THINKING
SKILLS: INTEGRATING LIBRARY RESOURCES WITH
LEARNING OBJECTIVES
Keeley Library Revised August 21, 2000 

COURSES: 10111, 10152 Algebra II 
NUMBER 
OBJECTIVES 
Page numbers below refer to Glenco Algebra 2 Standard numbers with M = assumptions of prior knowledge  
Keeley Library Resources : Click on the Internet Links in the First Column on the Left.  

1H3
IM16

CONTENT:
Discovering Closure via Complex Number Simplification: Describe
;the structure and properties of the real number system, and the relationships
between the real number system and its various subsets.Identify the properties
of operations on integers and rational numbers, including closure, associatively,
commutativiity, distributivity, identity and inverse.
PERFORMANCE Essay: Students will work alone writing an essay explaining what happens, with regard to form, when complex numbers are simplified to their simplest form. Short essay 

1H4
IH2

CONTENT:
Operating with Complex Numbers: Define
complex numbers and operate with them. Use Estimation to judge the reasonableness
of results of computations and of solutions to problems involving real
numbers.
PERFORMANCE: Problem Solving Students will work in groups on a real world application using complex numbers. Short answer. 

1H5
2H2

CONTENT:
Dilations of Geometric Figures: Represent
finite graphs using matrices and apply them to the solution of problems.
identify problem situations that lead to linear, quadratic, or exponential
equations and solve by applying appropriate graphical, tabular, or symbolic
methods.
PERFORMANCE: Explanation and Drawing: Students will work in groups to explain what happens to a triangle when its vertex matrix is scalar multiplied by a factor and then draw the figure to verify their expectations. Short answer. 

1H6
5H7

CONTENT
The Game o Five: Use permutations
and combinations to solve problems. Apply basic counting principles
to describe simple events, and compute probabilities of events with
outcomes that are not equally likely .
PERFORMANCE Problem Solving: Students will work in groups to analyze the "Game of Five" and draw conclusions about possible as well as impossible combinations. Game 
(to construct graphs etc. See below)

2H7
2H5

CONTENT:
Exploring Quadratic Functions. Describe
and model phenomena using functions, including exponential, logarithmic,
trigonometric, polynomial, rational, step, absolute value, and square root.
Describe similarities and differences among the families of linear, quadratic,
and exponential functions using graphs, tables, formulas and verbal descriptions
Describe the graphical significance of parameters.
PERFORMANCE Graph and Explanation : Students will be asked to find the axis of symmetry, the vertex, an d graph the function in the Y=(Xh)/\ 2C form, then explain the difference between the graph and the model f(x)=X/\2. Short answer 
(to construct graphs etc. See below)

2H8
2H3

CONTENT:
Solving Quadratic Equations by Graphing and Factoring Solve
polynomial, exponential, logarithmic trigonometric equations, and
equations with rational expressions by symbokic (quadratic) graphical and
numerical methods. Apply each method when appropriate. Use Algebra and
graphical methods to solve systems of linear equations and
inequalities, and describe relationships between different solution
methods.
PERFORMANCE: Graph, Problem Solving: Students working in groups will first graph a quadratic equation listing its Xintercepts. Students will then solve the quadratic equation by factoring and draw a conclusion between the solutions and the Xintercepts of the given function. Short Answer 
(to construct graphs etc. See below)

2H9
2H4

CONTENT:
Solving Systems of Equations: Solve
systems of equations and inequalities involving algebraic , exponential,
logarithmic, and trigonometric expressions using symbolic, numeric, and
graphical methods. Describe the relationship among the methods. Use systems
of equations or inequalities to represent mathematical relationships
and to solve problems.
PERFORMANCE: Graph, Problem Solving, Matrix Array Students working alone will be asked to solve a system of equations by graphing, by algebraic methods, and by use of determinates . Students will then be asked what was the most effective method for solving the given system of equations. Short answer. 
(to construct graphs etc. See below)

2H10
2H5

CONTENT:
Exploring Quadratic Functions Classify
functions into families. Describe the effects of parameter changes on different
representations of polynomial, rational, logarithmic, exponential and trigonometric
functions. Describe similarities and differences among the families
of linear, quadratic, and exponential functions using graphs, tables, formulas
and verbal descriptions Describe the graphical significance of parameters.
PERFORMANCE: Graph and Explanation Students will be asked to find the axis of symmetry, the vertex, and graph the function in the Y=(Xh)/\ 2C form, then explain the difference between the graph and the model f(x)=X/\2.Short answer. 

2H11
2M11

CONTENT:
Maximizing Profits and Minimizing costs Identify
maximum and minimum values of a function and use them in applications.
Explain and generalize how a change in one variable results in a change
in another variable in functional relationships...
PERFORMANCE: Problem Solving: Students working in groups will analyze manufacturing constraints in a real world problem, translate these constraints to a system of inequalities, and use the information to maximize profits and minimize costs of manufacturing. Openended response. 
(to construct graphs etc. See below)

2H12
2H1

CONTENT:
Composite Functions Perform
operations on functions, including compositions. Find inverses of functions.
Demonstrate facility in transforming polynomial expressions by rearranging
and collecting terms, factoring, and applying and applying the properties
of exponents in order to solve problems.
PERFORMANCE: Problem Solving : Students working individually will be given two defined functions f(x)and g(x) and ge asked to find fog(x) and gof (x )for the two defined functions. Short answer. 
Writing Essays

2H13
3H6

CONTENT:
Examples of Period Functions in the Real World Model
real work pehnomena involving growth, decay, and periodic processes. Apply
and interpret transformations on figures in the coordinate plane.
PERFORMANCE: Essay Students working alone will be asked to research real world phenomena to find examples in nature that can be modeled after a periodic function. Short essay 
Mathematics

2H14
3H8

CONTENT:
Finding the Sum of an Arithmetic Sequence
Identify arithmetic and geometric sequences and series and their properties.
Solve problems including the nth term recursively and explicitly.
Identify and describe geometric patterns of change using recursive notations.
PERFORMANCE: Problem Solving Students will be asked to find the sum of the first 937 odd integers. Short answer. 
Mathematics

2H15
3H8

CONTENT:
Using the Binomial Theorem: Define linear,
exponential and quadratic functions recursively, and to find closed form
expressions. Identify and describe geometric patterns of change using
recursive notations.
PERFORMANCE: Problem Solving Students working alone will use the Binomial Theorem in summation notation form to expand a binomial to some nth power. Fill in the blank 

3H9
3H5

CONTENT:
Navigation Derive and apply
trigonometric identities and the law of sines and cosines. Apply trigonometric
ratios in right triangles to solve problems.
PERFORMANCE: Problem Solving Students working in groups will solve navigation word problems using both the law of cosines and the law of sines to solve the problem. Short answer. 

3H10
3H6

CONTENT:
Dilations of Geometric Figures Use transformation
and coordinate geometry to represent real world and mathematical situations.
Apply and interpret transformations on figures in the coordinate plane.
PERFORMANCE: Explanation and Drawing Students will work in groups to explain what happens to a triangle when its vertex matrix is scalar multiplied by a factor and then draw the figure to verify their explanation. Short answer. 

3H11
3H6

CONTENT:
Rotational Transformations Use
vector geometry to solve problems. Describe addition of vectors and scalar
multiplication both symbolically and pictorially. Use vector methods to
obtain geometric results.. Apply and interpret transformations on figures
in the coordinate plane.
PERFORMANCE: Problem Solving: Students working in groups will utilize multiplication of matrices via a rotational matrix in order to transform a vector through a given rotation and find its new coordinates. Short answer. 

4H6
4M10

CONTENT:
Determining the Period of a Pendulum Describe
the relationship between degree and radian measures ,and use radian measure
in the solution of problems. Use proportions to model and solve indirect
measurement problems .
PERFORMANCE: Diagram, Problem Solving: Studentsworking in groups will solve real world problems involving the length and period of a pendulum which involves angular measures in radians. Short answer. 
Collaborative Work

5H8
5H2

CONTENT:
Predicting Stopping Distance: Apply regression
results and curve fitting to make predictions form data. Find the "line
of best fit" from a series of data. Use tables and graphs to compare linear,
quadratic, and exponential growth patterns.
PERFORMANCE: Graph, Problem Solving Students working in groups will analyze a set if data comparing speed with stopping distance. Students will create a prediction equation from the data and use that equation to make predictions for speeds not listed in the original data. Short answer. 

5H11
5H7

CONTENT:
Finding the Probability of Independent Events Use
simulations (e.g., random number tables, random functions, and area models)
to determine experimental probabilities. Apply basic counting principles
to describe simple events, and compute probabilities of events with
outcomes that are not equally likely .
PERFORMANCE: Problem solving Students working in groups will be given a black numbered spinner wheel (16), and a red numbered spinner wheel (16). Students will then be asked to find the probability that the sum or the numbers on both wheels will be more than or equal to 10 when both wheels are spun. Short answer. 
(to construct graphs etc. See below) 
5H12
5H1

CONTENT:
Analysis of Some Common Distributions Apply
uniform , normal, and binomial distributions to the solutions of
problems. Represent data in a scatter plot. Use the scatter plot to make
predictions. Describe data sets using the concepts of median, mean, mode,
maximum and minimum, and range.
PERFORMANCE: Graphs and Explanation Groups of students will work to produce line plots, and stem and leaf plots. Short answer, graph 
Note.he
following guide may also be useful for students who need to locate statistics
for projects. Statistics
We would also like to add links for online tutorials to cover items assumed to be already learned, and to help students who missed learning these concepts because of illness, etc. Microsoft has a number of tutorials. As we locate this information, we will place it as links in the file, Using Computers for Assignments. Constructive criticism and suggestions are welcomed. 