2013 Making Connections Conference MS Gulf Coast Coliseum and Convention Center

1. “What’s In the Box?”(Creative Techniques for Teaching Those Difficult Common Core State Standards) 2013 Making Connections Conference MS Gulf Coast Coliseum and Convention Center Friday, June 7, 2013 Marla Davis, Ph.D., NBCT, Office Director for Mathematics Office of Curriculum and Instruction

2. Goals of this Session Introducing New Vocabulary Unpacking Grade Level Standards Using Appropriate Tools Strategically Preparing for the PARCC Assessment

3. Introducing New Vocabulary Students do not learn how to “speak mathematics” by memorizing the definitions of new words, but they learn by hearing these words frequently and having many opportunities to use them in context.

4. Introducing New Vocabulary

5. Introducing New Vocabulary Directions: Examine the question below and write your response on the lines provided. “What does it mean to KNOW what a fraction is?” ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

6. Introducing New Vocabulary For example, if “fraction” is a vocabulary word that students must learn in Grade 3, does “knowing” it mean they are able to: identify or recognize a fraction? model a fraction? describe a fraction? compare and contrast fractions with unlike numerators? explain where to place a fraction on the number line? determine when two fractions are equivalent?

7. Activity #1 Directions: In your groups, locate the three charts post on the wall closest to you. Review each vocabulary word. As a group, determine what does it mean for a student to know the indicated vocabulary word. (Hint: Ask yourself what should a student be able to do with the indicated word?) Repeat this exercise for the remaining two charts.

8. Activity #1 This slide is left blank intentionally.

9. Without saying a word or looking at another group member, complete the following task: Locate a sheet of scratch paper. Fold the paper in half. Fold the paper in half again. Tear the top right part of the paper off. Hold your sheet of paper up for your entire group to see. What do you notice?

10. Using the five guiding questions below, address this Essential Question: “How is it that everyone read the exact same directions but obtained different results?” What was the first thing you did when you saw the task? Can you demonstrate how you completed this task? At any time, were there any directions that seemed unclear or ambiguous? If so, which ones? Why? Should there be one “correct” solution/outcome? How does this task relate to teaching the CCSSM?

11. Standard #1 (K.NBT.1) K. NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objectsordrawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

12. Unpacking K.NBT.1 This slide is left blank intentionally.

13. Unpacking K.NBT.1 A student should be able to given -or- using a student should be able to Given -or- using

14. Unpacking K.NBT.1 Write three “I Can” statements for the standard K.NBT.1. ______________________________ ______________________________ ______________________________ Write three Essential Questions for the standard K.NBT.1. _______________________________ _______________________________ _______________________________

15. Unpacking K.NBT.1 • This will be the first time that some students will move beyond the number 10 with representations. • Special attention must be given to these numbers because they do not follow a consistent pattern in the verbal counting sequence: • 11 and 12 are special number words. • “Teen” means one “ten” plus ones. • The verbal counting sequence for teen numbers is backwards. • Teaching the teen numbers as one group of ten and extra ones is foundational to understanding both the concept and the symbol that represents each teen number.

16. Activity #2 Think outside the box!! Directions: Locate the small box on your table. Select the grid paper and any other object(s) of your choice that could be used to teach and assess the standard K.NBT.1. Be prepared to share with the entire group.

17. Possible Strategy

18. Assessment Item for K.NBT.1 Write an equation for the number that is modeled by the drawing on the left and justify your response.

19. 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. Place a check mark next to the Mathematical Practice(s) demonstrated in the Assessment Task for K.NBT.1.

20. Standard #2 (7.NS.1) 7.NS.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

21. Unpacking 7.NS.1 This slide is left blank intentionally.

22. Unpacking 7.NS.1 A student should be able to given -or- using a student should be able to Given -or- using

23. Unpacking 7.NS.1 Write three “I Can” statements for the standard 7.NS.1. ______________________________ ______________________________ ______________________________ Write three Essential Questions for the standard 7.NS.1. _______________________________ _______________________________ _______________________________

24. Unpacking 7.NS.1 7.NS.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. What do the circled words indicate? What are the implications for instruction? assessment?

25. Activity #3 Think outside the box!! Directions: Locate the small box on your table. Select the cash register tape and any other object(s) of your choice that could be used to teach and assess the standard 7.NS.1. Be prepared to share with the entire group.

26. Possible Strategy Without using any tools, brainstorm about the following questions: • What point must be clearly indicated first? • Where would 16 be on your number line? • Where would 4 have to be? • Where would you place the number “a”? What about the number “b”? • Does a relationship exist between the numbers “a” and “b”? • How can you plot the numbers “a” and “b” on your number line?

27. Possible Strategy (continued) Directions: Select two separate “tools” (other than a ruler). Let your first “tool” represent the length “a”. Let your second “tool” represent the length “b”.

28. Possible Strategy (continued) Directions: Place the following ten “numbers” on your number line and discuss your work as a team. a b -a -b b – a a – b a + b b + a ½a ¾b

29. Assessment Item for 7.NS.1 Given the number line above, create a list of expressions that would yield a negative value. Provide a complete justification for each of your responses.

30. 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. Place a check mark next to the Mathematical Practice(s) demonstrated in the Assessment Task for 7.NS.1.

31. Directions: On a Post-it note, draw a symbol or small picture that depicts how your feelings have changed about introducing new vocabulary words to your student. (Be creative! ) Place your Post-it note on the back door.

32. Standard #3 (4.MD.5a, 5b) 4.MD.5a, 5b Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

33. Unpacking 4.MD.5a, 5b This slide is left blank intentionally.

34. Unpacking 4.MD.5a, 5b A student should be able to given -or- using a student should be able to Given -or- using

35. Unpacking 4.MD.5a, 5b Write three “I Can” statements for the standard 4.MD.5a and 4.MD.5b. ______________________________ ______________________________ ______________________________ Write three Essential Questions for the standard 4.MD.5a and 4.MD.5b. _______________________________ _______________________________ _______________________________

36. Sample Progression of 4.MD.5a, 5b

37. Activity #4 Think outside the box!! Directions: Locate the small box on your table. Select any object(s) of your choice that could be used to teach and assess the standard 4.MD.5a and 4.MD.5b. Be prepared to share with the entire group.

38. Assessment Item for 4.MD.5a,5b Create two separate assessment items for the diagram (angles 1-4) above. Use the space below to record your response.

39. 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. Place a check mark next to the Mathematical Practice(s) demonstrated in the Assessment Task for 4.MD.5a,5b.

40. Key Note about 4.MD.5a,5b The diagram below will help students understand that an angle measurement is not related to an area since the area between the 2 rays is different for both circles yet the angle measure is the same.

41. Reflections Planning Instruction Assessment Directions: Take a few minutes to reflect on today’s presentation. In the space provided, identify how this session has impacted your perception in the following areas.

42. CCSSM Exemplar Assessment Prototypes PARCC http://www.parcconline.org/samples/item-task-prototypes Smarter Balanced (SBAC) http://www.ode.state.org.us/serach/page/?id=3747 Illustrative Mathematics (IM) www.illustrativemathematics.org Mathematics Assessment Resources Service (MARS) http://map.mathshell.org/materials/lessons.php New York City Dept of Education (NYC) http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsStudentWork/default.htm

43. CCSSM Resources Common Core Website www.corestandards.org PARCC Assessment Administration Guidance http://www.parcconline.org/assessment-administration-guidance PARCC Grade Level Assessment Blueprints and Test Specifications http://www.parcconline.org/assessment-blueprints-test-specs Progression Documents for CCSSM http://math.arizona.edu/~ime/progressions/ PARCC Model Content Frameworks for Mathematics http://www.parcconline.org/parcc-model-content-frameworks SEDL CCSSM Support Videos http://secc.sedl.org/common_core_videos/

44. MDE Resources Office of Curriculum and Instruction www.mde.k12.ms.us/ci MDE iTunes U (archived webinars) www.mde.k12.ms.us/itunes MDE Common Core Website www.mde.k12.ms.us/ccss CCSS and PARCC training materials https://districtaccess.mde.k12.ms.us/commoncore/ Curriculum and Instruction Listserv http://fyt.mde.k12.ms.us/subscribe/subscribe_curriculum.html

45. MDE Contact Information Office of Curriculum and Instruction 601.359.2586 Nathan Oakley – Director of Curriculum and Instruction noakley@mde.k12.ms.us Dr. Marla Davis – Office Director for Mathematics mdavis@mde.k12.ms.us