1. SHIFTING FROM MATHEMATICAL WORKSHEETS TO MEANINGFUL TASKS FACILITATED BY: CYNTHIA BELL NUMERACY SPECIALIST LITERACY ASSISTANCE CENTER

2. OBJECTIVES  Build understanding of the effects of meaningful tasks  Understand the levels of cognitive demand as they relate to depth of knowledge and be able to identify the levels in a task  Discuss how the 8 Standard Mathematical Practices can be the focus when developing tasks

3. WHAT IS A MEANINGFUL TASK?  A mathematical task is a problem or set of problems that focuses students’ attention on a particular mathematical idea and/or provides an opportunity to develop or use a particular mathematical habit of mind  Is engaging, relatable, and can maintain student interest

4. WHY ARE TASKS/ACTIVITIES IMPORTANT?  Tasks and activities lead to prolonged retention  Tasks help educators shift their instruction from how to get the answer to understanding mathematics

5. IMPLEMENT TASKS THAT PROMOTE REASONING AND PROBLEM SOLVING  “Student learning is greatest in classrooms where the tasks consistently encourage high-level thinking and reasoning and least in classrooms where the tasks are routinely procedural in nature” (Boaler and Staples 2008; Hibert and Wearne 1993; stein and Lane 1996)  Tasks need to have a range of cognitive demand both low and high. They should range from complex challenges to a routine exercise

6. ADDRESSING COGNITIVE COMPLEXITY

8. COMPARE THE TWO TASKS Task # 1Task # 2 You are trying to decide which of two smartphone plans would be better. Plan A charges a basic fee of $30 per month and 10 cents per text message. Plan B charges a basic fee of $50 per month and 5 cents per text message. How many text messages would you need to send per month for plan B to be the better option? Explain your decision. Solve each of the following systems. 4x + y =2 x – y = 3 x + 7y = 0 2x – 8y = 22 -6x + 5y = 1 6x + 4y = -10 Adapted from Illustrative Mathematics Illustrations & Kutasoftware.com

9. WORKSHEET FOR TASK #2

10. LET’S TRY IT!

11. (6x 2 + 3x) - (2x 2 + 8x) This problem was simplified to 4x 2 + 11x which is incorrect. Explain why this is incorrect by citing any mathematical property or connecting the concept to another mathematical skill.

12. CONNECTING THE PRACTICES Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problems solving and allow multiple entry points and varied solution strategies. Source: Principles to Actions – Ensuring mathematical success for all by the NCTM 2014

14. EXPERIENCES OF THE PRACTICES Habits of MindReasoning & ExplainingModeling & Using ToolsSeeing Structure & Generalizing

15. EXAMPLE WORKSHEET

16. EXAMPLE TASK SMP #3 Is the statement p – 1 = 5p + 3p – 8 Always, Sometimes or Never True

17. LET’S REVIEW To build a meaningful task you should consider these two things: Meaningful Task Standard Mathematical Practices Cognitive Complexity

18. THINGS YOU COULD TRY!  Class discussion  Game  Group task  Individual task  Rotating partners  Create your own problems  Fix someone’s homework  Tutor another  Peer to peer tutoring  Puzzle

19. Cynthia Bell Numeracy Specialist Literacy Assistance Center Phone: 212-803-3306 Email: cynthiab@lacnyc.org CONTACT INFORMATION