F.2.ATMM.2 Represent constraints or inequalities using systems of equations and/or inequalities; interpret solutions as viable or non-viable options in a modeling context for functions beyond the level of linear and quadratic.
F.2.ATMM.3 Compose functions (e.g., If T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time).
V.3.ATMM Students will represent and model vector quantities and perform operations on vectors
V.3.ATMM.1 Recognize vector quantities as having both magnitude and direction; represent vector quantities by directed line segments and use appropriate symbols for vector and their magnitudes (e.g., v, |v|, ||v||, v)
V.3.ATMM.6 Understand vector subtraction; v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w pointing in the opposite direction; represent vector subtraction graphically by connecting the tips in the appropriate order and perform vector subtraction component-wise.
V.3.ATMM.8 Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v; compute the direction of cv knowing that when the |c|v ≠ 0, the direction cv is either along v (for c > 0) or against v(c < 0).
MO.4.ATMM.4 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
MO.4.ATMM.5 Understand that zero and identity matrices play a role in matrix addition and multiplication similar to 0 and 1 in real numbers; the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
PS.5.ATMM Students will interpret linear models, calculate expected values to solve problems, and use probability to evaluate outcomes of decisions
PS.5.ATMM.1 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
PS.5.ATMM.3 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value (e.g., find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices; find the expected grade under various grading schemes).
PS.5.ATMM.4 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value (e.g., find a current data distribution on the number of TV sets per household in the United States and calculate the expected number of sets per household; how many TV sets would you expect to find in 100 randomly selected households?).
PS.5.ATMM.5 Find the expected payoff for a game of chance (e.g., find the expected winnings from a state lottery or a game at a fast-food restaurant).
PS.5.ATMM.6 Evaluate and compare strategies on the basis of expected values (e.g., compare a high-deductible versus a low-deductible automobile insurance policy using various but reasonable chances of having a minor or major accident).