Mathematics DOK Level 3 (Strategic Thinking). Requires reasoning, planning, using evidence, and a higher level of thinking than the previous two levels. In most instances, requiring students to explain their thinking is at Level 3. Activities that require students to make conjectures are also at this level. The cognitive demands at Level 3 are complex and abstract. The complexity does not result from the fact that there are multiple answers, a possibility for both Levels 1 and 2, but because the task requires more demanding reasoning. An activity, however, that has more than one possible answer and requires students to justify the response they give would most likely be at Level 3.

Other Level 3 activities include drawing conclusions from observations; citing evidence and developing a logical argument for concepts; explaining phenomena in terms of concepts; and deciding which concepts to apply in order to solve a complex problem.

Subject:
Mathematics

## HSG.MG.B.IA.10

Compare and contrast vertex-edge graph topics and models in terms of:★

• properties
• algorithms
• optimization
• types of problems that can be solved

## HSG.MG.B.IA.9

Model and solve problems using at least two of the following fundamental graph topics and models: Euler paths and circuits, Hamilton paths and circuits, the traveling salesman problem (TSP), minimum spanning trees, critical paths, vertex coloring.★

## HSG.MG.B.IA.8

Understand, analyze, evaluate, and apply vertex-edge graphs to model and solve problems related to paths, circuits, networks, and relationships among a finite number of elements, in real-world and abstract settings.★

## HSN.Q.B.IA.3

Understand, analyze, apply, and evaluate some common voting and analysis methods in addition to majority and plurality, such as runoff, approval, the so-called instant-runoff voting (IRV) method, the Borda method and the Condorcet method.

## 2.MD.D.IA.2

Use interviews, surveys, and observations to collect data that answer questions about students' interests and/or their environment.

## 2.MD.C.IA.1

Describe the relationship among standard units of time: minutes, hours, days, weeks, months and years.

## 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).

## HSS.MD.B.5

(+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

1. Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast–food restaurant.
2. Evaluate and compare strategies on the basis of expected values. For example, compare a high–deductible versus a low–deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.

## HSS.MD.A.4

(+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?

## 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. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple–choice test where each question has four choices, and find the expected grade under various grading schemes.