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Problem Solving Sequences

Problem solving sequences demonstrate or ask the learner to solve a sequence of related problems that are in increasing order of complexity from an initial problem. Three types problems that can be used in the sequence, in order of complexity, are applications, variations, and extensions.

They are utilized in varied repetition and aggregate varied repetition via sequences where the content is revisited from a different perspective.

Problem solving sequences are a subset of prerequisite sequences.

Application sequence​

Two types of applications are direct applications and inferred applications.

Direct application sequence​

An example that is demonstrated or solved the same way as the initial problem. When referring to an application without the word "direct", a direct application is implied.

Example​

A module on order of operations explains that multiplication and division are evaluated before addition and subtraction. A worked example of 6 + 3 * 2 - 1 is shown. Following that, the learner is asked to solve the problem 8 - 2 + 5 * 3 - 1, which is a direct application of the worked example.

Inferred application sequence​

A problem that is demonstrated or solved based on the initial problem, where the solution can be inferred from what is presented in the initial problem.

Example​

A module on adding numbers using place value (from elementary school arithmetic) shows learners how to add numbers that have multiple digits. The module gives examples of adding 2 numbers together and examples add 3 numbers together. One of the examples is:

  435
  286
  128
+ ===
  849

Using the above examples and other ones (not shown), the learner is expected to answer this question, which is an inferred application:

When adding 3 numbers using place value, what is the maximum carry that would need to be added to the digits in any place (tens place, hundreds place, etc)?

Variation sequence​

A problem that is demonstrated or solved in a similar way to the initial problem, where one or more parts of the prior example are substituted. Optionally, the variation can explicitly state the parts of the prior example that need to be substituted.

Examples​

See these examples:

Extension sequence​

A problem that requires the learner to use ideas, learned in the initial problem, in a new way. As compared to a variation, the solution has more possibilities for the solution because substitutions are not used against the initial problem.

This example contains a variation with an extension.