 # Secondary Math 1 - Course Standards

## A-SSE

Interpret the structure of expressions.

## A-SSE-1

Interpret expressions that represent a quantity in terms of its context.

## A-SSE-1-a

Interpret parts of an expression, such as terms, factors, and coefficients.

## A-SSE-1-b

Interpret complicated expressions by viewing one or more of their parts as a single entity. For Example interpret p(1+r)n as the product of P and a factor not depending on P.

## A-CED

create equations that describe numbers or relationships.

## A-CED-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

Understand solving equations as a process of reasoning and explain the reasoning.

## A-REI-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-REI-3

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

## A-REI-5

Prove that, given a system of two equations in two variables, replacing one equations by the sum of that equation and a multiple of the other produces a system with the same solutions.

## A-REI-6

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

## A-REI-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-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, polynomial, rational, absolute value, exponential, and logarithmic functions.

## A-REI-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-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)

## F-IF-2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

## F-IF-3

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0)=f(1)=1,f(n+1)=f(n)+f(n-1) for n > 1

## F-IF-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.

## F-IF-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.

## F-IF-6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

## F-IF-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-IF-7.a

Graph linear and quadratic functions and show intercepts, maxima, and minima.

## F-IF-7.e

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

## F-IF-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.

## F.IF.1

Build new linear or exponential functions from existing functions.

## F.BF.3

Interpret the structure of linear expressions or exponential expressions with integer exponents.

## F.LE.5

Construct and compare linear and exponential models and solve problems. Interpret expressions for functions in terms of the situation they model.

## G.CO.1

Understand congruence in terms of rigid motions.

## G.Co.6

Make geometric constructions.

## G.PE.4

Use coordinates to prove simple geometric theorems algebraically.

## G.PE.5

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

## G.PE.6

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

## G.PE.7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

## S.ID

Summarize,represent, and interpret data on a single count or measurement variable.

## S.ID.1

Represent data with plots on the real number line (dot plots, histograms, and box plots,).

## S.ID.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

## S.ID.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

## S.ID.5

Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

## S.ID.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

## S.ID.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.

## S.ID.6.b

Informally assess the fit of a function by plotting and analyzing residuals.

## S.ID.6.c

Fit a linear function for a scatter plot that suggests a linear association.

## S.ID.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

## S.ID.8

Compute (using technology) and interpret the correlation coefficient of a linear fit.

## S.ID.9

Distinguish between correlation and causation.

## N.VM.1

Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.

## N.VM.2

Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

## N.VM.3

Solve problems involving velocity and other quantities that can be represented by vectors.

## N.VM.4.a

Add vectors end-to-end, component-wise, and by the parallelogram rule. understand that the magnitude of a sum of two vectors is typically not the sum of magnitudes.

## N.VM.4.b

Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

## N.VM.4.c

Understand vector subtraction v-w as v+(-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

## N.VM.5

Multiply a vector by a scalar.

## N.VM.5a

Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(Vx,Vy)=(CVx,CVy).

## N.VM.5b

Compute the magnitude a scalar multiple cv using //cv//=/c/v. Compute the direction of cv knowing that when /c/v=0, the direction of cv is either along v(for c>0) or against vs (for c<0)

## N.VM.6

Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

## N.VM.7

Multiply matrices by scalars to produce new matrices, e.g., as when all of the pay-offs in a game are doubled.

## N.VM.8

Add, subtract, and multiply matrices of appropriate dimensions.

## N.VM.9

Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

## N.VM.10

Understand that zero and the identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. I determinant of a square matrix is nonzero if an only if the matrix has a multiplicative inverse.

## N.VM.11

Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. work with matrices as transformations of vectors.

## N.VM.12

Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of data.

## N.VM.13

Solve systems of linear equations up to three variables using matrix row reduction.

Back to Main Course Page