book 4 page 21 Quadrilateral Query Book 1 page 18 Name That Triangle Book 1 page 20 Altitudes, Bisectors, and Medians Book 1 page 21 Triangle Relationships Book 1 pages 22 23 Medians, Altitudes, and Bisectors Book 2 pages 2 3 Opposites Attract Book 2 page 9 Proportional Segments 4
MA.912.G.4.6 Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles. (Also assesses MA.912.D.6.4 and MA.912.G.8.5.) MA.912.G.4.7 Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem. MA.912.G.5.1 Prove and apply the Pythagorean Theorem and its converse. (Assessed with MA.912.G.5.4.) MA.912.G.5.2 State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle. (Assessed with MA.912.G.5.4.) MA.912.G.5.3 Use special right triangles (30-60 - 90 and 45-45 - 90 ) to solve problems. (Assessed with MA.912.G.5.4.) MA.912.G.5.4 Solve real-world problems involving right triangles. (Also assesses MA.912.G.5.1, MA.912.G.5.2, MA.912.G.5.3.) MA.912.G.6.2 Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles. (Assessed with MA.912.G.6.5.) MA.912.G.6.4 Determine and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents). (Assessed with MA.912.G.6.5.) Activity 3:13 Identifying What is Needed to Prove Triangles Daily Warm-Up 40 Corresponding are Congruent Parts of Congruent Triangles Activity 3:14 Proving Triangles Similar Daily Warm-Up 50 The Pythagorean Theorem Daily Warm-Up 57 Pythagorean Triples Daily Warm-Up 58 Converse of the Pythagorean Theorem Daily Warm-Up 59 Special Right Triangles 1 Daily Warm-Up 60 Special Right Triangles 2 Daily Warm-Up 109 Angle of Depression Daily Warm-Up 65 Concentric Circles Daily Warm-Up 79 Circumference of a Circle Daily Warm-Up 166 Chord and Diameter of a Circle Daily Warm-Up 78 Arc of a Circle Daily Warm-Up 168 Tangent of a Circle Daily Warm-Up 169 Secant of a Circle Daily Warm-Up 170 Tangent Circles Activity 3:10 What Type of Triangle? Activity 3:11 Right Triangles and Special Right Triangles Activity 3:11 Right Triangles and Special Right Triangles Activity 6:2 Finding Perimeter - Fencing a Yard Activity 4:1 Crossword Puzzle of Circle Vocabulary Activity 4:7 Circles: Symbols of Segments and Angles (Double-Sided Geoboards) Activity 4:8 The Big Circle Puzzle (Double-Sided Geoboards) Activity 4:9 The Bigger Circle Puzzle (Double-Sided Geoboards) Activity 4:10 The Biggest Circle Puzzle (Double-Sided Geoboards) Lessons for instruction on this specific standard can be found on illumations.nctm. org. Also, this skill can be embedded into the instruction of MA.912.G.5.4. Book 2 pages 4 5 Proving Triangles Congruent Book 2 page 6 CPCTC Book 2 page 7 Oh, So Similar Book 2 page 1 To Be or Not To Be a Triangle? Book 2 page 8 The Pythagorean Theorem Book 2 pages 14 15 Special Right Triangles Book 2 pages 16 17 Angles of Elevation and Depression Book 5 page 1 Parts of Circles Book 5 pages 6 7 Segment Lengths Book 5 pages 8 9 Angle Properties Book 5 pages 10 11 Arc and Angle Measures Book 5 page 17 Circle Graphs and Central Angles 5
MA.912.G.6.5 Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors. (Also assesses MA.912.G.6.2 and MA.912.G.6.4.) MA.912.G.6.6 Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle. (Also assesses MA.912.G.6.7.) MA.912.G.6.7 Given the equation of a circle in center-radius form or given the center and the radius of a circle, sketch the graph of the circle. (Assessed with MA.912.G.6.6.) Daily Warm-Up 79 Circumference of a Circle Daily Warm-Up 80 Area of a Circle Activity 4:12 Circles and Coordinate Geometry Activity 5-:1 Visualizing with Pentominoes Lessons for instruction on this specific standard can be found on illumations.nctm.org. Also, this skill can be embedded into the instruction of MA.912.G.6.7. Book 5 pages 2 3 Circumference and Area of Circles Book 5 pages 4 5 Around the Bend Book 5 page 16 Equations of Circles Book 5 pages 14 15 A Round of Graphing MA.912.G.7.1 Describe and make regular, non-regular, and oblique polyhedra, and sketch the net for a given polyhedron and vice versa. (Also assesses MA.912.G.7.2.) Activity 5:4 Creating Prisms from Nets Activity 5:5 Constructing Nets and Regular Pyramids (Relational GeoSolids and SAGE Kit) Activity 5:8 Creating Three-Dimensional Models (AngLegs and Relational GeoSolids and SAGE Kit) Investigation 3: How Do you Make a Net for a Solid? (Relational Investigation 5: How Do You Find the Surface Area of a Solid? (Relational Book 3 page 1 Naming Three-Dimensional Figures Book 3 pages 2 3 Nothing but Net MA.912.G.7.2 Describe the relationships between the faces, edges, and vertices of polyhedra. (Assessed with MA.912.G.7.1.) Daily Warm-Up 96 Properties of Polyhedrons Activity 5:2 Opposite Faces of a Cube Activity 5:6 Platonic Solids Investigation 2: How Do You Make a Key? (Relational Investigation 7: What Patterns Exist Among Vertices, Faces, and Edges? (Relational Investigation 5: How Do You Find the Surface Area of a Solid? (Relational Book 3 page 6 Euler s Formula MA.912.G.7.4 Identify chords, tangents, radii, and great circles of spheres. (Assessed with MA.912.G.7.5.) Activity 4:6 Tangents: Circles and Lines Book 3 page 16 On the Ball 6
MA.912.G.7.5 Explain and use formulas for lateral area, surface area, and volume of solids. (Also assesses MA.912.G.7.4, MA.912.G.7.6.) MA.912.G.7.6 Identify and use properties of congruent and similar solids. (Assessed with MA.912.G.7.5.) MA.912.G.7.7 Determine how changes in dimensions affect the surface area and volume of common geometric solids. (Also assesses MA.912.G.2.7.) MA.912.G.8.1 Analyze the structure of Euclidean geometry as an axiomatic system. Distinguish between undefined terms, definitions, postulates, and theorems. (Embedded throughout.) MA.912.G.8.2 Use a variety of problemsolving strategies, such as drawing a diagram, making a chart, guess-andcheck, solving a simpler problem, writing an equation, and working backwards. (Embedded throughout.) Daily Warm-Up 86 Lateral Area of a Prism Daily Warm-Up 88 Volume of a Right Rectangular Prism Daily Warm-Up 90 Lateral Area of a Pyramid Daily Warm-Up 91 Volume of a Pyramid Daily Warm-Up 92 Surface Area of a Cylinder Daily Warm-Up 93 Volume of a Cylinder Daily Warm-Up 94 Surface Area of a Cone Daily Warm-Up 95 Volume of a Cone Daily Warm-Up 97 Surface Area of a Sphere Daily Warm-Up 98 Volume of a Sphere Daily Warm-Up 67 Circles: Central Angles Activity 6:7 Surface Area and Wrapping Paper Activity 6:8 Volumes of Containers (Relational GeoSolids and SAGE Kit) Activity 6:9 Surface Area and Volume of A Rectangular Prism Embedded throughout activities. Specific examples follow: Activity 2:8 Angles of Triangles Activity 3:14 Proving Triangles Similar Activity 4:11 Explain the Reason-Circles Investigation 5: How Do You Find the Surface Area of a Solid? (Relational Investigation 8: How Do You Find the Volumes of Prisms and Cylinders? (Relational Investigation 8: How Do You Find the Volumes of Prisms and Cylinders? (Relational Investigation 9: How Do the Volumes of Different Solids Relate? (Relational Lessons for instruction on this specific standard can be found on illumations.nctm.org. Also, this skill can be embedded into the instruction of MA.912.G.7.5. Book 3 page 7 Volume of Prisms Book 3 pages 8 9 Volume of Pyramids Book 3 page 10 Volume of Cylinders Book 3 page 11 Volume of Cones Book 3 pages 12 13 Surface Area of Prisms and Cylinders Book 3 pages 14 15 Surface Area of Pyramids and Cones Book 3 page 17 Surface Area and Volume of Spheres Book 3 pages 18 19 Congruent and Similar Solids Book 3 pages 22 23 Out and About Book 3 page 24 Dynamic Dimensions Embedded throughout activities. 7
MA.912.G.8.3 Determine whether a solution is reasonable in the context of the original situation. (Embedded throughout.) Embedded throughout activities. MA.912.G.8.4 Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture. Embedded throughout activities. Embedded throughout activities. MA.912.G.8.5 Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and indirect proofs. (Assessed with MA.912.G.3.4 and MA.912.G.4.6.) Embedded throughout activities. MA.912.G.8.6 Perform basic constructions using straightedge and compass, and/or drawing programs describing and justifying the procedures used. Distinguish between sketching, constructing, and drawing geometric figures. (Not assessed.) Embedded throughout activities. Daily Warm-Up 99 Sine Ratio Daily Warm-Up 100 Cosine Ratio MA.912.T.2.1 Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right triangles. Daily Warm-Up 101 Tangent Ratio Daily Warm-Up 102 Cosecant Ratio Daily Warm-Up 103 Secant Ratio Daily Warm-Up 104 Cotangent Ratio Daily Warm-Up 105 Area of an Acute Triangle Using Sine Daily Warm-Up 106 Law of Sines Daily Warm-Up 107 Law of Cosines Activity 3:12 Explaining the Sine, Cosine, and Tangent Ratios Activity 4:15 The Circular Definitions of the Trigonometric Functions Book 2 page 12 Sine, Cosine, and Tangent Ratios Book 2 page 13 Trigonometric Ratios Book 2 page 18 Law of Sines and Law of Cosines 8