Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Intermediate, 6th Grade
Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude
for a positive or negative quantity in a real-world situation. For
example, for an account balance of -30 dollars, write |-30| = 30 to
describe the size of the debt in dollars.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Intermediate, 6th Grade
Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Intermediate, 8th Grade
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the
function from a description of a relationship or from two (x, y) values,
including reading these from a table or from a graph. Interpret the rate
of change and initial value of a linear function in terms of the situation
it models, and in terms of its graph or a table of values.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Intermediate, 8th Grade
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15
t can be rewritten as (1.15
1/12)
12t ≈ 1.012
12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
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.★
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and
classify them as representing exponential growth or decay
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Distinguish between situations that can be modeled with linear functions and with exponential functions.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or
two input-output pairs (include reading these from a table).
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Interpret the parameters in a linear or exponential function in terms of a context.
