Explain why this alteration promotes reasoning and problem solving. Cite evidence from one of the module readings or from another source.

Open Up!
Closed mathematical tasks are the types of problems most often seen in mathematics textbooks: short performance task which can be completed quickly with only one correct answer. Open-ended tasks, on the other hand, have a range of appropriate responses and help develop a problem-solving and growth mindset in students.
Small (2009) offers five strategies that mathematics instructors can use to turn closed mathematics tasks into more open tasks to promote reasoning and problem solving: (1) turn around a question, (2) ask for similarities and differences, (3) allow for choice in numbers, (4) construct word problems from a number sentence, and (5) change questions to allow for multiple answers.”
Find an existing problem or performance task from a middle school textbook or online resource involving ratio and/or proportion which could be classified as a “closed mathematics task” (Small, 2009). Then create an alternative task or problem which promotes reasoning and problem solving. In an original response, address these prompts:
State the existing problem and explain what makes it a closed mathematical task. Be sure to cite the source properly.
Rewrite the task using one of Small’s guidelines.
Explain why this alteration promotes reasoning and problem solving. Cite evidence from one of the module readings or from another source.
Small, M. (2009). Good questions: Great ways to differentiate mathematics instruction. National Council of Teachers of Mathematics.

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