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# TN Geometry Standards - 2008-2009 Implementation

Mathematical Processes | Number & Operations | Algebra | Geometry & Measurement | Data Analysis, Statistics, and Probability | Review Help
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 Mathematical Processes Mathematics Curriculum Standards 3108 - Geometry Internet Resources Checks for Understanding (Formative/Summative Assessment) 1.1 | 1.2 | 1.3 | 1.4 | 1.5 | 1.6 | 1.7 | 1.8 | 1.9 | 1.10 1.11 | 1.12 | 1.13 | 1.14 Check solutions after making reasonable estimates in appropriate units of quantities encountered in contextual situations. 3108.1.1 � Determine position using spatial sense with two and three-dimensional coordinate systems. 3108.1.2 � Comprehend the concept of length on the number line. 3108.1.3 � Recognize that a definition depends on undefined terms and on previous definitions. 3108.1.4 � Use technology, hands-on activities, and manipulatives to develop the language and the concepts of geometry, including specialized vocabulary (e.g. graphing calculators, interactive geometry software such as Geometer�s Sketchpad and Cabri, algebra tiles, pattern blocks, tessellation tiles, MIRAs, mirrors, spinners, geoboards, conic section models, volume demonstration kits, Polydrons, measurement tools, compasses, PentaBlocks, pentominoes, cubes, tangrams). 3108.1.5 Algebra Tiles -Using tiles to represent variables and constants, learn how to represent and solve algebra problem. Graphing Calculator Tutorials - from Texas Instruments T1-83 and 84- Free online courses using these in your classroom Calculators On-Line�provides links to almost 7000 calculators Easy Calculation�offers several types of calculators How Old Are You?�- use this calculator to see how many years, months, days, minutes or seconds you are old.� Graphing Calculator Tutorials�from Texas Instruments Metric Conversion�- includes; length, area, volume, mass, force, pressure, work, power, temperature, and fuel mileage Creating Tessellations Using Microsoft Paint Tessellate!�- an interactive device for making a tessellation Tessellation Tutorials�- Tutorials and templates for making your own tessellations Tessellations�- Step by step with "Paintbrush" or "Paint". [Note: this document was retrieved from the Internet Archive known as theWayback Machine. The site may be blocked by school filters, so consider printing the document at home.] Tessellations Theme Page�- links to information about Tessellations What are Tessellations�- how to make them from Cool Math 4 Kids What Is a Tessellation?�- from Math Foru Use inductive reasoning to write conjectures and/or conditional statements. 3108.1.6 Inductive Reasoning - video explanation for making predictions Inductive Reasoning Examples - Find a logical sequence of five boxes. Your task is to decide which of the boxes completes this sequence. Making conjectures - video lesson Inductive Reasoning - Use inductive reasoning to make conjectures about sequences of numbers and shapes; lesson plan Recognize the capabilities and the limitations of calculators and computers in solving problems. 3108.1.7 � Understand how the similarity of right triangles allows the trigonometric functions sine, cosine, and tangent to be defined as ratio of sides. 3108.1.8 � Expand analysis of units of measure to include area and volume. 3108.1.9 � Use visualization, spatial reasoning, and geometric modeling to solve problems. 3108.1.10 � Identify and sketch solids formed by revolving two-dimensional figures around lines. 3108.1.11 � Connect the study of geometry to the historical development of geometry. 3108.1.12 � Use proofs to further develop and deepen the understanding of the study of geometry (e.g. two-column, paragraph, flow, indirect, coordinate). 3108.1.13 � Identify and explain the necessity of postulates, theorems, and corollaries in a mathematical system. 3108.1.14 � State Performance Indicators | 1.4 Give precise mathematical descriptions or definitions of geometric shapes in the plane and space. SPI 3108.1.1 Figures and Polygons - definitions and illustrations of numerous shapes. Geometry 3-D Shapes - An interactive Web site where students can learn about three-dimensional shapes, calculate surface area and volume, and discover some of the mathematical properties of shapes. Geometry Glossary - Thinkquest site that defines most of the words you'll ever need in geometry. � Determine areas of planar figures by decomposing them into simpler figures without a grid. SPI 3108.1.2 � Use geometric understanding and spatial visualization of geometric solids to solve problems and/or create drawings. SPI 3108.1.3 � Use definitions, basic postulates, and theorems about points, lines, angles, and planes to write/complete proofs and/or to solve problems. SPI 3108.1.4 �

 Number & Operations Mathematics Curriculum Standards 3108 - Geometry Internet Resources Checks for Understanding (Formative/Summative Assessment) 2.1 | 2.2 | 2.3 | 2.4 | 2.5 | 2.6 Analyze properties and aspects of pi (e.g. classical methods of approximating pi, irrational numbers, Buffon�s needle, use of dynamic geometry software). 3108.2.1 �Buffon's Needle Problem - Animated site showing this problem. Buffon's Needles Lab Report -Explore a Monte Carlo method of estimating the value of pi. Discovering pi - This particular activity allows students to discover why pi works in solving problems dealing with finding circumference. Computing Pi - Interactive tool; This activity allows for the investigation and comparison Approximate pi from a table of values for the circumference and diameter of circles using various methods (e.g. line of best fit). 3108.2.2 � Recognize and apply real number properties to vector operations and geometric proofs (e.g. reflexive, symmetric, transitive, addition, subtraction, multiplication, division, distributive, and substitution properties). 3108.2.3 � Add vectors graphically and algebraically. 3108.2.4 Learning about Properties of Vectors and Vector Sums Using Dynamic Software- Lessons that help students develop an understanding of vectors and their properties. Students manipulate a two vectors to control the movement of a plane in a gamelike setting. Vector Addition - explanation of concept. Vector Addition - Interactive site that lets students explore vector addition. Vector Addition - Interactive site; Drag two vectors around to see the sum of the vectors. The magnitude and direction of each vector can be manipulated. Components of all vectors are shown in equation form Multiply a vector by a scalar graphically and algebraically. 3108.2.5 � Analyze precision, accuracy, and approximate error in measurement situations. 3108.2.6 � State Performance Indicators Analyze, apply, or interpret the relationships between basic number concepts and geometry (e.g. rounding and pattern identification in measurement, the relationship of pi to other rational and irrational numbers) SPI 3108.2.1 � Perform operations on vectors in various representations. SPI 3108.2.2 � National Library of Virtual Manipulatives Number & Operations [Grades 9-12] Algebra Mathematics Curriculum Standards 3108 - Geometry Internet Resources Checks for Understanding (Formative/Summative Assessment) 3.1 | 3.2 | 3.3 | 3.4 | 3.5 | 3.6 Prove two lines are parallel, perpendicular, or oblique using coordinate geometry. 3108.3.1 � Connect coordinate geometry to geometric figures in the plane (e.g. midpoints, distance formula, slope, and polygons). 3108.3.2 � Find the equation of a circle given its center and radius and vice versa. 3108.3.3 Circle Equations - excellent information from Math is Fun, followed by twelve multiple-choice questions to check for understanding Find the equation of a circle - Java applet; use an analytical method to find the equation of the circle and then use the applet to change h, k and r to solve the same question graphically. Finally compare the two results. This exercise helps you in problem solving and also to gain a deep undertanding of the properties of the circle.� The equation of a circle - Example of how to find the equation of a circle and practice questions. The equation of a circle - how to obtain and use the�standard form�of the�equation of a circle in Geometry. Apply the midpoint and distance formulas to points and segments to find midpoints, distances, and missing information in two and three dimensions. 3108.3.4 � Use mapping notation to identify the image of a transformation given the coordinates of the pre-image. 3108.3.5 � Identify a transformation given its mapping notation. 3108.3.6 � State Performance Indicators Use algebra and coordinate geometry to analyze and solve problems about geometric figures (including circles). SPI 3108.3.1 Circle Equations - excellent information from Math is Fun, followed by twelve multiple-choice questions to check for understanding Use coordinate geometry to prove characteristics of polygonal figures. SPI 3108.3.2 � Describe algebraically the effect of a single transformation (reflections in the x- or y-axis, rotations, translations, and dilations) on two-dimensional geometric shapes in the coordinate plane. SPI 3108.3.3 � National Library of Virtual Manipulatives Algebra [Grades 9-12] Geometry & Measurement Mathematics Curriculum Standards 3108 - Geometry Internet Resources Checks for Understanding (Formative/Summative Assessment) 4.1 | 4.2 | 4.3 | 4.4 | 4.5 | 4.6 | 4.7 | 4.8 | 4.9 | 4.10 | 4.11 | 4.12 | 4.13 | 4.14 | 4.15 | 4.16 | 4.17 | 4.18 | 4.19 | 4.20 | 4.21 | 4.22 | 4.23 | 4.24 | 4.25 | 4.26 | 4.27 | 4.28 | 4.29 | 4.30 | 4.31 | 4.32 | 4.33 | 4.34 | 4.35 | 4.36 | 4.37 | 4.38 | 4.39 | 4.40 | 4.41 | 4.42 | 4.43 | 4.44 | 4.45 | 4.46 | 4.47 | 4.48 | 4.49 Recognize that there are geometries, other than Euclidean geometry, in which the parallel postulate is not true and discuss unique properties of each. 3108.4.1 � Compare and contrast inductive reasoning and deductive reasoning for making predictions and valid conclusions based on contextual situations. 3108.4.2 Inductive and Deductive Reasoning - video explanation Inductive Reasoning - video explanation for making predictions Solve problems involving betweeness of points and distance between points (including segment addition). 3108.4.3 � Describe and recognize minimal conditions necessary to define geometric objects. 3108.4.4 � Use vertical, adjacent, complementary, and supplementary angle pairs to solve problems and write proofs. 3108.4.5 � Describe the intersection of lines (in the plane and in space), a line and a plane, or of two planes. 3108.4.6 � Identify perpendicular planes, parallel planes, a line parallel to a plane, skew lines, and a line perpendicular to a plane. 3108.4.7 � Apply properties and theorems about angles associated with parallel and perpendicular lines to solve problems. 3108.4.8 � Classify triangles, quadrilaterals, and polygons (regular, non-regular, convex and concave) using their properties. 3108.4.9 � Identify and apply properties and relationships of special figures (e.g., isosceles and equilateral triangles, family of quadrilaterals, polygons, and solids). 3108.4.10 � Use the triangle inequality theorems (e.g., Exterior Angle Inequality Theorem, Hinge Theorem, SSS Inequality Theorem, Triangle Inequality Theorem) to solve problems. 3108.4.11 Triangle Inequality Property � Seven questions to use as an assessment of student understanding Triangle Inequality theorem from OnlineMath The Triangle Inequality - explore a relationship between the lengths of the three sides of a triangle Practice with Triangle Inequality�- five multiple choice questions with explanation� �[This expired page is brought to you by the Internet archive, the�Wayback Machine.] Triangle Inequality�- from Math for Morons Like Us, a ThinkQuest entry Triangle Inequalities�- explanation from the Regents Prep assessment prep site The Triangle Inequality Theorem�- explanation that any side of a triangle is always shorter than the sum of the other two sides - includes an interactive java applet� �or� Triangle Inequality Theorem�- with worked solutions and a video� Apply the Angle Sum Theorem for polygons to find interior and exterior angle measures given the number of sides, to find the number of sides given angle measures, and to solve contextual problems. 3108.4.12 The Exterior Angle Sum of a Polygon - investigate the sum of the exterior angles of a polygon Locate, describe, and draw a locus in a plane or space (e.g., fixed distance from a point on a plane, fixed distance from a point in space, fixed distance from a line, equidistant from two points, equidistant from two parallel lines, and equidistant from two intersecting lines). 3108.4.13 � Identify and use medians, midsegments, altitudes, angle bisectors, and perpendicular bisectors of triangles to solve problems (e.g., find segment lengths, angle measures, points of concurrency). 3108.4.14 � Identify, write, and interpret conditional and bi-conditional statements along with the converse, inverse, and contra-positive of a conditional statement. 3108.4.15 � Analyze and create truth tables to evaluate conjunctions, disjunctions, conditionals, inverses, contra-positives, and bi-conditionals. 3108.4.16 Truth Tables - table explanation (beware of the numerous ads on this page) Truth Tables - practice page Truth Tables - definition and examples Use the Law of Detachment, Law of Syllogism, conditional statements, and bi-conditional statements to draw conclusions. 3108.4.17 � Use counterexamples, when appropriate, to disprove a statement. 3108.4.18 � Use coordinate geometry to prove properties of plane figures. 3108.4.19 � Prove key basic theorems in geometry (i.e., Pythagorean Theorem, the sum of the angles of a triangle is 180 degrees, characteristics of quadrilaterals, and the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length). 3108.4.20 Pythagorean Theorem Interactive - [Free activity provided by a commercial site] Learn that the Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Discover visual and algebraic proofs. Apply the Pythagorean Formula to find missing side lengths. Derive the distance formula for points in the coordinate plane. Use properties of and theorems about parallel lines, perpendicular lines, and angles to prove basic theorems in Euclidean geometry (e.g., two lines parallel to a third line are parallel to each other, the perpendicular bisectors of line segments are the set of all points equidistant from the endpoints, and two lines are parallel when the alternate interior angles they make with a transversal are congruent). 3108.4.21 � Perform basic geometric constructions using a straight edge and a compass, paper folding, graphing calculator programs, and computer software packages (i.e., bisect and trisect segments, congruent angles, congruent segments, a line parallel to a given line through a point not on the line, angle bisector, and perpendicular bisector). 3108.4.22 � Describe the polyhedron or solid that can be made from a given net including the Platonic Solids. 3108.4.23 � Develop and use special formulas relating to polyhedra (e.g., Euler�s Formula). 3108.4.24 � Use properties of prisms, pyramids, cylinders, cones, spheres, and hemispheres to solve problems. 3108.4.25 � Describe and draw cross-sections (including the conic sections) of prisms, cylinders, pyramids, spheres, and cones. 3108.4.26 � Use right triangle trigonometry to find the area and perimeter of quadrilaterals (e.g. square, rectangle, rhombus, parallelogram, trapezoid, and kite). 3108.4.27 Areas of Triangles, Trapezoids, and Kites - discover or demonstrate the formulas for the areas of triangles, trapezoids, and kites. (three activities) Derive and use the formulas for the area and perimeter of a regular polygon. (A=1/2 ap) 3108.4.28 � Extend the effect of a scale factor k in similar objects to include the impact on volume calculations and transformations. 3108.4.29 � Use right triangle relationships or the Pythagorean Theorem to find the lateral area (if possible), surface area, and volume of prisms, cylinders, cones, pyramids, spheres, and hemispheres. 3108.4.30 Pythagorean Theorem Interactive - [Free activity provided by a commercial site] Learn that the Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Discover visual and algebraic proofs. Apply the Pythagorean Formula to find missing side lengths. Derive the distance formula for points in the coordinate plane. Use properties of single transformations and compositions of transformations to determine their effect on geometric figures (e.g. reflections across lines of symmetry, rotations, translations, glide reflections, and dilations). 3108.4.31 � Recognize, identify and apply types of symmetries (point, line, rotational) of two- and three- dimensional figures. 3108.4.32 � Use transformations to create and analyze tessellations and investigate the use of tessellations in architecture, mosaics, and artwork. 3108.4.33 � Create and analyze geometric designs using rigid motions (compositions of reflections, translations, and rotations). 3108.4.34 � Prove that two triangles are congruent by applying the SSS, SAS, ASA, AAS, and HL congruence statements. 3108.4.35 � Use several methods, including AA, SSS, and SAS, to prove that two triangles are similar. 3108.4.36 � Identify similar figures and use ratios and proportions to solve mathematical and real-world problems (e.g., Golden Ratio). 3108.4.37 � Use the principle that corresponding parts of congruent triangles are congruent to solve problems. 3108.4.38 � Identify lines and line segments associated with circles. 3108.4.39 Circle Equations - excellent information from Math is Fun, followed by twelve multiple-choice questions to check for understanding Find angle measures, intercepted arc measures, and segment lengths formed by radii, chords, secants, and tangents intersecting inside and outside circles. 3108.4.40 � Use inscribed and circumscribed polygons to solve problems concerning segment length and angle measures. 3108.4.41 � Use geometric mean to solve problems involving relationships that exist when the altitude is drawn to the hypotenuse of a right triangle. 3108.4.42 � Apply the Pythagorean Theorem and its converse to triangles to solve mathematical and contextual problems in two- or three-dimensional situations. 3108.4.43 Pythagorean Theorem Interactive - [Free activity provided by a commercial site] Learn that the Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Discover visual and algebraic proofs. Apply the Pythagorean Formula to find missing side lengths. Derive the distance formula for points in the coordinate plane. Identify and use Pythagorean triples in right triangles to find lengths of an unknown side in two- or three-dimensional situations. 3108.4.44 Pythagorean Theorem Interactive - [Free activity provided by a commercial site] Learn that the Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Discover visual and algebraic proofs. Apply the Pythagorean Formula to find missing side lengths. Derive the distance formula for points in the coordinate plane. Use the converse of the Pythagorean Theorem to classify a triangle by its angles (right, acute, or obtuse). 3108.4.45 � Classifying Triangles - showing how triangles can be classified according to some of their features (followed by a four-question quiz) Linkage Strip Construction - A triangle has three sides, but not just any set of three lengths will make a triangle. Use this linkage-strip Interactive Activity to answer a set of problems. Triangle Homework - Eight problems to solve Three Types of Angles - explore three types of angles - right, acute, and obtuse; and begin to visually recognize the three types of angles Apply properties of 30� - 60� - 90� and 45� - 45� - 90� to determine side lengths of triangles. 3108.4.46 � Find the sine, cosine and tangent ratios of an acute angle of a right triangle given the side lengths. 3108.4.47 � Define, illustrate, and apply angles of elevation and angles of depression in real-world situations. 3108.4.48 � Use the Law of Sines (excluding the ambiguous case) and the Law of Cosines to find missing side lengths and/or angle measures in non-right triangles. 3108.4.49 � State Performance Indicators 4.1 | 4.2 | 4.3 | 4.4 | 4.5 | 4.6 | 4.7 | 4.8 | 4.9 | 4.10 | 4.11 | 4.12 | 4.13 | 4.14 | 4.15 Differentiate between Euclidean and non-Euclidean geometries. SPI 3108.4.1 � Define, identify, describe, and/or model plane figures using appropriate mathematical symbols (including collinear and non-collinear points, lines, segments, rays, angles, triangles, quadrilaterals, and other polygons). SPI 3108.4.2 � Identify, describe and/or apply the relationships and theorems involving different types of triangles, quadrilaterals and other polygons. SPI 3108.4.3 � Analyze different types and formats of proofs. SPI 3108.4.4 � Describe solids and/or surfaces in three-dimensional space when given two-dimensional representations for the surfaces of three-dimensional objects. SPI 3108.4.5 � Use various area of triangle formulas to solve contextual problems (e.g., Heron�s formula, the area formula for an equilateral triangle, and A = � ab sin C). SPI 3108.4.6 � Compute the area and/or perimeter of triangles, quadrilaterals and other polygons when one or more additional steps are required (e.g. find missing dimensions given area or perimeter of the figure, using trigonometry). SPI 3108.4.7 � Solve problems involving area, circumference, area of a sector, and/or arclength of a circle. SPI 3108.4.8 Circle Equations - excellent information from Math is Fun, followed by twelve multiple-choice questions to check for understanding Use right triangle trigonometry and cross-sections to solve problems involving surface areas and/or volumes of solids. SPI 3108.4.9 � Identify, describe, and/or apply transformations on two and three dimensional geometric shapes. SPI 3108.4.10 � Use basic theorems about similar and congruent triangles to solve problems. SPI 3108.4.11 � Solve problems involving congruence, similarity, proportional reasoning and/or scale factor of two similar figures or solids. SPI 3108.4.12 � Identify, analyze and/or use basic properties and theorems of circles to solve problems (including those relating right triangles and circles). SPI 3108.4.13 � Use properties of right triangles to solve problems (such as involving the relationship formed when the altitude to the hypotenuse of a right triangle is drawn). SPI 3108.4.14 � Determine and use the appropriate trigonometric ratio for a right triangle to solve a contextual problem. SPI 3108.4.15 � National Library of Virtual Manipulatives Geometry [Grades 9-12] Measurement [Grades 9-12] Data Analysis, Statistics, & Probability Mathematics Curriculum Standards 3108 - Geometry Internet Resources Checks for Understanding (Formative/Summative Assessment) Determine the area of each sector and the degree measure of each intercepted arc in a pie chart. 3108.5.1 Circles - twenty-three java applets for investigating circles Translate from one representation of data to another (e.g., bar graph to pie graph, pie graph to bar graph, table to pie graph, pie graph to chart) accurately using the area of a sector. 3108.5.2 � Estimate or calculate simple geometric probabilities (e.g., number line, area model, using length, circles). 3108.5.3 � State Performance Indicators 5.1 Use area to solve problems involving geometric probability (e.g. dartboard problem, shaded sector of a circle, shaded region of a geometric figure). SPI 3108.5.1 � National Library of Virtual Manipulatives Data Analysis & Probability [Grades 9-12] Review Help Practice Tests Geometry Chapter Test - designed to let you test your skills with a sampling of problems from each chapter in a Glencoe textbook. Online Study Tools - Glencoe resources SOL Standardized Test Practice from Glencoe Mathematics (thirteen chapters covered) Virginia Standards of Learning - Select Geometry and 10, 20 or 40 questions - Repeat for a new set of questions Released Test & Others California Released Test Georgia End of Course Geometry Test (Spring 2004) 84 questions, answers not included Virginia Released Test Interactive items [reinforcement given after each answer ] - 2006 | 2005 | 2004 | 2003 | 2002 | (each test has 45 questions)  Virginia Released Test Printable items - 2006 | 2005 | 2004 | 2003 | 2002 | 2001 (each test has 45 questions - answers are included)   Internet4classrooms is a collaborative effort by Susan Brooks and Bill Byles. 