78228ISISBN 978-0-7406-9565-0

FLORIDAGEOMETRYEOC TOOLKIT CORRELATIONCorrelated to the Geometry End-of-Course Benchmarks

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2

Geometry EOC Benchmarks Daily Warm-Ups: Geometry Geometry Teacher’s Activities Kit

Investigating with Relational GeoSolids Illuminations.nctm.org VersaTiles® Geometry

MA.912.D.6.2 Find the converse, inverse, and contrapositive of a statement. (Also assesses MA.912.D.6.3.)

Daily Warm-Up 28 Conditional Statements (AngLegs)

Activity 1:24 If-Then Statements (converse only)

Book 1 pages 12–13 Converse, Inverse, and Contrapositive

MA.912.D.6.3 Determine whether two propositions are logically equivalent. (Assessed with MA.912.D.6.2.)

Daily Warm-Up 28 Conditional Statements (AngLegs)

Activity 1:24 If-Then Statements (converse only)

Book 1 page 15 Conditionals and Logical Equivalents

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 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

Daily Warm-Up 40 Corresponding Parts of Congruent Triangles

Book 1 pages 16–17 Laws of Logic and Indirect Proof

MA.912.G.1.1 Find the lengths and midpoints of line segments in two-dimensional 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)

MA.912.G.1.3 Identify and use the relationships between special pairs of angles formed by parallel lines and transversals.

Daily Warm-Up 13 Complementary Angles and Complements (AngLegs)

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

Daily Warm-Up 27 Alternate Interior and Alternate Exterior 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

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)

3

Geometry EOC Benchmarks Daily Warm-Ups: Geometry Geometry Teacher’s Activities Kit

Investigating with Relational GeoSolids Illuminations.nctm.org VersaTiles® Geometry

MA.912.G.2.2 Determine the measures of interior and exterior angles of polygons, justifying the method used.

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

Activity 3:5 Finding the Sum of the Interior Angles of a Polygon

Activity 3:20 The Big Quadrilateral Puzzle

Book 2 page 19 Angles in Polygons

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.)

Daily Warm-Up 52 Similar Polygons

Daily Warm-Up 53 Congruent Polygons

Daily Warm-Up 54 Corresponding Vertices

Daily Warm-Up 55 Corresponding Sides

Book 2 pages 20–21 Congruent and Similar Polygons

Book 4 page 21 Quadrilateral Query

Book 4 pages 22–23 Polygon Plot

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.

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

Activity 3:23 The Basics of Transformations (XY Coordinate Pegboard)

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

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.)

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

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)

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

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.)

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 24 Those Changing Dimensions

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 47 Rectangles

Daily Warm-Up 48 Squares

Daily Warm-Up 49 Rhombuses

Activity 2:15 Sorting Quadrilaterals

Activity 2:16 Charts and Quadrilaterals

Activity 3:18 Classifying Quadrilaterals

4

Geometry EOC Benchmarks Daily Warm-Ups: Geometry Geometry Teacher’s Activities Kit

Investigating with Relational GeoSolids Illuminations.nctm.org VersaTiles® Geometry

MA.912.G.3.2 Compare and contrast special quadrilaterals on the basis of their properties. (Assessed with MA.912.G.3.4.)

Activity 3:17 Attributes of Quadrilaterals

Activity 3:22 Identifying Attributes of Quadrilaterals

Book 1 page 24 Special Quadrilaterals

MA.912.G.3.3 Use coordinate geometry to prove properties of congruent, regular, and similar quadrilaterals.

Lessons for instruction on this specific standard can be found on illumations.nctm.org.

Book 4 page 21 Quadrilateral Query

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.)

Activity 3:19 Diagonals of Quadrilaterals

Activity 3:20 The Big Quadrilateral Puzzle

Activity 3:21 The Bigger Quadrilateral Puzzle

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.)

Daily Warm-Up 30 Classifying Triangles by Sides

Daily Warm-Up 31 Classifying Triangles by Angles

Activity 2:7 Try your Hand at Drawing Triangles

Activity 3:9 Attributes of Triangles

Book 1 page 18 Name That Triangle

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.)

Daily Warm-Up 12 Bisector of an Angle

Daily Warm-Up 44 Isosceles Triangles: Median and Altitude

Activity 3:7 Medians of Triangles

Book 1 page 20 Altitudes, Bisectors, and Medians

Book 1 page 21 Triangle Relationships

Book 1 pages 22–23 Medians, Altitudes, and Bisectors

MA.912.G.4.3 Construct triangles congruent to given triangles. (Not assessed.)

Not assessed independently, but lessons for this skill can be found on illumations.nctm.org.

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.)

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

Activity 3:13 Identifying What is Needed to Prove Triangles are Congruent

Activity 3:14 Proving Triangles Similar

Book 2 pages 2–3 Opposites Attract

MA.912.G.4.5 Apply theorems involving segments divided proportionally. (Assessed with MA.912.G.2.3.)

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

Book 2 page 9 Proportional Segments

5

Geometry EOC Benchmarks Daily Warm-Ups: Geometry Geometry Teacher’s Activities Kit

Investigating with Relational GeoSolids Illuminations.nctm.org VersaTiles® Geometry

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.)

Daily Warm-Up 40 Corresponding Parts of Congruent Triangles

Activity 3:13 Identifying What is Needed to Prove Triangles are Congruent

Activity 3:14 Proving Triangles Similar

Book 2 pages 4–5 Proving Triangles Congruent

Book 2 page 6 CPCTC

Book 2 page 7 Oh, So Similar

MA.912.G.4.7 Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem.

Activity 3:10 What Type of Triangle?

Book 2 page 1 To Be or Not To Be a Triangle?

MA.912.G.5.1 Prove and apply the Pythagorean Theorem and its converse. (Assessed with MA.912.G.5.4.)

Daily Warm-Up 50 The Pythagorean Theorem

Daily Warm-Up 57 Pythagorean Triples

Daily Warm-Up 58 Converse of the Pythagorean Theorem

Activity 3:11 Right Triangles and Special Right Triangles

Book 2 page 8 The Pythagorean Theorem

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.)

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.

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.)

Daily Warm-Up 59 Special Right Triangles 1

Daily Warm-Up 60 Special Right Triangles 2

Activity 3:11 Right Triangles and Special Right Triangles

Book 2 pages 14–15 Special Right Triangles

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.)

Daily Warm-Up 109 Angle of Depression

Activity 6:2 Finding Perimeter - Fencing a Yard

Book 2 pages 16–17 Angles of Elevation and Depression

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.)

Daily Warm-Up 65 Concentric Circles

Daily Warm-Up 79 Circumference of a Circle

Daily Warm-Up 166 Chord and Diameter of a Circle

Activity 4:1 Crossword Puzzle of Circle Vocabulary

Book 5 page 1 Parts of Circles

Book 5 pages 6–7 Segment Lengths

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.)

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 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)

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

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Geometry EOC Benchmarks Daily Warm-Ups: Geometry Geometry Teacher’s Activities Kit

Investigating with Relational GeoSolids Illuminations.nctm.org VersaTiles® Geometry

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.)

Daily Warm-Up 79 Circumference of a Circle

Daily Warm-Up 80 Area of a Circle

Book 5 pages 2–3 Circumference and Area of Circles

Book 5 pages 4–5 Around the Bend

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.)

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 page 16 Equations of Circles

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.)

Activity 4:12 Circles and Coordinate Geometry

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-:1 Visualizing with Pentominoes

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 GeoSolids)

Investigation 5: How Do You Find the Surface Area of a Solid? (Relational GeoSolids)

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 GeoSolids)

Investigation 7: What Patterns Exist Among Vertices, Faces, and Edges? (Relational GeoSolids)

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

Investigation 5: How Do You Find the Surface Area of a Solid? (Relational GeoSolids)

Book 3 page 16 On the Ball

7

Geometry EOC Benchmarks Daily Warm-Ups: Geometry Geometry Teacher’s Activities Kit

Investigating with Relational GeoSolids Illuminations.nctm.org VersaTiles® Geometry

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.)

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

Activity 6:7 Surface Area and Wrapping Paper

Activity 6:8 Volumes of Containers (Relational GeoSolids and SAGE Kit)

Investigation 5: How Do You Find the Surface Area of a Solid? (Relational GeoSolids)

Investigation 8: How Do You Find the Volumes of Prisms and Cylinders? (Relational GeoSolids)

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

MA.912.G.7.6 Identify and use properties of congruent and similar solids. (Assessed with MA.912.G.7.5.)

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 pages 18–19 Congruent and Similar Solids

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.)

Activity 6:9 Surface Area and Volume of A Rectangular Prism

Investigation 8: How Do You Find the Volumes of Prisms and Cylinders? (Relational GeoSolids)

Investigation 9: How Do the Volumes of Different Solids Relate? (Relational GeoSolids)

Book 3 pages 22–23 Out and About

Book 3 page 24 Dynamic Dimensions

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.)

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

MA.912.G.8.2 Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards. (Embedded throughout.)

Daily Warm-Up 67 Circles: Central Angles Embedded throughout activities.

8

Geometry EOC Benchmarks Daily Warm-Ups: Geometry Geometry Teacher’s Activities Kit

Investigating with Relational GeoSolids Illuminations.nctm.org VersaTiles® Geometry

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.

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 99 Sine Ratio

Daily Warm-Up 100 Cosine Ratio

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