Algebra I Curriculum

 Section A          Graphing
  1. Plotting points on a coordinate plane – Quadrant 1 only
  2. Evaluating linear algebraic expressions and equations
  3. Concept of undefined (algebraic expression)
  4. Discussion of associative property
  5. Graphing an equation on a coordinate plane – Quadrant 1
  6. Solution of equation in two variables (one equation, infinite many solutions)
  7. Finding a common solution of a system of two linear equations graphically
  8. Interpretation of graphs (discussion of relation versus function).

Section B          Algebra

  1. Order of operations – Addition/Subtraction, Multiplication/Division
  2. Order of operations – Exponents as a unique type of multiplication, parentheses
  3. Combining like terms
  4. Solving equations with one variable:  ax + b = cx + d
  5. Check answer
  6. Discussion of multiplicative inverse
  7. Discussion of commutative property
  8. Distributive Property in Arithmetic  Distributive Property in Algebra
  9. Solving linear equations with parentheses – Distributive property and
  10. Order of Operations

Section C        Problem Solving

  1. Solving literal equations
  2. Solving consecutive integer problems (non-negative integers)
  3. Find the common solution of two equations in two variables algebraically
  4. Arithmetic problems with distance, coin problems
  5. Algebraic solution of distance, coin problems, science, finance
  6. Translating quantitative phrase into an algebraic expression and equation 

 

Section D       Ratio/Proportion/Percent

  1. Proportions as equivalent ratios
  2. Solving verbal problems using ratios
  3. Using proportions to show direct variation.
  4. Percent
  5. Percent  solving by proportion
  6. Solving verbal problems involving percent
  7. Increases and decreases and discount.
  8. Discussion of relative error
  9. Solving equations with fractional expressions
  10. Discussion of Rates

 

Section E        Algebra with Integers           

  1. The four quadrants in a coordinate system
  2. Revisit Section A and Section B with integers and the 4 quadrants
  3. Discussion of Additive Inverse

 Section F      Graphs of parallel and perpendicular lines

  1. Graphing lines parallel to the axes
  2. Finding the slope of a line (given two points)
  3. Explain concept of rate of change.
  4. Discussion of rational numbers.
  5. Identifying the slope and y-intercept of a straight line from its equation
  6. Writing a linear equation given a slope and a point.
  7. Writing a linear equation given two points.
  8. Graphing a linear equation using the point-slope method
  9. Graphing a linear equation using the slope-intercept method
  10. How does a coefficient change affect its graph?
  11.  Tangent function in the first quadrant
  12. Slopes of parallel lines (determining if two lines are parallel).
  13. Finding a line parallel to a given line through a point, (x,y) on the given line
  14. Slopes of perpendicular lines; Using slope to prove lines are perpendicular
  15. Find perpendicular line given a line and a point on the given line
  16. Writing equations of a line:  y = mx + b;  Ax + By = C
  17. Determine if given point is on a line given the equation.

Section G        Systems of Linear Equations in Two Variables

  1. Graph of systems of linear equations. (Manually and using calculators)
  2. Solution of systems of linear equations by graphing (finding point of intersection)
  3. Solution of systems of linear equations by Addition/Multiplication; Substitution
  4. Determinants and the solution of linear equations in two variables

 

Section H      Operations with polynomials

  1. Adding monomials and polynomials
  2. Subtracting monomials and polynomials
  3. Multiplying monomials
  4. Dividing monomials
  5. Meaning of a negative exponent and a zero exponent
  6.  Writing numbers in scientific notation
  7. AREA:  Developing idea in algebraic framework.
  8.  Multiplying polynomials (Distributive Property.)
  9.  Dividing polynomials

 

Section I        Inequalities

  1.  Graphing inequalities
  2.  Solving systems of linear inequalities and graphing.
  3. Checking solutions
  4.  Solving inequalities in one variable.
  5.  Solving verbal problem through inequalities.

Section J       Variation

  1. What is direct variation?
  2. Finding parts of similar polygons
  3. Applications of similarity
  4. Finding the ratios of perimeters and areas of similar triangles
  5. Volume of regular solids and cylinders
     

Section K      Quadratic Functions and Factoring

  1. Graphs of non-linear equations
  2. How does a coefficient change affect its graph?
  3. Quadratic equations in two variables; Parabolas; x-intercepts
  4. Factoring and its relationship to area
  5. Factoring quadratic trinomials
  6. Factoring the difference of two squares
  7. Complete factorization of a polynomial:  common factors
  8. Solving quadratic equations through factoring with the use of zero property of multiplication.
  9. Solving quadratic equations by graphing.
  10. Solving verbal problems with quadratic equations
  11. Solving number and consecutive integer problems using quadratic equations
  12. Solving area problems using quadratic equations
  13. Solving fractional equations with integer and monomial denominators.
  14. Solving algebraic proportions with one variable which result in quadratic equations.

 

Section L         Irrational numbers and Pythagoras

  1. Irrational numbers
  2. The use of the radical sign
  3. Simplifying radicals no variable in radicand
  4. Operations with radicals (using like and unlike terms).

 

Section M        Right Triangle Trig

  1. Trig ratios of an acute angle of a right triangle
  2. Find an acute angle of a right triangle given the lengths of its sides
  3. Find the length of a side of a right triangle given the measure of an acute angle and the measure of one side.
  4. Application of Pythagorean theorem

 

Section N        Solution of linear/quadratic systems

  1. Parabola – The graph of a function of degree 2
  2. What are the characteristics of the following functions:
  3. Exploring quadratic equations
  4. Intersection of parabola and linear equation, y = f(x), y = 0, y = c for some
  5. constant c.  (Only factoring and quadratic formula)
  6. Characteristics of a Parabola:   
  7. Axis of symmetry (-b/2a)
  8. Finding the Vertex (maximum/minimum)
  9. Finding the Vertex (maximum/minimum)  using the graph
  10. Root Theory:  x-intercept
  11. Using the graphing calculator and a series of equations, find the
  12. roots/zeroes/solutions of each equation.
  13. Quadratic Formula; discriminant.
  14. Determine the nature of the roots using discriminant. b2 - 4ac

Section O         Functions:

  1. ABS Value: Meaning and how it relates to the length of a line segment.
  2. ABS Value Equations and Expressions.
  3. Graphing ABS Value functions. 
  4. ABS Val Inequalities
  5. Factorial Notation.

Section P        Rational Expressions

  1. Operations on algebraic fractions containing monomial denominators
  2. Reducing fractions containing polynomials.
  3. Multiplying and dividing fractions containing polynomials denominators
  4. Combining fractions with polynomial denominators
     

Section Q       Statistics of the Median

1.      Finding the median  - is there a mode?

2.      Stem and Leaf Plot

3.      Finding the quartile using the median

4.      Analyze and Interpret Box and whisker plots

5.      Setting up a frequency table/intervals other than one

6.      Finding the median from a frequency table.

7.      Analyze and Interpret Histograms

8.      What is meant by cumulative frequency histogram?

9.      How can we use a cumulative frequency histogram to determine formation on percentile scores, quartile scores and the median?

10.  Scatter plots of bivariate data.

11.  Line of best fit and equation for scatter plot

12.  Identify the relationship between the independent and dependent variables from a scatter plot.

 

Section R         Statistics of the Mean

1.      What does the mean of a set of data tell you?

2.      Finding the mean.

3.      Finding a data point which will change the mean to a given number.
 

Section S        Applications of Statistics

1.      Categorize data as qualitative or quantitative

2.      Determine whether the data to be analyzed is univariate or bivariate

3.      Determine when collected data or display of data maybe be biased

4.      Compare and contrast the appropriateness of different measures of central tendency for a given data set.

5.      Evaluate published reports and graphs that are based on data by considering: experimental design, appropriateness of the data analysis, and the soundness of the conclusions.

6.      Find the percentile rank of an item in a data set and identify the point values for the first, second, and third quartiles.

7.      Understand the difference between correlations but not a causal relationship.

8.      Identify and describe sources of bias and its effect, drawing conclusion from

9.      data.

10.  Recognize how linear transformations of one variable data affect the data of

11.  the mean, median, mode, and range.

12.  Use a reasonable line of best fit to make a prediction involving interpolation or extrapolation.

 

Section T        Probability

1.      Conditional probability

2.      Sample space and favorable events

3.      Probability of an event and its complement

4.      Determine empirical probabilities based on specific sample data.

5.      Determine, based on calculated probability of a set of events, if:

6.      Some or all are equally likely to occur

7.      One is more likely to occur than another

8.      Whether or not an event is certain to happen or not to happen

9.      Calculate the probability of:

10.  Series of independent events

11.  Series of dependent events

12.  Two mutually exclusive events

13.  Two events that are not mutually exclusive

Section U       Permutations

1.      Developing permutations

2.      Solving permutation problems involving n things taken r at a time

3.      Counting Principle

Section V       Set theory

1.      Set builder notation and/or interval notation to represent the elements of a set

2.      Complement of a set

3.      Intersection of sets

Section W       Exponential Growth and Decay

1.      Analyze and solve verbal problems that involve exponential growth and decay

2.      Exponential growth and decay:  Expressions, equations, inequalities and word problems.

3.      Graph exponential growth and decay

 

 

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