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THINKING SKILLS: INTEGRATING LIBRARY RESOURCES WITH LEARNING OBJECTIVES 
Keeley Library     Revised August 21, 2000
Algebra 2
COURSES:  10111, 10152          Algebra II
STANDARD
NUMBER
CONTENT AND PERFORMANCE
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.
  • Mathematics
  • Writing Essays

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    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
  • Mathematics
  • Collaborative Work

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    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.
  • Mathematics
  • Collaborative Work

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    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.
  • Mathematics
  • Collaborative Work

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    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
  • Mathematics
  • Using Computers for Assignments

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    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=(X--h)/\ 2-C form, then explain the difference between the graph and the model f(x)=X/\2. Short answer
  • Mathematics
  • Collaborative Work
  • Using Computers for Assignments

  •   (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 X-intercepts. Students will then solve the quadratic equation by factoring and draw a conclusion between the solutions and the X-intercepts of the given function. Short Answer
  • Mathematics
  • Using Computers for Assignments

  •   (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. 
  • Mathematics
  • computers
  • Using Computers for Assignments

  •    (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=(X--h)/\ 2-C form, then explain the difference between the graph and the model f(x)=X/\2.Short answer. 
  • Mathematics
  • Collaborative Work

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    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. Open-ended response.
  • Mathematics
  • Using Computers for Assignments

  •   (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. 
  • Mathematics

  • 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 n-th 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 n-th power. Fill  in the blank
  • Mathematics
  • Collaborative Work

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    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. 
  • Mathematics
  • Collaborative Work

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    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. 
  • Mathematics
  • Collaborative Work

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    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. 
  • Mathematics
  • Collaborative Work

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    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. 
  • Mathematics

  • 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. 
  • Mathematics
  • Collaborative Work

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    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 (1-6), and a red numbered spinner wheel (1-6). 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. 
  • Mathematics
  • Collaborative Work
  • Using Computers for Assignments

  •    (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.
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    Jane Constant, Reference Librarian
    Keeley Library, B.M.C.Durfee High School of Fall River
    September, 1978  to  June, 2001