HIS Mathematics (Algebra II)

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 Advanced Algebra, Scott Foresman Integrated Mathematics, Scott Foresman and Company, c. 1996, 1998
    Teacher’s Resource File
    Visual Aids
    Activity Kit
    Algebra Software Tools



    Instructional Objectives:

    Unit 1
    1. Evaluate expressions and formulas, including correct units in answers
    2. Use function notation
    3. Solve and check linear equations
    4. Rewrite formulas
    5. Evaluate sequences
    6. Write a recursive definition for a sequence
    7. Determine whether a relation defined by a table, a list or ordered pairs, or a simple equations is a function
    8. Determine the domain and range of a function defined by a table, list of ordered pairs, or a simple equation
    9. Use addition, subtraction, multiplication, and division to write expressions which model real-world situations
    10. Use functions to solve real-world problems
    11. Use linear equations to solve real-world problems
    12. Determine the domain, range, and values of a function from its graph
    13. Apply the Vertical-Line Test for a function

    Unit 2
    1. Translate variation language into formulas and formulas into variation language
    2. Solve variation problems
    3. Find slopes (rates of change)
    4. Use the Fundamental Theorem of Variation
    5. Identify the properties of variation functions
    6. Recognize variation situations
    7. Solve real-world variation problems
    8. Fit an appropriate model to data
    9. Graph variation equations
    10. Identify variation equations from graphs
    11. Recognize the effects of a change in scale or viewing window on a graph of a variation equation

    Unit 3
    1. Determine the slope and intercepts of a line given its equation
    2. Find an equation for a line given two points on it or given a point on it and its slope
    3. Evaluate expressions based on step functions
    4. Evaluate or find explicit and recursive formulas for arithmetic sequences
    5. Recognize properties of linear functions
    6. Recognize properties of arithmetic sequences
    7. Model constant-increase or constant-decrease situations or situations involving arithmetic sequences
    8. Model situations leading to linear combinations
    9. In a real-world context, find an equation for a line containing two points
    10. Fit lines to data
    11. Model situations leading to piecewise-linear functions or step functions
    12. Graph or interpret graphs of linear equations
    13. Graph or interpret graphs of piecewise-linear functions or step functions

    Unit 4
    1. Add, subtract, and find scalar multiples of matrices
    2. Multiply matrices
    3. Determine equations of lines perpendicular to given lines
    4. Recognize properties of matrix operations
    5. Recognize relationships between figures and their transformation images
    6. Relate transformations to matrices, and vice versa
    7. Use matrices to store data
    8. Use matrix addition, matrix multiplication, and scalar multiplication to solve real-world problems
    9. Graph figures and their transformation images

    Unit 5
    1. Solve 2 x 2 and 3 x 3 systems using the Linear Combination Method or substitution
    2. Find the determinant and the inverse of a square matrix
    3. Use matrices to solve systems of two or three linear equations
    4. Recognize properties of systems of equations
    5. Recognize properties of systems of inequalities
    6. Use systems of two or three linear equations to solve real-world problems
    7. Use linear programming to solve real-world problems
    8. Solve and graph linear inequalities in one variable
    9. Estimate solutions to systems by graphing
    10. Graph linear inequalities in two variables
    11. Solve systems of inequalities by graphing

    Unit 6
    1. Expand squares of binomials
    2. Transform quadratic equations from vertex from to standard form, and vice versa
    3. Solve quadratic equations
    4. Perform operations with complex numbers
    5. Apply the definition of absolute value and the Absolute Value-Square Root Theorem
    6. Use the discriminant of a quadratic equation to determine the nature of the solutions to the equation
    7. Use quadratic equations to solve area problems or problems dealing with velocity and acceleration
    8. Fit a quadratic model to data
    9. Use the Graph-Translation Theorem to interpret equations and graphs
    10. Graph quadratic functions or absolute value functions and interpret them
    11. Use the discriminant of a quadratic equation to determine the number of x-intercepts of the graph

    Unit 7
    1. Evaluate bn when b > 0 and n is a rational number
    2. Simplify expressions or solve equations using properties of exponents
    3. Describe geometric sequences explicitly and recursively
    4. Solve equations of the form xn = b, where n is a rational number
    5. Recognize properties of nth powers and nth roots
    6. Solve real-world problems which can be modeled by expressions with nth powers or nth roots
    7. Apply the compound interest formula
    8. Solve real-world problems involving geometric sequences
    9. Graph nth power functions

    Unit 8
    1. Find values and rules for composites of functions
    2. Find the inverse of a relation
    3. Evaluate radicals
    4. Rewrite or simplify expressions with radicals
    5. Solve equations with radicals
    6. Apply properties of the inverse relations and inverse functions
    7. Apply properties of radicals and nth root functions
    8. Solve real-world problems which can be modeled by equations with radicals
    9. Make and interpret graphs of inverses of relations

    Unit 9
    1. Determine values of logarithms
    2. Use logarithms to solve exponential equations
    3. Solve logarithmic equations
    4. Recognize properties of exponential functions
    5. Identify or apply properties of logarithms
    6. Apply exponential growth and decay models
    7. Fit an exponential model to data
    8. Apply logarithmic scales (pH, decibel), models, and formulas
    9. Graph exponential functions
    10. Graph logarithmic curves

    Unit 10
    1. Approximate values of trigonometric functions using a calculator
    2. Find exact values of trigonometric functions of multiples of 30o or 45o or their radian equivalents
    3. Determine the measure of an angle given its sine, cosine, or tangent
    4. Convert angle measures from radians to degrees or from degrees to radians
    5. Identify and use definitions and theorems relating to sines, cosines, and tangents
    6. Solve real-world problems using the trigonometry of right angles
    7. Solve real-world problems using the Law of Sines or Law of Cosines
    8. Find missing parts of a triangle using the Law of Sines or Law of Cosines
    9. Use the properties of a unit circle to find trigonometric values
    10. Identify properties of the sines, cosines, and tangent functions using their graphs

    Unit 11
    1. Use the Extended Distributive Property to multiply polynomials
    2. Factor polynomials
    3. Find zeros of polynomial functions by factoring
    4. Determine an equation for a polynomial function from data points
    5. Use technical vocabulary to describe polynomials
    6. Apply the Zero-Product Theorem, Factor Theorem, and Fundamental Theorem of Algebra
    7. Apply the Rational-Zero Theorem
    8. Use polynomials to model real-world situations
    9. Use polynomials to describe geometric situations
    10. Graph polynomial functions
    11. Estimate zeros of functions of polynomials using tables or graphs
    12. Be familiar with the history of the solving of polynomial equations

    Unit 12
    1. Rewrite an equation for a conic section in the general form of a quadratic equation in two variables
    2. Write equations of inequalities for quadratic relations given sufficient conditions
    3. Find the area of an ellipse
    4. Solve systems of one linear and one quadratic equation or two quadratic equations by substitution or linear combination
    5. Find points on a conic section using the definition of the conic
    6. Identify characteristics of parabolas, circles, ellipses, and hyperbolas
    7. Classify curves as circles, ellipses, parabolas, or hyperbolas using algebraic or geometric properties
    8. Use circles, ellipses, and hyperbolas to solve real-world problems
    9. Use systems of quadratic equations to solve real-world problems
    10. Graph quadratic relations given sentences for them, and vice versa
    11. Solve systems of quadratic equations graphically

    Unit 13
    1. Calculate values of a finite arithmetic series
    2. Calculate values of finite geometric series
    3. Use summation (?) or factorial (!) notation
    4. Calculate permutations and combinations
    5. Expand binomials
    6. Recognize properties of Pascal’s triangle
    7. Solve real-world problems using arithmetic or geometric series
    8. Solve problems involving permutations or combinations
    9. Use measures of central tendency or dispersion to describe data or distributions
    10. Solve problems using probability
    11. Give reasons for sampling
    12. Graph and analyze binomial and normal distributions