Download Coding Expectations Strand (First Letter) Big Idea (Number

Coding Expectations
Strand
(First Letter)
(N = Numbers & Operations)
(A = Algebraic Relationships)
(G = Geometric & Spatial Relationships)
(M = Measurement)
(D = Data & Probability)
Big Idea
(Number)
Concept
(Row letter)
Expectation (Grade or Course Level)
(Since College Algebra is above the state
expectations I used A+ as the code to
indicate anything from Algebra I up)
Strand: Numbers and Operations (N)
1. Understand numbers, ways of representing numbers, relationships
among numbers and number systems.
A. Read, write, and compare numbers
(compare and order rational and irrational numbers including
finding their approximate locations on a number line)
B. Represent and use rational numbers
(use real numbers and various models, drawings etc. to solve
problems)
C. Compose and decompose numbers
(use a variety of representations to demonstrate an understanding
of very large and very small numbers)
D. Classify and describe numeric relationships
2. Understand meanings of operations and how they relate to one
another.
A. Represent operations
B. Describe effects of operations
(Describe the effects of operations, such as multiplication,
division, computing powers and roots on the magnitude of
quantities)
C. Apply properties of operations
(apply properties of operations to all rational numbers including
order of operations and inverse operations)
D. Apply operations of real and complex numbers
(apply operations to real numbers, matrices and complex numbers
using mental computation or paper-pencil calculations and
technology for more complicated cases)
3. Compute fluently and make reasonable estimates.
A. Describe or represent mental strategies.,
B. Develop and demonstrate fluency
C. Compute problems
D. Estimate and justify solutions
E. Use proportional reasoning
Strand: Algebraic Relationships (A)
1. Understand patterns, relations and functions
A. Recognize and extend patterns
B. Create and analyze patterns
(generalize patterns using explicitly or recursively defined functions)
C. Classify objects and representations
(compare and contrast various forms of representations of patterns)
D. Identify and compare functions
(understand and compare properties of linear, nonlinear,
exponential, logarithmic and rational functions and apply properties of
exponents to simplify expressions and solve equations)
E. Describe the effects of parameter changes
(on linear, exponential and quadratic functions include intercepts)
2. Represent and analyze mathematical situations and structures using
algebraic symbols.
A. Represent mathematical situations
(use symbolic algebra to represent and solve problems that involve linear,
quadratic, exponential and logarithmic relationships)
B. Describe and use mathematical manipulations
(including factoring and rules of integer exponent and properties of
exponents to simplify expressions, inverse and composition of functions)
C. Utilize equivalent forms
(use and solve equivalent forms of equations and inequalities- linear,
piece-wise and quadratic)
D. Utilize systems
(use and solve systems of linear and quadratic equations or inequalities
with 2 variables)
3. Use mathematical models to represent and understand quantitative
relationships
A. Use mathematical models
(identify quantitative relationships and determine the type of functions that
might model the situation to solve the problem)
4. Analyze change in various contexts
A. Analyze change
(analyze linear, quadratic, exponential and logarithmic functions by
investigating rate of change, intercepts and zeros, and asymptotes)
Strand: Geometric and Spatial Relationships (G)
1. Analyze characteristics and properties of two- and three-dimensional
geometric shapes and develop mathematical arguments about geometric
relationships
A. Describe and use geometric relationships
(use inductive & deductive reasoning to establish the validity of
geometric conjectures to prove theorems and critique arguments
of others. Also use trigonometric relationships with right triangles to
determine lengths and angles measure)
B. Apply geometric relationships
(such as similarity and angle relationship to solve multi-step problems
in 2 dimensions)
C. Compose and decompose shapes
2. Specify locations and describe spatial relationships using coordinate
geometry and other representational systems
A. Use coordinate systems
(make conjectures and solve problems involving 2-dimensional
objects represented with Cartesian coordinates)
3. Apply transformations and use symmetry to analyze mathematical
situations
A. Use transformations on objects
(use and apply constructions and the coordinate plane to represent
translations, reflections, rotations and dilations of objects)
B. Use transformations on functions
(in algebra II translate, dilate, and reflect functions)
C. Use symmetry
(identify types of symmetries of 2 and 3-dimensional figures)
4. Use visualization, spatial reasoning and geometric modeling to solve
problems
A. Recognize and draw three-dimensional representations.
(draw and use vertex-edge graphs or networks to find optimal solutions
and draw representations of 3-dimensional geometric objects from
different perspectives)
B. Draw and use visual models (to solve problems)
Strand: Measurement (M)
1. Understand measurable attributes of objects and the units, systems
and processes of measurement
A. Determine unit of measurement
B. Identify equivalent measures
C. Tell and use units of time
D. Count and compute money
2. Apply appropriate techniques, tools and formulas to determine
measurements
A. Use standard or non-standard measurements
B. Use angle measurement
(solve problems of angle measure, including those involving triangles or
other polygons and of parallel lines cut by a transversal)
C. Apply geometric measurements
(solve problems involving circumference and/or area of a circle and
surface area/volume of geometric solids including rectangular or
triangular prisms, cylinders, cones, and spheres.
D. Analyze precision
(describe the effects of computations on precision which includes
judging the reasonableness of numerical computations and their results
And applying concepts of successive approximation.
E. Use relationships within a measurement system
(use unit analysis to solve problems involving rates, such as speed,
density or population density)
Strand: Data and Probability (D)
1. Formulate questions that can be addressed with data and collect,
organize and display relevant data to answer them
A. Formulate questions
(formulate and collect data about a characteristic which include
sample spaces and distributions)
B. Represent and interpret data
C. Classify and organize data
(select and use appropriate graphical representation of data and
given one-variable quantitative data, describe its shape and calculate
summary statistics)
2. Select and use appropriate statistical methods to analyze data
A. Describe and analyze data
(apply statistical measure of center to solve problems)
B. Compare data representations
C. Represent data algebraically
(find line of best fit/determine a type of function which models the data)
3. Develop and evaluate inferences and predictions that are based on
data
A. Develop and evaluate inferences
(make conjectures about possible relationships between 2 characteristics
of a sample on the basis of scatter plots of data)
B. Analyze basic statistical techniques
4. Understand and apply basic concepts of probability
A. Apply basic concepts of probability
(describe the concepts of sample space and probability distribution)
B. Use and describe compound events
(use and describe the concepts of conditional probability and independent
Events and how to compute the probability of a compound event)
The Show-Me Standards for Mathematics
Summary of Performance Outcomes and Indicators for VSI in College Algebra 110
Unit 0: Basics: Remembrance of Things Past
Outcome: Be able to define, relate, and understand basic concepts of the real number system, the
formulation of mathematics as a language, exponents, polynomial expressions, the complex number
system, and basic geometry.
Coding:
MA-4, 5; Goal 1.8, 3.1;
N1DA+
MA-4, 5; Goal 1.8, 3.1;
N1AA+; N1DA+
MA-5; Goal 1.8, 3.2;N1AA+
MA-5, 6; Goal 1.8;G2A5+
MA-1, 5; Goal 3.6;N1B7+
MA-1; Goal 1.5, 2.1;N1AA+
MA-5; Goal 1.5, 2.1;A2AA+
MA-1; Goal 1.5, 2.1;N1AA+
MA-5, 6; Goal 1.5, 3.2;G1AG
MA-5, 6; Goal 3.1; N1CA+
MA-5, 6; Goal 3.1, 3.2;
N2BA+
MA-5, 6; Goal 3.1, 3.2;
N2BA+
MA-5, 6; Goal 3.1, 3.2;N2CA+
MA-1, 4, 5; Goal 1.5, 3.4;
A1CA+
MA-1, 4, 5; Goal 1.5, 3.4;
A1DA+
MA-1, 4, 5; Goal 1.5, 3.4;
A1DA+
MA-1, 4, 5; Goal 1.5, 3.4;
A1DA+
MA-1, 4, 5; Goal 1.5, 3.4;
A2BA+
MA-5; Goal 1.6, 3.4; A2BA+
MA-1, 4, 5; Goal 1.10, 3.2;
A2BA+
MA-1, 4, 5; Goal 1.10, 3.2;
A2BA+, A2CA+
MA-1, 4, 5; Goal 1.5,
3.4;A2CA+
Performance Indicators:
a) Proper notation for denoting sets of objects
b) Classify and define the following sets of the Real Number System:
Natural Numbers, Integers, Rational Numbers,
Irrational Numbers, Real Numbers
c) Construct and label the points on a real number line.
d) Calculate the distance between two points
e) Represent real numbers as decimals
f) Identify key concepts in learning to read mathematics
g) Write and understand the basic symbols used in algebra
h) Relate mathematical concepts to a language context as the Nouns,
Pronouns, and The Main Verb of Algebra
i) Describe and define theorems, corollaries, lemmas, etc.
j) Identify and define integer exponents
k) Perform operations with integer exponents
l) Recognize square roots as a pair of equal factors, and simplify
expressions containing radicals
m) Perform operations with nth roots and rational exponents
n) Define, identify, and classify polynomials on general and specific
levels
o) Perform operations on polynomials such as adding, subtracting,
and multiplying
p) Identify and correct common errors associated with performing
operations on polynomials
q) List and identify handy polynomial products
r) Factor various polynomials
s) Complete perfect squares and be able to describe the reasoning and
processes
t) Perform the operation of dividing polynomials (simplify rational
expressions)
u) Simplify polynomial expressions, rational expressions, and a
combination of the two expressions (polynomial and rational) in
dealing with various operations (adding, subtracting, multiplying, and
dividing)
v) Develop skills to solve polynomial & rational equations
Copyrights by The Curators of the University of Missouri, 1999
MA-1, 4, 5; Goal 1.5, 3.1, 3.2,
3.3; N1DA+, A2BA+, A2CA+
MA-1, 2, 4, 5; Goal 1.6, 3.4;
M2C7+
MA-2, 4, 5; Goal 3.3, 3.4;
G2A8+
w) Define, simplify, and manipulate complex numbers; compare and
relate complex numbers to real numbers
x) Calculate area, perimeter, and volume using geometric area
formulas; list formulas; explain processes used
y) Understand and use The Pythagorean Theorem and its applications
as an introduction to further studies in trigonometry
Copyrights by The Curators of the University of Missouri, 1999
Unit 1: Graphs
Outcome: Be able to graph, relate, and understand equations of lines & circles in the Rectangular
Coordinate System by hand and with the aid of a graphing utility; calculate and classify information
about the equations and graphs produced.
Coding:
MA-2, 4, 6; Goal 1.6, 2.2, 4.1;
G2AA+
MA-1, 2, 6; Goal 3.2,
3.4; G2AA+
MA-4, 6; Goal 1.4, 3.4;
Performance Indicators:
a) Describe the organization of the Rectangular Coordinate System
where geometry meets algebra
b) Evaluate the distance between two points, the midpoint of a line
segment, and applications
c) Explore, understand, and use the functions and applications of
graphing utilities
MA-6; Goal 1.5, 1.8; G2AA+, d) Understand the basic concepts associated with graphing; Classify
A1DA+
and graph equations
MA-6; Goal 1.5, 1.6, 2.2, 4.1; e) Describe, define, and find intercepts of the x and y axes given
A4AA+, A1EA+
equations and/or graphs
MA-2, 4, 6; Goal 1.5, 1.6, 2.2; f) Determine and describe symmetry relating to graphs of equations
G3CA+
MA-2, 4, 6; Goal 1.5, 2.2, 4.1; g) Define and correctly represent the slope of a line from linear equaA4AA+
tions and linear graphs
MA-4, 6; Goal 1.5, 1.8, 3.4,
h) Identify lines & their equations; graph a line from its equation; de4.1; A1DA+, A4AA+, G2AA+ scribe the characteristics of a line and its equation
MA-4, 6; Goal 1.5, 1.6, 2.2,
i) Compare and contrast between parallel & perpendicular lines; name
4.1; A1EA+, A4AA+
parallel and perpendicular lines’ slope from given equations
MA-4, 6; Goal 1.5, 1.6, 1.8,
j) Graph circles from a given equation; describe the characteristics of
2.2, 4.1;A4AA+, G2AA+
a given circle and its equation
MA-6; Goal 1.5, 1.8, 4.1;
k) Evaluate and graph given equations and their applications
A1DA+, A4AA+, G2AA+
Copyrights by The Curators of the University of Missouri, 1999
Unit 2: Functions and Their Graphs
Outcome: Be able to graph, describe, and understand the basic concepts of functions and their graphs
Coding:
MA-4, 5; Goal 1.8, 2.3, 3.2,
3.6; A1BA+, A1DA+
MA-4; Goal 2.3, 4.1; A1DA+
MA-4, 6; Goal 1.1; A1DA+
MA-1, 4; Goal 1.1, 1.7;
A1DA+
MA-4, 6; Goal 1.7; A1DA+
MA-6; Goal 1.6, 4.6; A4AA+
MA-4; Goal 1.6; A4AA+,
G3BA+, G3CA+
MA-4; Goal 1.5, 4.4; A1DA+,
A2CA+, G2AA+
MA-1; Goal 2.1; A1DA+,
A2CA+, G2AA+
MA-4, 6; Goal 1.4; G3AA+,
G3BA+, G3CA+
MA-1, 5; Goal 4.1; A2BA+
MA-1, 6; Goal 1.10, 3.5, 4.1,
4.8; A3AA+
Performance Indicators:
a) Understand and explain the central idea of mathematics, the
function, using ideas presented
b) Define and describe functions using the proper language and
notation of functions
c) Evaluate the domain of given functions
d) Evaluate functions using given values for the domain
e) Correctly define and evaluate functions using graphs of (x, f(x))
pairs to enhance visualization
f) Identify: increasing & decreasing functions, local maximums &
local minimums of functions, and even & odd functions
g) Draw, describe, and memorize the graphs of the library of
important functions as presented
h) Evaluate, graph, and understand the concept of Piecewise Defined
Functions
i) Demonstrate knowledge of the graphs of functions by working
given exercises
j) Use, manipulate, and graph functions using the graphing
techniques as listed: Vertical & Horizontal Shifts, Compressions &
Stretches, Reflections Across the Axes
k) Understand and evaluate function compositions
l) Relate the study of functions and their graphs to real world
problems using mathematical models
Copyrights by The Curators of the University of Missouri, 1999
Unit 3: Equations & Inequalities
Outcome: Be able to solve, graph, and understand the concepts of linear and quadratic equations; relative
mathematical models; general, polynomial, and rational inequalities; and equations and inequalities
containing absolute values
Coding:
MA-3, 6; Goal 3.1, 3.2, 3.4,
3.6 ; A1DA+, G2AA+
MA-3, 6; Goal 3.1, 3.2, 3.4,
3.6 ; A1DA+, G2AA+
MA-4; Goal 3.1, 3.2, 3.4, 3.6;
A1DA+, A2AA+, A2BA+
MA-4, 6; Goal 3.1, 3.2, 3.4,
3.6; A1DA+, A2BA+, G2AA+
MA-1; Goal 3.1, 3.2, 3.4, 3.6;
N1DA+
MA-1, 4; Goal 3.1, 3.2, 3.4,
3.6; A1DA+, A2AA+
MA-4, 6; Goal 3.1, 3.2, 3.4,
3.6; A4AA+, G2AA+
MA-1, 4; Goal 3.1, 3.2, 3.3,
3.4, 3.6, 3.7; A3AA+
MA-1, 4; Goal 3.1, 3.2, 3.3,
3.4, 3.6, 3.7, 3.8; A1DA+,
A2BA+, A2CA+
MA-1, 4; Goal 3.1, 3.5, 3.6;
N1DA+, A2CA+
MA-1, 4; Goal 3.1, 3.2, 3.3,
3.4, 3.6, 3.7, 3.8; A2CA+
MA-1, 4; Goal 3.1, 3.2, 3.3,
3.4, 3.5, 3.6, 3.7, 3.8; N1DA+,
A2CA+
MA-1, 5; Goal 3.1, 3.2, 3.4,
3.6, 3.7; A2CA+
MA-1, 5; Goal 3.4, 3.5, 3.7,
3.8; N1DA+, A1EA+, A3AA+
Performance Indicators:
a) Solve equations (approximately) with a graphing device & The
Intermediate Value Theorem
b) Solve linear equations by the “Linear Formula” and by graphing
c) Solve non-linear equations that lead to linear equations
d) Solve quadratic equations by factoring and graphing
e) Understand and define the principle square root of a negative
number
f) Solve quadratic equations using the “Quadratic Formula”;
understand the concept and applications of the discriminant
g) Graph and list the processes in graphing quadratic equations
h) Set up equations to be used to solve mathematical models
i) Solve equations in various forms including: Equations involving
radicals, Equations quadratic in form, Factorable Equations
j) Describe the properties of inequalities
k) Understand and use the steps for solving inequalities in general
l) Solve and classify inequalities of the following nature: Linear
inequalities Quadratic inequalities Higher-degree polynomial
inequalities Rational inequalities
m) Solve equations and inequalities when absolute values appear
n) Understand the concept of absolute values, why they are used and
what they represent
Copyrights by The Curators of the University of Missouri, 1999
Unit 4: Polynomial & Rational Functions
Outcome: Be able to graph, evaluate, and explain the concepts of quadratic functions, general
polynomial functions, rational functions; understand and explain the many facets of zeros of polynomial
functions, strategies and exercises involving zeros
Coding:
MA-1, 4, 5; Goal 1.6, 3.4, 4.1;
N1DA+, A1DA+
MA-4, 6; Goal 1.4, 1.5, 1.8,
2.7; A4AA+, A1EA+, G2AA+
MA-4, 5; Goal 1.6, 1.8, 3.1,
3.6, 4.1; A3AA+
MA-4, 5; Goal 1.6, 1.8, 4.1;
A1CA+
MA-1, 4, 5; Goal 1.4, 1.5, 1.6,
1.8, 2.7; A1DA+, G2AA+
MA-1, 4, 5; Goal 1.4, 1.6, 1.8;
A4AA+, G2AA+
MA-1, 4, 5; Goal 1.2, 1.6, 2.1,
2.7, 3.1; A1DA+, A2AA+,
A2BA+
MA-3, 4; Goal 1.1, 1.6, 1.8,
2.1, 2.7, 3.1, 3.4, 4.1; A1BA+,
A1EA+, A4AA+
MA-4, 5; Goal 1.4, 1.6, 1.8
2.1, 2.7; A4AA+, G2AA+
Performance Indicators:
a) Describe and define the concept of quadratic functions
b) Graph quadratic functions using the properties, theorems, and
explanations presented
c) Describe and express quadratic functions as mathematical models
d) Describe and define general polynomial functions
e) Graph and understand the concept of power functions
f) Graph general polynomial functions after considering and defining
the following concepts: Zeros, Multiplicity, Turning Points, End
Behavior
g) Explain the answers and concepts of the following questions
regarding zeros of polynomial functions:
How Many Zeros Are There?
How Many Zeros Are Real?
How Many Real Zeros Are Positive? Negative?
Where (On What Interval) Are All Real Zeros?
How Can You Guess The Location of Real Zeros?
How Can You Reduce The Number of Real Zeros?
h) List strategies and tools for working exercises involving
polynomials and their zeros
i) Define and graph rational functions; understand explain, and find
appropriate asymptotes
Copyrights by The Curators of the University of Missouri, 1999
Unit 5: Exponential & Logarithmic Functions
Outcome: Be able to graph, evaluate, and explain the concepts of exponential functions, logarithmic
functions, and their applications.
Coding:
MA-1, 4; Goal 3.1; A1DA+
MA-4, 6; Goal 1.8; G2AA+,
A1DA+, A1EA+, A3AA+
MA-4, 6; Goal 1.8; G2AA+,
A1DA+, A4AA+
MA-1, 4, 5; Goal 3.4; A2BA+
MA-4, 6; Goal 1.8; A1DA+,
G2AA+
MA-4, 6; Goal 1.8; A1DA+,
G2AA+
MA-1, 4; Goal 3.4; N1DA+,
A1DA+
MA-1, 5; Goal 3.4; A1DA+
MA-1, 2, 3; Goal 1.10;
A3AA+
MA-1, 2; Goal 3.4; A1DA+
MA-1, 2, 3; Goal 1.5; A3AA+,
A4AA+
Performance Indicators:
a) Define and classify one-to-one functions
b) Graph, describe, and evaluate exponential functions and their
applications
c) Graph, describe, and evaluate natural exponential functions
d) Manipulate, evaluate, and define inverse functions
e) Graph, define, and evaluate logarithmic functions and their applications
f) Graph, define, and evaluate natural logarithmic functions
g)List and describe the properties of logarithms
h) Solve logarithmic equations
i) Calculate and relate the models of sound (loudness) and fury
(earthquakes) to logarithmic applications
j) Solve exponential equations
k) Apply and calculate results from the exponential models of
compounded interest and growth & decay
Copyrights by The Curators of the University of Missouri, 1999
Unit 6: Systems of Equations
Outcome: Be able to evaluate, solve, and explain the concepts of solving systems of linear equations by
substitution or elimination; applications and exercises involving systems of linear equations; systems of
non-linear equations.
Coding:
MA-4, 5, 6; Goal 1.6, 2.1, 2.3;
A2DA+
MA-1, 4, 5; Goal 3.2, 3.6;
A2DA+
MA-1, 4, 5; Goal 2.3, 3.2, 3.3,
3.6, 4.1; A2DA+
MA-1, 2, 5; Goal 3.4, 3.7, 4.6;
A2CA+
Performance Indicators:
a) Understand and explain the concept of systems of linear equations
in general
b) Solve a system of 2 (or 3) linear equations in 2 (or 3) variables
using the methods of substitution or the method of elimination.
c) Solve and explain exercises involving systems of linear equations
d) Understand and evaluate an application regarding writing proper
rational functions as sums of simpler proper rational functions
(otherwise known as partial fractions)
MA-2, 4, 6; Goal 3.6, 3.7; e) Solve by mostly graphical means systems of 2 non-linear equations
G2AA+
in 2 variables
Copyrights by The Curators of the University of Missouri, 1999
Unit 7: Some Discrete Topics
Outcome: Be able to construct, explain, understand, and evaluate the concepts of sequences and finite
sums; arithmetic and geometric sequences; series and induction; and the binomial theorem.
Coding:
MA-1, 2, 5; Goal 1.5, 3.2, 4.1;
A1BA+
MA-1, 5, 6; Goal 3.2, 4.1;
N2CA+, N1DA+
MA-1, 4, 5; Goal 3.2, 3.3;
N2AA+, N2DA+
MA-1, 4, 5; Goal 1.6, 3.3, 4.1;
A1BA+, N1DA+
MA-1, 4, 5; Goal 1.4, 1.5, 3.2;
N3CA+
MA-1, 4, 5; Goal 3.2, 4.1;
N1DA+
MA-4, 5; Goal 3.2, 3.5, 4.1;
A1BA+
MA-4, 5, 6; Goal 1.5, 3.2, 4.1;
N1DA+, A1AA+
MA-1, 2, 4, 5; Goal 1.8, 3.2,
3.6; A1AA+
MA-1, 2, 4, 5; Goal 1.4, 1.5,
3.2; A1AA+
Performance Indicators:
a) Define and evaluate infinite sequences (functions with domain n)
b) Define, manipulate and evaluate expressions involving the factorial
symbol
c) Add the first n terms of a sequence: nth partial sums & summation
notation
d) Compare and contrast arithmetic sequences and geometric
sequences
e) Evaluate arithmetic sequences and geometric sequences
f) Define and evaluate geometric series and their (infinite) sums
g) Understand and explain the concept of the principle of
mathematical induction
h) Evaluate and explain the use for the “binomial coefficient” symbol
i) Understand and relate Pascal’s Triangle
j) Know how to expand binomials raised to the nth power using the
binomial theorem
Copyrights by The Curators of the University of Missouri, 1999
X-Y Files: The Proof is in Here
Outcome: Be able to understand and relate the extensions presented in the X-Y Files as further
information and proofs for the various topics in this course.
Coding:
MA-1, 4, 5, 6; Goal 1.1, 1.6,
2.1, 2.2, 3.1 - 3.7, 4.1
N1AA+
MA-5; Goal 1.5, 2.4, 3.2;
A3AA+, A4AA+
MA-1, 4, 5; Goal 1.1, 3.2, 3.3,
3.6, 3.7; A2BA+
MA-1, 4, 5; Goal 1.6, 2.1, 2.3,
3.7, 4.1; N1AA+
Performance Indicators:
a) Understand and describe proofs of the following topics presented in
Unit 0:
• A Proof That 2 is Irrational
• A Proof That There Are The Same Number of Rational
Numbers as Natural Numbers!
• A Proof That There Are More Real Numbers Than Natural
Numbers!
b) Define and understand the applications of variation (algebra for
science) as presented in Unit 2
c) Understand and answer the following question as an extension to
Unit 4: How Can You Find Rational Zeros (if any) of a Polynomial
Function?
d) Understand and describe the proof that “e” is irrational as the topic
was introduced in Unit 7
Copyrights by The Curators of the University of Missouri, 1999