Algebra 1 Scope and Sequence

Students will be able to:

  • Determine the slope of a line given a table of values, the coordinates of two points on the line, or an equation in slope-intercept form.
  • Write and solve equations involving direct variation.
  • Write linear equations in slope-intercept form given a table of values or a verbal description.
  • Decide whether relations represented verbally, tabularly, graphically, and symbolically define a function.
  • Evaluate functions, expressed in function notation, given one or more elements in their domains.
  • Determine the domain and range of a linear function in mathematical problems, and represent domain and range using inequalities.
  • Determine reasonable domain and range values for real-world situations, both continuous and discrete.

Suggested Activities

  • Models, Models
  • Bouncing Ball
  • Mathman on the Slopes
  • Walk It!
  • The Concorde and a Bike Race
  • Guess My Coefficient
  • The Prom Project
  • Slope-Intercept in Real Life
  • This is the Way We Vary

Students will be able to:

  • Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems.
  • Determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of abc, and d.
  • Calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems.

Suggested Activities

  • As Time Goes By
  • The Wave
  • Representing Functions
  • Shark Attack

Students will be able to:

  • Solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides.
  • Write linear equations in two variables in various forms, including y = mx + bAx + By = C, and y - y1 = m(x - x1), given one point and the slope and given two points.
  • Determine the slope of a line given a graph or an equation written in various forms, including Ax + By = C, and y - y1 = m(x - x1).
  • Write the equation of a line that contains a given point and is parallel to a given line.
  • Write the equation of a line that contains a given point and is perpendicular to a given line.
  • Write an equation of a line that is parallel or perpendicular to the X or Y axis and determine whether the slope of the line is zero or undefined.

Suggested Activities

  • Oh, The Pressure!
  • Points, Lines and Slopes-Oh My!
  • Linear Functions Here and There
  • Linear Equations Art Project

Students will be able to:

  • Write systems of two linear equations given a table of values, a graph, or a verbal description.
  • Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist.
  • Estimate graphically the solutions to systems of two linear equations with two variables in real-world problems.
  • Solve systems of two linear equations with two variables for mathematical and real-world problems.

Suggested Activities

  • How You Gonna Call?
  • Ready Copy
  • How Many Solutions to a System?
  • Understanding Solutions of Systems
  • Let’s Be Systematic

Students will be able to:

  • Solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides.
  • Write linear inequalities in two variables given a table of values, a graph, or a verbal description.
  • Graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.
  • Solve mathematic and scientific formulas, and other literal equations, for a specified variable.
  • Graph the solution set of linear inequalities in two variables on the coordinate plane

Suggested Activities

  • Applications of Linear Inequalities
  • One Variable Linear Inequalities
  • Inequalities Foldable/Scavenger Hunt
  • Working Teen
  • Literal Equations Practice

Students will be able to:

  • Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association.
  • Compare and contrast association and causation in real-world problems.
  • Write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.

Suggested Activities

  • Monopoly and Line of Best Fit
  • Trashcan Bball and Line of Best Fit
  • Correlation Investigation
  • Correlation Practice

Students will be able to:

  • Add and subtract polynomials of degree one and degree two.
  • Multiply polynomials of degree one and degree two.
  • Divide polynomials of degree one and two.
  • Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property;
  • Factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two.
  • Decide if a binomial can be written as the difference of two squares and, if possible, rewrite the binomial as two factors.

Suggested Activities

  • Multiplying-Box Method
  • Factoring-Box Method
  • Number Tricks
  • Operations with Polynomials Scavenger Hunt

Students will be able to:

  • Identify terms of arithmetic and geometric sequences when the sequences are given in recursive or explicit form.
  • Write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms.

Suggested Activities

  • Introduction to Arithmetic and Geometric Sequences
  • Generating Sequences Numerically
  • Arithmetic and Geometric Sequences Maze
  • Sequences Scavenger Hunt
  • Sequences Practice-Mixed

Students will be able to:

  • Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.
  • Simplify numerical radical expressions involving square roots.

Suggested Activities

  • Exponent Rules Investigation
  • Exponent Rules Calculator Exploration
  • Exponent Rules Puzzle
  • Negative Exponents Number Line Game
  • Simplifying Rational Exponents Error Detection
  • Simplifying Radicals Maze

Students will be able to:

  • Determine the domain and range of quadratic functions and represent the domain and range using inequalities;
  • Write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)2+ k), and rewrite the equation from vertex form to standard form (f(x) = ax2+ bx + c.)
  • Write quadratic functions when given real solutions and graphs of their related equations.
  • Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry.
  • Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions.
  • Determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of abc, and d.
  • Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula.
  • Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.

Suggested Activities

  • What Goes Up Must Come Down
  • Getting to Know Parabolas
  • Ball Toss
  • Graphing Quadratic Functions
  • Manual Fit – Parabolas
  • Quadratic Graphs 3 Forms
  • Rectangles and Quadratics
  • Applications of Quadratic Functions

Students will be able to:

  • Determine the domain and range of exponential functions of the form f(x) = abx and represent the domain and range using inequalities.
  • Interpret the meaning of the values of a and b in exponential functions of the form f(x) = abx in real-world problems.
  • Write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay.
  • Graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems.
  • Write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems.

Suggested Activities

  • Growing Money, Shrinking Value
  • Last Man Standing
  • Spreading Doom
  • Do You Want to Be a Millionaire?
  • Exponential Functions Matching Game