Secondary Math 1 - Course Standards
Interpret the structure of expressions.
Interpret expressions that represent a quantity in terms of its context.
Interpret parts of an expression, such as terms, factors, and coefficients.
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.
create equations that describe numbers or relationships.
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.
Understand solving equations as a process of reasoning and explain the reasoning.
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.
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
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.
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
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.)
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.
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.
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)
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
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
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.
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.
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.
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
Graph linear and quadratic functions and show intercepts, maxima, and minima.
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
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.
Build new linear or exponential functions from existing functions.
Interpret the structure of linear expressions or exponential expressions with integer exponents.
Construct and compare linear and exponential models and solve problems. Interpret expressions for functions in terms of the situation they model.
Understand congruence in terms of rigid motions.
Make geometric constructions.
Use coordinates to prove simple geometric theorems algebraically.
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).
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Summarize,represent, and interpret data on a single count or measurement variable.
Represent data with plots on the real number line (dot plots, histograms, and box plots,).
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.
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
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.
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
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.
Informally assess the fit of a function by plotting and analyzing residuals.
Fit a linear function for a scatter plot that suggests a linear association.
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Compute (using technology) and interpret the correlation coefficient of a linear fit.
Distinguish between correlation and causation.
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.
Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
Solve problems involving velocity and other quantities that can be represented by vectors.
Add and subtract vectors.
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.
Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
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.
Multiply a vector by a scalar.
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).
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)
Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
Multiply matrices by scalars to produce new matrices, e.g., as when all of the pay-offs in a game are doubled.
Add, subtract, and multiply matrices of appropriate dimensions.
Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
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.
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.
Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of data.
Solve systems of linear equations up to three variables using matrix row reduction.