In Algebra 1, we learn to reason abstractly and use the language of mathematics to model change in the world. The key content involves writing, solving, and graphing linear equations, including systems of two linear equations in two unknowns. The course also includes study of inequalities, exponential and quadratic functions, ratio, and proportion. Algebraic skills are applied in a wide variety of problem-solving situations.
Curriculum source: Desmos
How can mathematical ideas be represented?
How do you translate a relationship between quantities into an algebraic expression?
How can the numerical values of such quantities be predicted from an understanding of the rate at which each quantity changes with respect to the others?
How do we represent algebraic expressions visually?
Major Concepts:
Tables, equations, and graphs provide structure for communicating mathematical thinking.
Linear relationships grow at a constant rate.
Exponential relationships grow by a constant factor.
Major Content:
Use tables, equations, and graphs to describe relationships and make predictions
Distinguish between linear and exponential relationships shown in tables, graphs, equations, and situations.
Write and interpret equations of linear and exponential relationships
Major Concepts:
We create equivalent relationships by applying the same operation to both sides of an equation.
Linear relationships can be represented graphically as straight lines.
The solution to an equation or inequality is the set of values that make the equation or inequality true.
Major Content:
Solve linear equations with one variable, including equations with no solution or many solutions.
Solve multi-variable equations for a given variable.
Write equations to represent linear situations.
Determine solutions to an inequality algebraically and graphically.
Write inequalities in one and two variables to represent constraints.
Major Concepts:
Measures of center and spread are key features of data sets we use to make sense of....
Visual representations of data sets help us describe them.
Major Content:
Represent data with a dot plot, histogram, or box plot.
Calculate the mean and standard deviation or median and IQR for a data set.
Use shape, center, spread, and outliers to compare data sets.
Describe data using correlation coefficients and lines of best fit.
Use technology to generate lines of best fit and make predictions.
Major Concepts:
Functions are relationships between inputs and outputs for which each input has exactly one output.
Functions come with mathematical shorthand that facilitates mathematical communication.
Functions have various features we use to describe and compare them.
We can model many different situations with functions and use representations of functions to help us interpret those situations.
Major Content:
Describe whether or not a relationship is a function.
Interpret statements in function notation using tables, equations, and graphs.
Describe functions using their key features, including average rate of change.
Compare graphs of functions using function notation and key features.
Describe the domain and range of a function using its graph
Interpret functions representing situations.
Major Concepts:
The solution to a system of equations or inequalities is the set of all values that make every equation/inequality in the system true.
The intersection of the graphs of each equation in a system is the solution set.
Major Content:
Solve systems of linear equations with elimination, substitution, and graphing.
Write systems of linear equations to represent constraints and interpret their solutions in context.
Graph the solutions to a system of inequalities.
Write systems of linear inequalities to represent constraints and interpret their solutions in context.
Major Concepts:
Linear functions have a constant rate of change, while exponential functions have a constant ratio (and not a constant rate of change).
Many real-life situations involving money can be modeled with exponential functions.
Major Content:
Distinguish between situations modeled by linear and exponential functions.
Compare representations of linear and exponential functions.
Interpret and write exponential equations to model situations that involve percent increase or decrease.
Use equations of exponential functions to solve problems in context.
Use properties of exponents to make sense of compound interest rates.
Fit a linear or exponential function to data and informally assess the fit.
Major Concepts:
Quadratic functions have a variable rate of change with a constant second difference.
The square of any number is positive, which creates vertical symmetry in quadratic functions.
The product of any expression and zero is zero.
Major Content:
Justify whether a function is linear, quadratic, exponential, or none.
Identify and interpret key features of quadratics in graphs and tables.
Graph quadratics in standard form and factored form.
Write quadratic equations in factored form from a graph or description.
Use key features to graph quadratics in vertex form.
Write quadratic functions in factored form or vertex form.