Algebra 1 Scope & Sequence
Common Core State Standards
Unit 1.1 Expressions & Equations
CCSS Standards:
•HSA.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
•HSA.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.
•HSA.SSE.A.2 Use the structure of an expression to identify ways to rewrite it.
•HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems.
•HSA.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Lessons, Objectives, & Activities:
I can simplify expressions using properties and combining like terms.
Combining Like Terms & Distributing with Context Practice
Rewriting Algebraic Expressions Group Activity
Collecting Like Terms & Distributing Practice Activities
I can use mathematical vocabulary to talk about expressions and equations.
Expressions and Equation Vocab Bifold
Expressions Vocabulary Challenge
I can translate words into expressions and equations.
Translating Expressions Around the Room
Translating Expressions and Equations Game
I can solve equations using inverse operations.
Do Undo Method for Solving Equations
I can solve word problems with equations.
Word Problems and Equations Match Up
Additional Practice
Equations Practice with Error Analysis
Solving Equations & Multiplying by the Reciprocal Analysis
Unit 1.2 Equations with Variables on Both Sides + Literal Equations
CCSS Standards:
•HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems.
•HSA.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
•HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
Lessons, Objectives, & Activities:
I can determine if an equation has one, many, or no solutions.
I can solve equations with variables on both sides.
PowerPoint Intro Lesson for Variables on Both Sides
Equations with Variables on Both Sides Practice
I can solve equations that have infinitely many solutions or no solution.
I can solve literal equations for a specific variable.
Literal Equations and Rearranging Formulas
I can use strategies to solve many types of equations and rearrange formulas.
Equations Centers with Variables on Both Sides
Unit 2.1
CCSS Standards:
•HSF.IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
Lessons, Objectives, & Activities:
I can sketch graphs for real world situations.
Interpreting Graphs PowerPoint and Tasks
I can describe relationships shown on graphs and sketch graphs based on descriptions.
I can relate graphs to descriptions.
Interpreting Graphs: Distance and Speed
Unit 2.2
CCSS Standards:
•HSA.F.IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
•HSA.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
•HSA.REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
•HSF.IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
•HSF.BF.A.1 Write a function that describes a relationship between two quantities.
•HSF.BF.A.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.
Lessons, Objectives, & Activities:
I can graph and compare proportional relationships.
Proportional Relationships Multiple Representations
Comparing Proportional Relations Tasks
I can calculate slopes of linear relationships.
I can create a graph to show a linear relationship.
I can identify initial values and rates from descriptions.
Practice Powerpoint: Identifying Initial Values & Rates
Initial Values and Rates Activity
I can create tables of values and graphs from stories.
(Continue Initial Values and Rates Activity)
I can write an equation in slope-intercept form to represent a story, table, or graph.
Graphing Linear Equations Multiple Representations
Extra Practice: Discovering y=mx+b through Graphing
I can compare linear relationships.
Equations and Graphing Challenges
Graphing and Comparing Linear Relationships Project
I can write an equation given a slope and a point (point-slope form).
Point-Slope Form Inquiry Lesson
I can use standard form to write equations, find intercepts, and graph.
Multiple Representations of Linear Equations, Standard Form
I can graph any linear equation.
Remediation: Graphing Skills Worksheets or Graphing Practice
Extension: Rates Business Startup Project
Unit 2.3 Scatter Plots
CCSS Standards:
•HSS.ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
•HSS.ID.B.6.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
•HSS.ID.B.6.b Informally assess the fit of a function by plotting and analyzing residuals.
•HSS.ID.B.6.c Fit a linear function for a scatter plot that suggests a linear association.
•HSS.ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
•HSS.ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
•HSS.ID.C.9 Distinguish between correlation and causation.
Lessons, Objectives, & Activities:
I can graph a scatter plot and use math vocabulary to describe features.
I can interpret real world scatter plots.
Math Meets Science Scatter Plot
I can interpret correlation coefficients.
Correlation Coefficients Lesson with Card Match
I can use technology for graphing scatter plots, linear regression, and correlation coefficients.
Scatter Plot Task for Graphing Calculator
I can distinguish between correlation and causation.
Correlation vs Causation Info Sheet
Extension Project:
Unit 2.4 Systems of Equations
CCSS Standards:
•HSA.REI.C.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
•HSA.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
•HAS.REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations.
Lessons, Objectives, & Activities:
I can interpret a system of equations.
Intro to Systems: The Growth of Trees
Bug Race, Comparing Lines Practice
I can solve systems of equations using graphs and tables.
Systems: Multiple Representations
I can use substitution to solve systems of equations.
(Complete Multiple Representations activity)
Graphic Organizer: Types of Solutions
I can use elimination to solve systems of equations.
Elimination Guided Learning and Practice
I can problem solve with systems.
I can graph all types of linear equations and systems.
Unit 3 Functions
CCSS Standards:
•HSF.IF.A.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
•HSF.IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
•HSF.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
Lessons, Objectives, & Activities:
I can identify functions.
I can use function notation.
(Continue Functions Lesson Pack)
I can determine an appropriate domain and range for a function and identify domains and ranges.
(Continue Functions Lesson Pack)
I can determine if a relation is linear and if it is a function.