Our Algebra 1 Lessons for Grade Students

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 a, b, c, 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 + b, Ax + 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.

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 n^th 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 a, b, c, 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