HIS Mathematics (Trig & Stats)

Children are a heritage from the Lord. .......Psalm 127:3


Instructional Philosophy:

Order is one of the hallmarks of God’s creation and mathematics is a discipline that teaches about the precision of this order. By understanding God’s use of numbers to symbolize many things throughout the entirety of scripture and exploring the detail of the use of numbers in scripture we can better appreciate God’s creation and its order. Upon examining the construction of the Temple by Solomon (II Chronicles 3,4), God gave Solomon specific measurements to be used. The sea (a huge circular-washing basin) was built using measurements for diameter and circumference in its consideration. On closer examination we find that within the measurements the number PI (3.14….) can be found from God’s provided measurements, yet no one on earth at that time understood the significance of this number until many years later. This example shows the mathematical precision in God’s instruction. The same can be said of the building of the ark as it was made to withstand the only worldwide flood in conjunction with being a house for all the kinds of animals on the earth. Hebrew, the Old Testament’s original language, itself is a compilation of numbers. We also can see that certain numbers such as 3, 7, 12 and 40 have special significance with God. Through the above-mentioned we can see that mathematics is an important part of the wisdom that we are all called to ask for (James 1:5).


Instructional Goals:

  • Upgrade student achievement in mathematics
  • Update the mathematics curriculum
  • Increase the number of students who take mathematics beyond algebra and geometry
  • Problem-solving activities that engage students’ intellects
  • Connections with the real world and other disciplines that motivate the need to study meaningful mathematics
  • The use of geometry, statistics, and probability in each course
  • Text support for development of students’ communications skills
  • The use of appropriate technology as a tool for discovery and learning mathematics
  • Daily review questions that lead to mastery of concepts


    Resources:

    Textbook – The University of Chicago School of Mathematics Project Functions, Statistics, and Trigonometry, Scott Foresman Integrated Mathematics, Addison Wesley Longman, Inc., c. 1998
    Teacher’s Resource File
    Visual Aids



    Instructional Objectives:

    Unit 1
    1. Use samples to make inferences about populations
    2. Determine relationships and interpret data presented in a table
    3. Read and interpret bar graphs, circle graphs, and coordinate graphs
    4. Draw graphs to display data
    5. Calculate measure of center and spread for data sets
    6. Use statistics to describe data sets and to compare or contrast data sets
    7. Read and interpret dotplots and histograms
    8. Compare measures of center and compare measures of spread
    9. Read and interpret box plots
    10. Use ?-notation to represent variance or standard deviation

    Unit 2
    1. Evaluate functions described with Euler’s notation
    2. Identify the independent and dependent variables, domain, and range of a function
    3. Identify properties of regression lines and of the correlation coefficient
    4. Describe properties of quadratic and exponential functions
    5. Find and interpret linear models
    6. Find and interpret exponential models
    7. Find and interpret quadratic models
    8. Use step functions to model situations
    9. Graph linear, exponential, quadratic, and step functions
    10. Interpret properties of relations from graphs
    11. Use scatter plots to draw conclusions about models for data

    Unit 3
    1. Find formulas and values of composite of functions
    2. Find inverses of functions
    3. Use the Graph-Translation Theorem or the Graph Scale-Change Theorem to find transformation images
    4. Describe the effects of translations or scale changes on functions and their graphs
    5. Describe the effects of translations or scale changes on measures of center or spread
    6. Describe the symmetries of graphs
    7. Identify properties of composite and inverses
    8. Identify properties of z-scores
    9. Use translations, scale changes, or z-scores to analyze data
    10. Recognize and graph parent functions
    11. Apply the Graph-Translation Theorem or the Graph Scale-Change Theorem to make or identify graphs.
    12. From a graph of a function, determine its symmetries or whether its inverse is a function
    13. Graph inverses of functions

    Unit 4
    1. Convert between degrees, radians, and revolutions
    2. Find lengths of circular arcs, and areas of sectors
    3. Find sines, cosines, and tangents of angles
    4. Apply the definitions of the sine, cosine, and tangent functions
    5. Apply theorems about sine, cosine, and tangents
    6. Identify the amplitude, period, frequency, phase shift, and other properties of circular functions.
    7. Solve problems involving lengths or arcs or areas of sectors
    8. Use equations of circular functions to solve problems about real phenomena
    9. Find equations of circular functions to model periodic phenomena
    10. Use the unit circle to find values of sines, cosines, and tangents
    11. Draw or interpret graphs of the parent sine, cosine, and tangent functions
    12. Graph transformation images of circular functions
    13. State equations for graphs of circular functions

    Unit 5
    1. Find sines, cosines, and tangents of angles
    2. Evaluate inverse trigonometric functions
    3. Use trigonometry to find lengths, angles, or areas
    4. Solve trigonometric equations
    5. Interpret the Law of Sines, Law of Cosines, and related theorems
    6. State properties of inverse trigonometric functions
    7. Solve problems using trigonometric ratios in right triangles
    8. Solve problems involving the Laws of Sines and Cosines
    9. Write and solve equations for phenomena described by trigonometric and circular functions
    10. Graph or identify graphs of inverse trigonometric functions

    Unit 6
    1. Evaluate bm/n for b>0
    2. Solve exponential equations
    3. Evaluate logarithms
    4. Describe properties of rational power, nth root, and logarithm functions
    5. Use properties of logarithms
    6. Use rational exponents to model situations
    7. Solve problems arising from exponential or logarithmic models
    8. Use rational power functions or logarithm functions to model data
    9. Graph nth root, rational power, and logarithm functions
    10. Interpret graphs of nth root, rational power, and logarithmic functions

    Unit 7
    1. List sample spaces and events for probabilistic experiments
    2. Compute probabilities
    3. Find the number of ways of selecting or arranging objects
    4. Evaluate expressions using factorials
    5. State and use properties of probabilities
    6. Determine whether events are mutually exclusive, independent, or complementary
    7. Solve equations using factorials
    8. Calculate probabilities in real situations
    9. Use counting principles and theorems to find the number of ways of arranging objects
    10. Design and conduct simulations without technology
    11. Design and conduct simulations using technology
    12. Construct, graph, and interpret probability distributions

    Unit 8
    1. Find terms of sequences from explicit or recursive formulas
    2. Find explicit or recursive formulas for the nth term of an arithmetic or geometric sequence
    3. Evaluate arithmetic or geometric series
    4. Expand binomials
    5. Determine whether a sequence is arithmetic or geometric
    6. Determine limits of certain sequences
    7. Tell whether an infinite series converges and if it does, give the limit
    8. Prove and apply properties involving combinations.
    9. Solve problems involving arithmetic and geometric sequences and series
    10. Use combinations to compute the number of ways of selecting objects.
    11. Determine probabilities in situations involving binomial experiments
    12. Locate numerical properties represented by the patterns in Pascal’s Triangle

    Unit 9
    1. Use infinite differences and systems of equations to determine an equations for a polynomial functions from data points
    2. Calculate or approximate zeros and relative extrema of polynomial functions
    3. Divide polynomials
    4. Factor polynomials and solve polynomial equations using the Factor Theorem, sums or differences of powers, grouping terms, or trial and error.
    5. Perform operations with complex numbers
    6. Apply the vocabulary of polynomials
    7. Apply the Remainder Theorem, Factor Theorem, and Factor-Solution-Intercept Equivalence Theorem
    8. Apply the Fundamental Theorem of Algebra and Conjugate Zeros Theorem
    9. Construct and interpret polynomials that model real situations
    10. Represent two- or three-dimensional figures with polynomials
    11. Relate properties of polynomial functions and their graphs

    Unit 10
    1. Calculate the mean and standard deviations of a binomial probability distribution
    2. Use the Standard Normal Distribution to find probabilities
    3. Compare and contrast characteristics of different binomial probability distribution graphs
    4. Use properties of normal distributions and their parent function
    5. Solve probability problems using binomial or normal distributions
    6. Use binomial and normal distributions to test hypotheses
    7. Apply the Central Limit Theorem
    8. Apply confidence intervals to real-world problems
    9. Graphs and interpret a binomial probability distribution
    10. Graph and interpret normal distributions

    Unit 11
    1. Multiply matrices when possible
    2. Use matrices to solve systems of equations
    3. Find the inverse of a 2x2 matric
    4. Apply properties of matrices and matrix multiplication
    5. Apply the Addition and Double Angle Formulas
    6. Use a matrix to organize information
    7. Represent reflections, rotations, scale changes, and size changes as matrices
    8. Represent composites of transformations as matrix products
    9. Use matrices to find the image of a figure under a transformation

    Unit 12
    1. Use properties of ellipses and hyperbolas to write equations describing them
    2. Find equations for rotation images of figures
    3. Rewrite equations of conic sections in the general form of a quadratic relation in two variables
    4. State and apply properties of ellipses and hyperbolas to draw or describe them
    5. Describe the intersections of a plane and a cone of 2 nappes
    6. Determine information about elliptical orbits
    7. Graph or identify graphs of ellipses and hyperbolas give their equations
    8. Graph transformation images of parent ellipses and hyperbolas
    9. Describe graphs of quadratic equations

    Unit 13
    1. Evaluate the reciprocal trigonometric functions
    2. Perform operations with complex numbers in polar or trigonometric form
    3. Represent complex numbers in different forms
    4. Find powers and roots of complex numbers
    5. Apply properties of the reciprocal trigonometric functions
    6. Prove trigonometric identities
    7. Describe singularities of functions
    8. Use and automatic grapher to test a proposed identity
    9. Given polar coordinates of a point, determine its rectangular coordinates and vice versa
    10. Plot points in a polar coordinate system
    11. Graph and interpret graphs of polar equations
    12. Graph complex numbers