Developing and Using Meaningful Math Tasks

1. Developing and Using Meaningful Math Tasks The Key to Math Common Core Take a moment to record on a sticky: What is a meaningful Math Task?

2. Norms Courtesy • Be on time • Cell phones on silent, vibrate, or off • Be mindful of side-bar conversations • Focus on the task at hand • Collaborative • Promote a sense of inquiry • Frame meaningful questions • Pay attention of self and others • Assume positive intentions • Be reflective

3. Today’s Outcomes • Participants will have a better understanding of what they need to expect from their students in math. • Participants will have a better understanding of how to select and set up a challenging math task. • Participants will have a better understanding of facilitate a math task. • Participants will have a better understanding of how to increase the cognitive demands of a math task.

4. What are we asking our students to: • Think about? • Talk about? • Understand? “Never memorize something you can look up” Einstein

5. Let’s Watch • Notice what the teacher does to start the lesson, what skills do students develop through daily mental math? • How is this task differentiated for every child? • What do you gain as a teacher by doing a task like the one in the video?

6. Mathematical Tasks:A Critical Starting Point for Instruction There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics. Lappan & Briars, 1995

7. Animals and Fences at the Zoo • The Problem: A zookeeper was promised that she could have some special animals called mathemals. She has twenty connecting cubes to be used as fencing to build a pen for the mathemals. What type of pen can she make to hold the most mathemals?

8. Materials: • Twenty connecting cubes of one color to use as fencing and a large supply of connecting cubes of another color to use as mathemals when testing various solutions. • Grid paper for recording the results.

9. Rules: • Work in teams to use all twenty connecting cubes to build the pen, with each cube joining another cube, face against face. • The pen must be closed, with no doors or openings, so that the mathemals cannot get out. • Mathemals cannot be allowed to stand on top of one another in the pen. • Each mathemal in the pen uses the space of one cube.

10. What learning took place? • Take a moment at your table to decide which standards this covers at your grade level. • How could this task be adapted to fit every student’s ability? • How could you adapt it to fit better at your grade level?

11. Mathematical Tasks:A Critical Starting Point for Instruction If we want students to develop the capacity to think, reason, and problem solve then we need to start with high-level, cognitively complex tasks. Stein & Lane, 1996

12. Candy Shop • Melissa went to the candy store and grabbed a large bag to fill with candy. There were 5 jars of yummy candy. At the first jar, she put 2 pieces of candy in the bag. At the second jar, she put 4 pieces in the bag and at the third jar, she put 6 pieces in the bag. If this pattern continues, how many pieces of candy will Melissa have after she visits all 5 jars?

13. Candy Shop Part II • Brent went to the new Candy Shop in town. He grabbed a large bag to fill with goodies. There were 4 jars of yummy candy. At the first jar, he put 5 pieces of candy in the bag. At the second jar, he put 10 pieces in the bag and at the third jar he put 15 pieces in the bag. If this pattern continues, how man pieces of candy will Brent have after he visits all 4 jars? • While Brent was leaving the candy store his brother stopped by. Brent walked with his brother to all 4 jars. At each jar, he ate 5 pieces of candy from his bag that he had already collected. How man pieces of candy does he have when he finally leaves the candy store?

14. Your principal would like your class to create greeting cards in honor of Geometry Day. The cards will decorate the halls of your school. The principal has put some requirements for the cover of the cards. • Design Rules: • The design must include 11 polygons and at least 44 sides. • You must include at least one triangle, one quadrilateral, one pentagon, and one hexagon. • Consider using a straight edge to draw your polygons. • Work with your partner to check and make sure you both have followed the rules on your design.

15. Report the information in a chart like this on the inside of your card. Use the back of the card to complete the following sentences: I learned That… Sometimes I need to remember…

16. Where is the balance? • When do you do whole class tasks? • How often? • Where do centers fit into the day? • How do you find the right balance?

17. Things to Think about… • What is the purpose of the task or center? • What are the students going to be learning or practicing? • How are you going to hold them accountable?

18. Selecting a Math Task • What are your goals for this lesson? • What mathematical content and processes do you hope students will learn from their work on this task? • In what ways does this task build on students’ previous knowledge? • What definitions, concepts, or ideas do students need to know in order to begin to work on the task?

19. Setting Up a Math Task • What are all the ways the task can be solved? • How will you ensure that students remain engaged in the task? • What are your expectations for students as they work on and complete this task? • How will you introduce students to the activity so as not to reduce the demands of the task? • What will you hear that lets you know students understand the task?

20. Supporting Students’ Exploration • What questions will you ask to focus their thinking? • What will you see or hear that lets you know how students are thinking about mathematical ideas? • What questions will you ask to assess students’ understanding?

21. Where does Investigations fit in to all of this work? • What makes a number even or odd? • Imagine a group of 12 students. Can they make two equal teams? How do you know? Can they make partners with no one left over? How do you know? What about a group of 13 students? • Let’s think abut what happens when you put two groups together. Think about this problem: In Ms. Ortega’s class, there are 4 students in the blue group and 6 students in the yellow group. If we put the two groups together, could everyone have a partner? How many pairs would there be?

22. Kindergarten

24. First Grade

26. Second Grade

27. Games • How can games be used like tasks to further student understanding of math standards? • Take a moment to turn and talk.

28. Mathematical Tasks:A Critical Starting Point for Instruction Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking. Stein, Smith, Henningsen, & Silver, 2000

29. Mathematical Tasks:A Critical Starting Point for Instruction If we want students to develop the capacity to think, reason, and problem solve then we need to start with high-level, cognitively complex tasks. Stein & Lane, 1996

30. Increase the Cognitive Demand of the Task • Increase complexity • Introduce ambiguity • Synthesize strand of mathematics • Invite conceptual connections • Require explanation and justification • Propose solutions that reveal misconceptions or common errors

31. Invite students to: • Describe their process • Reflect on their decisions • Explain their vigilance • Confirm their thinking • Make connections • Promote discourse

32. Questions or Concerns? Fill out exit slip