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Secondary Curriculum

Mathematics - Accelerated Geometry

District Course #0823

Course Description

Open to: Grade 9, One Year Course
Prerequisite: Accelerated Algebra and Instructor/counselor approval
Content: Students study solid geometry and solving more difficult geometric problems as well as studying coordinate geometry.

Adopted Materials

Title: Geometry: for Enjoyment and Challenge
Edition: 1991
Publisher: McDougal, Littell & Company
ISBN: 0-86609-965-4

Mathematics Curriculum Map
Course overview, activities, vocabulary, supplemental materials in pdf format.

Copyright Resources

Course Scope

Unit 1	Introduction to Geometry	2 weeks
Unit 2	Basic Concepts and Proofs	3 weeks
Unit 3	Congruent Triangles	3 weeks
Unit 4	Lines in the Plane	3 weeks
Unit 5	Parallel Lines and Quadrilaterals	4 weeks
Unit 6	Lines and Planes in Space	1 week
Unit 7	Polygons	2 weeks
Unit 8	Similar Polygons	2 weeks
Unit 9	Pythagorean Theorem	4 weeks
Unit 10	Circles	3 weeks
Unit 11	Area	3 weeks
Unit 12	Surface Area and Volume	3 weeks
Unit 13	Coordinate Geometry	2 weeks

Assessment Correlation acronyms key

Mathematics Curriculum Matrix K-12 pdf or Word document

For specific Standard References please see: Idaho State Assessment Standards
Download this curriculum and standards documentation as a "Printer Friendly" pdf file
Curriculum updated 6/18/09

Unit 1

Geometry Overview

2 weeks

Instructional Objective 0823.01 Understand and apply basic geometric concepts.			Standard Reference G.4.1.1, G.4.3.1, G.4.2.1
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Apply basic terminology and notation (points, lines, planes, rays, angles, segments, vertex, union, intersection and triangle).	pp. 3-6		EOC, TMA
02	Find lengths of segments.	p.9		EOC, TMA
03	Find the measure of angles.	pp. 9-12		EOC, TMA
04	Classify angles by their measure.	p. 11		EOC, TMA
05	Apply congruence to angles and segments.	p. 12		EOC, TMA
06	Recognize co linearity and betweenness.	p. 18		EOC, TMA
07	Interpret geometric diagrams.	p. 19		EOC, TMA
08	Apply the triangle inequality.	p. 19		EOC, TMA
09	Write simple two column proofs.	p. 23		EOC, TMA
10	Identify bisectors and trisectors of segments and angles.	pp. 28-30		EOC, TMA
11	Write a paragraph proof.	pp. 36-37		EOC, TMA
12	Understand elements of deductive structure.	pp. 39-41		EOC, TMA
13	Write and apply statements of logic (conditionals, negations, converses, inverses, contra positives and the chain rule).	pp. 44-46		EOC, TMA
14	Solve basic probability problems.	pp. 49-50		EOC, TMA

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Unit 2	Basic Concepts and Proofs	3 weeks

Instructional Objective 0823.02 Apply vocabulary and understand the foundations for proof.			Standard Reference G.4.4.1, G.4.2.1, G.4.1.2., G.3.2.1, G.4.1.1
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Apply perpendicularity to lines, rays and segments.	pp. 61-63		EOC, TMA
02	Recognize and compute angle supplements and complements.	pp. 66-68		EOC, TMA
03	Develop a framework from which to draw conclusions.	pp. 72-73		EOC, TMA
04	Prove angles are congruent.	pp. 76-78		EOC, TMA
05	Apply the addition property to segments and angles.	pp. 82-84		EOC, TMA
06	Apply the multiplication property to segments and angles.	pp. 89-91		EOC, TMA
07	Apply the transitive/substitution property to angles and segments.	pp. 95-97		EOC, TMA
08	Recognize opposite rays and vertical angles.	pp. 100-101		EOC, TMA

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Unit 3	Congruent Triangles	3 weeks

Instructional Objective 0823.03 Prove triangles and their corresponding parts congruent.			Standard Reference G.4.1.2, G.4.1.3, G.2.2.2
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Understand congruent figures and their corresponding parts.	pp. 111-113		EOC, TMA
02	Prove triangles congruent (SSS, SAS, ASA, HL).	pp. 115-119, 156-158		EOC, TMA
03	Apply the principle of CPCTC.	pp. 125		EOC, TMA
04	Identify medians and altitudes of triangles.	pp. 131-133		EOC, TMA
05	Use overlapping triangles in proofs.	pp. 138-139		EOC, TMA
06	Classify triangles by their angle measure and side length.	pp. 142-143		EOC, TMA

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Unit 4	Lines in the Plane	3 weeks

Instructional Objective 0823.04 Determine the relationship between lines in a plane and the angles they form.			Standard Reference G.4.2.1, G.3.2.1, G.2.2.2,, G.3.1.1,
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Apply the midpoint formula.	pp. 170		EOC, TMA
02	Prove that angles are right angles.	pp. 180-181		EOC, TMA
03	Apply the relationship between equidistance and perpendicularity.	pp. 184-186		EOC, TMA
04	Identify the relationship between the angles formed by two parallel lines and a transversal.	pp. 192-195		EOC, TMA
05	Determine if lines are parallel or perpendicular by their slopes.	pp. 198-200		EOC, TMA

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Unit 5	Parallel Lines and Quadrilaterals	4 weeks

Instructional Objective 0823.05 Prove lines parallel and specificity of a quadrilateral.			Standard Reference G.4.1.3, G.2.2.2
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Write indirect proof.	p. 212		EOC, TMA
02	Prove that lines are parallel.	pp. 216-218		EOC, TMA
03	Identify and apply the relationships of the angles formed by two parallel lines and a transversal.	pp. 224-227		EOC, TMA
04	Define quadrilaterals.	p. 236		EOC, TMA
05	Identify properties of quadrilaterals.	pp. 241-242		EOC, TMA
06	Prove that a four- sided figure is a specific quadrilateral.	p. 249, 255-256		EOC, TMA

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Unit 6	Lines and Planes in Space	1 week

Instructional Objective 0823.06 Understand the relationships between lines and planes of a given plane.			Standard Reference G.2.2.2, G.3.1.1
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Understand basic concepts of lines and planes in three dimensional spaces.	pp. 269-271		EOC, TMA
02	Determine if lines and planes are perpendicular.	pp. 276-277		EOC, TMA
03	Determine the relationship between planes.	pp. 282-283		EOC, TMA

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Unit 7	Polygons	2 weeks

Instructional Objective 0823.07 Calculate the number of sides and angle measures for a specific polygon.			Standard Reference G.2.2.2
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Apply triangle application theorems.	pp. 295-296, 302		EOC, TMA
02	Calculate the side and or angle measures in a polygon.	pp. 307-308, 314-315		EOC, TMA

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Unit 8	Similar Polygons	2 weeks

Instructional Objective 0823.08 Determine lengths and angle measures in similar triangles.			Standard Reference G.4.1.3, G.4.1.2
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Apply ratios and proportions to solve problems.	pp. 325-328		EOC, TMA
02	Identify the characteristics of similar figures.	pp. 332-334		EOC, TMA
03	Prove triangles similar (AA,SSS, SAS)	pp. 339-340		EOC, TMA
04	Determine congruencies and proportions in similar triangles.	pp. 345-346, 351-352		EOC, TMA

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Unit 9	Pythagorean Theorem	4 weeks

Instructional Objective 0823.09 Solve right triangle problems using the Pythagorean Theorem or the quadratic formula.			Standard Reference G.1.3.1, G.2.2.2, G.4.1.4, G.2.2.2
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Simplify radical expressions.	p. 368		EOC, TMA
02	Solve quadratic equations.	p. 368		EOC, TMA
03	Solve problems involving circles.	pp. 370-371		EOC, TMA
04	Attempt the geometric mean problems.	pp. 377-378		EOC, TMA
05	Identify properties of quadrilaterals.	pp. 241-242		EOC, TMA
06	Solve problems by applying the Pythagorean Theorem and its converse.	pp. 384-386, 398-399, 413-414		EOC, TMA
07	Compute the lengths of segments in the coordinate plane.	pp. 392-394		EOC, TMA
08	Solve special right triangles.	pp. 405-406		EOC, TMA
09	Apply the trigonometric ratios to right triangle.	pp. 418-419, 423		EOC, TMA

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Unit 10	Circles	3 weeks

Instructional Objective 0823.10 Solve problems involving circles.			Standard Reference G.2.2.1, G.2.2.2, G.1.3.1, G1.1.1, G.4.1.1
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Solve problems involving chords, radii, and diameters.	pp. 439-441		EOC, TMA
02	Apply the relationships of segments on a circle.	pp. 446. 459-462, 493-494		EOC, TMA
03	Apply the relationships of angles and arcs on a circle.	pp. 450-453, 468-472, 479-480, 499-500		EOC, TMA
04	Apply the characteristics of inscribed and circumscribed polygons.	pp. 486-488		EOC, TMA

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Unit 11	Area	3 weeks

Instructional Objective 0823.11 Calculate the areas of two dimensional shapes.			Standard Reference G.2.2.1, G.2.2.2, G.4.1.2, G.2.1.1, G.1.1.1
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Calculate the areas of polygons.	pp. 512, 516-517, 523-524, 528, 531-532, 550-551		EOC, TMA
02	Calculate the areas of circles, sectors and segments.	pp. 537-538		EOC, TMA
03	Find and interpret the ratios of the areas of similar figures.	pp. 543-544		EOC, TMA

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Unit 12	Surface Area and Volume	3 weeks

Instructional Objective 0823.12 Calculate the surface area and volume of three dimensional shapes.			Standard Reference G.2.2.1, G.2.2.2, G.4.1.1, G.1.1.1
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Find the surface area of a three dimensional shape.	pp. 561-562, 565, 570-571		EOC, TMA
02	Find the volume of a three dimensional shape.	pp. 575-577,583-584, 589		EOC, TMA

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Unit 13	Coordinate Geometry	2 weeks

Instructional Objective 0823.13 Solve problems using coordinate geometry.			Standard Reference G.3.1.1, G.2.2.2, G.3.2.1, G.4.2.1
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Graphing lines and circles.	pp. 605-607, 638		EOC, TMA
02	Write equations of lines.	pp. 610-612, 638		EOC, TMA
03	Solve systems of equations.	pp. 618, 636, 638		EOC, TMA
04	Graph inequalities.	pp. 622-624, 638		EOC, TMA
05	Three dimensional graphing.	pp. 626-628, 638		EOC, TMA
06	Write the equation of a circle.	pp. 633-634, 638		EOC, TMA

Secondary Mathematics Curriculum	Curriculum Home	Download this curriculum as a pdf file
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Boise School District
8169 W. Victory Rd., Boise, ID 83709