Poyen School
Poyen School Curriculum K - 12 2007-2008

Mathematics - ALE 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
Vocabulary, Reasoning, Application Master 1.0 2004 Arkansas Mathematics Frameworks LG.1.G.1 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Inductive Reasoning lesson 1.2 [Textbook].  
- Geometry Concepts and Skills, Deductive Reasoning: Lesson 2.5 [Textbook].  
- Add to lesson, Venn Diagrams: Worksheets [Teaching Strategies].  
- Add to lesson, Matrix Logic: Worksheets [Teaching Strategies].  
- Add to lesson, Pattern: Open Response [Teaching Strategies].  
- Geometry Concepts and Skills, matrix logic puzzle page 100 [Textbook].  
  
    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
Vocabulary, Reasoning, Application Master 1.0 2004 Arkansas Mathematics Frameworks LG.1.G.2 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Kinds of angles: p. 34 [Textbook].  
- Geometry Concepts and Skills, Exploring Intersections page 21 [Textbook].  
- Geometry Concepts and Skills, Exploring Intersections lesson 1.4 [Textbook].  
- Geometry Concepts and Skills, Lesson 1.5 Segments and their Measures [Textbook].  
- Geometry Concepts and Skills, Lesson 1.6 Angles & their Measures [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
Vocabulary, Reasoning, Application Master 1.0 2004 Arkansas Mathematics Frameworks LG.1.G.3 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Lesson 1.4 Sketching & Exploring Intersections [Textbook].  
- Geometry Concepts and Skills, Lesson 2.1 Segment Bisectors [Textbook].  
- Geometry Concepts and Skills, Folding Angle Bisectors page 60 [Textbook].  
- Geometry Concepts and Skills, Lesson 2.2 Angle Bisectors [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
Vocabulary, Reasoning, Application Master 1.0 2004 Arkansas Mathematics Frameworks LG.1.G.4 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Lesson 2.3 Complentary/Supplementary [Textbook].  
- Geometry Concepts and Skills, Page 74 Angles & Intersecting Lines [Textbook].  
- Geometry Concepts and Skills, Lesson 2.4 Vertical Angles [Textbook].  
- Geometry Concepts and Skills, Lines in Space page 107 [Textbook].  
- Geometry Concepts and Skills, Lesson 3.1 Parallel, Perpendicular [Textbook].  
- Geometry Concepts and Skills, Lesson 3.2 Theorems about perpendicular lines [Textbook].  
- Geometry Concepts and Skills, Brain Game page 166 Review types of angles [Textbook].  
  
    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
Vocabulary, Reasoning, Application Master 1.0 2004 Arkansas Mathematics Frameworks LG.1.G.5 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Parallel Lines and Angles pg 126-127 [Textbook].  
- Geometry Concepts and Skills, Lesson 3.4 Parallel LInes and transversals [Textbook].  
- Geometry Concepts and Skills, Lesson 3.5 Showing Lines are Parallel [Textbook].  
- Geometry Concepts and Skills, Lesson 3.6 Using Perpindicular & Parallel Lines [Textbook].  
- Geometry Concepts and Skills, Page 150-151 Technology Act, Parallel Lines & Slop [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
Vocabulary, Reasoning, Application Master 1.0 2004 Arkansas Mathematics Frameworks LG.1.G.6 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Lesson 2.6 Properties of equality and congruence [Textbook].  
- Geometry Concepts and Skills, page 191 activity 4.4 Discover Pythagorean Theorem [Textbook].  
  

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
Triangles: classify, logic, trig Master 1.0 2004 Arkansas Mathematics Frameworks T.2.G.1 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Lesson 5.1 Congruence & Triangles [Textbook].  
- Geometry Concepts and Skills, Lesson 5.2 Congruent Triangles [Textbook].  
- Geometry Concepts and Skills, Lesson 5.2 proving triangles congruent SSS & SAS [Textbook].  
- Geometry Concepts and Skills, Lesson 5.3 Proving triangles congruent ASA & AAS [Textbook].  
- Geometry Concepts and Skills, Lesson 5.4 Hypotnuse-leg [Textbook].  
- Geometry Concepts and Skills, Technology Activity p 264, investigating congruenc [Textbook].  
- Geometry Concepts and Skills, lesson 5.5 using congruent triangles [Textbook].  
- Geometry Concepts and Skills, lesson 7.1 ratio and proportion [Textbook].  
- Geometry Concepts and Skills, lesson 7.2 similar polygons [Textbook].  
- Geometry Concepts and Skills, lesson 7.3 showing triangles are similar, AA [Textbook].  
- Geometry Concepts and Skills, Lesson 7.4 shoeing triangles are similar SSS, SAS [Textbook].  
- Geometry Concepts and Skills, lesson 7.5 proportions & similar triangles [Textbook].  
- Geometry Concepts and Skills, Brain Game, page 406 [Textbook].  Use tangrams to create congruent and similar figures
  
    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
Triangles: classify, logic, trig Master 1.0 2004 Arkansas Mathematics Frameworks T.2.G.2 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Triangle inequality: lesson 4.7 [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
Triangles: classify, logic, trig Master 1.0 2004 Arkansas Mathematics Frameworks T.2.G.3 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Lesson 4.1, Classifying Triangles [Textbook].  
- Geometry Concepts and Skills, Lesson 4.3 Isosceles & Equilateral Triangles [Textbook].  
- Geometry Concepts and Skills, Activity 4.6 Intersecting Medians [Textbook].  
- Geometry Concepts and Skills, Lesson 4.6 Medians of a triangle [Textbook].  
- Geometry Concepts and Skills, Brain Game p 226, Review/Identify Vocabulary terms [Textbook].  
- Geometry Concepts and Skills, Activity 5.6 Investigating Bisectors [Textbook].  
- Geometry Concepts and Skills, Lesson 5.6 Angle & Perpendicular Bisectors [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
Triangles: classify, logic, trig Master 1.0 2004 Arkansas Mathematics Frameworks T.2.G.4 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Lesson 4.4 The Pythagorean Theorem & Distance Form [Textbook].  
- Geometry Concepts and Skills, Technology Activity Page 199, Application of Pytha [Textbook].  
- Geometry Concepts and Skills, Lesson 10.1 Simplifying square roots [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
Triangles: classify, logic, trig Master 1.0 2004 Arkansas Mathematics Frameworks T.2.G.5 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Lesson 10.2, 45-45-90 [Textbook].  
- Geometry Concepts and Skills, Activity p. 548, Special Right Triangles [Textbook].  
- Geometry Concepts and Skills, Lesson 10.3, 30-60-90 [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
Triangles: classify, logic, trig Master 1.0 2004 Arkansas Mathematics Frameworks T.2.G.6 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Lesson 10.4 Tangent [Textbook].  
- Geometry Concepts and Skills, Lesson 10.5 Sine & Cosine [Textbook].  
- Geometry Concepts and Skills, Lesson 10.6 Solving Right Triangles [Textbook].  
- Geometry Concepts and Skills, P 582 Brain Game, Right Triangle Bingo [Textbook].  
  
    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
Triangles: classify, logic, trig Master 1.0 2004 Arkansas Mathematics Frameworks T.2.G.7 amended 2006
Instructional Resources
- Geometry Concepts and Skills, p 556 Right Triangle Ratio [Textbook].  
  

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
Measure, Apply Formulas, Solve Problems Master 1.0 2004 Arkansas Mathematics Frameworks M.3.G.1 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Appendix 2 pg 713-714 Geometric Probability [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
Measure, Apply Formulas, Solve Problems Master 1.0 2004 Arkansas Mathematics Frameworks M.3.G.2 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Lesson 8.3 Area Squares & Rectangles [Textbook].  
- Geometry Concepts and Skills, Activity p 430 Finding Area of Triangles [Textbook].  
- Geometry Concepts and Skills, Lesson 8.4 Area of Triangles [Textbook].  
- Geometry Concepts and Skills, Lesson 8.5 Area of Parallelograms [Textbook].  
- Geometry Concepts and Skills, Lesson 8.6 Area of Trapezoids [Textbook].  
- Geometry Concepts and Skills, p 451 activity, finding area of circle [Textbook].  
- Geometry Concepts and Skills, Lesson 8.7 circumference & area of circle [Textbook].  
- Geometry Concepts and Skills, p 468-469 CH. 7-8 project, similarity & area [Textbook].  
- Geometry Concepts and Skills, activity p 481, investigating surface area [Textbook].  
- Geometry Concepts and Skills, Lesson 9.2, Surface area of prisms & cylinders [Textbook].  
- Geometry Concepts and Skills, lesson 9.3 surface area of pyramids & cones [Textbook].  
- Geometry Concepts and Skills, lesson 9.4 volume of prisms & cylinders [Textbook].  
- Geometry Concepts and Skills, Activity pg 508-509 Investigating Volume [Textbook].  
- Geometry Concepts and Skills, Lesson 9.5 volume of pyramids-cones [Textbook].  
- Geometry Concepts and Skills, Lesson 9.6 Surface area & volume of spheres [Textbook].  
- Geometry Concepts and Skills, Brain Games pg 530, volume [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
Measure, Apply Formulas, Solve Problems Master 1.0 2004 Arkansas Mathematics Frameworks M.3.G.3 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Technology Activity pg. 438 Area of Similar Triang [Textbook].  
- Geometry Concepts and Skills, Appendix 3 pg 715-716 changing dimensions of a fig [Textbook].  
  
    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
Measure, Apply Formulas, Solve Problems Master 1.0 2004 Arkansas Mathematics Frameworks M.3.G.4 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Lesson 7.1 Ratio and Proportion [Textbook].  
- Geometry Concepts and Skills, p468-469, ch 7-8 project, similarity & area [Textbook].  
- Geometry Concepts and Skills, ch 9-10 project, pg 584-585, indirect measurement [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
Measure, Apply Formulas, Solve Problems Master 1.0 2004 Arkansas Mathematics Frameworks M.3.G.5 amended 2006
Instructional Resources
- Geometry Concepts and Skills, lesson 3.1, parallel & perpendicular [Textbook].  
  

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
2&3-D: Characteristics, properties Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.1 amended 2006
Instructional Resources
- Geometry Concepts and Skills, activity 6.2 investigating parallelograms [Textbook].  
- Geometry Concepts and Skills, lesson 6.2, properties of parallelograms [Textbook].  
- Geometry Concepts and Skills, lesson 6.3 showing quadrilaterals are parallelogra [Textbook].  
- Geometry Concepts and Skills, Technology Activity p 324, making parallelograms [Textbook].  
- Geometry Concepts and Skills, lesson 6.4 Rhombuses, Rectangles, and Squares [Textbook].  
- Geometry Concepts and Skills, Technology Activity p 331, midsegment of a trapez [Textbook].  
- Geometry Concepts and Skills, lesson 6.5, Trapezoids [Textbook].  
- Geometry Concepts and Skills, lesson 6.6 reasoning about special quadrilaterals [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
2&3-D: Characteristics, properties Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.2 amended 2006
Instructional Resources
- Geometry Concepts and Skills, lesson 4.2 Measures of a triangle [Textbook].  
- Geometry Concepts and Skills, lesson 6.1 polygons [Textbook].  
- Geometry Concepts and Skills, lesson 8.1 classifying polygons [Textbook].  
- Geometry Concepts and Skills, activity p 416, angle sum of polygons [Textbook].  
- Geometry Concepts and Skills, lesson 8.2 angles in polygons [Textbook].  
  
    Tessellations
The learner will be able to identify and explain why figures tessellate.
Strand Bloom's Scope Hours Source
2&3-D: Characteristics, properties Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.3 amended 2006
Instructional Resources
- Geometry Concepts and Skills, tessellations chapter 5-6 [Textbook].  
- Geometry Concepts and Skills, Add to lesson: tessalation activity: math crusades [Textbook].  
  
    Five Platonic Solids
The learner will be able to identify the attributes of the five Platonic Solids.
Strand Bloom's Scope Hours Source
2&3-D: Characteristics, properties Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.4 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Platonic solids: lesson 9.1; 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
2&3-D: Characteristics, properties Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.5 amended 2006
Instructional Resources
- Geometry Concepts and Skills, lesson 11.1 parts of circle [Textbook].  
- Geometry Concepts and Skills, activity pg 594 tangents & circles [Textbook].  
- Geometry Concepts and Skills, lesson 11.2 properties of tangents [Textbook].  
- Geometry Concepts and Skills, lesson 11.3 arcs & central angles [Textbook].  
- Geometry Concepts and Skills, lesson 11.4 arcs & chords [Textbook].  
- Geometry Concepts and Skills, lesson 11.6 properties of chords [Textbook].  
- Geometry Concepts and Skills, technology activity p 626, intersecting secants [Textbook].  
  
    Inscribed and Circumscribed figures
The learner will be able to solve problems using inscribed and circumscribed figures.
Strand Bloom's Scope Hours Source
2&3-D: Characteristics, properties Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.6 amended 2006
Instructional Resources
- Geometry Concepts and Skills, activity p 613 exploring inscribed angles [Textbook].  
- Geometry Concepts and Skills, lesson 11.5 inscribed angles & polygons [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
2&3-D: Characteristics, properties Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.7 amended 2006
Instructional Resources
- Geometry Concepts and Skills, lesson 2.7 isometric & orthographic drawings [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
2&3-D: Characteristics, properties Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.8 amended 2006
Instructional Resources
- Geometry Concepts and Skills, lesson 2.7 crosssections page 113 [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
2&3-D: Characteristics, properties Master 1.0 2004 Arkansas Mathematics Frameworks R.4.G.9 amended 2006
Instructional Resources
- Geometry, Prentice Hall, lesson 7.5, exploring spherical Geometry [Textbook].  
  

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
Location, Transformations, Relationships Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.1 amended 2006
Instructional Resources
- Geometry Concepts and Skills, lesson 2.1, midpoint formula [Textbook].  
- Geometry Concepts and Skills, lesson 4.4 The Pythagorean Theorem & Distance Form [Textbook].  
- Geometry, Prentice Hall, lesson 2.3, slopes parralles & perpendicular lines [Textbook].  
- Geometry Concepts and Skills, Yellow WB: pg 77, 85, 91-92 [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
Location, Transformations, Relationships Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.2 amended 2006
Instructional Resources
- Geometry Concepts and Skills, YELLOW WB pg 91-92 [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
Location, Transformations, Relationships Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.3 amended 2006
Instructional Resources
- Geometry Concepts and Skills, YELLOW WB pg 91-92 [Textbook].  
  
    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
Location, Transformations, Relationships Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.4 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Add to Lesson: Yellow WB pg 91-92 [Textbook].  
- Geometry Concepts and Skills, Add to Lesson: Teacher made WS [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
Location, Transformations, Relationships Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.5 amended 2006
  
    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
Location, Transformations, Relationships Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.6 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Lesson 11.7 Equations of Circles [Textbook].  
  
    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
Location, Transformations, Relationships Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.7 amended 2006
Instructional Resources
- Geometry Concepts and Skills, Lesson 3.7, Translations [Textbook].  
- Geometry Concepts and Skills, Activity 5.7 Investigating Reflections [Textbook].  
- Geometry Concepts and Skills, Lesson 5.7 Reflections & Symmetry [Textbook].  
- Geometry Concepts and Skills, Brain Game pg 298, Reflection & Symmetry [Textbook].  
- Geometry Concepts and Skills, Lesson 7.6 Dilations [Textbook].  
- Geometry Concepts and Skills, Technology Activity p 399, Dilations using coordin [Textbook].  
- Geometry Concepts and Skills, Lesson 11.8, Rotations [Textbook].  
  

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