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Essential Outcomes Geometry 1. Know and use the correct symbols for lines, rays, angles, segments, perpendicular and parallel. (Standard 1, 8 Core Standard 1) Learning Goals A) Students will understand and be able to use appropriate symbols for lines, rays, segments, and angles (1.1, 1.2, 8.1) B) Students will understand, be able to differentiate and use correct symbols for segments, length of segments, angles and measure of angles (1.1, 1.2, 8.1) C) Students will understand and be able to use correct symbols for parallel and perpendicular lines. (1.1, 1.2, 1.3, 1.4, 8.1) 2. Find slope, length, and midpoint of segments. (Standard 1, 2, 3, 8, Core Standard 7) Learning Goals A) Students will understand and be able to apply the formula for slope given two points, the equation of a line, or given a graph (1.4, 8.1, 8.2) B) Students will understand and be able to apply the formula for midpoint of a segment and find an endpoint given the midpoint and the second endpoint. (1.1, 8.1, 8.2) C) Students will understand and be able to identify congruent segments (1.2, 2.6, 3.4, 8.1) D) Students will understand and be able to apply the distance formula given two points (1.1,1.4, 5.1, 8.1, 8.2) 1 3. Identify angles and triangles by measure, by markings, and determine angle measure by using symbols or special angle relationships (Standard 4, 8 Core Standard 2, 9) Learning Goals A) Students will understand and be able to identify acute, right, obtuse, straight and congruent angles (4.1, 8.1) B) Students will understand and be able to identify the relationship between complementary and supplementary angles (4.2, 4.4, 4.6, 8.1) C) Students will understand and be able to classify triangles by side length and angle measure (4.1, 4.2, 4.3, 4.4, 8.1) D) Students will understand and be able to use Isosceles Triangle Theorem (4.8, 4.9, 8.1, 8.6) 4. Identify and use special angles formed by lines and a transversal, vertical angles, and linear pairs. (Standard 1, 3, 4, 8 Core Standard 1, 7) Learning Goals A) Students will understand and be able to identify corresponding angles, same-side interior (exterior) angles, alternate interior (exterior) angles, vertical angles, and linear pairs. (1.3, 3.4, 8.1) B) Students will understand and be able to apply the rules for the above angle pairs when two lines are parallel or not (1.4, 4.9, 8.2) 2 5. Identify polygons and find interior and exterior angle measures. (Standard 2, 6, 8 Core Standard 4) Learning Goals A) Students will be able to identify and name polygons by number of sides (2.1, 2.2, 8.1) B) Students will understand and be able to apply the formula for interior angle sum of all polygons (2.3, 2.2, 2.5, 8.1, 8.2, 8.9) C) Students will understand and be able to apply the formula for exterior angles (2.3, 2.5, 8.1, 8.2, 8.9) D) Students will understand the relationship between the interior and exterior angles of polygons (2.2, 2.6) 6. Write equations of lines in slope-intercept, standard, and point-slope forms; be able to graph lines. (Standard 1, 3, 4, 8 Core Standard 7) Learning Goals A) Students will understand and be able to change between various forms of linear equations (1.4, 8.1, 8.9) B) Students will understand and be able to identify the necessary information to graph a line (1.2, 1.4, 4.9, 8.1, 8.9) C) Students will understand and be able to distinguish whether lines are parallel, perpendicular or neither by looking at the slope (1.4, 8.1) D) Students will understand and be able to use slopes of parallel and perpendicular lines to write equations of related lines (1.2, 1.4, 3.4, 4.9, 8.1) 3 7. Know what information is needed to prove triangles congruent and do simple proofs in different forms including 2-column, paragraph, indirect, flow, and coordinate. (Standard 2, 3, 4, 8 Core Standard 2, 7, 9) Learning Goals A) Students will understand and be able to identify the five ways of proving triangles are congruent (2.3, 4.3, 4.6, 8.3) B) Students will understand and be able to use CPCTC after proving triangles are congruent (2.3, 2.4, 4.4, 8.3) C) Students will understand the logical sequencing and be able to write an original proof (2.6, 3.4, 8.3, 8.7, 8.8) 8. Know the relationships and find the parts of special right triangles and use the Pythagorean Theorem. (Standard 5, 8 Core Standard 2, 3) Learning Goals A) Students will understand and be able to identify the parts of a right triangle (5.3, 8.1) B) Students will understand and be able to use the relationship between sides of special right triangles (30-60-90, 45-45-90) to find other sides (5.3, 8.1) C) Students will understand and be able to use the Pythagorean Theorem its converse and its corollary (5.1, 8.1) D) Students will understand and be able to reduce radials to simplest radical form (A 1.1.2) E) Students will understand and be able to use the Triangle Inequality Theorem to determine possible third side lengths (5.6, 8.1) F) Students will understand and be able to identify whether 3 side lengths are possible for a triangle (5.1) 4 9. Use basic trigonometric functions. (Standard 5, 8 Core Standard 3) Learning Goals A) Students will understand and be able to identify sine, cosine and tangent ratios and use their symbols correctly (5.4, 5.5, 8.1, 8.2) B) Students will understand and be able to use trigonometric functions to find missing angles and sides (5.6, 8.1, 8.2) 10. Correctly use formulas for area, volume, perimeter, circumference, arc length, surface area, and sector area with correct units. (Standard 3, 7, 8 Core Standard 4, 5, 6) Learning Goals A) Students will understand and be able to use formulas to find areas of squares, rectangles, triangles, parallelograms, trapezoids, rhombi, kite, regular polygons and circles (3.3, 3.4, 4.7, 7.7, 8.1, 8.2) B) Students will understand and be able to use formulas for perimeter of polygons, and circumference of circles (3.3, 3.4, 4.7, 7.5, 8.1) C) Students will understand and be able to use formulas for arc length, area of sectors and circle segments (6.5, 6.7, 7.5, 8.1) D) Students will understand and be able to use formulas for surface area and volume of cylinders, cones, pyramids, prisms, and spheres (7.3, 7.7, 8.1) 11. Identify and know the properties of the family of quadrilaterals. (Standard 3, 8 Core Standard 4, 7, 9) Learning Goals A) Students will understand and be able to identify quadrilaterals by their special properties and vice versa (3.1, 3.2, 3.3, 3.4, 8.1, 8.2) 5 12. Figures can be reflected, rotated, translated, and dilated. (Standard 2 Core Standard 2, 8) Learning Goals A) Students will understand and be able to identify transformations from pictures (2.4) B) Students will understand and be able to use rules for transformations to draw an image transformed from a preimage ( 2.4) C) Students will understand and be able to use scalar multiplication to draw a dilation (2.4) 13. Identify, use, and prove similar figures. (Standard 3 Core Standard 2, 7) Learning Goals A) Students will understand and be able to identify similar figures (3.4, 4.4) B) Students will understand and be able to use properties of similar figures to find missing parts (3.4, 4.4, 5.2) C) Students will understand and be able to prove figures are similar (3.4, 4.9) 14. Find and use the equation of a circle, use formulas to determine segments and angles related to circles (Standard 6,8 Core Standard 5, 7) Learning Goals A) Students will understand and be able to identify the various parts (center and radius) of a circle given the equation and vice versa (6.1, 6.2, 6.8) B) Students will understand and be able to identify relationships among radii, chords, secants, tangents, and diameters (6.2) C) Students will understand, be able to identify and find the measures of central angles, inscribed angles (by chords), exterior angles (formed by secants and tangents) and interior angles (by chords) (6.3, 6.5) 6 15. Use logic and conditional statements to make conclusions (Standard 8 Core Standard 9) Learning Goals A) Students will understand and be able to write conditional statements, converses, bi-conditionals, inverses and contra-positive statements (8.4, 8.5, 8.7) B) Students will understand and be able to determine the truth value of statements, find counter examples. (8.7, 8.8, 8.9) 7 MICHIGAN CITY HIGH SCHOOL Geometry Ongoing/All Year 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter Course Title Assessment Assessment Assessment Assessment GEOMETRY 1, 15, 2, 6, 4, QTR1 Standard 1.1 3.4 8.4 Standard 1.2 1.3 1.4 4.9 5.1 8.1 8.5 8.7 8.8 3, 7, 13, 8, QTR2 2.6 8.2 8.9 2.3 4.2 4.9 8.1 Standard 2.4 2.6 3.4 4.3 4.4 4.6 5.1 5.2 5.3 8.3 8.6 8.7 9, 5, 11, 14, QTR3 4.1 4.8 5.6 8.8 2.1 3.1 5.5 6.5 Standard 2.2 2.3 2.5 3.2 3.3 3.4 5.6 6.1 6.2 6.8 8.1 8.2 10A, 10B, 10C, 12 QTR4 2.6 5.4 6.3 8.9 2.4 6.7 8.2 3.3 7.3 Standard 3.4 4.7 7.7 7.5 6.5 8.1 Bundles 1, 9, 2, 8 Bundles 2, 3, 6 Bundles 3, 4, 7 Bundles 5, 10 Best Practice Methods Best Practice Methods Best Practice Methods Best Practice Methods Similarities and Differences Frequent and Immediate Feedback Graphic Organizers Construct Investigate Re-teaching Similarities and Differences Frequent and Immediate Feedback Graphic Organizers Construct Investigate Re-teaching Similarities and Differences Frequent and Immediate Feedback Graphic Organizers Construct Investigate Re-teaching Similarities and Differences Frequent and Immediate Feedback Graphic Organizers Construct Investigate Re-teaching 8 GEOMETRY Bundle #1 Standard Indicator: Geometry Standard 1: Points, Lines, Angles & Planes 1.1, 1.4 Declarative Knowledge Concepts There are formulas for finding segment lengths, midpoints, slopes and equations for lines. Organizing Ideas Students will understand: 1. How to find the length and midpoints of segments. 2. How to find slopes and different forms of linear equations. Details Vocabulary 1. 2. 3. 4. 5. Distance formula Midpoint formula Slope formula Parallel lines have the same slope. Perpendicular slopes are opposite reciprocals. 6. Slope – Intercept form 7. Point – Slope form 8. Order of Operations 9. Properties of equalities 10. Steps to simplify radicals Parallel, Perpendicular, Slope, skew, Midpoint, Segment, Distance, Linear, Coordinates, Reciprocals, Intercept, Equation, X& Y axes, Slope – intercept form, Point – slope form, positive & negative slopes, variable, symbols for parallel, perpendicular, segment, angles, lines, rays, slope, measurements of angles and segments Procedural Knowledge Processes 1. 2. Reading Process Order of Operations Skills 1. Multiply, Divide, Add, Subtract, and simplify fractions. Adding and subtracting integers. Plot points and graph equations on the coordinate plane. Use Order of Operations to solve problems Simply radicals Problem Solving 2. 3. 4. 5. 6. 9 GEMOMETRY Bundle #2 Standard Indicator: Geometry Standard 1: Points, Lines, Angles, and Planes 1.3 Declarative Knowledge Concepts Organizing Ideas Details Vocabulary Procedural Knowledge There are relationships between special pairs of angles formed by parallel lines and transversals. Students will understand that transversals create special pairs of angles. Processes 1. Order of operations 2. Reading Process 1. Alternate interior angles are congruent. 2. Same side interior angles are supplementary 3. Corresponding angles are congruent. 4. Vertical angles are congruent. 5. Linear pairs are supplementary. 6. Steps to solve and write equations Alternate, Interior, Exterior, Corresponding, Vertical Angles, Linear pair, Supplementary, Complementary, Adjacent, Congruent, Transversal, Parallel, Same – side, Angles Skills 1. Adding and subtracting 2. Identify if angles are on the same side or alternate sides of the transversal. 3. Identify if angles are interior or exterior in relationship to the parallel lines. 4. Solve Equations by Showing Work. 10 GEOMETRY Bundle #3 Standard Indicator: Geometry Standard 5: Right Triangles 5.1, 5.2, 5.3, 5.4, 5.6 Declarative Knowledge Concepts Organizing Ideas Details Vocabulary Procedural Knowledge There are rules for finding sides and angles in right triangles. Students will understand: 1. How to use the Pythagorean Theorem to solve problems. 2. How to identify and use the trigonometric functions. 3. How to use special right triangles to solve problems. 4. How to use the Geometric Mean relationships. Processes 1. Pythagorean Theorem 2. Sine, Cosine, Tangent 3. Special right triangles ( 30-60 and 45 -45) 4. Geometric Mean formulas 5. Order of operations Pythagorean Theorem, Geometric mean, Sine, Cosine, Tangent, Right triangle, inverse, Isosceles triangle, Similar triangles, Hypotenuse, Opposite leg, Adjacent leg, arcsine, arccosine, arctangent Skills 1. Reading Process 2. Writing Process 3. Order of Operations 1. Proper use of a scientific calculator. 2. Identify the parts of a right triangle. 3. Simplify radicals. 4. Cross multiplication 5. Solve Equations by Showing Work. 6. Use Order of Operations to Problem Solving 11 GEOMETRY Bundle #4 Standard Indicator: Geometry Standard 6: Circles 6.2, 6.5, 6.6, 6.7, 6.8 Declarative Knowledge Concepts Organizing Ideas Details Vocabulary 1. There are relationships for finding area, arc length, angles, and segment lengths of circles. 2. There are equations for circles. Students will: 1. Write an equation for a circle 2. Calculate circumference, arc length, and area of circles and sectors. 3. Use measures of arcs and related angles. 4. Use the relationships among parts of a circle. 1. Equation of a circle 2. Formulas for area and circumference. 3. Arc length and area of sectors. 4. Relationships among radii, chords, secants, tangents and diameters. 5. Relationships among arcs, central and inscribed angles, angles formed by tangents and secants and chords. 6. Steps for solving quadratic equations - Quadratic formula - Factoring Circle, Center, Radius, Diameter, Arc, Sector, Central Angle, Inscribed Angle, Chord, Tangent, Secant, Concentric, Circumference, Midpoint, Distance, π, congruent, circumscribed Procedural Knowledge Processes Skills 1. 2. 3. Writing Process Reading Process Order of Operations 1. 2. 3. 4. Use the Distance formula Use the Midpoint formula Solving quadratic equations Calculator usage 5. Basic Rounding Rules 12 GEOMETRY Bundle #5 Standard Indicator: Geometry Standard 7: Polyhedra and Other Solids 7.1, 7.2, 7.3, 7.5, 7.6, 7.7 Declarative Knowledge Concepts Organizing Ideas Details Vocabulary There are rules describing relationships and symmetries, using congruence and similarity for polyhedra and other solids. Students will understand: 1. How to describe regular and nonregular polyhedra. 2. How to use Euler’s Formula. 3. How to calculate volumes and surface areas of solids. 4. How to use properties of congruent and similar solids. 1. Euler’s Formula 2. Formulas for volumes of solids. 3. Formulas for lateral and surface areas of solids. 4. Similarity ratios. Regular, Non-regular, Net, Prism, Polyhedra, Cylinder, Pyramid, Cone, Sphere, Base, Composite, Oblique, Right, Edge, Polygon, Similar, Apothem, Face, Slant height, Height, Vertices, Volume, Area, Surface Area, Lateral Area, Perimeter, Cross-Section, π, Circumference, Square and Cubic Units, Congruent Procedural Knowledge 1. Reading Process 2. Writing Process 3. Order of Operations Processes Skills 1. 2. 3. 4. 5. 6. 7. Multiplying Fractions. Using a Scientific Calculator. Reducing Fractions. Identifying Perfect Squares and Cubes. Basic Rounding Rules Basic Conversion Units. Break Apart an Irregular Shape into Basic Solids. 8. Use order of operations to solve problems 9. Find Cube Roots 10. Use Pythagorean Theorem to solve problems 13 GEOMETRY Bundle # 6 Standard Indicator: Geometry Standard 4: Triangles 4.1, 4.2, 4.4, 4.5, 4.6, 4.8 Declarative Knowledge Concepts Organizing Ideas Details Vocabulary 1. There are rules for proving triangles similar and congruent. 2. Triangles have special properties. Students will understand: 1. How to classify triangles. 2. How to prove triangles congruent and similar. 1. Triangles are classified by their angles and sides. 2. Triangle Angle Sum Theorem 3. SSS, SAS, ASA, AAS, HL. 4. AA~, SAS~, SSS~. 5. Longest side is opposite largest angle. 6. Properties of Midsegments. 7. Triangle Inequality Theorem 8. Properties of Altitudes, Medians, Perpendicular and Angle Bisectors. 9. Steps for writing a proof. Altitude, Median, Angle Bisector, Perpendicular Bisector, Acute, Scalene, Obtuse, Right, Segment, Equilateral, Isosceles, Vertex, Equiangular, Exterior Angle, Remote Interior Angle, Sum, Congruent, Similar, Inequality, Corresponding Parts, CPCTC, Midsegment, Included Angle, Included Side, Triangle Angle Sum Theorem Procedural Knowledge Processes 1. 2. 3. Writing Process Reading Processs Order of Operations Skills 1. 2. 3. Logical Reasoning. Solving Equations. Drawing Diagrams and marking congruent parts. Write a proof 4. 14 GEOMETRY Bundle # 7 Standard Indicator: Geometry Standards 2 and 3: Polygons 2.1, 2.2, 2.3, 2.5, 3.1, 3.2, 3.3, 4.7 Declarative Knowledge Procedural Knowledge Concepts Organizing Ideas Details Vocabulary 1. There are rules for finding the area, perimeter, and angle measures. 2. Polygons have specific properties. Students will understand: 1. How to calculate perimeter and area. 2. How to find interior and exterior angle measures. 3. How to classify different polygons. 1. Properties of Triangles. 2. Properties of Quadrilaterals. 3. Properties of Regular Polygons. 4. Formulas for Area and Perimeter 5. Formula for Finding Interior Angles of a Polygon. Kite, Trapezoid, Isosceles Trapezoid, Parallelogram, Rhombus, Rectangle, Square, Triangle, Pentagon, Hexagon, Octagon, Height, Decagon, Diagonals, Base, Opposite Angles, Apothem, Perimeter, Perpendicular, Altitude, Radius, Side, Exterior/Interior Angles, Similar, Congruent, Square Units, Regular, n-gon, Convex, Concave, Composite Processes 1. Writing Process 2. Reading Process 3. Order of Operations Skills 1. Solving Equations. 2. Writing Equations. 3. Drawing and Marking Diagrams. 4. Recognize Parts of a Polygon. 5. Basic Calculator Skills. 6. Basic Rounding Rules. 7. Knowing Place Values. 8. Using Correct Units. 9. Basic Conversion Units. 10. Break Apart an Irregular Shape into Basic Polygons. 11. Use Pythagorean Theorem to Solve problems 15 GEOMETRY Bundle # 8 Standard Indicator: Geometry Standard 8: Mathematical Reasoning 8.1, 8.2 Declarative Knowledge Procedural Knowledge Concepts Organizing Ideas 1. 2. 3. 1. 2. 3. Details Vocabulary 1. 2. 3. 4. 5. 6. 7. 8. Problems may be solved in a variety of ways. Solutions should be reasonable. Steps taken to solve problems are justifiable. Students will choose an appropriate method to solve problems. Students will be able to justify steps when solving problem. Students will determine and verify whether a solution is valid. Draw a diagram Make a chart Solve a simpler problem Work backwards Write an equation Properties for equality and inequality Look for a pattern Choose the appropriate formula, or method Formula, equation, diagram, solution, reasonable, graph dimensions, Processes 1. 2. 3. Skills 1. Reading Process Writing Process Order of Operations Solving equations and showing work 2. Apply appropriate strategies 3. Proper use of a scientific calculator 4. Basic rules for rounding 5. Interpret information and results 6. Explain reasoning 7. Make Charts 8. Write an equation 9. Classify by patterns 10. Use order of operations to solve problems 11. Draw diagrams to assist in solving problems 16 GEOMETRY Bundle # 9 Standard Indicator: Geometry Standard 8: Mathematical Reasoning 6.3, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8 Declarative Knowledge Procedural Knowledge Concepts Organizing Ideas Details Vocabulary 1. Mathematical arguments follow logical patterns 2. Statements are justified by reasons 1. Students will write and interpret if-then statements 2. Students will apply theorems, postulates, corollaries, and definitions to form logical arguments 3. Students will write a variety of styles of proofs 1. Write proofs in various forms a. two column b. paragraph c. indirect d. coordinate e. flow 2. Determine coordinates for coordinate geometry proofs 3. Identify the hypothesis Inverse, converse, contra-positive, bi-conditional, conditional, conjecture, theorem, corollary, postulate, counter-example, coordinate, inductive, deductive Processes 1. Writing Process 2. Reading Process Skills 1. Draw conclusions 2. Draw and label a diagram from given information 3. Follow the steps to write a proof 4. Use rules of logic to solve problems 17 GEOMETRY Bundle # 10 Standard Indicator: Geometry Standard 8: Mathematical Reasoning 1.2, 2.4, 2.6, 3.4, 4.3, 4.9, 6.1, 6.4, 7.4, 8.9 Declarative Knowledge Procedural Knowledge Concepts Organizing Ideas Details Vocabulary 1. Constructions can be used in problem solving 2. Transformations of figures follow specific rules 1. Students will choose an appropriate method for constructing figures. 2. Students will choose appropriate rules to transform figures 1. Construct: a. Copy segments b. Copy angles c. Perpendicular bisectors of segments d. Angle bisectors 2. Apply transformations to polygons to determine congruence, similarity, symmetry, and create tessellations Transformation, reflection, translation, dilation, rotation, tessellation, symmetry, “strike an arc”, convenient radius, copy, construct, draw, sketch, compass, straight-edge, glide-reflection, intersect, isometry, similar, congruent, corresponding parts, trace Processes 1. Writing Process 2. Reading Process 3. Order of Operations Skills 1. 2. 3. 4. 5. 6. 7. 8. 9. Draw a line with a straight-edge Use a compass appropriately Trace Use scissors safely Following directions Scalar multiplication Matrix addition Graph on the coordinate plane Use a compass to and straight edge for constructions 10. Create tessellations 18 Assessment Plan Essential Outcome 1: Know and use the correct symbols for lines, rays, angles, segments, perpendicular and parallel. Summative Assessment: Selected response: symbols, measures of segments and angles Describe assessment and timeline Method Knowledge Types of Reasoning Formative: Worksheet generated by Geometry teachers X multiple choice and matching Students will understand and be able to use appropriate symbols for lines, rays, segments, angles, length of segments, planes, angles and measure of angles, symbols for parallel and perpendicular lines. Students will understand and be able to use congruent segments (segment midpoints and segment bisectors) and angles (angle bisectors) as well as segment and angle addition to solve for missing measures. Understand and use the terms collinear, coplanar, and skew. Performance Products Skills X Short answer, solving equations 10 question Timeline: 7 days, assess on day 8 19 Assessment Plan Essential Outcome 2: Find slope, length, and midpoint of segments. Summative Assessment: Selected Response: slope of lines, distance formula, midpoint formula Describe assessment and timeline Method Knowledge Types of Reasoning Formative: Students will understand and be able to apply the formula for slope given two points, the equation of a line (slopeintercept, point-slope, or standard form), or given a graph. Students will understand and be able to apply the formula for midpoint of a segment and find an endpoint given the midpoint and the second endpoint. Identify congruent segments (using midpoint), apply the distance formula Timeline: 6 days, assess day 7 Worksheet by Geometry teachers X Count spaces on a graph Know the forms of a line X Know the formulas Performance Products Skills X Changing linear equations from one form to another Apply the slope formula. X Use the equations for midpoint and distance 20 Essential Outcome 3: Identify angles and triangles by measure, by markings, and determine angle measure by using symbols or special angle relationships Summative Assessment: Selected response: identify angles, classify triangles, use special angle relationships, use isosceles triangle theorem Describe assessment and timeline Formative: Students will understand and be able to identify acute, right, obtuse, straight, congruent angles and the relationship between complementary and supplementary angles. Students will be able to use the Triangle Angle Sum Theorem. Students will understand and be able to classify triangles by side length and angle measure, and use Isosceles Triangle Theorem Timeline: 10 days teaching, day 6 assess Method Worksheet made by Geometry teachers Knowledge Types of Reasoning X X Matching or Solving equations multiple given algebraic choice values for identification complementary and of types of supplementary angles angles X X Multiple Solve for side choice lengths and angle identification measures using the of types of ITT. triangles Performance Products Skills 21 Essential Outcome 4: Identify and use special angles formed by lines and a transversal, vertical angles, and linear pairs. Summative Assessment: Selected response: identify types of angles, find angle measures Describe assessment and timeline Formative: Students will understand and be able to identify corresponding angles, same-side interior (exterior) angles, alternate interior (exterior) angles, vertical angles, and linear pairs. Students will understand and be able to apply the rules for the above angle pairs when two lines are parallel or not. Timeline: 6 days, assess day 7 Method Worksheet made by Geometry teachers Knowledge Types of Reasoning X X Know how Solve for missing each angle angle measures is related to knowing how the every other angles are related angle Performance Products Skills 22 Essential Outcome 5: Identify polygons and find interior and exterior angle measures. Summative Assessment: Selected Response: identify polygons, find interior angles sums, find interior and exterior angles of regular polygons. Describe assessment and Method Knowledge Types of Performance Products timeline Reasoning Skills Worksheet X X Formative: Students will be able to identify made by Matching, Short answer, solve and name polygons by number of Geometry short equations. sides teachers answer Students will understand and be X able to apply the formulas for Know interior angle sum of all formulas polygons, exterior angle sum, and understand the relationship between the interior and exterior angles of polygons Timeline: 6 days, assess day 7 23 Essential Outcome 6: Write equations of lines in slope-intercept, standard, and point-slope forms; be able to graph lines. Summative Assessment: Selected response: graph a line, write the equation of a line give the graph, use slope to determine relationship of lines, Describe assessment and timeline Formative: Students will understand and be able to identify the necessary information to graph a line Students will understand and be able to distinguish linear relationships by looking at the slope, write equations of related lines Timeline: 4 days, assess day 5 Method Worksheet made by Geometry teachers Knowledge Types of Reasoning X X Find the Write the equation slope and of new line given a the yrelationship to a intercept line and a point X Identify equal slopes and opposite inverses Performance Products Skills * Assessment should take only the first 10-15 minutes 24 Essential Outcome 7: Know what information is needed to prove triangles congruent and do simple proofs in different forms including 2-column, paragraph, indirect, flow, and coordinate Summative Assessment: Selected response: identify SSS, SAS, ASA, AAS & HL. Use CPCTC to prove secondary triangles are congruent. Write proofs. Describe assessment and Method Knowledge Types of Performance Products timeline Reasoning Skills Formative: Students will Teacher X X X understand and be able to generated Given 2 Given two triangles Write an identify the five ways of proving worksheet triangles with markings and original triangles are congruent or activity with common parts proof Students will understand and be markings X able to use CPCTC after proving Fill in the blank or triangles are congruent, and use matching reasons, logical sequencing and be able to given the write an original proof statements Timeline: 6 days assess on day 7 25 Essential Outcome 8: Know the relationships and find the parts of special right triangles and use the Pythagorean Theorem. Summative Assessment: Selected response: Use Pythagorean Theorem, special right triangles, and triangle inequality theorem Describe assessment and Method Knowledge Types of Performance Products timeline Reasoning Skills Formative: Students will understand and be able to identify the parts of a right triangle, use the Pythagorean Theorem, its converse and corollary. Be able to reduce radials to simplest radical form. Worksheet made by Geometry teachers Worksheet (Geometry IF Students will understand and be able to Wkst p. 58) use the relationship between sides of special right triangles (30-60-90, 4545-90) to find other sides X Identify the parts of a right triangle X Just do it! X Use the Pythagorean theorem, corollary and converse X Given three sides, will they make a triangle? Given two sides, what are the range of possible third sides Students will understand and be able to use the Triangle Inequality Theorem to determine possible third side lengths. Timeline: 9 days, assess on day 10 26 Essential Outcome 9: Use basic trigonometric functions Summative Assessment: Selected response: Find angle measures, given side lengths, find side lengths given angle measures Describe assessment and Method Knowledge Types of Performance Products timeline Reasoning Skills Teacher X X Be able to use their Formative: Students will understand and be able to identify sine, cosine and tangent ratios and use their symbols correctly. generated worksheet or activity Know the ratios, solve rations Apply the rations to find missing measures own calculator correctly Students will understand and be able to use trigonometric functions (sin, cos, tan)to find missing angles and sides. Timeline: 6 days assess on day 7 27 Revisit-We may want to break this apart into smaller units or something Essential Outcome 10: Correctly use formulas for area, volume, perimeter, circumference, arc length, surface area, and sector area with correct units Summative Assessment: Find perimeters and areas of polygons and circles, arc length, arc measure, sector area, circle segment area Describe assessment and timeline Method Knowledge Types of Performance Products Reasoning Skills Formative: Students will understand and be able to use formulas to find perimeters and areas of squares, rectangles, triangles, parallelograms, trapezoids, rhombi, kite, regular polygons Timeline: 8 days, assess on day 9* Formative: Students will understand and be able to use formulas for area of circles, circumference of circles, arc length, area of sectors and circle segments Timeline: 4 days assess on day 5 Teacher generated worksheet X Matching, know the formulas Teacher generated worksheet or activity X Know the formulas X Use the correct formula correctly, use special right triangles and Pythagorean theorem X Correctly use the formulas and apply to given information, use special right triangles Formative: Students will understand and be able to use formulas for surface area and volume of cylinders, cones, pyramids, prisms, and spheres Timeline: 5 days assess on day 6 28 Essential Outcome 11: Identify and know the properties of the family of quadrilaterals. Summative Assessment: Selected response, know the 5 ways of proving a quadrilateral is a parallelogram, know the special properties of: triangles, rhombuses, squares, trapezoids, isosceles trapezoids, kites, and parallelograms. Be able to use the properties to solve for missing measures Describe assessment and Method timeline 15 questions Formative: Students will understand and be able to identify quadrilaterals by their special properties and vice versa Timeline: 8 days, assess on day 8 Formative: Students will be 5 question short response able to understand and use properties of quadrilaterals to solve for missing measures. Timeline: 3-4 days assess on day 4 Knowledge Types of Reasoning Performance Skills X Solving equations X Be able to solve equations Products X Matching properties with shape or checklist X Know how measures are related using properties 29 Essential Outcome 12: That figures can be reflected, rotated, translated, and dilated Summative Assessment: Product: booklet made illustrating the various transformations Describe assessment and timeline Method Knowledge Formative: Students will understand and be able to identify transformations from pictures Timeline: 2 days, assess on day 3 5 questions X matching Formative: Students will understand and be able to use rules for transformations to draw an image transformed from a pre-image Timeline: 4 days, assess on day 4 Formative: : Students will understand and be able to use scalar multiplication to draw a dilation 4 questions X Know the rules for transformations and apply them to draw images X Be able to multiply by rational numbers Timeline: 1 day 3 questions Given A and A’ find the sf, given the other coordinates, use the sf to find the remaining, graph Types of Reasoning Performance Products Skills X Be able to draw a reasonable image X Be able to draw a dilation 30 Essential Outcome 13: Identify, use and prove similar figures Summative Assessment: Selected response, Describe assessment and Method timeline 15 questions Formative: Students will understand and be able to identify similar figures Timeline: 2 days, assess on day 3 Formative: Students will understand and be able to use properties of similar figures to find missing parts. Timeline: 5 days, assess on day 6 Formative: Students understand and be able to prove figures are similar Timeline: 3 days, assess day 4 Knowledge X Be able to check cross products. Be able to simplify fractions 5 question short X response Use side splitter thm, triangle angle, bisector thm, right triangle similarity thm. Proof, given X statements, Know methods of student provides proving reasons similarity (AA~, SSS~, SAS~) Types of Reasoning Performance Skills Products X If similar give sf, if not, tell why X Use scale factors to find missing measures. Solve equations. X Be able to solve equations X Write a proof 31 Essential Outcome 14: Find and use the equation of a circle, use formulas to determine segments and angles related to circles Summative Assessment: Selected response, Describe assessment and timeline Method Knowledge Formative: Students will understand and be able to identify the various parts (center and radius) of a circle given the equation and vice versa Timeline: 2, assess on day 3 Formative: Students will understand, identify and use relationships among radii, chords, secants, tangents, and diameters Timeline: 3, assess day 4 5 questions, short response Be able to recognize the equations and identify the various parts Know the formulas for finding segment lengths Be able to draw a circle given the equation or the center and radius Solve equations Formative: : Students will understand, be able to identify and find the measures of central angles, inscribed angles (by chords), exterior angles (formed by secants and tangents) and interior angles (by chords) Timeline: 5 10 questions Know the formulas for finding angles and arcs (360 in a circle, 180 in a triangle) Solve equations 10 questions Types of Reasoning Performance Products Skills 32 Essential Outcome 15: Use logic and conditional statements to make conclusions Summative Assessment: Selected response, Describe assessment and timeline Method Formative: Students will understand 5 matching questions and be able to write conditional statements, converses, biconditionals, inverses and contrapositive statements, hypothesis, conclusions, negation, contradiction. Timeline: 3, assess on day 4 Formative: Students will understand and be able to determine the truth value of statements, find counter-examples, use Laws of Detachment, Syllogism Timeline: 2, assess day 3 5 questions Knowledge Types of Reasoning Identify H and C. Understand negation Know conditional and contrapositive statements have the same truth value as do inverses and converses Performance Products Skills Write statements Use Laws of Syllogism, and Detachment to make conclusions 33 34