School City of Hobart Mathematics The ISTEP+ assessment measures the academic performance of students in Mathematics. IN: Geometry The Indiana Academic Standards for Mathematics include standards for students in Geometry. |
Functions |
The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. |
Trigonometric Functions: Define
The learner will be able to define the trigonometric functions with regard to the angles of right triangles.
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Trigonometric Functions: Apply
The learner will be able to apply the trigonometric functions with regard to the angles of right triangles.
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Geometry |
The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. Students study properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving. |
Figures: Explain/Points on Spheres
The learner will be able to explain sets of points on spheres including chords, tangents, and great circles.
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Solids: Recognize/Understand
The learner will be able to recognize and understand properties of congruent and similar three-dimensional solids.
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Figures: Polyhedra
The learner will be able to explain relationships and symmetries, and apply congruence and similarity of polyhedra.
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Triangles: Recognize/Explain
The learner will be able to recognize and explain triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.
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Circles: Define/Determine/Apply
The learner will be able to define, determine, and apply measures of circumference, arc length, and areas of circles and sectors and solve problems using these measures.
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Circles: Define/Recognize
The learner will be able to define and recognize congruent, similar, and concentric circles.
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Circle Concepts: Relating
The learner will be able to identify, define, and determine how the following circle parts are related: arc, radius, diameter, chord, secant, and tangent.
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Circles: Measure/Angles/Lengths/Areas
The learner will be able to determine measures of angles, lengths, and areas of circles.
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Circle Concepts: Define/Determine/Apply
The learner will be able to identify, define, and apply arc measures and related angles.
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Proofs: Write
The learner will be able to compose geometric proofs, including proofs by contradiction and proofs using coordinate geometry.
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Proving: Circles
The learner will be able to prove and/or apply theorems involving the properties of circles.
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Proof: Recognize/Example
The learner will be able to recognize and give examples of undefined terms, axioms, and theorems and inductive and deductive proofs.
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Proofs: Apply/Compare
The learner will be able to apply and make comparisons of many different ways to present deductive proofs.
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Logic: Write/Interpret
The learner will be able to write and interpret "if - then" and "if and only if" statements.
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Logic: Converse/Inverse/Contrapositive
The learner will be able to express, apply, and examine the validity of the converse, inverse, and contrapositive of "if - then" statements.
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Constructions: Segments/Angles
The learner will be able to construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines applying a straight edge and compass, describing and justifying the steps used.
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Constructions: Geometric/Perform
The learner will be able to perform basic geometric constructions (copy line and angle, bisect line segments and angles, perpendicular lines and parallel lines).
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Congruence/Similarity: Apply
The learner will be able to apply the properties of congruent and similar quadrilaterals to obtain solutions to problems involving length and area.
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Inequality Theorems
The learner will be able to verify, comprehend, and use the inequality theorems: triangle inequality, inequality in one triangle, and hinge theorem.
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Theorem: Triangle Inequality
The learner will be able to obtain problem solutions through the application of the Triangle Inequality Theorem.
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Prove: Use/Theorems
The learner will be able to prove and use theorems involving segments divided proportionally.
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Quadrilaterals: Explain/Classify
The learner will be able to explain, classify, and comprehend relationships among the following quadrilaterals: square, rectangle, rhombus, parallelogram, trapezoid, and kite.
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Polygons: Determine/Apply
The learner will be able to determine and apply measures of sides, perimeters, and areas of polygons, and associate these measures with each other using formulas.
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Polygons: Apply
The learner will be able to apply symmetry, tessellations, and transformations of polygons.
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Polygons: Recognize/Explain
The learner will be able to recognize and explain convex, concave, and regular polygons.
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Polygons: Describe/Identify
The learner will be able to describe and identify geometric polygons.
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Polygons: Exterior/Interior Angles
The learner will be able to determine the measures of interior and exterior angles of polygons, justifying the strategy used.
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Figures: Describe/Polyhedron
The learner will be able to explain the polyhedron that can be created from a given net.
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Figures: Describe/Polyhedron/Net
The learner will be able to explain the net for a given polyhedron.
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Figures: Explain/Polyhedra
The learner will be able to explain polyhedra.
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Angle Relationships: Comprehend
The learner will be able to comprehend the relationships between special pairs of angles formed by parallel lines and transversals.
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Angle Relationships: Apply
The learner will be able to apply the relationships between special pairs of angles formed by parallel lines and transversals.
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Solids: Describe Characteristics
The learner will be able to describe relationships among faces, edges, and vertices of different polyhedra.
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Solids: Symmetry/Describe
The learner will be able to describe symmetry within three-dimensional solids.
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Solids: Describe
The learner will be able to describe three-dimensional solids.
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Solids: Construct/Polyhedra
The learner will be able to construct polyhedra.
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Solids: Create
The learner will be able to create solid figures.
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Shapes: Construct/Polyhedra
The learner will be able to construct a model and describe regular and non-regular polyhedra.
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Congruent/Similar: Triangles
The learner will be able to prove triangles congruent and similar.
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Line Segment: Length
The learner will be able to determine line segment lengths.
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Line Segment: Midpoint
The learner will be able to determine the midpoint of a line segment.
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Angles: Bisector/Define
The learner will be able to define an angle bisector.
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Triangles: Identify/Altitude
The learner will be able to recognize altitudes of any triangle.
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Triangles: Identify/Median
The learner will be able to recognize medians of any triangles.
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Triangles: Perpendicular Bisector
The learner will be able to recognize perpendicular bisectors of any triangle.
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Triangles: Angle Bisector
The learner will be able to recognize angle bisectors of any triangle.
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Triangles: Recognize
The learner will be able to recognize various types of triangles.
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Triangles: Perpendicular Bisector
The learner will be able to define perpendicular bisectors of triangles.
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Triangles: Define/Median
The learner will be able to define the median of a triangle.
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Triangles: Define/Altitude
The learner will be able to define the altitude of a triangle.
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Triangles: Explain
The learner will be able to explain various types of triangles.
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Triangles: Draw/Altitude
The learner will be able to draw the altitude of a triangle.
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Triangles: Draw/Median
The learner will be able to draw the medians of the sides of a triangle.
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Triangles: Draw/Perpendicular Bisector
The learner will be able to draw the perpendicular bisectors of the sides of a triangle.
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Triangles: Measure/Sides
The learner will be able to find the measure of the sides of a triangle.
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Triangles: Corresponding Parts
The learner will be able to apply concepts involving the corresponding parts of congruent triangles.
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Triangles: Draw/Angle Bisector
The learner will be able to construct the angle bisectors of any triangle.
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Circle: Center
The learner will be able to identify the center point of a circle.
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Circle: Define/Concepts
The learner will be able to define concepts related to circles.
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Circles: Circumscribe
The learner will be able to circumscribe circles.
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Circles: Inscribe
The learner will be able to inscribe circles.
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Circle: Equation
The learner will be able to determine equations of circles.
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Circle: Equation/Coordinate Plane
The learner will be able to determine the equation of a circle in the coordinate plane with regard to its center and radius.
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Circle: Construct/Tangents
The learner will be able to construct circle tangents.
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Circle: Construct/Non-Collinear Points
The learner will be able to construct a circle which contains three non-collinear points.
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Pythagorean Theorem: Apply
The learner will be able to apply the Pythagorean Theorem.
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Pythagorean Theorem: Problem Solving
The learner will be able to solve problems using the Pythagorean Theorem.
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Pythagorean Theorem: Prove
The learner will be able to create a proof for the Pythagorean Theorem.
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Transformation: Apply/Polygons
The learner will be able to determine congruence, similarity, symmetry, and tessellations by applying transformations to polygons.
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Translation: Understand/Congruence
The learner will be able to understand that images that are made by translations are congruent to the original image.
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Geometric Concepts: Conjectures
The learner will be able to formulate conjectures about geometric concepts.
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Similarity: Apply/Quadrilaterals
The learner will be able to apply the similarity of quadrilaterals.
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Similarity: Apply/Triangles
The learner will be able to apply the similarity of triangles.
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Constructions: Explain/Procedures
The learner will be able to explain the procedures used for basic geometric constructions.
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Constructions: Distinguish
The learner will be able to distinguish between drawing figures and constructing figures.
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Constructions: Procedures/Justify
The learner will be able to make justifications for the procedures for basic geometric constructions.
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Properties: Apply/Triangles
The learner will be able to apply the properties of congruent and similar triangles to obtain solutions to problems involving lengths and areas.
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Congruence: Apply/Quadrilaterals
The learner will be able to apply the congruence of quadrilaterals.
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Congruence: Apply/Triangles
The learner will be able to apply the congruence of triangles.
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Congruency: Triangles/Construct
The learner will be able to construct a triangle which is congruent to a given triangle.
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Problem Solving: Polygons
The learner will be able to use the properties of similar polygons in obtaining problem solutions.
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Problem Solving: Polygons
The learner will be able to use the properties of congruent polygons in obtaining problem solutions.
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Perpendicular Lines: Describe
The learner will be able to describe perpendicular lines.
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Parallel Lines: Describe
The learner will be able to describe parallel lines.
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Parallel Lines: Use
The learner will be able to use parallel lines.
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Perpendicular Lines: Use
The learner will be able to use perpendicular lines.
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Quadrilaterals: Identify/Simple
The learner will be able to recognize simple quadrilaterals.
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Quadrilaterals: Explain/Simple
The learner will be able to explain simple quadrilaterals.
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Quadrilaterals: Prove/Properties
The learner will be able to prove properties of quadrilaterals using coordinate geometry.
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Polygons: Apply/Congruence
The learner will be able to apply congruence to polygons.
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Polygons: Apply/Similarity
The learner will be able to apply similarity to polygons.
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Polygons: Measure/Interior Angles
The learner will be able to measure the interior angles of polygons.
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Polygons: Measure/Exterior Angles
The learner will be able to measure the exterior angles of polygons.
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Polygons: Prove/Properties
The learner will be able to prove properties of polygons using coordinate geometry.
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Mathematics Processes |
The Mathematics Processes Unit includes Competencies/Objectives which focus on mathematical connections. Students communicate and model concepts and procedures. |
Math as Reasoning: Create/Evaluate
The learner will be able to create and evaluate mathematical arguments and proofs.
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Argument: Formulate/Judge Validity
The learner will be able to formulate logical arguments, assess their validity, and give counterexamples that disprove statements.
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Conjecture: Distinguish
The learner will be able to distinguish between data that supports a conjecture and proof of a conjecture.
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Measurement |
The Measurement Unit includes Competencies/Objectives which focus on measurement concepts, applications, and analysis. Students study length, area, circumference, perimeter, volume, weight, formulas, distance, calendar, money, tools, accuracy, units, constructions, patterns, and problem solving. |
Length/Perimeter/Area: Measure
The learner will be able to determine the side length, perimeter, and area of polygons by measuring.
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Length/Perimeter/Area Quadrilaterals
The learner will be able to determine the side length, perimeter, and area of quadrilaterals by measuring.
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Perimeter: Triangle
The learner will be able to determine the perimeter of a triangle.
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Length/Perimeter/Area: Quadrilaterals
The learner will be able to apply the side, perimeter, and area measure of quadrilaterals.
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Length/Perimeter/Area: Relating
The learner will be able to use formulas to determine how the side length, perimeter, and area of quadrilaterals are related.
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Perimeter/Area: Applying Formulas
The learner will be able to use formulas to relate the measures of sides, perimeters, and areas of triangles to each other.
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Area of a Triangle: Determine
The learner will be able to find the area of a triangle.
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Problem Solving |
The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems. |
Solutions: Evaluate Reasonableness
The learner will be able to evaluate the reasonableness of a given solution within the context of the original problem.
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Strategies: Use
The learner will be able to use a variety of strategies to solve problems.
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Real Numbers and the Coordinate Plane |
The Real Numbers and the Coordinate Plane Unit includes Competencies/Objectives which focus on graphing concepts. Students graph equations and make connections between algebraic concepts and their geometric correspondences. |
Coordinate Geometry: Length/Midpoint
The learner will be able to determine the lengths and midpoints of line segments in one- or two-dimensional coordinate systems.
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Linear Equations
The learner will be able to find the slope, equation of the line, or properties of parallelism or perpendicularity of given lines using concepts of coordinate geometry.
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Slope: Determine/Line
The learner will be able to determine the slope of a line.
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Coordinate Geometry: Triangles
The learner will be able to prove properties of triangles using coordinate geometry.
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Equations of the Line: Determine
The learner will be able to determine the equations of lines.
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Trigonometry |
The Trigonometry Unit includes Competencies/Objectives which focus on trigonometric concepts. Students study triangles, trigonometric ratios, and triangle measurements; apply triangle properties; and solve right triangle problems. |
Trigonometric Concepts: Define/Use
The learner will be able to define and use the trigonometric relations of sine, cosine, and tangent.
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Right Triangle: Relationships
The learner will be able to state and use the relationships that are present when the altitude is drawn to the hypotenuse of a right triangle.
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Right Triangle: Use/Understand
The learner will be able to apply and understand the relationship sin^2 (x) + cos^2 (x) = 1.
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Right Triangles: Solve/Word Problems
The learner will be able to obtain solutions to word problems using right triangles.
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Right Triangles: Use/Special
The learner will be able to obtain solutions to problems using special right triangles.
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