OhioDiscrete Mathematics/Computer Science
Ohio Discrete Mathematics/Computer Science Curriculum
Video lessons and practice for every Discrete Mathematics and Computer Science topic. Aligned to Ohio's Learning Standards for high school math.
Ohio Discrete Mathematics/Computer Science | StudyPugHelp
​
ID | Standard | StudyPug Topic |
|---|---|---|
CC.HSS.CP.B.9 | Use permutations and combinations to compute probabilities of compound events and solve problems. |
CC.HSS.CP.A.1 | Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not"). |
CC.HSS.CP.A.2 | Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. |
CC.HSS.CP.A.3 | Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. |
CC.HSS.CP.A.5 | Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. |
CC.HSS.MD.A.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. |
CC.HSS.MD.A.2 | Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. |
CC.HSS.MD.A.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. |
CC.HSS.MD.B.7 | Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). |
CC.HSF.IF.A.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). |
CC.HSF.IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. |
CC.HSF.IF.A.3 | Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. |
CC.HSF.IF.B.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. |
CC.HSF.BF.A.2 | Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. |
CC.HSF.BF.B.4 | Find inverse functions. |
CC.HSF.LE.A.2 | 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). |
CC.HSA.SSE.B.4 | Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. |
CC.HSN.VM.C.6 | Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. |
CC.HSN.VM.C.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. |
CC.HSN.VM.C.10 | Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. |
CC.HSN.VM.C.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. |
CC.HSA.REI.C.8 | Represent a system of linear equations as a single matrix equation in a vector variable. |
CC.HSA.REI.C.9 | Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). |
CC.HSS.ID.A.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. |
CC.HSS.ID.A.3 | Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). |
CC.HSS.IC.A.1 | Understand statistics as a process for making inferences about population parameters based on a random sample from that population. |
CC.HSS.IC.B.3 | Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. |
CC.HSS.IC.B.4 | Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. |
CC.HSN.VM.A.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. |
CC.HSN.VM.A.2 | Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. |
CC.HSN.VM.B.4 | Add and subtract vectors. |
CC.HSN.VM.B.5 | Multiply a vector by a scalar. |
Ohio Discrete Mathematics and Computer Science Curriculum
Ohio high school students taking Discrete Mathematics and Computer Science cover a wide range of topics that connect mathematical reasoning to real-world problem solving. This course is aligned to Ohio's Learning Standards for Math and prepares students for college-level mathematics and computer science programs.
Probability and Statistics
A major portion of this course focuses on probability. Students learn to use permutations and combinations to compute probabilities of compound events. They explore sample spaces, independent events, and conditional probability using the formula P(A|B) = P(A and B)/P(B). Two-way frequency tables help students determine whether events are independent and approximate conditional probabilities from real data.
- Permutations and combinations for compound events
- Independent events and the multiplication rule
- Conditional probability and two-way frequency tables
- Random variables, probability distributions, and expected value
- Applying probability to analyze decisions and strategies
Functions and Sequences
Students develop a solid understanding of functions, including function notation, domain and range, and inverse functions. Arithmetic and geometric sequences are studied both recursively and explicitly, and students derive the formula for the sum of a finite geometric series.
- Function notation and domain/range relationships
- Arithmetic and geometric sequences — recursive and explicit forms
- Inverse functions
- Linear and exponential function construction from graphs and tables
- Sum of a finite geometric series
Matrices and Linear Systems
This course introduces matrices as tools for representing and manipulating data. Students learn matrix addition, multiplication, and the role of identity and zero matrices. They work with matrix inverses to solve systems of linear equations and apply matrix transformations to vectors.
- Matrix addition and multiplication
- Determinants and multiplicative inverses
- Matrix representation of linear systems
- Vector transformations using matrices
- Solving 3×3 systems using technology
Data Analysis and Vectors
Students compare data sets using measures of center and spread, interpret correlation coefficients, and distinguish between correlation and causation. The course also introduces vectors — representing vector quantities with directed line segments, finding components, and performing vector operations.
- Center and spread: mean, median, IQR, standard deviation
- Correlation and causation
- Sample surveys, experiments, and observational studies
- Margin of error through simulation
- Vector addition, subtraction, and scalar multiplication