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Proportional Reasoning How Do You Know? January 10, 2012

Proportional Reasoning How Do You Know? January 10, 2012. Connie Laughlin Hank Kepner Rosann Hollinger Kevin McLeod Mary Mooney Heath Garland. We are learning to…. deepen our understanding of proportionality and its application. We will know we are successful when.

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Proportional Reasoning How Do You Know? January 10, 2012

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  1. Proportional Reasoning How Do You Know?January 10, 2012 Connie Laughlin Hank Kepner Rosann Hollinger Kevin McLeod Mary Mooney Heath Garland

  2. We are learning to… deepen our understanding of proportionality and its application.

  3. We will know we are successful when • we can explain when two quantities are in or not in a proportional relationship. • we can use proportional relationships to solve multistep ratio and percent problems.

  4. Making Sense • Does the conclusion make sense? Make a convincing argument to your peers about the quantities being in or not in a proportional relationship. • What distinguishes those that make sense from those that don’t make sense?

  5. Essential Understanding Superficial cues present in the context of a problem do not provide sufficient evidence of proportional relationships between quantities.

  6. Standards for Mathematical Practice #1 Make sense of problems and persevere in solving them. #3 Construct viable arguments and critique the reasoning of others. #6 Attend to precision.

  7. Farrah’s Faucet You put a measuring cup under a dripping faucet. The measuring cup had 6 ounces in it to begin with. You come back in 8 minutes and notice that there are now 10 ounces in the measuring cup. How many ounces will be in the measuring cup after 17 minutes? Is there a proportional relationship? If so, identify the two quantities. If not, explain why not.

  8. Paint By Numbers One man can paint a bedroom by himself in 3 hours. How long will it take two men to paint the room if both men paint at the same pace? Is there a proportional relationship? If so, identify the two quantities. If not, explain why not.

  9. CCSSM • Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.RP.2 Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship.

  10. Cognitive Demand “The kind and level of thinking required of students in order to successfully engage with and solve the task.” Stein, Smith, Henningsen, & Silver, (2000)

  11. Student Learning TASKS As they appear in curricular/ instructional materials TASKS As set up by teachers TASKS As implemented by students Mathematical Tasks Framework A representation of how mathematical tasks unfold during classroom instruction. (Stein & Smith, 1998, Mathematics Teaching in the Middle School)

  12. Four Levels of Cognitive Demand in Mathematical Tasks Low Level Cognitive Demands • Memorization Tasks • Procedures Without Connections to understanding, meaning or concepts Tasks High Level Cognitive Demands • Procedures With Connections to understanding, meaning or concepts Tasks • Doing Mathematics Tasks

  13. Making Connections • What have I learned in this session? • What will I share at my schools? With whom/why? How?

  14. Feedback Question Describe one new insight you had as a result of today’s session.

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