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 2008 by Mahomet-Seymour Schools.
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Mahomet-Seymour Schools

Curriculum

Mathematics - Geometry

 

Discovering Points, Lines, Planes and Angles

 

The learner will be able to graph ordered pairs on a coordinate plane.

 

  

 

The learner will be able to identify collinear points.

 

  

 

The learner will be able to identify and model points, lines and planes.

 

  

 

The learner will be able to identify coplanar points and intersecting lines and planes.

 

  

 

The learner will be able to solve problems by listing the possibilities.

 

  

 

The learner will be able to solve problems by listing the possibilities.

 

  

 

The learner will be able to solve problems by using formulas.

 

  

 

 

The learner will be able to find maximum areas of a rectangle for a given perimeter.

 

  

 

The learner will be able to find the distance between two points on a number line and between points in a coordinate plane.

 

The learner will be able to use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle.

 

The learner will be able to find the midpoint of a segment.

 

The learner will be able to complete proofs involving segment theorems.

 

The learner will be able to identify angles and classify angles.

 

The learner will be able to use the Angle Addition Postulate to find the measures of angles.

The learner will be able to identify and use congruent angles and the bisectors of angles.

 

The learner will be able to identify and use adjacent, vertical, complementary, supplementary, and linear pairs of angles and perpendicular lines.

 

The learner will be able to determine what information can and cannot be assumed from a diagram.

 

The learner will be able to use a compass and straight edge to do basic geometric constructions (copy angles and segments, bisect angles and segments, perpendicular bisectors).

 

  

 

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Connecting Reasoning and Proof

 

The learner will be able to make conjectures based on inductive reasoning.

 

  

 

The learner will be able to write a statement in if-then form.

 

  

 

The learner will be able to write the converse, inverse and contrapositive of an if-then statement.

 

  

 

The learner will be able to identify and use basic postulates about points, lines and planes.

 

  

 

The learner will be able to use the Law of Detachment and the Law of Syllogism in deductive reasoning.

 

  

 

The learner will be able to solve problems by looking for a pattern.

 

  

 

The learner will be able to use properties of equality in algebraic and geometric proofs.

 

  

 

The learner will be able to complete proofs involving segment theorems.

 

  

 

The learner will be able to complete proofs involving angle theorems.

 

  

 

 

 

  

 

 

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Using Perpendicular and Parallel Lines

 

The learner will be able solve problems by drawing a diagram.

 

  

 

The learner will be able identify the relationships between two lines or between two planes.

 

  

 

The learner will be able to name angles formed by a pair of lines to determine angle measures.

 

The learner will be able to use the properties of parallel lines to determine angle measures.

 

  

 

The learner will be able to find slopes of lines.

 

  

 

The learner will be able use slope to identify parallel and perpendicular lines.

 

  

 

The learner will be able to recognize angle conditions that produce parallel lines.

 

  

 

The learner will be able to prove two lines are parallel based on given angle relationships.

 

  

 

The learner will be able to recognize and use distance relationships among points, lines and planes.

 

  

 

 

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Identifying Congruent Triangles

 

The learner will be able to identify the parts of triangles and classify triangles by their parts.

 

  

 

The learner will be able to apply the Angle Sum Theorem.

 

  

 

The learner will be able to apply the Exterior Angle Theorem.

 

  

 

The learner will be able to name and label corresponding parts of congruent triangles.

 

  

 

 

The learner will be able to use SSS, SAS and ASA postulates to test for triangle congruence.

 

  

 

The learner will be able to use the AAS Theorem to test triangle congruence.

 

  

 

The learner will be able to solve problems by eliminating the possibilities.

 

  

 

The learner will be able to use properties of isosceles and equilateral triangles.

 

  

 

 

 

 

 

 

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Applying Congruent Triangles

 

The learner will be able to identify and use medians, altitudes, angle bisectors, and perpendicular bisectors in a triangle.

 

The learner will be able to recognize and use tests for congruence of right triangles (Hypotenuse Leg HL).

 

The learner will be able to use indirect reasoning and indirect proofs to reach a conclusion.

 

The learner will be able to recognize and apply properties of inequalities to the measures of segments and angles.

 

The learner will be able to solve problems by working backwards.

 

The learner will be able to recognize and apply relationships between sides and angles in a triangle.

 

The learner will be able to apply the Triangle Inequality Theorem.

 

The learner will be able to apply the SAS Inequality and the SSS Inequality.

 

 

 

 

 

 

 

 

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Exploring Quadrilaterals

 

The learner will be able to recognize and apply the properties of a parallelogram.

 

The learner will be able to recognize and apply the conditions that ensure a quadrilateral is a parallelogram. 

 

The learner will be able to identify and use sub goals in writing proofs.

 

The learner will be able to recognize and apply the properties of rectangles.

 

The learner will be able to recognize and apply the properties of squares and rhombi.

 

The learner will be able to recognize and apply the properties of trapezoids.

 

 

 

 

 

 

 

 

 

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Connecting Proportion and Similarity

 

The learner will be able to recognize and use ratios and proportions.

 

The learner will be able to apply the properties of proportions.

 

The learner will be able to identify similar figures.

 

The learner will be able to solve problems involving similar figures.

 

The learner will be able to identify similar triangles.

 

The learner will be able to use similar triangles to solve problems.

The learner will be able to use proportional parts of triangles to solve problems.

 

The learner will be able to recognize and use the proportional relationships of corresponding perimeters, altitudes, angle bisectors, and medians of similar triangles.

 

 

 

 

 

 

 

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Applying Right Triangles and Trigonometry

 

The learner will be able to find the geometric mean between two numbers.

 

The learner will be able to solve problems involving relationships between parts of a triangle and the altitude to its hypotenuse.

 

The learner will be able to use the Pythagorean Theorem and its converse.

 

The learner will be able to use the properties of 45-45-90 and 30-60-90 triangles.

 

The learner will be able to find trigonometric ratios using right triangles.

 

The learner will be able to solve problems using trigonometric ratios.

 

The learner will be able to use trigonometry to solve problems involving angles of elevation and depression.

 

 

  

 

 

 

 

 

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Applying Circles

 

The learner will be able to identify and use parts of circles.

 

The learner will be able to solve problems involving the circumference of a circle.

 

The learner will be able to recognize major arcs, minor arcs, semicircles, and central angles.

 

The learner will be able to find measures of arcs and central angles.

 

The learner will be able to solve problems by making circle graphs.

 

The learner will be able to recognize and use relationships among arcs, chords, and diameters.

 

The learner will be able to recognize and find measures of inscribed angles.

 

The learner will be able to apply properties of inscribed figures.

 

The learner will be able to recognize tangents and use properties of tangents.

The learner will be able to find the measures of angles formed by intersecting secants and tangents in relation to intercepted arcs.

 

The learner will be able to use properties of chords, secants, and tangents to solve segment measure problems.

 

The learner will be able to write and use the equation of a circle in the coordinate plane.

 

 

  

 

 

 

 

 

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Exploring Polygons and Area

 

 

 

The learner will be able to identify and name polygons.

 

The learner will be able to find the sum of the measures of interior and exterior angles of a convex polygon and find the measures of interior and exterior angles of a regular polygon.

 

The learner will be able to solve problems involving angle measures of polygons.

 

The learner will be able to find the area of a parallelogram.

 

The learner will be able to find the areas of triangles, rhombi, and trapezoids.

 

The learner will be able to find the areas of regular polygons.

 

The learner will be able to find the areas of circles.

 

 

 

 

 

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Investigating Surface Area and Volume

 

The learner will be able to name and identify three-dimensional figures.

 

The learner will be able to find the lateral area and surface area of a right prism.

 

The learner will be able to find the lateral area and surface area of a right cylinder.

 

The learner will be able to find the lateral area and surface area of a right pyramid.

 

The learner will be able to find the lateral area and surface area of a right circular cone.

 

The learner will be able to find the volume of a right prism.

 

The learner will be able to find the volume of a right cylinder.

 

The learner will be able to Find the volume of a right pyramid.

 

The learner will be able to find the volume of a right circular cone.

 

The learner will be able to recognize and define basic properties of spheres.

 

The learner will be able to find the surface area and volume of a sphere.

 

The learner will be able to identify congruent or similar solids.

 

The learner will be able to state properties of congruent solids.

 

 

  

 

 

 

 

 

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Continuing Coordinate Geometry

 

The learner will be able to graph linear equations using the intercepts method and the slope-intercept method.

 

The learner will be able to write an equation of a line given information about its graph.

 

The learner will be able to solve problems by using equations.

 

The learner will be able to relate statistics and equations of lines to geometric concepts.

 

The learner will be able to prove theorems using coordinate geometry.

 

The learner will be able to find the magnitude and direction of a vector.

 

The learner will be able to determine if two vectors are equal.

 

The learner will be able to perform operations with vectors.

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