Download Concepts in Algebra and Geometry

Concepts in Algebra and Geometry
Introduction
The following outline represents one possible way to structure Concepts in Algebra and
Geometry, which we envision as a replacement for the current Geometry B course. It is based on
the Glencoe texts Algebra: Concepts and Applications and Geometry: Concepts and
Applications. All chapter and section headings in the outline are those used in the 2008 editions
of those books.
Our purpose in redesigning the Geometry B course is to strengthen the Algebra skills of the
students, not only to bolster their performance in this course, but also to better prepare them for
the Algebra IIB course that follows it. Many incoming SHS freshmen have achieved a modicum
of success in Pre-Algebra and Algebra I, but have not attained the level of mastery needed for the
demands of the high-school curriculum. We believe that by strengthening their Algebra skills
early in the Geometry course, and then throughout the course as the subject linkages demand it,
these students will achieve a level of success that will in turn enhance their confidence as math
students.
Much of the Algebra sequence that follows is already an informal part of Geometry B. But the
formal and specific emphasis on these topics means that we will be unable to cover some of the
current Geometry sequence. We believe that the Glencoe text mitigates this sacrifice by
ensuring adequate coverage of the Massachusetts Curriculum Framework’s Grades 9–10
Learning Standards for Geometry and Measurement.
In the outline, the chapter and section numbers and titles are those of the Geometry text.
Sections from the Algebra text are labeled A1-2, A2-2, and so on. Sections in italics are to be
considered optional because they repeat Algebra topics or because historically they have not
been covered in the Geometry B course. In addition, the outline omits Chapter 14 (Circle
Relationships) and Chapter 16 (More Coordinate Graphing and Transformations).
Finally, it should be noted that the outline as presented has some flexibility built into it, to
accommodate (as much as possible) the vagaries of the school’s overall schedule. It assumes a
school calendar that permits 14 full cycles (approximately 77 hours) of instruction and
assessment per semester.
Concepts in Algebra and Geometry
Term 1
35 Days of Instruction and Assessment; 23 Topics, 6 Assessments
Unit One.
The Basics
Chapter 1
Reasoning in Geometry (9 days, 2 assessments)
A1-2
A1-4
1-1
1-2
1-3
1-4
1-5
1-6
Order of Operations
The Distributive Property
Patterns and Inductive Reasoning
Points, Lines, and Planes
Postulates
Conditional Statements and Their Converses
Tools of the Trade
A Plan for Problem Solving
Chapter 2
A2-2
A3-4
A3-6
A4-4
A4-5
A4-6
2-1
2-2
2-3
2-4
2-5
Segment Measure and Coordinate Graphing (14 days, 2 assessments)
The Coordinate Plane
Equations
Solving Addition and Subtraction Equations
Solving Multiplication and Division Equations
Solving Multi-Step Equations
Variables on Both Sides
Real Numbers and Number Lines
Segments and Properties of Real Numbers
Congruent Segments
The Coordinate Plane
Midpoints
Unit Two.
Angles
Chapter 3
Angles (12 days, 2 assessments)
3-1
3-2
3-3
3-4
3-5
3-6
3-7
Angles
Angle Measure
The Angle Addition Postulate
Adjacent Angles and Linear Pairs of Angles
Complementary and Supplementary Angles
Congruent Angles
Perpendicular Lines
Concepts in Algebra and Geometry
Term 2
35 Days of Instruction and Assessment; 22 Topics, 6 Assessments
Unit Two.
Angles (continued)
Chapter 4
Parallels (13 days, 3 assessments)
A7-1
A7-2
A7-3
A7-5
A7-6
A7-7
4-1
4-2
4-3
4-4
4-5
4-6
Slope
Writing Equations in Point–Slope Form
Writing Equations in Slope–Intercept Form
Graphing Linear Equations
Families of Linear Graphs
Parallel and Perpendicular Lines
Parallel Lines and Planes
Parallel Lines and Transversals
Transversals and Corresponding Angles
Proving Lines Parallel
Slope
Equations of Lines
Unit Three. Triangles
Chapter 5
5-1
5-2
5-3
10-6
5-4
5-5
5-6
A8-1
A8-2
A8-3
A8-5
A8-7
A14-1
A14-2
A14-3
Triangles and Congruence (22 days, 3 assessments)
Classifying Triangles
Angles of a Triangle
Geometry in Motion
Symmetry
Congruent Triangles
SSS and SAS
ASA and AAS
Powers and Exponents
Multiplying and Dividing Powers
Negative Exponents
Square Roots
The Pythagorean Theorem
The Real Numbers
The Distance Formula
Simplifying Radical Expressions
Concepts in Algebra and Geometry
Term 3
35 Days of Instruction and Assessment; 28 Topics, 8 Assessments
Unit Three. Triangles (continued)
Chapter 6
6-1
6-2
6-3
6-4
6-5
6-6
6-7
Medians
Altitudes and Perpendicular Bisectors
Angle Bisectors of Triangles
Isosceles Triangles
Right Triangles
The Pythagorean Theorem
Distance on the Coordinate Plane
Chapter 7
A12-1
A12-2
A12-3
A12-4
7-1
7-2
7-3
7-4
More About Triangles (8 days, 2 assessments)
Triangle Inequalities (10 days, 2 assessments)
Inequalities and Their Graphs
Solving Addition and Subtraction Inequalities
Solving Multiplication and Division Inequalities
Solving Multi-Step Inequalities
Segments, Angles, and Inequalities
Exterior Angle Theorem
Inequalities Within a Triangle
Triangle Inequality Theorem
Unit Four.
Other Shapes
Chapter 8
Quadrilaterals (8 days, 1 assessment)
8-1
8-2
8-3
8-4
8-5
Quadrilaterals
Parallelograms
Tests for Parallelograms
Rectangles, Rhombi, and Squares
Trapezoids
Chapter 9
9-1
9-2
9-3
9-4
9-5
9-6
9-7
Proportions and Similarity (9 days, 2 assessments)
Using Ratios and Proportions
Similar Polygons
Similar Triangles
Proportional Parts and Triangles
Triangles and Parallel Lines
Proportional Parts and Parallel Lines
Perimeters and Similarity
Concepts in Algebra and Geometry
Term 4
35 Days of Instruction and Assessment; 22 Topics, 8 Assessments
Unit Four.
Other Shapes (continued)
Chapter 11 Circles (9 days, 2 assessments)
11-1
11-2
11-3
11-4
11-5
11-6
Parts of a Circle
Arcs and Central Angles
Arcs and Chords
Inscribed Polygons
Circumference of a Circle
Area of a Circle
Unit Five.
Area and Volume
Chapter 10 Polygons and Area (8 days, 2 assessments)
10-1
10-2
10-3
10-4
10-5
10-7
Naming Polygons
Diagonals and Angle Measure
Areas of Polygons
Areas of Triangles and Trapezoids
Areas of Regular Polygons
Tessellations
Chapter 12 Surface Area and Volume (10 days, 2 assessments)
12-1
12-2
12-3
12-4
12-5
12-6
12-7
Solid Figures
Surface Areas of Prisms and Cylinders
Volumes of Prisms and Cylinders
Surface Areas of Pyramids and Cones
Volumes of Pyramids and Cones
Spheres
Similarity of Solid Figures
Unit Six.
Special Topics
Chapter 13 Right Angles and Trigonometry (3 days, 1 assessment)
13-1
13-2
13-3
13-4
13-5
Simplifying Square Roots
45°-45°-90°Triangles
30°-60°-90°Triangles
The Tangent Ratio
Sine and Cosine Ratios
Chapter 15 Formalizing Proof (5 days, 1 assessment)
15-1
15-2
15-4
15-5
Logic and Truth Tables
Deductive Reasoning
Preparing for Two-Column Proofs
Two-Column Proofs