Search the California Content Standards

Standard:
Evaluate algorithms in terms of their efficiency.

Descriptive Statement:
Algorithms that perform the same task can be implemented in different ways, which take different amounts of time to run on a given input set. Algorithms are commonly evaluated using asymptotic analysis (i.e., “Big O”) which involves exploration of behavior when the input set grows very large. Students classify algorithms by the most common time classes (e.g., log n, linear, n log n, and quadratic or higher). For example, students could read a given algorithm, identify the control constructs, and in conjunction with input size, identify the efficiency class of the algorithm.

Standard:
Compare and contrast fundamental data structures and their uses.

Descriptive Statement:
Data structures are designed to provide different ways of storing and manipulating data sets to optimize various aspects of storage or runtime performance. Choice of data structures is made based on expected data characteristics and expected program functions. Students = compare and contrast how basic functions (e.g.., insertion, deletion, and modification) would differ for common data structures including lists, arrays, stacks, and queues. For example, students could draw a diagram of how different data structures change when items are added, deleted, or modified. They could explain tradeoffs in storage and efficiency issues. Alternatively, when presented with a description of a program and the functions it would be most likely to be running, students could list pros and cons for a specific data structure use in that scenario.

Standard:
Demonstrate the flow of execution of a recursive algorithm.

Descriptive Statement:
Recursion is a powerful problem-solving approach where the problem solution is built on solutions of smaller instances of the same problem. A base case, which returns a result without referencing itself, must be defined, otherwise infinite recursion will occur. Students represent a sequence of calls to a recursive algorithm and show how the process resolves to a solution. For example, students could draw a diagram to illustrate flow of execution by keeping track of parameter and returned values for each recursive call. Alternatively, students could create a video showing the passing of arguments as the recursive algorithm runs.

Standard:
Evaluate the ability of models and simulations to test and support the refinement of hypotheses.

Descriptive Statement:
A model could be implemented as a diagram or a program that represents key properties of a physical or other system. A simulation is based on a model, and enables observation of the system as key properties change. Students explore, explain, and evaluate existing models and simulations, in order to support the refinement of hypotheses about how the systems work. At this level, the ability to accurately and completely model and simulate complex systems is not expected. For example, a computer model of ants following a path created by other ants who found food explains the trail-like travel patterns of the insect. Students could evaluate if the output of the model fits well with their hypothesis that ants navigate the world through the use of pheromones. They could explain how the computer model supports this hypothesis and how it might leave out certain aspects of ant behavior and whether these are important to understanding ant travel behavior. Alternatively, students could hypothesize how different ground characteristics (e.g., soil type, thickness of sediment above bedrock) relate to the severity of shaking at the surface during an earthquake. They could add or modify input about ground characteristics into an earthquake simulator, observe the changed simulation output, and then evaluate their hypotheses.