A. Data Analysis

1. Collect, generate, organize, and display data.
   • Data generated from surveys
2. Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data.
   • Bar graph, line graph, circle graph, table, histogram
   • Range, median, and mean
   • Calculators and computers used to record and process information
3. Respond to questions about data, generate their own questions and hypotheses, and formulate strategies for answering their questions and testing their hypotheses.

B. Probability

1. Determine probabilities of events.
   • Event, complementary event, probability of an event
   • Multiplication rule for probabilities
   • Probability of certain event is 1 and of impossible event is 0
   • Probabilities of event and complementary event add up to 1
2. Determine probability using intuitive, experimental, and theoretical methods (e.g., using model of picking items of different colors from a bag).
   • Given numbers of various types of items in a bag, what is the probability that an item of one type will be picked
   • Given data obtained experimentally, what is the likely distribution of items in the bag
3. Explore compound events.
4. Model situations involving probability using simulations (with spinners, dice) and theoretical models.
5. Recognize and understand the connections among the concepts of independent outcomes, picking at random, and fairness.

C. Discrete Mathematics-Systematic Listing and Counting

1. Solve counting problems and justify that all possibilities have been enumerated without duplication.
   • Organized lists, charts, tree diagrams, tables
   • Venn diagrams
2. Apply the multiplication principle of counting.
   • Simple situations (e.g., you can make 3 x 4 = 12 outfits using 3 shirts and 4 skirts).
   • Number of ways a specified number of items can be arranged in order (concept of permutation)
   • Number of ways of selecting a slate of officers from a class (e.g., if there are 23 students and 3 officers, the number is 23 x 22 x 21)
3. List the possible combinations of two elements chosen from a given set (e.g., forming a committee of two from a group of 12 students, finding how many handshakes there will be among ten people if everyone shakes each other person's hand once).

D. Discrete Mathematics-Vertex-Edge Graphs and Algorithms

1. Devise strategies for winning simple games (e.g., start with two piles of objects, each of two players in turn removes any number of objects from a single pile, and the person to take the last group of objects wins) and express those strategies as sets of directions.
2. Analyze vertex-edge graphs and tree diagrams.
   • Can a picture or a vertex-edge graph be drawn with a single line? (degree of vertex)
   • Can you get from any vertex to any other vertex? (connectedness)
3. Use vertex-edge graphs to find solutions to practical problems.
   • Delivery route that stops at specified sites but involves least travel
   • Shortest route from one site on a map to another