Transcript Math II - Cabarrus County Schools

MATH II
An overview of the new math II
course and a comparison to the
traditional geometry course
MATH II CONTENT
Topics of study
 Functions, graphs and
operations
 Systems of linear and non-linear
equations
 Transformations of graphs and
objects on a graph
 Triangle congruence and proofs
 Right triangle trig
 Law of Sines and Cosines
 Complex functions
 Graphing functions
 Independent and dependent
probability
 Rules of probability
GEOMETRY VS. MATH II
Geometry by Units
Unit 1:
 Basic Geometric Terms
 Points, lines, and planes
 Rays
 Segment and Angle Addition
 Graphing on the coordinate plane
 Writing linear equations
 Parallel and Perpendicular lines
Unit 2:
 Parallel lines cut by a transversal
 Special angle relationships
 Geometric proofs
 Algebraic properties
Unit 1:
Math II by Units
 Function notation
 Function operations
 Function structure
 Literal Equations
 Domain and Range (linear, exponential,
quadratic, absolute value)
 Graphically and equations
 Graphing equations in 2 variables
 Building functions
 Systems of equations (linear and linear)
 Systems of equations (linear and quadratic)
 Writing and solving inequalities
 Systems of inequalities
GEOMETRY VS. MATH II
Geometry Cont.
Unit 3:
 Triangle Congruence
 Triangle Congruence Proofs
 CPCTC and proofs
Unit 4:
 Triangle angle sum
 Triangle properties

Angles and Sides
 Exterior angle of triangles
 Triangle Proofs
Math II Cont.
Unit 2:
 Isometry
 Translations, Dilations,
Reflections, and Rotations
 Combinations of
transformations
 Transformation of functions
(linear quadratics)
 Write functions from vertex
to standard form
GEOMETRY VS. MATH II
Geometry cont.
Math II cont.
Unit 5:
Unit 3:
 Polygon angle sums
 Algebraic proofs
 Triangle segments
 Triangle Angle Sum
 Triangle midsegments
 Triangle Congruence
 Points of Concurrency
 Congruence Proofs
 Graphing triangle segments
 Dividing Segments into portions
 Construct triangle, square, and
hexagon
GEOMETRY VS. MATH II
Geometry cont.
Unit 6:
 Properties of parallelograms

Parallelogram

Rectangle

Rhombus

Square
 Trapezoids
 Kites
 Quadrilaterals
Math II cont.
Unit 4:
 Right triangle trig
 Sine and Cosine complements
 Law of Sines
 Law of Cosines
 Area of Triangle (A= 1/2absinC)
GEOMETRY VS. MATH II
Geometry cont.
Math II cont.
Unit 7:
 Special Right Triangles
 Area of quadrilaterals
 Area of regular polygons
 Geometric Probability
Unit 8:
 Similar figures
 Triangle similarity
 Similarity proofs
Unit 5:
 Complex Functions
 Graphing

Exponential

Logs

Quadratics

Sine

Cosine

Tangent

Circles
 Solving for Zeros
 Inverse Functions
GEOMETRY VS. MATH II
Geometry cont.
Math II cont.
Unit 9:
Unit 6:
 Right Triangle Trig
 Angle of elevation and
depression
 Area of regular polygons
Unit 10:
 Volume, Surface Area, and
Lateral Area
 Independent and Conditional
Probability
 Addition Rule of Probability
 Multiplication Rule of
Probability
 Permutations and Combinations
 Two way frequency tables
GEOMETRY VS. MATH II
Geometry cont.
Unit 11:
 Circles

Segments and angles

Arcs and lengths
Unit 12:
 Transformations

Reflections, Rotations,
Translations, Dilations
Math II cont.
FINAL EXAM INFORMATION
 State will provide us with a Common Exam/MSL
 The exam will count as 25% of the overall grade
 There will be no exam exemptions
An overview of the
geometry in Math II
Number and
Operations
N-RN.2
Geometry topics include:
•
Congruence
•
Congruence proofs
•
Similarity of triangles
•
Similarity of transformed objects
•
•
Right Triangles
Trigonometry
•
•
Laws of Sines and Cosines
Graphing trigonometric
functions
•
Modeling given situations
•
Probability
•
Conditional probability
•
Rules of probability
Quantities*
N-Q.1*
N-Q.2*
N-Q.3*
Statistics and
Probability
Interpreting Functions
Congruence
Making Inferences &
Justifying Conclusions
S-IC.2
Functions
M
Real Numbers
Geometry
Algebra
Seeing Structure in
Expressions
A-SSE.1.a*
A-SSE.1.b*
A-SSE.2
A-SSE.3.c*
Arithmetic with
Polynomials and Rational
Expressions
O
D
E
L
I
N
G
F-IF.2
G-CO.2
F-IF.4*
G-CO.3
S-IC.6
F-IF.5*
G-CO.4
F-IF.7.b*
G-CO.5
Conditional Probability
and the Rules of
Probability
F-IF.7.e*
G-CO.6
S-CP.1
F-IF.8.a
G-CO.7
S-CP.2
F-IF.9
G-CO.8
S-CP.3
A-APR.1
Building Functions
G-CO.10
S-CP.4
A-APR.3
F-BF.1.a*
G-CO.13
S-CP.5
F-BF.1.b*
Creating Equations*
F-BF.3
Similarity, Right Triangles,
& Trigonometry
S-CP.6
S-CP.7
A-CED.1*
G-SRT.1.a
S-CP.8
A-CED.2*
G-SRT.1.b
S-CP.9
A-CED.3*
G-SRT.6
A.CED.4*
Reasoning with Equations
and Inequalities
A-REI.1
A-REI.2
G-SRT.7
G-SRT.8*
G-SRT.9
G-SRT.11
A-REI.4.b
Expressing Geometric
Properties with Equations
A-REI.7
G-GPE.1
G-GPE.6
A-REI.10
A-REI.11*
Geometric Measurement
and Dimension
G-GMD.4
Modeling with Geometry
G-MG.1*
G-MG.2*
G-MG.3*
WHERE IS ALL THE GEOMETRY NOW?
The traditional geometry material is spread over the curriculum from
grades 6 – 11. The integrated math approach is introducing students to the
strands of geometry as it applies to algebraic concepts.
For example:
Math II continues a progression of the standards established in Math I. In
addition to these standards, Math II includes polynomials, congruence and
similarity of figures, trigonometry with triangles, modeling with geometry,
probability, making inferences and justifying conclusions.
WHAT IS THE NEXT COURSE?
 Students are on a graduation track that has Math III as the next course.
 Math III will not be offered until next year.
 The integrated curriculum of Math II overlaps with the traditional
Algebra II curriculum.
 Students will gain more of the topics of geometry in Math III
 If students are planning to go into chemistry next semester, math II will
meet the requirements of algebra 2. (No need to double up for
science)
An overview to show the
geometry in Math III
Number and
Operations
Algebra
M
Functions
O
D
E
L
I
N
Geometry
Statistics and
Probability
G
Real Numbers
Seeing Structure in
Expressions
Interpreting
Functions
Congruence
Interpreting
Categorical and
Quantitative Data
N-RN.3
A-SSE.1.a*
F-IF.2
G-CO.1
S-ID.4
A-SSE.1.b*
F-IF.4*
G-CO.9
A-SSE.2
F-IF.5*
G-CO.10
Making
Inferences &
Justifying
Conclusions
N-Q.1*
A-SSE.3.b*
F-IF.7.c
G-CO.11
S-IC.1
N-Q.2*
A-SSE.4*
F-IF.7.e*
G-CO.12
S-IC.3
Similarity, Right
Triangles, &
Trigonometry
S-IC.4
The Complex
Number System
Arithmetic with
Polynomials and
Rational Expressions
F-IF.8.a*
N-CN.1
A-APR.1
• Circles
N-CN.2
A-APR.2
F-BF.1.a*
G-SRT.3
Using Probability
to Make Decisions
N-CN.7
A-APR.3
F-BF.1.b*
G-SRT.4
S-MD.6
• Geometric properties and
N-CN.9
A-APR.4
F-BF.2*
G-SRT.5
S-MD.7
A-APR.6
F-BF.3
Circles
A.APR.7
F-BF.4a
G-C.1
G-C.2
Creating Equations*
Linear, Quadratic,
and Exponential
Models*
A-CED.1*
F-LE.3*
G-C.5
• Proofs
A-CED.2*
F-LE.4*
A-CED.3*
Expressing Geometric
Properties with
Equations
• Trigonometric Functions
A.CED.4*
Trigonometric
Functions
Reasoning with
Equations and
Inequalities
F-TF.1
G-GPE.1
F-TF.2
G-GPE.2
A-REI.1
F-TF.5
A-REI.2
F-TF.8
Modeling with
Geometry
• Congruence
• Similarity
• Right Triangles
• Trigonometry
equations
• Modeling with geometry
Quantities*
N-Q.3*
A-REI.4.a
A-REI.4.b
A-REI.10
F-IF.9
Building Functions
G-SRT.2
G-C.3
G-MG.3*
S-IC.5
S-IC.6
QUESTIONS????