A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.

A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Embed with A-REI.B.3, A-REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Embed with A-REI.B.3, A-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.

A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A−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. Include cases where f(x) and/or g(x) are linear...

Embed with A-REI.D.11, A−REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Embed with A-REI.D.11, A−REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

F-IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables,

or by verbal descriptions). 

Embed with F-IF.C.9, 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.

F-BF.A.1 Write a function that describes a relationship between two quantities.

Embed with F-BF.A.1, F-BF.A.2 Write arithmetic [this unit] and geometric [end of this unit or beginning of the next] sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Achievement Level Descriptors

Evidence

Achievement Level Descriptors

Evidence

Achievement Level Descriptors

Evidence

Achievement Level Descriptors

Evidence

Achievement Level Descriptors

Evidence

Embed with A-REI.B.3, A-REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A-SSE.A.1 Interpret parts of an expression, such as terms, factors, and coefficients.

A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it.

A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. 

Embed with A-REI.B.3, A-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.

Embed with A-REI.D.11, A−REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Embed with A-REI.D.11, A−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).

A-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.

N-Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

Embed with A-REI.D.11, A−REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Embed with F-IF.C.9, 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.

Embed with F-BF.A.1, F-BF.A.2 Write arithmetic [this unit] and geometric [end of this unit or beginning of the next] sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

F-IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.