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Scenarios

This document examines five distinct mathematical problem-solving scenarios to evaluate the various stages of understanding demonstrated by learners. From calculating the number of cars that can be made with wheels to determining how many ripe tomatoes are in a box, these examples highlight how students approach and break down mathematical problems. Each scenario includes student responses and a question about the stage of mathematical understanding they represent. Educators can use this to assess and guide students in their mathematical journey.

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Scenarios

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  1. Scenarios

  2. Scenario 1 • At the car factory they need 4 wheels to make each car. How many cars can they make with 72 wheels? • Stephanie said: • Nine 8’s are 72. • So we double the 9 to get 18. • What stage is Stephanie at?

  3. Scenario 2 • You have 37 lollies and you eat 9 of them. • How many lollies do you have left? • Arita says: • The answer is 28 because four 9’s is 36, and 1 is 37. So the answer is three 9’s and 1, or 28. • What stage is this?

  4. Scenario 3 • There are 6 baskets. There are 24 muffins in each basket. How many muffins are there altogether? • Tim says: • It’s six 25’s and you take away 6. • What stage is this?

  5. Scenario 4 • In a box of 240 tomatoes there are 65% that are ripe. How many tomatoes are ripe? • Tom says: • Well 50% is 120, and 25% is 60, • and 12.5% is 30. • So it must be close to 150. • What stage is this?

  6. Scenario 5 • What is of 28? • Steve says: • I get 21 because half of 28 is 14 and half of 14 is 7. Then 7+7+7 = 21 • What stage is this?

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