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Algebra 1

Course Outline

Teaching Units Competencies and Objectives
Number Sense Competency: Perform basic operations with fractions, decimals and integers.
6 days

Review operations on integers

  • Include order of operations
  • Include absolute value
  • Include exponents
  • Include operations with fractions
  • Include operations with decimals
  Competency: Communicate using the language of algebra
1 day

Evaluate algebraic expressions

  • Include fractions and decimals
2 days

Simplify algebraic expressions using the distributive property

  • Include combine like terms
  • Include fractions
1 day Simplify radical expressions
2 days

Apply the Pythagorean Theorem

  • Include word problems
  Competency: Analyze data and apply concepts of probability
4 days

Probability

  • Single events
  • Independent events (two-stage with replacement)
  • Dependent events (two-stage without replacement)

Statistics

  • Calculate mean, median, mode
  • Answer questions given graphical representations of data:
    • Scatterplots
    • Stem-and-leaf plots
    • Histograms
    • Line graphs
    • Box-and-whisker plot
2 days
18 days total
Review and Test
Linear equations and inequalities Competency: Solve equations and inequalities in one variable
2 days

Develop and use elementary transformations to solve one-step equations and inequalities:

  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Include work with fractions and decimals
2 days

Solve two-step equations and inequalities in the form ax + b = c

  • Graph solutions to inequalities on number lines
2 days

Solve multi-step equations and inequalities with variables on both sides of the equal sign

  • Graph solutions on number lines
  • Include multiply by LCD to clear fractions
3 days

Solve multi-step equations and inequalities involving the distributive property and combining like terms

  • Graph solutions to inequalities on number lines
  • Include multiply by LCD to clear fractions
  Competency: Apply algebraic methods to problem solving
3 days

Solve equations resulting from applications involving:

  • Complementary and supplementary angles
  • Vertical angles
  • Parallel lines cut by a transversal
  • Sum of the interior angles of triangles and quadrilaterals
3 days

Solve problems dealing with similar polygons

  • Include solve proportion equations
1 day

Translate word phrases into algebraic expressions

Translate sentences into algebraic equations and inequalities

4 days

Solve word problems including the following types:

  • Number
  • Age
  • Consecutive integers
  • Angle relationships (dealt with above)
  • Rate-time-distance
  • Cost
  • Wage
2 days
22 days total
Review and Test
Polynomials Competency: Examine and apply the characteristics of operations on polynomials
4 days

Classify polynomials as monomial, binomial, trinomial, or polynomial
Use laws of exponents to simplify algebraic expressions

  • Definition of exponents
  • Product of powers
  • Power of a power
  • Power of a product
  • Definition of negative exponent
  • Definition of zero as an exponent
  • Quotient of powers
  • Power of a quotient
  • Divide polynomials by a monomial

Add and subtract polynomials (review of combining like terms)

3 days

Multiply polynomials

  • Monomial times a polynomial
  • Binomial times a binomial
  • Binomial times a trinomial
  • Difference of two squares type
  • Square of a binomial
2 days Apply polynomial operations to problems involving perimeter and area
8 days

Factor polynomials using algebraic methods:

  • GCF
  • Grouping
  • Trinomials a = 1
  • Trinomials a > 1
  • Perfect square trinomials
  • Difference of two squares
  • Multiple steps
2 days

Solve quadratic equations using the Zero Product Property

  • Include area applications
2 days
21 days total
Review and Test
Relations, functions and their graphs Competency: Discriminate between relations and functions.
1 day Plot points on the Cartesian plane
1 day

Determine if a relation is a function from:

  • Graph
  • Mapping
  • A list of ordered pairs
  • A table of values
  • Match an algebraic equation to a table of values and vice-versa
1 day

Find the range of a function from its:

  • Graph
  • Table of values
  • List of ordered pairs
  • Algebraic expressions given the domain
  Competency: Investigate graphing techniques for linear equations and inequalities in two variables
1 day Graph linear equations by making a table of values and plotting points
2 days

Find the slope of a line using:

  • Given points
  • The graph of a line
  • Slope-intercept equations
  • Standard form equations
4 days

Graph linear equations using the slope and y-intercept (Slope-intercept form)
Graph linear equations using the x- and y-intercepts (Standard form)

  • Show how to transform standard form into slope-intercept form

Graph linear equations given certain conditions:

  • 2 points
  • x- and y-intercepts
  • Point and slope
  • Slope and either x- or y-intercept
1 day Find the midpoint and the length of a segment
3 days

Write the equation of a line given:

  • 2 points
  • x- and y-intercepts
  • Slope and a point
  • Graph
1 day Write an equation for the line of best fit from scatterplots. (Use scatterplots from unit 1.)
1 day

Identify the graphs of common relations:

  • x = constant
  • y = constant
  • y = x
1 day Graph linear inequalities
2 days

Solve systems of linear equations by:

  • Graphing
  • Substitution
2 days
21 total days
Review and test
2 days Review and final exam


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