HIS Mathematics (Algebra)

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 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 ever as well as house all 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
  • In addition to traditional mathematical content, the student will engage in problem solving in real-life situations in mathematics.
  • 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 Algebra, Scott Foresman Integrated Mathematics, Scott Foresman and Company, c. 1996, 1998
    Teacher’s Resource File
    Visual Aids
    Activity Kit
    Geometry Template
    Algebra Software Tools



    Instructional Objectives:

    Unit 1
    1. Find solutions to open sentences using trial and error
    2. Find unions and intersections
    3. Evaluate numerical and algebraic expressions
    4. Evaluate square roots with and without a calculator
    5. Read and interpret set language and notation
    6. Use the Square of the Square Root Property
    7. Give instances or counterexamples of patterns
    8. Use variables to describe patterns in instances or tables
    9. In real situations, choose a reasonable domain for a variable
    10. Evaluate formulas in real situations
    11. Apply the Pythagorean Theorem to solve problems in real situations
    12. Draw and interpret graphs of solution sets to inequalities

    Unit 2
    1. Multiply and simplify algebraic fractions
    2. Multiply positive and negative numbers
    3. Solve and check equations of the form ax = b
    4. Solve and check inequalities of the form ax < b
    5. Evaluate expressions containing a factorial symbol
    6. Identify properties of multiplication
    7. Apply the Area Model of Multiplication to real situations
    8. Apply the Rate Factor Model of Multiplication to real situations
    9. Apply the Multiplication Counting Principle and Permutation Theorem
    10. Use rectangles, rectangular solids, or rectangular arrays to picture multiplication

    Unit 3
    1. Use the Distributive Property and the properties of addition to simplify expressions
    2. Solve and check equations of the form x + a = b and ax + b = c
    3. Add algebraic fractions
    4. Solve and check inequalities of the form ax + b < c
    5. Identify and apply properties of addition or the Distributive Property
    6. Use the Distributive Property to perform calculations in your head
    7. Apply models of addition to write linear expressions or to solve sentences of the forms x + a = b, ax + b = c, ax + b < c
    8. Write expressions and solve problems involving linear patterns with two variables
    9. Draw and interpret two-dimensional graphs
    10. Draw and interpret two-dimensional slides on a coordinate graph
    11. Use balance scales or area models to represent expressions or sentences
    12. On a number line graph solutions to inequalities of the form ax + b < c

    Unit 4
    1. Simplify expressions involving subtraction
    2. Solve and check linear equations involving subtraction
    3. Solve and check linear inequalities involving subtraction
    4. Use the Opposite of a Sum or Difference Property to simplify expressions and solve sentences
    5. Apply the algebraic definition of subtraction
    6. Use the definitions of supplements and complements, and the Triangle Sum Theorem
    7. Use Triangle Inequality to determine possible lengths of sides of triangles
    8. Use models for subtraction to write expressions and sentences involving subtraction
    9. Solve problems using linear sentences involving subtraction
    10. Apply the Triangle Inequality in real situations
    11. Use a spreadsheet to show patterns and make tables from formulas
    12. Graph equations of the forms x + y = k and x – y =k or ax + b and ax – b by making a table of values

    Unit 5
    1. Solve linear equations of the form ax + b = cx + d
    2. Solve linear inequalities of the form ax + b < cx + d
    3. Use chunking to simplify or evaluate expressions or to solve equations
    4. Find equivalent forms of formulas and equations
    5. Apply and recognize properties associated with linear sentences
    6. Use linear equations and inequalities of the form ax + b = cx + d or ax + b < cx + d to solve real-world problems 7. Use tables or spreadsheets to solve real-world problems involving linear situations
    8. Graph horizontal and vertical lines
    9. Use graphs to solve problems involving linear expressions
    10. Given an equation, be able to use an automatic grapher to draw and interpret a graph

    Unit 6
    1. Divide real numbers and algebraic fractions
    2. Solve percent problems
    3. Solve proportions
    4. Use the language of proportions and the Means-Extremes Property
    5. Use the Rate Model for Division
    6. Use ratios to compare two quantities
    7. Calculate relative frequencies or probabilities in situations with a finite number of equally likely outcomes
    8. Solve percent problems in real situations
    9. Solve problems involving proportions in real situations
    10. Find probabilities involving geometric regions
    11. Apply the Size Change Model for Multiplication
    12. Find lengths and ratios of similitude in similar figures

    Unit 7
    1. Find the slope of the line through two given points
    2. Find an equation for a line given two points on it, or its slope and one point on it
    3. Write an equation for a line in standard form or slope-intercept form, and from either form find its slope and y-intercept
    4. Use the definition and properties of slope
    5. Calculate rates of change from real data
    6. Use equations for lines to describe real situations
    7. Given data whose graph is approximately linear, find a linear equation to fit the graph
    8. Graph a straight line given its equation, or given a point and the slope
    9. Graph linear inequalities

    Unit 8
    1. Evaluate integer powers of real numbers
    2. Simplify products, quotients, and powers of powers
    3. Rewrite powers of products and quotients
    4. Test a special case to determine whether a pattern is true
    5. Identify properties of exponents and use them to explain operations with powers
    6. Calculate compound interest
    7. Solve problems involving exponential growth and decay
    8. Use and simplify expressions with powers in real situations
    9. Graph exponential relationships

    Unit 9
    1. Solve quadratic equations
    2. Simplify square roots
    3. Evaluate expressions and solve equations using absolute value
    4. Identify and use properties of quadratic equations
    5. Use quadratic equations to solve problems about paths of projectiles
    6. Graph equations of the form y = ax2 + bx + c and interpret these graphs
    7. Calculate and represent distances on the number line or in the plane

    Unit 10
    1. Add and subtract polynomials
    2. Multiply polynomials
    3. Multiply a polynomial by a monomial or multiply two binomials
    4. Expand squares of binomials
    5. Classify polynomials by their degree or number of terms
    6. Write whole numbers as polynomials in base 10
    7. Translate investment situations into polynomials
    8. Use the chi-square statistic to determine whether or not an event is likely
    9. Represent areas and volumes of figures with polynomials

    Unit 11
    1. Solve systems using substitution
    2. Solve systems by addition
    3. Solve systems by multiplying
    4. Recognize sentences with no solution, one solution, or all real numbers as solutions
    5. Determine whether a system has no solution, one solution, or infinitely many solutions
    6. Use systems of linear equations to solve real-world problems
    7. Use systems of linear inequalities to solve real-world problems
    8. Find solutions to systems of equations by graphing
    9. Graphically represent solutions to systems of linear inequalities

    Unit 12
    1. Factor positive integers into primes
    2. Find common monomial factors of polynomials
    3. Factor quadratic expressions
    4. Solve quadratic equations by factoring
    5. Apply the definitions and properties of primes and factors
    6. Recognize and use the Zero Product Property
    7. Determine whether a quadratic polynomial can be factored over the integers
    8. Apply the definitions and properties of rational and irrational numbers
    9. Solve quadratic equations in real situations
    10. Represent quadratic expressions and their factorizations with areas


    Unit 13
    1. Evaluate functions and solve equations involving functions notation
    2. Use function keys on a calculator
    3. Determine whether a set of ordered pairs is a function
    4. Find the domain and the range of a function from its formula, graph, or rule
    5. Use function notation and language in real situations
    6. Determine values of probability functions
    7. Find lengths of sides or tangents of angles in right triangles using the tangent function
    8. Determine whether or not a graph represents a function
    9. Graph functions