220.127.116.11 E.2 Recognize that the volume of a pyramid or cone is one-third of the volume of the prism or cylinder with the same base and height (e.g., use rice to compare volumes of figures with same base and height).
8.4.4 All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.
18.104.22.168 A Data Analysis
22.214.171.124 A.1 Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode).
126.96.36.199 A.1.a Type of display most appropriate for given data
188.8.131.52 B.3 Explore the probabilities of conditional events (e.g., if there are seven marbles in a bag, three red and four green, what is the probability that two marbles picked from the bag, without replacement, are both red).
184.108.40.206 B.6 Play and analyze probability-based games, and discuss the concepts of fairness and expected value.
220.127.116.11 C Discrete Mathematics-Systematic Listing and Counting
18.104.22.168 C.1 Apply the multiplication principle of counting.
22.214.171.124 C.1.a Permutations: ordered situations with replacement (e.g., number of possible license plates) vs. ordered situations without replacement (e.g., number of possible slates of 3 class officers from a 23 student class)
126.96.36.199 C.2 Explore counting problems involving Venn diagrams with three attributes (e.g., there are 15, 20, and 25 students respectively in the chess club, the debating team, and the engineering society; how many different students belong to the three clubs if there are 6 students in chess and debating, 7 students in chess and engineering, 8 students in debating and engineering, and 2 students in all three?).
188.8.131.52 D.1.d Finding the shortest circuit on a map that makes a tour of specified sites
184.108.40.206 D.1.e Limitations of computers (e.g., the number of routes for a delivery truck visiting n sites is n!, so finding the shortest circuit by examining all circuits would overwhelm the capacity of any computer, now or in the future, even if n is less than 100)
8.4.5 All students will use mathematical processes of problem solving, communication, connections, reasoning, representations, and technology to solve problems and communicate mathematical ideas.
8.4.5 A Problem Solving
8.4.5 A.1 Learn mathematics through problem solving, inquiry, and discovery.
8.4.5 A.2 Solve problems that arise in mathematics and in other contexts.
8.4.5 A.2.a Open-ended problems
8.4.5 A.2.b Non-routine problems
8.4.5 A.2.c Problems with multiple solutions
8.4.5 A.2.d Problems that can be solved in several ways