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Inquiry Learning: Exploring Quality Tasks and Creating Quality Tasks

Inquiry Learning: Exploring Quality Tasks and Creating Quality Tasks. Diane Leighty November 5, 2013 Colonial Heights, VA. Email: mthmtcs@verizon.net Website: http://mthmtcs.net. Case Study on Teaching a Math Class.

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Inquiry Learning: Exploring Quality Tasks and Creating Quality Tasks

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  1. Inquiry Learning: Exploring Quality Tasks and Creating Quality Tasks Diane Leighty November 5, 2013 Colonial Heights, VA Email: mthmtcs@verizon.net Website: http://mthmtcs.net

  2. Case Study on Teaching a Math Class • 30 minutes to explore 3 problems Jerome Robinson uses in his classroom. Discussion of the problems • 20 minutes - Read the Case Study – Jerome Robinson • 10 minutes – Discussion of the Case Study

  3. Three squares are placed next to each other as shown. The vertices A, B, and C are collinear. Find the dimension n. • Replace the lengths 4 and 7 by m and k, respectively. Express k in terms of m and n. C B A 4 7 n

  4. 3 Squares Problem • What is the mathematics? • Where could you use the problem? • What standards are incorporated? Or can be incorporated?

  5. Exploring Paired Data West Nile Virus Data

  6. Graph

  7. Reported Cases vs. Deaths

  8. Explore Ratio

  9. Statistics Used to Explore Singular Data • Measures of Central Tendency • Box-and-Whiskers Plot • Normal Distribution • Histogram (if there is enough data) • Regression Analysis (including Piece-wise)

  10. Suggested Problems: • Flight Data • Algebra 1 and/or Algebra 2 • FlightAware website to gather data • http://flightaware.com/live/findflight/KRIC/KATL/ • Braking Distances • Algebra 1 and/or Algebra 2 • http://forensicdynamics.com/stopping-distance-calculator • http://www.stoppingdistances.org.uk/

  11. Midge Problem • Perfect for Algebra 2 or Pre-Calculus • Sidewalk Stones • Ice-Cream Cones

  12. Creating Open-Ended Problems • Take textbook problems and eliminate or change some of the information to open the problem up to • discussion, • thinking, • problem-solving, • multiple solutions.

  13. Original Textbook Problem • A carpenter is building a handicapramp to a platform that is nine feet off the ground. The ground is perfectly level, and he begins 16 feet away from the structure. How long will the face of the ramp be?

  14. Revised Textbook Problem • A carpenter is building a handicap ramp to a platform that is nine feet off the ground. The ground is perfectly level, and he begins 16 feet away from the structure. How long will the face of the ramp be?

  15. Original Textbook Problem Tickets to a concert cost $2.50 for students and $3.75 for adults. Suppose x represents the number of student tickets sold and y represents the number of adult tickets sold. Write an inequality that describes the condition that total receipts must exceed $1500.

  16. REVISED….. Tickets to a concert cost $2.50 for students and $3.75 for adults. If the total receipts must exceed $1500 in order to make a profit, and there are only 480 seats in the auditorium, how many of each kind of ticket need to be sold? Try to find several combinations that will work. Can you generalize your solution?

  17. Mailing Costs - Original Recently the cost c, in dollars of shipping a FedEx Priority Overnight package weighing 1 lb. or more a distance of 1001 to 1400 miles was given by c = 3.1w + 29.07, where w is the package’s weight, in pounds. Graph the equation and use the graph to estimate the cost of shipping a 6 ½ lb package.

  18. Mailing Costs - Rewrite Recently the cost of shipping a FedEx Priority Overnight package weighing 1 lb. to Chicago was $32.17 while a package weighing 2 lbs. shipped to Chicago cost $35.27, and a package weighing 5 lbs. to Chicago cost $44.57. How much will it cost to ship a 6 ½ lb. package to Chicago?

  19. Plant Stand You buy a tall, three-legged plant stand. When you place a plant on the stand, it appears to be unstable under the weight of the plant. The diagram at right shows a coordinate plane superimposed on one pair of the plant stand’s legs. The legs are extended to form  OBC. Is  OBC an isosceles triangle? Explain why the plant stand may be unstable.

  20. “Rich” Tasks ….. • Are accessible and extendable. • Allow individuals to make decisions. • Involve learners in testing, proving, explaining, reflecting and interpreting. • Promote discussion and communication. • Encourage originality and invention. • Encourage “what if?” and “what if not?” questions. • Are engaging and contain opportunity to surprise.

  21. http://www.theproblemsite.com/problems/mathhs/2009/default.asphttp://www.theproblemsite.com/problems/mathhs/2009/default.asp Flowers! Flowers! • There are 3 rivers and after each river lies a grave. So there are 3 rivers and 3 graves. A man wants to leave the SAME amount of flowers at each grave, and be left with none at the end. What happens though is that each time he passes through one of the rivers the number of flowers he has doubles. So he has to start off with what number of flowers, taking into consideration that they double, so that he is left with no flowers whatsoever at the end?

  22. For additional resources…. • Capstone Website: • https://sites.google.com/site/mathematicscapstonecourseunits/ • Dan Meyer’s Blog: • http://blog.mrmeyer.com/ • Mathematics Assessment Project: • http://map.mathshell.org/materials/tasks.php • The Problem Site • http://www.theproblemsite.com/problems/mathhs/

  23. Exeter Mathematics • Math 1 – Mostly Algebra 1 • Math 2 – Mostly Geometry (incl. Algebra) • Math 3 – Mostly Algebra 2/Trig • Math 4 – Advanced Mathematics/Calculus • http://www.exeter.edu/academics/72_6539.aspx

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