Poyen School
Poyen School Curriculum K - 12 2007-2008

Mathematics - Investigating 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).
Strand Bloom's Scope Hours Source
Vocabulary, Reasoning, Application Master 1.0 2004 Arkansas Mathematics Frameworks LG.1.G.1
  
    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
  
    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
  
    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
  
    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
  
    Deductive reasoning/justify conclusions
The learner will be able to give justification for conclusions reached by deductive reasoning.
Strand Bloom's Scope Hours Source
Vocabulary, Reasoning, Application Master 1.0 2004 Arkansas Mathematics Frameworks LG.1.G.6
  

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
  
    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
  
    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
  
    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
  
    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
  
    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
  

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
  
    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, prims, 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
  
    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
  
    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
  
    Parallel lines: proportional reasoning
The learner will be able to use properties of parallel lines and proportional reasoning to find the lengths of segments.
Strand Bloom's Scope Hours Source
Measure, Apply Formulas, Solve Problems Master 1.0 2004 Arkansas Mathematics Frameworks M.3.G.5
  

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
  
    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
  
    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
  
    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
  
    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
  
    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
  
    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
  
    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
  

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
  
    Slope-intercept form
The learner will be able to write equations of lines in slope-intercept form and use slope to determine parallel and perpendicular lines.
Strand Bloom's Scope Hours Source
Location, Transformations, Relationships Master 1.0 2004 Arkansas Mathematics Frameworks CGT.5.G.2
  
    Use coordinates to classify 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.3
  
    Write equation of a 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.4
  
    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. Rotaions (90,180 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.5
  

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