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Same question, different representations

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Algebra discs

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Algebra tiles and partitioning

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Multiple methods

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Multiple representations

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One step equations

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Change one thing

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Developing Number Fluency - What, Why and How

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Developing Number Fluency - What, Why and How

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Efficiency - this implies that children do not get bogged down in too many steps or lose track of the logic of the strategy. An efficient strategy is one that the student can carry out easily, keeping track of sub-problems and making use of intermediate results to solve the problem.

Accuracy depends on several aspects of the problem-solving process, among them careful recording, knowledge of number facts and other important number relationships, and double-checking results.

Flexibility requires the knowledge of more than one approach to solving a particular kind of problem, such as two-digit multiplication. Students need to be flexible in order to choose an appropriate strategy for the numbers involved, and also be able to use one method to solve a problem and another method to check the results.

So fluency demands more of students than memorising a single procedure – they need to understand why they are doing what they are doing and know when it is appropriate to use different methods.

https://nrich.maths.org/10624

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Challenge quickly and often.