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Poyen School
Poyen School Curriculum K - 12 2007-2008
Mathematics - Geometry

Language of Geometry
Inductive and deductive reasoning
The learner will be able to define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations: 1. Venn Diagrams 2. Matrix logic 3. Conditions Statements (statement, inverse, converse, and contrapositive) 4. figural patterns.
Strand Bloom's Scope Hours Source Activities
Vocabulary, Reasoning, Application   Master 1.0 2004 Arkansas Mathematics Frameworks LG.1.G.1 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Inductive Reasoning [Textbook].  Lesson 1.1
· Geometry, McDougall Littell, Deductive Reasoning: Lesson 2.3 [Textbook].  
· Add to lesson, Venn Diagrams: Worksheets [Teaching Strategies].  
· Add to lesson, Matrix Logic: Worksheets [Teaching Strategies].  
· Geometry, McDougall Littell, Condition Statements: Leson 2.1 [Textbook].  
· Geometry, McDougall Littell, Lesson 1.1 [Textbook].  Pages 6 - 9: #24, 25, 29 - 33, 34-39, 42, 43
· Geometry, McDougall Littell, Lesson 2.1 [Textbook].  Pages 75 - 78: # 22 - 28, 50, 51, 55, 56
· Geometry, McDougall Littell, Lesson 2.3: Inductive/Deductive WS # 1 - 10 [Textbook].  
· Add to lesson, Pattern: Open Response [Teaching Strategies].  
  
Basic terms of geometry
The learner will be able to represent points, lines, and planes pictorially with proper identification, as well as basic concepts derived from these undefined terms, such as segments, rays, and angles.
Strand Bloom's Scope Hours Source Activities
Vocabulary, Reasoning, Application   Master 1.0 2004 Arkansas Mathematics Frameworks LG.1.G.2 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Points, Lines, Planes: Lesson 1.2 [Textbook].  
· Geometry, McDougall Littell, Segments, Rays: Lesson 1.2 [Textbook].  
· Geometry, McDougall Littell, Angles: Lesson 1.4 [Textbook].  
· Geometry, McDougall Littell, Lesson 1.2: [Textbook].  Page 13 - 16: # 9 - 42 (mult of 3), 52 - 54
· Geometry, McDougall Littell, Lesson 1.4 [Textbook].  Page 29 - 79: # 17 - 22, 26 - 28, 40 - 43
· Geometry, McDougall Littell, Lesson 1.2: Definition WS [Textbook].  
· Geometry, McDougall Littell, Quiz # 1 - 10 [Textbook].  
  
Relationships from geometric figures
The learner will be able to describe relationships derived from geometric figures or figural patterns.
Strand Bloom's Scope Hours Source Activities
Vocabulary, Reasoning, Application   Master 1.0 2004 Arkansas Mathematics Frameworks LG.1.G.3 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Figures & Patterns: Lesson 1.1 [Textbook].  
  
Properties of angles
The learner will be able to apply, with and wtihout appropriate technology, definitions, theorems, properties, and postulates related to such topics as complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines.
Strand Bloom's Scope Hours Source Activities
Vocabulary, Reasoning, Application   Master 1.0 2004 Arkansas Mathematics Frameworks LG.1.G.4 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Lesson 1.6 [Textbook].  Complementary, supplementary, vertical, linear pairs, & adjacent angles
· Geometry, McDougall Littell, Lesson 3.1 [Textbook].  Angles formed by perpendicular lines
  
Parallel lines/transversal/angles
The learner will be able to explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel.
Strand Bloom's Scope Hours Source Activities
Vocabulary, Reasoning, Application   Master 1.0 2004 Arkansas Mathematics Frameworks LG.1.G.5 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Angle pairs & transversals: lesson 3.1 [Textbook].  
  
Deductive reasoning/justify conclusions
The learner will be able to give justification for conclusions reached by deductive reasoning state and prove key basic theorems in geometry (i.e., the Pythagorean theorem, the sum of the measures of the angles of a triangle is 180 degrees, and the line joining the midpoints of two sides of a triangle is parallel to the third side and half it's length.
Strand Bloom's Scope Hours Source Activities
Vocabulary, Reasoning, Application   Master 1.0 2004 Arkansas Mathematics Frameworks LG.1.G.6 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Deductive reasoning: lesson 2.3 [Textbook].  # 23 - 25, 33 - 35, 45 - 48
  
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Triangles
Triangle congruence and similarity
The learner will be able to apply congruence (SSS...) and similarity (AA...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification.
Strand Bloom's Scope Hours Source Activities
Triangles: classify, logic, trig   Master 1.0 2004 Arkansas Mathematics Frameworks T.2.G.1 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Congruence: lesson 4.2 [Textbook].  
· Geometry, McDougall Littell, Similarity: lesson 8.4 [Textbook].  
· Geometry, McDougall Littell, Properties: Lesson 4.1 [Textbook].  
· Geometry, McDougall Littell, Lesson 4.2: page 207: # 24 - 29 [Textbook].  
  
Triangle inequality theorem
The learner will be able to investigate the measures of segments to determine the existence of triangles (triangle inequality theorem).
Strand Bloom's Scope Hours Source Activities
Triangles: classify, logic, trig   Master 1.0 2004 Arkansas Mathematics Frameworks T.2.G.2 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Triangle inequality: lesson 5.5 [Textbook].  
  
Special segments of triangles
The learner will be able to identify and use the special segments of triangles (altitude, median, angle bisector, perpendicular bisector, and midsegment) to solve problems.
Strand Bloom's Scope Hours Source Activities
Triangles: classify, logic, trig   Master 1.0 2004 Arkansas Mathematics Frameworks T.2.G.3 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Lesson 5.3: altitude, median [Textbook].  
· Geometry, McDougall Littell, Lesson 5.2: angle bisector, perpendicular bisector [Textbook].  
· Geometry, McDougall Littell, Lesson 5.4: midsegment [Textbook].  
  
Pythagorean Theorem
The learner will be able to apply the Pythagorean Theorem and its converse in solving practical problems.
Strand Bloom's Scope Hours Source Activities
Triangles: classify, logic, trig   Master 1.0 2004 Arkansas Mathematics Frameworks T.2.G.4 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Pythagorean theorem: lesson 9.2 [Textbook].  
· Geometry, McDougall Littell, Pythagorean theorem converse: Lesson 9.3 [Textbook].  
  
Special right triangles
The learner will be able to use the special right triangle relationships (30-60-90 and 45-45-90) to solve problems.
Strand Bloom's Scope Hours Source Activities
Triangles: classify, logic, trig   Master 1.0 2004 Arkansas Mathematics Frameworks T.2.G.5 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Lesson 9.4 [Textbook].  
  
Trig ratios
The learner will be able to use trigometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles in right triangles including angles of elevation and angles of depression.
Strand Bloom's Scope Hours Source Activities
Triangles: classify, logic, trig   Master 1.0 2004 Arkansas Mathematics Frameworks T.2.G.6 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Lesson 9.5 [Textbook].  
· Activity Page, Eagle WS [Classroom Materials].  
  
Similarity of Right Triangles
The learner will be able to use similarity of right triangles to express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given lengths of sides.
Strand Bloom's Scope Hours Source Activities
Triangles: classify, logic, trig   Master 1.0 2004 Arkansas Mathematics Frameworks T.2.G.7 amended 2006 Classroom
  
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Measurement
Geometric probability
The learner will be able to calculate probabilities arising in geometric contexts (Example: Find the probability of hitting a particular ring on a dartboard).
Strand Bloom's Scope Hours Source Activities
Measure, Apply Formulas, Solve Problems   Master 1.0 2004 Arkansas Mathematics Frameworks M.3.G.1 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Lesson 11.6 [Textbook].  
  
Application problems
The learner will be able to apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms.
Strand Bloom's Scope Hours Source Activities
Measure, Apply Formulas, Solve Problems   Master 1.0 2004 Arkansas Mathematics Frameworks M.3.G.2 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Area & perimeter: lesson 1.7 [Textbook].  
· Geometry, McDougall Littell, Surface area, prisms, cylinders: Lesson 12.2 [Textbook].  
· Geometry, McDougall Littell, Volume, prisms, cylinders: Lesson 12.4 [Textbook].  
· Geometry, McDougall Littell, Polygons: lesson 11.2 [Textbook].  
· Geometry, McDougall Littell, Pyramids, cones: Lesson 12.3; Lesson 12.5 [Textbook].  
· Geometry, McDougall Littell, Spheres: lesson 12.6 [Textbook].  
· Geometry, McDougall Littell, Composite figures: all of chapter 12 [Textbook].  
  
Affects of changing attributes
The learner will be able to relate changes in the measurement of one attribute of an object to changes in other attributes (Example: How does changing the radius or height of a cylinder affect its surface area or volume?).
Strand Bloom's Scope Hours Source Activities
Measure, Apply Formulas, Solve Problems   Master 1.0 2004 Arkansas Mathematics Frameworks M.3.G.3 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Lesson 12.2: page 734: # 45, 46 [Textbook].  
· Geometry, McDougall Littell, Lesson 12.3: # 49 [Textbook].  
· Geometry, McDougall Littell, Lesson 12.6: # 33 [Textbook].  
· Add to lesson, Teacher made worksheet [Teaching Strategies].  
  
Similarity and proportional reasoning
The learner will be able to use (given similar geometric objects) proportional reasoning to solve practical problems (including scale drawings).
Strand Bloom's Scope Hours Source Activities
Measure, Apply Formulas, Solve Problems   Master 1.0 2004 Arkansas Mathematics Frameworks M.3.G.4 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Proportional reasoning: lesson 12.7 [Textbook].  
  
Parallel/Perp lines: Euclidean construct
The learner will be able to identify and apply properties of and theorems about parallel and perpendicular lines to prove other theorems and perform basic Euclidean constructions.
Strand Bloom's Scope Hours Source Activities
Measure, Apply Formulas, Solve Problems   Master 1.0 2004 Arkansas Mathematics Frameworks M.3.G.5 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Parallel lines/proportional reasoning: lesson 8.6 [Textbook].  
  
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Relationships between 2 and 3 Dimensions
Quadrilaterals
The learner will be able to explore and verify the properties of quadrilaterals.
Strand Bloom's Scope Hours Source Activities
2&3-D: Characteristics, properties   Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.1 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Properties of quadrilaterals: lesson 6.6 [Textbook].  
  
Properties of polygons
The learner will be able to solve problems using properties of polygons: 1. Sum of the measures of the interior angles of a polygon. 2. Interior and exterior angle measure of regular polygon or irregular polygon. 3. Number of sides or angles of a polygon.
Strand Bloom's Scope Hours Source Activities
2&3-D: Characteristics, properties   Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.2 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Sum of angles of polygon: lesson 11.1 [Textbook].  
· Geometry, McDougall Littell, Interior/exterior measures: regular/irregular poly [Textbook].  Lesson 11.1
· Geometry, McDougall Littell, Number sides/angles polygon: lesson 6.1 [Textbook].  
  
Tessellations
The learner will be able to identify and explain why figures tessellate.
Strand Bloom's Scope Hours Source Activities
2&3-D: Characteristics, properties   Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.3 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Tesselations: chapter 7 project [Textbook].  
  
Five Platonic Solids
The learner will be able to identify the attributes of the five Platonic Solids.
Strand Bloom's Scope Hours Source Activities
2&3-D: Characteristics, properties   Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.4 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Platonic solids: lesson 12.1; website [Textbook].  
  
Circles
The learner will be able to investigate and use the properties of angles (central and inscribed), arcs, chords, tangents, and secants to solve problems involving circles.
Strand Bloom's Scope Hours Source Activities
2&3-D: Characteristics, properties   Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.5 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Central angles, arcs, chords: lesson 10.2 [Textbook].  
· Geometry, McDougall Littell, Inscribed angles: lesson 10.3 [Textbook].  
· Geometry, McDougall Littell, Chords, tangents, secants: lesson 10.1 [Textbook].  
  
Inscribed and Circumscribed figures
The learner will be able to solve problems using inscribed and circumscribed figures.
Strand Bloom's Scope Hours Source Activities
2&3-D: Characteristics, properties   Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.6 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Lesson 10.3 [Textbook].  
  
Orthographic and Isometric drawings
The learner will be able to use orthographic drawings (top, front, side) and isometric drawings (corner) to represent three-dimensional objects.
Strand Bloom's Scope Hours Source Activities
2&3-D: Characteristics, properties   Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.7 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Chapter 3 project [Textbook].  
  
Cross-sections of 3-D
The learner will be able to draw, examine, and classify cross-sections of three-dimensional objects.
Strand Bloom's Scope Hours Source Activities
2&3-D: Characteristics, properties   Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.8 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Lesson 12.1 [Textbook].  
· Geometry, McDougall Littell, Website [Textbook].  
  
Non-Euclidean Geometries
The learner will be able to explore non-Euclidean geometries, such as spherical geometry and identify its unique properties which result from a change in the parallel postulate.
Strand Bloom's Scope Hours Source Activities
2&3-D: Characteristics, properties   Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.9 amended 2006 Classroom
  
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Coordinate Geometry & Transformations
Distance/midpoint/slope:coordinate plane
The learner will be able to use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines.
Strand Bloom's Scope Hours Source Activities
Location, Transformations, Relationships   Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.1 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Distance formula: lesson 1.3 [Textbook].  
· Geometry, McDougall Littell, Midpoint formula: lesson 1.5 [Textbook].  
· Geometry, McDougall Littell, Parrallel slope: lesson 3.6 [Textbook].  
· Geometry, McDougall Littell, Perpendicular slope: lesson 3.7 [Textbook].  
· Geometry, McDougall Littell, Horizontal slope: page 794 [Textbook].  
· Geometry, McDougall Littell, Vertical slope: page 794 [Textbook].  
  
Write equation of line: parallel
The learner will be able to write an equation of a line parallel to a line through a given point not on the line.
Strand Bloom's Scope Hours Source Activities
Location, Transformations, Relationships   Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.2 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Write equations in slope-intercept form [Textbook].  Page 794, lesson 3.6, lesson 3.7
· Geometry, McDougall Littell, Parallel slopes: lesson 3.6 [Textbook].  
· Geometry, McDougall Littell, Perpendicular slope: lesson 3.7 [Textbook].  
  
Write equation of line: perpendicular
The learner will be able to write an equation of a line perpendicular to a line through a given point.
Strand Bloom's Scope Hours Source Activities
Location, Transformations, Relationships   Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.3 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Parallelograms: lesson 6.3 [Textbook].  
· Geometry, McDougall Littell, Isosceles triangles: lesson 4.1 [Textbook].  
· Geometry, McDougall Littell, trapezoid: lesson 6.5 [Textbook].  
· Geometry, McDougall Littell, Properties of quadrilaterals [Textbook].  Lesson 6.3, lesson 6.4, lesson 6.5, lesson 6.6
  
Perpendicular Bisector
The learner will be able to write the equation of the perpendicular bisector of a line segment.
Strand Bloom's Scope Hours Source Activities
Location, Transformations, Relationships   Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.4 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Lesson 10.6 [Textbook].  
  
Determine type of figure
The learner will be able to determine, given a set of points, the type of figure based on its properties (parallelogram, isosceles triangle, trapezoid).
Strand Bloom's Scope Hours Source Activities
Location, Transformations, Relationships   Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.5 amended 2006 Classroom
  Instructional Resources
 
· Geometry, McDougall Littell, Translations: lesson 7.4 [Textbook].  
· Geometry, McDougall Littell, Reflections: lesson 7.2 [Textbook].  
· Geometry, McDougall Littell, Rotations: lesson 7.3 [Textbook].  
· Geometry, McDougall Littell, Dilations: lesson 8.7 [Textbook].  
  
Equation of Circle
The learner will be able to write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle.
Strand Bloom's Scope Hours Source Activities
Location, Transformations, Relationships   Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.6 amended 2006 Classroom
  
Transformations
The learner will be able to draw and interpret the results of transformations and successive transformations on figures in the coordinate plane 1. translations 2. reflections 3. rotations (90 degrees, 180 degrees, clockwise and counterclockwise about the origin) 4. dilations (scale factor).
Strand Bloom's Scope Hours Source Activities
Location, Transformations, Relationships   Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.7 amended 2006 Classroom
  
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