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Oroville Union High School District |
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Mathematics Curriculum |
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Mathematics - Geometry |
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Geometry Content Standards
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Undefined Terms, Axioms, Theorems, Etc.
The learner will be able to
demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 1.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Unit 2: conjectures (BP-1); Unit 6: axioms (TK-49), theorems (TK-16 & 25). Deductive reasoning is the focus of Unit 2. Students often use inductive reasoning for problem-solving and conjecturing (see esp. Unit 3). Teacher notes: Many problems require students
to cite definitions and/or theorems to justify steps in their
solutions.
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PLATO Learning Inc., 2000, Modules: [Software]. Geometry and Measurement 2:
Postulates and Theorems.
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Geometric Proofs
The learner will be able to
write geometric proofs, including proofs by contradiction.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 2.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Problems requiring conjecturing, explaining, and proving occur
throughout the text from Unit 1 through Unit 12. Each problem of this
type--235 of them--is marked with an icon (falling dominos). Units 2,
6, and 9 emphasize proof. See Unit 6: proof (TK-16) and theorem
(TK-25), types of proof (TK-37-38 ff., 62, 74, 87, 100). Teacher notes: See introductory paragraph
above, as well as the
introductory notes for Units 2
and 6.
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PLATO Learning Inc., 2000, Modules: [Software]. Geometric proofs are presented throughout the Geometry and Measurement 2 curriculum. |
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Validity of a Logical Argument
The learner will be able to
construct and judge the validity of a logical argument and give counterexamples to disprove a statement.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 3.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. See #2. Also Unit 2: digit place and color square problems, plus BP-4, 20, 29, 40; Unit 3: converses (PS-94 ff.), PS-95; Unit 6: converses (TK-73 ff.), counterexample (TK-74 ff.), contradiction (TK-100 ff.), TK-79, 83, 114. Teacher notes encourage the use of class time to present and criticize student proofs. Developmental problems practice various kinds of logical
reasoning.
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PLATO Learning Inc., 2000, Modules: [Software]. No PLATO modules are available for this learning expectation at this time. |
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Congruence & Similarity: Basic Theor
The learner will be able to
prove basic theorems involving congruence and similarity.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 4.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Unit 5: congruence introduction (CG-21 thru 26, 31-34, 40-41, 51), proofs and practice follow, esp. Unit 5 (CG-66, 92), Unit 6 (TK-4, 26, 52, 57, 62-64, 76-77, 87-88, 90, 114), and Unit 7 homework; Unit 8: similarity introduced (S-1, 4, 9, 20-23, 25), used (S-28, 34, 45, 50, 95-96 ff.), plus spiraled work in Units 9-12.
Unit 5: CG-70 & 71, then several homework exercises spiraled
throughout the course and in the context of applications (e.g., Unit 9,
US-32, 78); projects #39. Teacher notes: Projects are found in the
Assessment Handbook in the
Teacher Version.
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PLATO Learning Inc., 2000, Modules: [Software]. Geometry and Measurement 1:
Using Geometry;
Geometry and Measurement 2:
Congruent Angles,
Supplementary and Complementary Angels,
Two of a Kind,
Congruent Triangles Part 1.
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Congruence & Similarity: Triangles
The learner will be able to
prove that triangles are congruent or similar, and they are able to use
the concept of corresponding parts of congruent triangles.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 5.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Unit 5: congruence introduction (CG-21 thru 26, 31-34, 40-41, 51), proofs and practice follow, esp. Unit 5 (CG-66, 92), Unit 6 (TK-4, 26, 52, 57, 62-64, 76-77, 87-88, 90, 114), and Unit 7 homework; Unit 8: similarity introduced (S-1, 4, 9, 20-23, 25), used (S-28, 34, 45, 50, 95-96 ff.), plus spiraled work in Units 9-12.
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PLATO Learning Inc., 2000, Modules: [Software]. Geometry and Measurement 2:
Congruent Triangles Part 1,
Congruent Triangles Part 2,
Congruent Triangle Problems,
Arcs and Chords.
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Triangle Inequality Theorem
The learner will be able to
know and are able to use the triangle inequality theorem.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 6.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Unit 5: CG-70 & 71, then several homework exercises spiraled throughout the course and in the context of applications (e.g., Unit 9, US-32, 78); projects #39. Teacher notes: Projects are found in the Assessment Handbook in the Teacher Version. |
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PLATO Learning Inc., 2000, Modules: [Software]. No PLATO modules are available for this learning expectation at this time. |
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Parallel Lines, Quadrilaterals & Cir
The learner will be able to
prove and use theorems involving the properties of parallel lines cut by
a transversal, the properties of quadrilaterals, and the properties of circles.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 7.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Unit 3: parallel lines (intro., PS-45 thru 49 ff.); Unit 6: parallel proofs (TK-49, 87-89 ff.); Unit 9: quadrilaterals (US-6, 27, 57-61, 67-72, 81, 82, 91-92, 101, 116-118), Unit 10 CS-60 ; Unit 10: circles (CS-21 & 22, 31 ff., 41 ff., 50-55, 59 ff.); Unit 11: GP-51, 54, 60, 69, 76; Unit 12: as sub problems throughout, circles (3D-44 thru 48 ff.). Teacher notes: Properties of quadrilaterals are
used to area and perimeter problems throughout the text.
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PLATO Learning Inc., 2000, Modules: [Software]. Geometry and Measurement 2:
Intersecting Lines and Planes,
Angles in Pairs,
Transitive Properties of Lines,
A Sense of Proportion;
Polygons:
Introduction to Polygons,
Summing Up Angles,
Angles in Regular Polygons,
Parallelograms Part 1,
Parallelograms Part 2,
Rhombuses and Trapezoids;
Circles:
Introduction to Circles,
Tangents,
Arcs and Chords,
Inscribed Angles,
Circles and Angles,
Circles and Segments,
Measuring Circumference,
The Length of Arcs,
The Area of Circles.
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Problems Solving: Geometric Figures
The learner will be able to
know, derive, and solve problems involving the perimeter, circumference,
area, volume, lateral area, and surface area of common geometric figures.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 8.0. |
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Instructional Resources |
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CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook]. Unit 0: PR-8 thru 14; Unit 1: RC-8 thru 61, esp. 8, 29-34, 41-43, 51-61, 93, 99, 101, 103, 104; Unit 2: BP-6 ff., 38-39, 71, 101, 103; Unit 3: PS-16, 23, 32, 105, 109 plus HW; Unit 4: SV-1 ff., 20, 35, 50, 77, 112; Unit 5: CG-56; Unit 6: TK-11, 59, 65, 71, 107, 115, 127; Unit 7: T-28, 48, 54, 87, 105; Unit 8: S-4, 6, 90, 108; Unit 9: dissecting polygons (US-39 thru 41, 48), regular polygons (US-57
thru 61), 95, 100, 102, 105, 113, 116; Unit 10: CS-3, 10, 16 ff., 48, 51 ff., 60 ff.; Unit 11: throughout, esp. GP-11, 13, 17, 26-27, 44-49, 83; Unit 12: in subproblems throughout, 3D-52, 82. Teacher notes: Area and perimeter problems spiral throughout the course. Many are in the context of broader problems. Second
semester problems incorporate right triangle trigonometry in more complex area and perimeter problems.
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PLATO Learning Inc., 2000, Modules: [Software]. Math Fundamentals:
Linear Measurement,
Area Measurement,
Volume and Capacity Measurement;
Geometry and Measurement 1:
Circles/Arcs/Circumferences,
Area Part 1,
Area Part 2,
Volume,
Using Measurement.
Geometry and Measurement 2
Area of Right Triangles and Parallelograms
Area of Any Triangle
Area of Trapezoids and Rhombuses
Measuring Circumference
The Length of Arcs
The Area of Circles
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Computing Volumes & Surface Areas
The learner will be able to
compute the volumes and surface areas of prisms, pyramids, cylinders,
cones, and spheres; and students commit to memory the formulas for prisms,
pyramids, and cylinders.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 9.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Unit 4: SV-65 thru 103, esp. 66, 71, 79, 94, 100, 101, 103, 110;
Unit 5: in HW (CG-10 ff., 36,100, 101); Unit 6: in HW (TK-47, 85, 98)
Unit 7: T-10; Unit 9: US-49, 63; Unit 10: CS-68 thru 96, esp. 68, 70,
76, 77, 88; Unit 11: GP-28; Unit 12: 3D-1 thru 41, esp. 1, 3, 11, 12,
20, 21, 29, 35; Unit 12 assessment rou quiz; -projects #31, 37, 38.
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PLATO Learning Inc., 2000, Modules: [Software]. Geometry and Measurement 2:
Volume,
Prisms,
Area and Volume of Cylinders,
Area and Volume of Cones.
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Computing Areas of Polygons
The learner will be able to
compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 10.0. |
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Instructional Resources |
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PLATO Learning Inc., 2000, Modules: [Software]. Geometry and Measurement 1:
Area Part 1,
Area Part 2;
Geometry and Measurement 2:
Area of Right Triangles and Parallelograms,
Area of Any Triangle,
Area of Trapezoids and Rhombuses.
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Changes in Dimensions
The learner will be able to
determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 11.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Unit 3: PS-64; Unit 8: S-55 thru 59, 66-70, 76, 77, 86-89, 111;
Unit 9: US-10, 22, 35, 43, 64, 86; Unit 10: CS-58; Unit 11: GP-10,
40; Unit 12: 3D-22, 72, 75.
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PLATO Learning Inc., 2000, Modules: [Software]. No PLATO modules are available for this learning expectation at this time. |
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Classifying Figures
The learner will be able to
find and use measures of sides and of interior and exterior angles of
triangles and polygons to classify figures and solve problems.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 12.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Calculate: Unit 1: RC-2 ff. (see Standard 15), 20, 55-60, 93; Unit 2:
BP-58; Unit 3: PS-53, 63; Unit 6: TK-18, 19, 29, 46, 58, 66, 69, 92,
94; Unit 7 throughout (sides: T-14, 18, 19, 26-30, 35 ff., esp. 51, 53;
angles T-41 ff.), T-86 thru 88, 96-99 ff., 120; Unit 8: throughout, esp.
S-12, 17, 25, 26 ff., 34 ff., 46 ff.; Unit 9: US-2, 7, 9, 14 ff., 29,
30 ff., 57-60, 87, 93, 96, 100, 101-104; Unit 11: GP-18, 19; projects
# 57; Classify: Unit 2: triangles (BP-77); Unit 3: related vocabulary;
Unit 5: congruence (CG-23 ff.); Unit 9: polygons (US-1),
quadrilaterals (US-80 ff., esp. 81, 82, 91, 92, 107-110);
projects #39, 44, 50. Teacher notes: Many of the perimeter and area
citations for Standards 8 and 10
also require subproblems that
find lengths of sides and
measures of angles.
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PLATO Learning Inc., 2000, Modules: [Software]. Geometry and Measurement 2:
Introduction to Polygons,
Summing Up Angles,
Angles in Regular Polygons.
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Relationships between Angles in Polygons
The learner will be able to
prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 13.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Preliminary work: Unit 3: PS-35 thru 39 (supplementary PS-36),
47-49, 58-61 (vertical angles PS-59, complementary angles PS-88,
exterior angles PS-103), calculations with justifications (PS-52, 64,
esp. 68 ff., 89); Proof: Unit 3: PS-62, 93, 94; Unit 4: SV-75, 107;
Unit 5: CG-16, 50, 52; Unit 6: TK-5, 16, 17, 26, 27, 49-52, 63, 76,
77, 80, 81, 87-91, 99, 102, 113, 114; Unit 7: T-106; Unit 8: S-28;
Unit 9: US-2 thru 6, 26, 27, 67, 69, 70, 81; projects #14, 18, 45. Teacher notes: Most polygon proofs prove
relationships between sides. See
units 6-12.
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PLATO Learning Inc., 2000, Modules: [Software]. Geometry and Measurement 1:
Special Angles Part 1,
Special Angles Part 2.
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Pythagorean Theorem
The learner will be able to
prove the Pythagorean theorem.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 14.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Introduction and practice: Unit 1: RC-1 ff. (see Standard 15);
proof : Unit 6: TK-64, 65, 127, 128. Teacher notes: Three proofs are included.
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PLATO Learning Inc., 2000, Modules: [Software]. Geometry and Measurement 1:
The Pythagorean Theorem Geometry and Measurement 1;
Geometry and Measurement 2:
The Pythagorean Theorem 2.
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Application of Pythagorean Theorem
The learner will be able to
use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 15.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Unit 1: RC-2, 3, 8, 22, 35, 36, 52, 58, 92 (distance RC-47, 70, 99,
105); BP-34, 59, 88, 94, 101, 103; Unit 3: PS-57, 63; Unit 4: SV-50,
52; Unit 5: CG-18, 38, 85; Unit 6: TK-11; Unit 7: T-53, 61-64, 91;
Unit 8: S-31= Unit 9: US-49; Unit 12: 3D-1. Teacher notes: The Pythagorean Theorem is a
subproblem in numerous
problems in units 1-6.
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PLATO Learning Inc., 2000, Modules: [Software]. Geometry and Measurement 2:
Solving Right Triangle Problems,
30° - 60° Right Triangles.
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Basic Constructions
The learner will be able to
perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 16.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Appendix: AP-1 thru AP-31. Teacher notes: May be taught as self-contained unit or as part of appropriately
related units.
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PLATO Learning Inc., 2000, Modules: [Software]. No PLATO modules are available for this learning expectation at this time. |
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Coordinate Geometry
The learner will be able to
prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 17.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Unit 1: Pythagorean Theorem (RC-1), distance (RC-47, 70), slope (74-79), midpoint (RC-88, 89), 99, 101, 102; Unit 2: writing equations (BP-33, 35, 69, 70 and Unit 3: PS-41, 42), midpoint (BP-57). Teacher notes: Significant work with linear and quadratic equations and systems
of equations makes proofs adaptable to a coordinate format.
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PLATO Learning Inc., 2000, Modules: [Software]. Intermediate Algebra:
Linear Equations and Inequalities;
Geometry and Measurement 2:
The Distance Formula,
Slope,
Coordinates in Three Dimensions.
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Trigonometric Functions
The learner will be able to
know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x))2 + (cos(x)) 2 = 1.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 18.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Unit 7: throughout, esp. T-1 thru 4, 12-18, 26-31,41, 95-99;
relationships explored in T-1, 33, 49-50, 79, 122-24., Assessment
Handbook, Unit 7 group tests.
Teacher notes: These are the developmental
problems.
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Right Angle Trigonometry,
Three More Trigonometric Functions.
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Application of Trigonometric Functions
The learner will be able to
use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 19.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Unit 7: T-18, 19, 27, 29, 31, 32, 35 ff., 97, 102, 116, including word
problems (T-44, 46, 51 ff.) and area (T-86, 87 ff.); Unit 8: S-7, 16, 17,
ff.; Unit 9: US-24, 32, 48, 57 ff.; Unit 10: CS-18, 27, 38, 52, 106;
Unit 11: GP-18, 47, 49, 51; Unit 12: 3D-12, 19, 20, 30, 37, 51, 52.
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Right Angle Trigonometry.
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Angle & Side Relationships
The learner will be able to
know and are able to use angle and side relationships in problems with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 20.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Unit 7: T-61-66, 82, 87, 90, 91, 101, 115; Unit 8: S-7, 12, 16, 40,83, 108; Unit 9: US-38-40, 93, 100, 112, 116; Unit 10: CS-44, 60,70, 85, 96, 105; Unit 11: GP-54, 57, 78; Unit 12: 3D-3, 28, 41, 70;project #5. Teacher notes: Emphasis on right triangletrigonometry gives studentsanother method to solve theseproblems. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Right Angle Trigonometry.
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Problems Regarding Relationships
The learner will be able to
prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 21.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Unit 10: throughout (CS-21-25, 30-34, 40-45, 50-55, 59 ff., 98,
100, 101, 103, 105-107); Unit 11: GP-7, 16, 42; Unit 12: 3D-44 thru
3D-48, 50, 61; projects #62, 65, 66.
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PLATO Learning Inc., 2000, Modules: [Software]. Geometry and Measurement 2:
Tangents,
Arcs and Chords,
Inscribed Angles,
Circles and Angles,
Circles and Segments.
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Effect of Rigid Motions on Figures
The learner will be able to
know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.
| Strand |
Scope |
Source |
| Geometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Geometry, 22.0. |
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Instructional Resources |
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CPM Mathematics 2 (Geometry) 2nd Ed. v. 4.0,, CPM Educational Program, 2000, Problems: [Textbook]. Unit 5: reflections (CG-2 through CG-5); translations (CG-11);
rotations (CG-12). Spiraled problems follow, esp. in Units 5 and 6
(e.g., CG-13, 15, 20, 42, 81, 90). Useful for introducing similarity in
Unit 8. Teacher notes: Teacher Version offers a
Tessellation project using
transformations at the end of
Unit 5.
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PLATO Learning Inc., 2000, Modules: [Software]. Geometry and Measurement 2:
Symmetry,
Translations,
Rotations.
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