Engaging Learners through Worthwhile Math Tasks Jenny Novak Secondary Math Resource Teacher

Warm-Up It's a hot summer day, and Eric the Sheep is at the end of a line of sheep waiting to be shorn. There are 50 sheep in front of him. Being an impatient sort of sheep, though, every time the shearer takes a sheep from the front of the line to be shorn, Eric jumps in front of the next two sheep in front of him. If he continues to do this how many sheep will be shorn before Eric? Be prepared to explain how you determined your answer. This task is excerpted from Driscoll, M. (2001). Fostering Algebraic Thinking Toolkit. Portsmouth, NH: Heinemann.

Outcomes By the end of this session participants will: Engage in mathematical tasks and generate multiple strategies for solving a problem Consider how worthwhile mathematical tasks can improve students mathematical practices Examine tools to evaluate mathematical tasks Become familiar with resources for finding math tasks

Standards for Mathematical Practice Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Revisit Eric the sheep problem—what standards are lifted up?

Revisiting the Warm-Up It's a hot summer day, and Eric the Sheep is at the end of a line of sheep waiting to be shorn. There are 50 sheep in front of him. Being an impatient sort of sheep, though, every time the shearer takes a sheep from the front of the line to be shorn, Eric jumps in front of the next two sheep in front of him. If he continues to do this how many sheep will be shorn before Eric? Be prepared to explain how you determined your answer. Share out strategies

Another approach Video screen capture of applet available on learner.org

The Candles Task You will be assigned either #1 or #2. Then complete #3. 3. Megan lights two candles of equal length at the same time. The red candle takes six hours to burn out and the green candle takes nine. How much time will pass until the slower-burning candle is exactly twice as long as the faster-burning one? Explain how you got your answer. This task is excerpted from Driscoll, M. (2001). Fostering Algebraic Thinking Toolkit. Portsmouth, NH: Heinemann.

The Locker Problem There are 20 closed lockers in one hallway of your school. Your class decides to conduct an experiment. The first student is going to run down the row and open each of the locker doors. The second student in line will start with locker #2 and close every second door. The third student will start at locker #3 and change the state of every third locker. The fourth student will start at locker #4 and change the state of every fourth locker, and so on, until 20 students have passed by the lockers. Which locker doors are still open after the twentieth student is finished? Which locker(s) changed the most? Now suppose there are 200 lockers. Which lockers are open after the 200th student is finished? Which locker or lockers changed the most? This task is excerpted from Driscoll, M. (2001). Fostering Algebraic Thinking Toolkit. Portsmouth, NH: Heinemann.

Evaluating a Math Task Select one of the math tasks we have completed today & use the evaluation sheet to rate the task What were the strongest areas represented in this task? How could we improve the task? How could this tool be used in your classroom?

Additional Resources Driscoll, M. (2001). Fostering Algebraic Thinking Toolkit. Portsmouth, NH: Heinemann. National Council of Teachers of Mathematics (2010). Focus in High School Mathematics: Reasoning and Sense Making. Reston, VA: National Council of Teachers of Mathematics, Inc. Small, M. & Lin, A. (2010). More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction. New York: Teachers College, Columbia University.

Web Resources Learner.org: Math tasks and video of lessons http://www.learner.org/index.html Secondary Mathematics Intranet Page-Math Tasks http://login.hcpss.org/Login/__WWW/Portal/Curricular_Programs/Math/MathTask Figure This! NCTM site with activities for families http://www.figurethis.org/index.html

In Closing What is one take-away you have from this session? What is one action step you plan to take?