A. Data Analysis

1. Collect, generate, record, and organize data in response to questions, claims, or curiosity.
   • Data collected from students' everyday experiences
   • Data generated from chance devices, such as spinners and dice
2. Read, interpret, construct, and analyze displays of data.
3. Pictures, tally chart, pictograph, bar graph, Venn diagram
4. Smallest to largest, most frequent (mode)

B. Probability

1. Use chance devices like spinners and dice to explore concepts of probability.
   • Certain, impossible
   • More likely, less likely, equally likely
2. Provide probability of specific outcomes.
   • Probability of getting specific outcome when coin is tossed, when die is rolled, when spinner is spun (e.g., if spinner has five equal sectors, then probability of getting a particular sector is one out of five)
   • When picking a marble from a bag with three red marbles and four blue marbles, the probability of getting a red marble is three out of seven

C. Discrete Mathematics—Systematic Listing and Counting

1. Sort and classify objects according to attributes.
   • Venn diagrams
2. Generate all possibilities in simple counting situations (e.g., all outfits involving two shirts and three pants).

D. Discrete Mathematics—Vertex-Edge Graphs and Algorithms

1. Follow simple sets of directions (e.g., from one location to another, or from a recipe).
2. Color simple maps with a small number of colors.
3. Play simple two-person games (e.g., tic-tac-toe) and informally explore the idea of what the outcome should be.
4. Explore concrete models of vertex-edge graphs (e.g. vertices as "islands" and edges as "bridges").
   • Paths from one vertex to another