Virginia

Virginia flag
Skills available for Virginia high school math standards

Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.

Show alignments for:

Actions

Graphs

  • DM.1 The student will model problems, using vertex-edge graphs. The concepts of valence, connectedness, paths, planarity, and directed graphs will be investigated.

    • DM.1.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

      • DM.1.a.1 Determine the valence of each vertex in a graph.

      • DM.1.a.2 Use graphs to model situations in which the vertices represent objects, and edges (drawn between vertices) represent a particular relationship between objects.

      • DM.1.a.3 Represent the vertices and edges of a graph as an adjacency matrix, and use the matrix to solve problems.

      • DM.1.a.4 Investigate and describe valence and connectedness.

      • DM.1.a.5 Determine whether a graph is planar or nonplanar.

      • DM.1.a.6 Use directed graphs (digraphs) to represent situations with restrictions in traversal possibilities.

  • DM.2 The student will solve problems through investigation and application of circuits, cycles, Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits. Optimal solutions will be sought using existing algorithms and student-created algorithms.

    • DM.2.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

      • DM.2.a.1 Determine whether a graph has an Euler circuit or path, and determine it, if it exists.

      • DM.2.a.2 Determine whether a graph has a Hamilton circuit or path, and determine it, if it exists.

      • DM.2.a.3 Count the number of Hamilton circuits for a complete graph with n vertices.

      • DM.2.a.4 Use an Euler circuit algorithm to solve optimization problems.

  • DM.3 The student will apply graphs to conflict-resolution problems, such as map coloring, scheduling, matching, and optimization.

    • DM.3.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

      • DM.3.a.1 Model projects consisting of several subtasks, using a graph.

      • DM.3.a.2 Use graphs to resolve conflicts that arise in scheduling.

      • DM.3.a.3 Determine the chromatic number of a graph.

  • DM.4 The student will apply algorithms relating to trees, networks, and paths. Appropriate technology will be used to determine the number of possible solutions and generate solutions when a feasible number exists.

    • DM.4.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

      • DM.4.a.1 Use Kruskal's algorithm to determine the shortest spanning tree of a connected graph.

      • DM.4.a.2 Use Prim's algorithm to determine the shortest spanning tree of a connected graph.

      • DM.4.a.3 Use Dijkstra's algorithm to determine the shortest spanning tree of a connected graph.

Election Theory and Fair Division

  • DM.5 The student will analyze and describe the issue of fair division in discrete and continuous cases.

    • DM.5.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

      • DM.5.a.1 Investigate and describe situations involving discrete division (e.g., estate division).

      • DM.5.a.2 Use an algorithm for fair division for a group of indivisible objects.

      • DM.5.a.3 Investigate and describe situations involving continuous division of an infinitely divisible set (e.g., cake cutting).

      • DM.5.a.4 Use an algorithm for fair division of an infinitely divisible set.

  • DM.6 The student will investigate and describe weighted voting and the results of various election methods. These may include approval and preference voting as well as plurality, majority, runoff, sequential runoff, Borda count, and Condorcet winners.

    • DM.6.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

      • DM.6.a.1 Determine in how many different ways a voter can rank choices.

      • DM.6.a.2 Investigate and describe the following voting procedures:

        • DM.6.a.2.1 weighted voting;

        • DM.6.a.2.2 plurality;

        • DM.6.a.2.3 majority;

        • DM.6.a.2.4 sequential (winners runoff);

        • DM.6.a.2.5 sequential (losers are eliminated);

        • DM.6.a.2.6 Borda count; and

        • DM.6.a.2.7 Condorcet winner.

      • DM.6.a.3 Compare and contrast different voting procedures.

      • DM.6.a.4 Describe the possible effects of approval voting, insincere and sincere voting, a preference schedule, and strategic voting on the election outcome.

  • DM.7 The student will identify apportionment inconsistencies that apply to issues such as salary caps in sports and allocation of representatives to Congress. Historical and current methods will be compared.

    • DM.7.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

      • DM.7.a.1 Compare and contrast the Hamilton and Jefferson methods of political apportionment with the Hill-Huntington method (currently in use in the U.S. House of Representatives) and the Webster-Willcox method.

      • DM.7.a.2 Solve allocation problems, using apportionment methods.

      • DM.7.a.3 Investigate and describe how salary caps affect apportionment.

Computer Mathematics

  • DM.8 The student will describe and apply sorting algorithms and coding algorithms used in sorting, processing, and communicating information.

    • DM.8.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

      • DM.8.a.1 Select and apply a sorting algorithm, such as a

        • DM.8.a.1.1 bubble sort;

        • DM.8.a.1.2 merge sort; and

        • DM.8.a.1.3 network sort.

      • DM.8.a.2 Describe and apply a coding algorithm, such as

        • DM.8.a.2.1 ISBN numbers;

        • DM.8.a.2.2 UPC codes;

        • DM.8.a.2.3 Zip codes; and

        • DM.8.a.2.4 banking codes.

  • DM.9 The student will select, justify, and apply an appropriate technique to solve a logic problem.

    • DM.9.a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

      • DM.9.a.1 Generate truth tables that encode the truth and falsity of two or more statements.

      • DM.9.a.2 Use Venn diagrams to represent set relationships, such as intersection and union.

      • DM.9.a.3 Interpret Venn diagrams.

      • DM.9.a.4 Use Venn diagrams to codify and solve logic problems.

      • DM.9.a.5 Use matrices as arrays of data to solve logic problems.

Recursion and Optimization