Basic Geometry Course Name: Geometry Unit: 1 Terminology & Fundamental Definitions Time Line: 4 to 6 weeks Building Blocks of Geometry Define & identify point, line, plane angle, segment, ray, midpoint, bisector Classify angles according to size Identify relationships between angles (vertical angles, parallel lines with transversal, perpendicular lines) Performance Objectives Develop dictionary terms and symbols Measure and construct specific angles with compass, protractor, & straight edge Determine angle measures dealing with vertical angles and parallel & perpendicular lines Assessment Teacher Resources Standards Teacher designed quizzes and chapter test using book generated tests & quizzes augmented by other problems. Teacher designed quizzes and chapter test using book generated tests & quizzes augmented by other problems. Teacher designed quizzes and chapter test using book generated tests & quizzes augmented by other problems. 2.3.11.B 2.9.11.C M11.C.3.1 2.3.11.B 2.9.11.C M11.B.2.1 2.3.11.B 2.9.11.C M11.B.2.1
Geometry Course Name: Geometry Unit: 2 Triangles, Congruence, & Similarity Time Line: 4 to 6 weeks Describing and Comparing Triangles Classify triangles with respect to the angles as well as with the sides Apply the Pythagorean Theorem Decide if triangles are congruent Determine similarity & solve problems using similarity Performance Objectives Define and identify acute, obtuse, and right triangles. Define and identify scalene, isosceles, and equilateral triangles. Determine the length of the hypotenuse of a right triangle. Determine whether a triangle is acute, right, or obtuse by applying the Pythagorean Theorem. Define congruence Apply congruence theorems: SSS, SAS, ASA, AAS, HL Determine corresponding parts of congruent triangles Review ratio & proportion Define similarity and similar triangles Assessment Teacher Resources Standards generated tests & quizzes generated tests & quizzes generated tests & quizzes generated tests & quizzes 2.9.11.B 2.9.11.D M11.B.2.1 2.9.11.B 2.9.11.D M11.A.1.1 M11.A.2.2 M11.C.1.4 M11.C.3.1 2.9.11.B 2.9.11.D M11.C.1.2 M11.C.1.3 2.9.11.B 2.9.11.D M11.A.2.1 M11.C.1.3
Geometry Course Name: Geometry Unit: 3 Quadrilaterals Time Line: 4 to 6 weeks Investigating 4 sided figures Identify polygons according to number of sides Find interior and exterior angle measurements for quadrilaterals Identify special quadrilaterals Performance Objectives Develop terminology for polygons and their parts Solve for missing angles in quadrilaterals Compare and contrast properties of parallelograms, rectangles, rhombuses, trapezoids, and squares. Solve for missing side lengths for various special quadrilaterals. Assessment Teacher Resources Standards generated problems sources generated problems sources generated problems sources 2.9.11.C 2.9.11.E 2.9.11.J M11.C.1.2 2.9.11.C 2.9.11.E 2.9.11.J M11.B.2.1 M11.C.1.2 2.9.11.C 2.9.11.E 2.9.11.J M11.C.1.2
Geometry Course Name: Geometry Unit: 4 Area & Volume Time Line: 4 to 6 weeks Using Ratio & Proportions to Determine Sizes in Shapes Determine the angles in polygons with the Angle Sum Theorem Use are formulas for common shapes; such as rectangles & parallelograms, triangles & trapezoids, circles & sectors, and regular polygons. Use formulas to solve surface area and volume problems for solid figures; such as prisms & cylinders, pyramids & cones, and spheres. Performance Objectives Calculate the angle sum for a polygon, given the number of sides. Solve for the missing angle for a polygon, using the Angle Sum Theorem. Calculate the area of standard shapes. Create a strategy, then apply it to solve the area of a complex shape. Dissect common 3-D figures into their respective bases and sides to apply the appropriate area formulas to calculate the surface area of the object. Calculate the volume for a solid figure using the appropriate formula. Assessment Teacher Resources Standards generated examples generated examples generated examples 2.3.11.B M11.B.2.1 M11.D.1.1 2.3.11.B M11.B.2.2 M11.B.2.3 2.3.11.B M11.B.2.2 M11.B.2.3
Geometry Course Name: Geometry Unit: 5 Right Triangles & Intro to Trigonometry Time Line: 3 weeks Common Right Triangles with Sine, Cosine, and Tangent Simplify radicals Apply the common right triangles whose sides are whole numbers Apply the 45-45-90 and 30-60- 90 right triangles Use sine, cosine & tangent to solve right triangle problems Performance Objectives Simplify square roots without the aid of a calculator Use special right triangles and the concept of similar triangles to solve the missing side in specific right triangles. 3-4 - 5 5-12-13 8-15-17 7-24-25 Apply the appropriate side ratios with the special degree right triangles to determine the missing sides. Convert proportions of the sides in right triangles to basic trigonometry functions Calculate the sine, cosine, and tangent ratios in right triangles. Assessment Teacher Resources Standards generated examples generated examples generated examples generated examples 2.1.11.A 2.8.11.S M11.A.1.1 M11.A.2.2 2.1.11.A 2.8.11.S M11.A.1.1 M11.A.1.2 M11.A.1.3 M11.A.2.1 M11.C.1.4 2.1.11.A 2.8.11.S M11.A.1.1 M11.A.1.3 M11.A.2.1 2.1.11.A 2.8.11.S M11.A.1.1 M11.A.1.3 M11.A.2.1 M11.A.2.2
Geometry Course Name: Geometry Unit: 6 Circles Time Line: 3 weeks Working with Circles, the Parts and the Whole Identify parts of circles Solve problems involving angles, circles, tangents Write and graph the equation of a circle. Performance Objectives Define: Radius, chord, diameter, secant, tangent, central & inscribed angles, arcs, sectors Apply properties of tangents, chords, arcs, and angles to solve problems with missing measures in components of a circle. Determine the radius and coordinates of the center of a circle given its equation. Determine the equation of a circle given its radius and coordinates of the center. Assessment Teacher Resources Standards generated tests & quizzes. generated tests & quizzes. generated tests & quizzes. 2.8.11.E 2.9.11.F M11.C.1.1 2.8.11.E 2.9.11.F M11.B.2.1 M11.C.2.3 M11.C.1.1 2.8.11.E 2.9.11.F
Unit: 1 Patterns/Basic Terms Time Line: 9 weeks Fundamental Building Blocks of Geometry classifying objects geometrically Identify geometric shapes Find nth term in a series (numeric & geometric) Define & identify point, line, plane, angle, segment, ray, midpoint, & bisector Classify angles according to size Classify triangles by sides & angles Recognize geometric shapes in art and nature Recognize and formulate numeric & geometric patterns Develop dictionary of terms and symbols Classify right, acute, & obtuse angles Classify right, acute, obtuse, scalene, and isosceles triangles Reproduce objects in 1 and 2 point perspective Geometrivia Cooperative Problem Solving Activity found on P. 131-132 of Discovering Geometry : An Inductive Approach Various from PSSA 2.8.11.C 2.9.11.J M11.B.2.1.1 M11.D.1.1.1 Classify polygons by sides Classify polygons having 3 12 sides with their proper terms: Triangle, Quadrilateral, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, Undecagon, & Dodecagon
Unit: 1 Patterns/Basic Terms Time Line: 9 weeks Fundamental Building Blocks of Geometry classifying objects geometrically Define special quadrilaterals (parallelogram, rhombus, rectangle, square) Convert to spatial figures (visualize in 3 dimensions) Classify Quadrilaterals as Parallelograms, Rhombi, Rectangles, and Squares Sketch 3 dimensional figures including prisms, pyramids, cylinders, cones, spheres, and hemispheres Use compass & straight edge Reproduce objects in 1 and 2 point perspective Geometrivia Cooperative Problem Solving Activity found on P. 131-132 of Discovering Geometry : An Inductive Approach Various from PSSA 2.8.11.C 2.9.11.J
Unit: 2 Constructions Time Line: 3 weeks Drawing accurate geometric models Duplicate the seven constructions Understand points of concurrency to inscribe & circumscribe circles Discover 7 basic constructions segment angles bisector drop perpendicular erect perpendicular bisect < II lines Define & construct points of concurrency 2.9.11.E M11.C.1.2.1
Unit: 3 Angles/Coordinate Plane Time Line: 3 weeks Understanding angle relationships & Geometry in the coordinate plane Solve complicated angle problems using all angle relationships Solve complicated angle problems using all angle relationships Solve complicated angle problems using all angle relationships Translate finding the midpoint of a line to the coordinate plane. Find equations of lines using parallel and perpendicular slopes. Determine equations of given lines Add vertical, complimentary & supplementary <s to dictionary Discover triangle & polygon angle sums Discover properties of parallel lines (defining alternate interior, corresponding, and alternate exterior angles) Discover midpoint and slope formulas Discover slope relationships between parallel and perpendicular lines Discover equations of lines in slope-intercept form Geometrivia II Cooperative Problem Solving Activity found on P. 221-222 of Discovering Geometry : An Inductive Approach Various from PSSA 2.8.11.J 2.8.11.L M11.B.2.1.1 M11.C.1.2.2 M11.C.3.1.1 M11.C.3.1.2 M11.D.3.2.2 M11.D.3.2.3
Unit: 3 Angles/Coordinate Plane Time Line: 3 weeks Understanding angle relationships & Geometry in the coordinate plane Determine the intersection point of given lines Determine the probability of a specified outcome Discover substitution method of solving 2 equations Define probability and learn to organize possible outcomes using tables Geometrivia II Cooperative Problem Solving Activity found on P. 221-222 of Discovering Geometry : An Inductive Approach 2.8.11.J 2.8.11.L M11.E.3.1.1 M11.E.3.1.2 Various from PSSA
Unit: 4 Congruence & Similarity Time Line: 4 weeks Determining congruent and similar triangles Decide if triangles are congruent Use congruent triangles to find corresponding parts Use congruent triangles to find corresponding parts Use flow chart to present deductive thinking Define congruence Investigate shortcuts (or determine triangle congruence) SSS SAS ASA AAS HL Understand that congruent triangles have corresponding parts (CPCTC) Locate corresponding parts of congruent triangles and use the information to find missing parts Develop understanding of reading and writing flow charts Various from PSSA 2.9.11.B 2.9.11.D 2.1.11.A M11.A.2.1.3 M11.C.1.2 M11.C.1.3.1 Use ratios and proportions to find missing components of similar polygons Define ratio and proportion
Unit: 4 Congruence & Similarity Time Line: 4 weeks Determining congruent and similar triangles Recognize the difference between similarity & congruence Recognize the difference between similarity & congruence Locate corresponding sides and angles of similar polygons Determine similarity using the AA, SAS, and SSS conjectures Various from PSSA 2.9.11.B 2.9.11.D 2.1.11.A M11.A.2.1
Unit: 5 Polygons & Triangles Time Line: 8 weeks Discovering the properties of geometric figures Solve complicated angle problems using all angle relationships Solve complicated angle problems using all angle relationships Solve complicated angle problems using all angle relationships Solve complicated angle problems using all angle relationships Solve complicated angle problems using all angle relationships Solve complicated angle problems using all angle relationships Calculate the sum of the angles in a triangle Discover the properties of isosceles triangles Discover the relationship between the exterior angles and the remote interior angles of triangles Calculate the sum of the interior angles of polygons Calculate the sum of the exterior angles of polygons Discover the properties of midsegments of triangles and trapezoids Various from PSSA 2.9.11.C M11.B.2.1 M11.C.1.2.1
Unit: 5 Polygons & Triangles Time Line: 8 weeks Discovering the properties of geometric figures Find all missing parts of right triangles and determine if triangles are right, acute, or obtuse using the Pythagorean Theorem. Find all missing parts of right triangles using the 30-60-90 and 45-45-90 triangle relationships. Develop Pythagorean Theorem and its converse Discover the 30-60-90 and 45-45-90 triangle relationships Various from PSSA 2.9.11.C
Unit: 5 Polygons & Triangles Time Line: 8 weeks Discovering the properties of geometric figures Use the properties of quadrilaterals to solve problems involving missing angles, sides, and diagonals of quadrilaterals. Discover the properties of the following quadrilaterals: Kite Trapezoid Parallelogram Rhombus Square Rectangle Various from PSSA 2.9.11.C M11.C.1.4.1
Unit: 6 Circles Time Line: 3 weeks Properties of circles Solve complex problems involving angles, circles, arcs, chords, tangents, and secants Solve complex problems involving angles, circles, arcs, chords, tangents, and secants Discover properties of circles Add terms to dictionary radius chord diameter secant tangent central & inscribed angles Find center of circle when only arc is given Find angle between clock hands Various from PSSA 2.9.11.F M11.C.1.2 M11.C.1.2.2 Solve complex problems involving angles, circles, arcs, chords, tangents, and secants Solve problems related to circumference, speed, distance Develop circle, tangent, chord, & angle properties Discover (review) circumference/diameter ratio
Unit: 6 Circles Time Line: 3 weeks Properties of circles Solve problems related to circumference, speed, distance Discover method to find arc length Find center of circle when only arc is given Find angle between clock hands 2.9.11.F M11.B.2.2.3 M11.B.2.2.4 M11.B.2.3.1 Various from PSSA
Unit: 7 Area & Volume Time Line: 6 weeks Calculating area & volume Demonstrate several ways to tessellate the plane using a variety of regular and irregular geometric shapes. Use formulas to solve simple & complex area & volume problems Use formulas to solve simple & complex area & volume problems Use formulas to solve simple & complex area & volume problems Use formulas to solve density & displacement problems Be familiar with transformation, isometrics, symmetry & regular tessellations Use previous knowledge to develop methods for finding area of all previously discussed shapes Expand knowledge to find surface area Move from 2 to 3 dimensional figures & develop volume formulas Move beyond volume to density & displacement Develop original tessellating design 2.5.11.A 2.9.11.H 2.9.11.I M11.B.2.2.1 M11.A.2.2.2 M11.B.2.2.4 M11.B.2.3.1 M11.C.2
Unit: 8 Deductive Reasoning (Supplemental Unit) Time Line: 2 weeks Proving geometric concepts using deductive reasoning Convert word arguments into symbolic form & use laws of logic to make conclusions Use all previous conjectures & logical structures and convert process to a 2 column proof Discuss logical arguments and use symbols of logic and laws of logic Use direct, conditional and indirect proofs 2.4.11.A 2.4.11.B 2.4.11.C 2.4.11.D