Geometry
October 9, 2003
Month |
Content Standard and Objective |
Learning Activity |
Assessment |
SEPT Unit 1 Intro to Geometry Unit 2 Coordinate Geometry |
Preliminaries: Review of basic Algebra 2.1.2 - Use hands-on, visual, geometric patterns to predict and extend design, drawing conjectures based on inductive reasoning a) 3.1.2 - write conditional statements b) 3.1.2 - write the converse statements c) 3.1.2 – write contrapositive and inverse statements d) 3.1.2 - determine the truth value e) 3.1.2 - write counter examples to prove a statement false, e.g. If a polygon is a quadrilateral, it is a square. Rectangle is the counter example. f) 3.1.2 - write good definitions for terms. Include symbolic representation where appropriate (point, line, plane, ray, opposite rays, congruent, similar, midpoint, perpend. bisector, between, exterior point, interior point; point, line and plane postulates on page 80 and any vocab and symbols of points, lines and planes) 3.1.5 - Sketch, label and recognize each of the following: parallel, perpendicular, oblique and skew lines; 3.3.1 – Construct parallel lines and perpendicular bisectors; copy and bisect segments 2.2.6 - Apply algebraic properties (Section 2.5) to the two segments created by the points between line segment and midpoint of a line segment. (Use algebra and arithmetic to find parts of segments); Apply Midpoint Formula in coordinate system 3.23 Distance Formula in coordinate system 3.1.7 - In a coordinate system, use slope to prove lines parallel or perpendicular (Review graphing of a line and slope-intercept form) 2.1.5 - Write the equation of a line perpendicular or parallel to a second line through a given point; Parallel and Perpend. Postulates |
Sort a set of objects by attributes. Use conditional statements and find converses, inverse, contrapositives. Find lengths of segments and measures of angles. Use straightedge and compass to make basic constructions. Sketch and label geometric objects. Use proper notation. Write good definitions. Use properties from algebra and properties of congruence. Use coordinate geometry to: find the midpoint, slope, parallel and perpendicular lines. Prove two lines are parallel using slope. Use coordinate geometry to find an equation of a line. |
Daily correction of homework (20% of grade). Missed problems are to be redone for understanding Daily feedback on Weekly quizzes (10% of grade) Unit Exams (Exams worth 70% of grade) |
OCTOBER Unit 3 Angles and Lines Unit 4 Properties of Triangles |
3.1.4 - Measure angles and review classifications 3.1.4 - Identify angle pairs as adjacent, complementary, supplementary, linear or vertical; Angle Addition Postulate 3.3.1 - Construct angles a) copy angles b) bisect angle to use in a real world situation, e.g. cutting molding in construction c) construct other angle measures including 45º, 60º and 90º, etc. 3.1.6, 3.1.7 - Classify angle pairs formed by two parallel lines cut by a transversal. Prove lines parallel through angle relationships. Introduce proofs (Section 3.4) 3.1.12 - Classify triangles using properties and discover those properties based on classification 3.1.12, 2.2.6 - Solve for unknown angle using sum of angles in a triangle (use algebra) 3.1.9 - Identify and construct a) a median using cut-out triangles and center of gravity (centroid) b) an angle bisector c) an altitude d)a median (not in core, but useful for algebra applications later) Not in core, but cover: Triangle Inequalities |
Use protractors to measure the angle of a triangle. Draw angle pairs. Straightedge and compass constructions. Identify and use properties of parallel lines. Write proofs. Draw and classify triangles. Use algebra to find missing angles of triangles. Identify, construct and use special segments of a triangle. . |
Daily correction of homework (20% of grade). Missed problems are to be redone for understanding Daily feedback on Weekly quizzes (10% of grade) Unit Exams (Exams worth 70% of grade) Comprehensive Term Final |
NOVEMBER Unit 5 Congruent Triangles Unit 6 Similar Triangles |
Term 3 3.1.1, 3.1.8, 3.3.4 – Review definition of congruent triangles and discover congruency using hands-on experiences a) formulate rules for proving congruency b) prove congruency 3.1.1, 3.1.8, 3.3.4 – Review proportional reasoning, e.g. scale drawings (pgs. 18-20), indirect measure 2.2.6, 3.1.8 – Review solving for a missing side of similar triangles 3.1.8 – Discover conditions that make triangles similar by increasing two sides of a triangle 3.1.8 – Prove similarity of triangles |
Compare the lengths of sides and angles of triangles Prove 2 triangles are congruent. Write proofs. Write and simplify ratios of two numbers. Use proportions to solve problems. |
Daily correction of homework (20% of grade). Missed problems are to be redone for understanding Daily feedback on Weekly quizzes (10% of grade) Unit Exams (Exams worth 70% of grade) |
DECEMBER Unit 7 Right Triangles |
2.2.3, 2.2.6, 3.3.4 – Using altitude to the hypotenuse of a right triangle and the geometric mean, find missing measures of right triangles 2.2.3 – Apply Pythagorean Theorem to find the missing measures of right triangles 3.2.3 – Develop the distance formula using the Pythagorean Theorem 3.2.3 – Apply Pythagorean Theorem/distance formula to prove diagonals of a rectangle are congruent 2.1.3 – Discover relationships between the side of a special right triangle (30-60-90 and 45-45-90 triangles) 2.1.3 – Solve problems using the properties of special right triangles |
Use the Pythagorean Theorem. Use special right triangles properties. |
Daily correction of homework (20% of grade). Missed problems are to be redone for understanding Daily feedback on Weekly quizzes (10% of grade) Unit Exams (Exams worth 70% of grade) |
JANUARY Unit 8 Trigonometry |
End of First Semester, January 15 Term 3 3.3.1 - Use similar right triangles to solve real world problems of indirect measurement 2.2.1 - Identify the adjacent side, opposite side and hypotenuse given any acute angle in a right triangle a) write ratios for these sides without using trigonometric terms b) write trigonometric ratios as a fraction and a decimal using trigonometric relations and terminology (sine, cosine, tangent) 2.2.1 - Using a calculator, find the angle measurement in degrees when given a trigonometric ratio 2.2.2 - Find the trigonometric ratio given the angle. Use a calculator 2.2.3, 3.3.4 - Solve real world problems using trig ratios e.g. height of immeasurable objects, distance, angle of elevation, angle of descent, etc. 2.2.4 - Find the missing part of a triangle using the law of sines and cosines |
Use indirect measurement to find missing lengths and measures. Use right triangle trigonometry. |
Daily correction of homework (20% of grade). Missed problems are to be redone for understanding Daily feedback on Weekly quizzes (10% of grade) Unit Exams (Exams worth 70% of grade) Comprehensive Term Final |
FEBRUARY Unit 9 Quadrilaterals Unit 10 Polygons |
3.1.10 - Review the classification of quadrilaterals, e.g. rhombus, square, rectangle, kite, trapezoid, parallelogram 3.2.3 - Verify the classification of these quadrilaterals using coordinate geometry a) review distance formula, slope of a line, and midpoint of a line b) using these formulas, classify quadrilaterals using properties listed in sections 6.3-6.7 3.2.3 - Verify that diagonals of a rectangle are congruent using the distance formula/Pythag Theorem 2.1.4 - Review the area of quadrilaterals and discover the effect on area when changing linear dimensions 2.1.2 – Review classification of polygons; Use patterns to determine the relationship between the measure of angles and the number of sides on a polygon a) find the sum of the interior angles in a polygon b) find the measure of an interior angle of a regular polygon c) find the sum of the exterior angles of a polygon 4.2.1, 4.2.4 - Solve real-world problems using the area of regular polygons and irregular regions |
Use properties of parallelograms. Prove quadrilaterals are parallelograms using coordinate geometry and characteristics. Find perimeter and area of quadrilaterals. Use perimeter and area to solve real-life problems. Draw polygons Discover polygon patterns and relationships. Find missing angles in polygons using formulas. Use and apply formulas for areas of regular polygons. |
Daily correction of homework (20% of grade). Missed problems are to be redone for understanding Daily feedback on Weekly quizzes (10% of grade) Unit Exams (Exams worth 70% of grade) |
MARCH Unit 11 Transformations Unit 12 Circles |
3.2.4 - Use coordinate geometry to analyze transformations of polygons discovering the change in coordinate values a) perform translations b) perform rotations (90º, 180º, 270º) c) perform reflections d) perform dilations 3.1.11 - Identify parts of circle (radii, diameters, chords, secants, arcs, sectors, central angles, inscribed angles, tangents of a circle) 3.3.3-Demonstrate the relationship between the measurement of intercepted an arc, an inscribed angle, and a central angle 3.3.2 - Define pi as a ratio between circumference and diameter 2.1.4-Review the area of circle given the formula and explore how a change in the length of the radius affects the area of a circle 4.2.2-Find the area of a sector 4.2.2-Discover arc length as a fraction of the circumference 3.2.1 - Introduce the circle on a coordinate system and graph a circle given the equation in the form (x-h)² + (y-k)² = r². Write the equation of a circle given a graph |
Use properties of isometries. Relate common characteristics of rigid transformations. Use compositions of transformations Use graphing calculators to explore isometries. Identify parts of circles. Use properties of tangents, chords, arcs and inscribes angles. Graph circles and write equations of circles. Discover pi. Apply and use circle formulas. |
Daily correction of homework (20% of grade). Missed problems are to be redone for understanding Daily feedback on Weekly quizzes (10% of grade) Unit Exams (Exams worth 70% of grade) Comprehensive Term Final |
APRIL Unit 13 Solids and Polyhedrons |
3.1.13 - Classify 3-D objects according to their properties a) use nets to build shapes b) 2.1.2 - use a table to derive Euler’s Formula relating faces edges and vertices 4.2.3 - Calculate the surface area and volume of 3-D objects (prisms, cones, spheres, cylinders, and pyramids) given the formulas 2.1.4 - Discover the effect on volume when changes are made in the linear dimensions of the shape 3.3.5 - Sketch the cross sections of solids |
Identify polyhedrons. Find surface area and volume. Use surface area and volume to solve real-life problems. Sketch cross sections of solids. Make nets. |
Daily correction of homework (20% of grade). Missed problems are to be redone for understanding Daily feedback on Weekly quizzes (10% of grade) Unit Exams (Exams worth 70% of grade) |
MAY |
May 5.2.1-Identify geometric probabilities by performing simulations involving area or length, e.g. areas on a target 5.2.2 - Calculate geometric probability using the area of two different regions All standards - Real world projects applying geometric knowledge - Review for CRT’s - Review for Semester Final (on all 4 terms) |
Daily correction of homework (20% of grade). Missed problems are to be redone for understanding Daily feedback on Weekly quizzes (10% of grade) Unit Exams (Exams worth 70% of grade) Term Final CRT |