1. CCGPS Mathematics Unit-by-Unit Grade Level Webinar Second Grade Unit 3: Understanding Measurement, Length, and Time September 6, 2012 Session will be begin at 3:15 pm While you are waiting, please do the following: Configure your microphone and speakers by going to: Tools – Audio – Audio setup wizard Document downloads: When you are prompted to download a document, please choose or create the folder to which the document should be saved, so that you may retrieve it later.

2. CCGPS Mathematics Unit-by-Unit Grade Level Webinar Grade Two Unit 3: Understanding Measurement, Length, and Time September 6, 2012 Turtle Toms– tgunn@doe.k12.ga.ustgunn@doe.k12.ga.us Elementary Mathematics Specialist These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

3. Expectations and clearing up confusion The intent of this webinar is to bring awareness to:  the types of tasks contained in the unit.  your conceptual understanding of the mathematics in this unit.  approaches to tasks which provide deeper learning situations for your students. We will not be working through each task during this webinar.

4. Welcome! Thank you for taking the time to join us in this discussion of Unit 3. At the end of today’s session you should have at least 3 takeaways:  The big ideas of Unit 3  Something to think about… food for thought  How can I support student understanding?  What is my conceptual understanding of the material in this unit?  a list of resources and support available for CCGPS mathematics

5. Please provide feedback at the end of today’s session.  Feedback helps us all to become better teachers and learners.  Feedback helps as we develop the remaining unit-by-unit webinars.  Please visit http://ccgpsmathematicsK-5.wikispaces.com/ to share your feedback.http://ccgpsmathematicsK-5.wikispaces.com/ After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars. Turtle Gunn Toms– tgunn@doe.k12.ga.ustgunn@doe.k12.ga.us Elementary Mathematics Specialist

8. Activate your Brain A snail and a turtle both started out on Monday toward a pond 32 inches away. An owl was watching them and told them how far they were at the beginning of each day of the race. By Tuesday both the snail and the turtle had gone 1 inch. By Wednesday the snail had traveled 2 inches, and the turtle had crawled 7 inches. By Thursday the snail was 4 inches from the start, and the turtle was 13 inches from it. By Friday the snail was 8 inches from the start, and the turtle was 19 inches from it. If the snail and the turtle kept moving in the same ways, on what day will each animal reach the pond? Write to help explain your best thinking using words, numbers, or pictures. Bonus for the curious : http://www.parentingscience.com/critical-thinking-in-children.html

9. Why do learners make mistakes? Lapses in concentration. Hasty reasoning. Memory overload. Not noticing important features of a problem. or…through misconceptions based on: alternative ways of reasoning; local generalisations from early experience.

10. A pupil does not passively receive knowledge from the environment - it is not possible for knowledge to be transferred holistically and faithfully from one person to another. A pupil is an active participant in the construction of his/her own mathematical knowledge. The construction activity involves the reception of new ideas and the interaction of these with the pupils existing ideas.

11. New Concept: Measure of length is a count of how many units are needed to match the length of the object being measured. Existing idea: When I use a number line, I count the numbers on the number line. Accommodation Misconception: The numbers are the important part of the ruler.

12. Misconception: The numbers are what I use on a ruler. Cognitive conflict: Measurements don’t fit understandings of benchmark sizes.

13. What do we do with mistakes and misconceptions? Avoid them whenever possible? "If I warn learners about the misconceptions as I teach, they are less likely to happen. Prevention is better than cure.” Use them as learning opportunities? "I actively encourage learners to make mistakes and to learn from them.”

14. Diagnostic teaching. Source: Swann, M : Gaining diagnostic teaching skills: helping students learn from mistakes and misconceptions, Shell Centre publications “ Traditionally, the teacher with the textbook explains and demonstrates, while the students imitate; if the student makes mistakes the teacher explains again. This procedure is not effective in preventing... misconceptions or in removing [them]. Diagnostic teaching..... depends on the student taking much more responsibility for their own understanding, being willing and able to articulate their own lines of thought and to discuss them in the classroom”.

15. Diagnosis of misconceptions. Misconception: To measure, I use the numbers on the ruler. Challenge: Measure a post-it using a broken ruler.

16. Example 1 of dealing with a misconception. One way to contrast or challenge this misconception might be to get agreement among students via discussion of the various measures of the post-it note.

17. Example 2 of dealing with a misconception. After discussion with a pupil holding a measuring misconception have students use an intact ruler to find objects that measure the same as the post-it, then compare the objects and the measure and discuss the differences.

18. Two ways to teach... M. Swann, Improving Learning in Mathematics, DFES

19. Importance of dealing with misconceptions 1) Teaching is more effective when misconceptions are identified, challenged, and ameliorated. 2) Pupils face internal cognitive distress when some external idea, process, or rule conflicts with their existing mental schema. 3) Research evidence suggests that the resolutions of these cognitive conflicts through discussion leads to effective learning.

20. Measurement Language- new vocabulary Confusion with units Measuring tools – ruler as number line Misconceptions

21. Time Students confuse the minute and hour hands. They have difficulty in estimating the duration of a given length of time. Digital clock and timers have a number scale based on 60 not 100. Misconceptions

22. Tools Students misread or misunderstand measuring tools. Students often misuse rulers by not beginning to measure a length from the zero mark. – They use the edge of the ruler or start at 1. – When measuring lengths longer than the ruler, some students flip the ruler over and over. Misconceptions

23. Some principles to consider Encourage learners to explore misconceptions through discussion. Focus discussion on known difficulties and challenging questions. Encourage a variety of viewpoints and interpretations to emerge. Ask questions that create a tension or ‘cognitive conflict' that needs to be resolved. Provide meaningful feedback. Provide opportunities for developing new ideas and concepts, and for consolidation.

24. Look at a task from the unit What major mathematical concepts are involved in the task? What common mistakes and misconceptions will be revealed by the task? How does the task: – encourage a variety of viewpoints and interpretations to emerge? – create tensions or 'conflicts' that need to be resolved? – provide meaningful feedback? – provide opportunities for developing new ideas?

25. Misconceptions It is important to realize that inevitably students will develop misconceptions… Askew and Wiliam 1995; Leinwand, 2010; NCTM, 1995; Shulman, 1996

26. Misconceptions Therefore it is important to have strategies for identifying, remedying, as well as for avoiding misconceptions. Leinwand, 2010; Swan 2001; NBPTS, 1998; NCTM, 1995; Shulman, 1986;

27. Activate your Brain A snail and a turtle both started out on Monday toward a pond 32 inches away. An owl was watching them and told them how far they were at the beginning of each day of the race. By Tuesday both the snail and the turtle had gone 1 inch. By Wednesday the snail had traveled 2 inches, and the turtle had crawled 7 inches. By Thursday the snail was 4 inches from the start, and the turtle was 13 inches from it. By Friday the snail was 8 inches from the start, and the turtle was 19 inches from it. If the snail and the turtle kept moving in the same ways, on what day will each animal reach the pond? Write to help explain your best thinking using words, numbers, or pictures. Bonus for the curious : http://www.parentingscience.com/critical-thinking-in-children.html

28. What’s the big idea? Time and distance can be measured. Measurement can be done using standard and non-standard units. Units can be compared, and different units are useful in different situations. Line plots show “how many” on a numeric scale.

29. What’s the other big idea? Standards for Mathematical Practice What might this look like in the classroom? Wiki- http://ccgpsmathematicsk-5.wikispaces.com/1st+Grade/ http://ccgpsmathematicsk-5.wikispaces.com/1st+Grade/ Inside math- http://bit.ly/RgKGrzhttp://bit.ly/RgKGrz Illustrative Mathematics- http://illustrativemathematics.org/standards/k8 http://illustrativemathematics.org/standards/k8 Edutopia- http://bit.ly/o1qaKfhttp://bit.ly/o1qaKf Teaching channel- http://bit.ly/LZ5DJRhttp://bit.ly/LZ5DJR Math Solutions- http://bit.ly/MqPf6whttp://bit.ly/MqPf6w

31. Activate your Brain A snail and a turtle both started out on Monday toward a pond 32 inches away. An owl was watching them and told them how far they were at the beginning of each day of the race. By Tuesday both the snail and the turtle had gone 1 inch. By Wednesday the snail had traveled 2 inches, and the turtle had crawled 7 inches. By Thursday the snail was 4 inches from the start, and the turtle was 13 inches from it. By Friday the snail was 8 inches from the start, and the turtle was 19 inches from it. If the snail and the turtle kept moving in the same ways, on what day will each animal reach the pond? Write to help explain your best thinking using words, numbers, or pictures. Bonus for the curious : http://www.parentingscience.com/critical-thinking-in-children.html

33. What’s the big idea? Enduring Understandings Essential Questions Common Misconceptions Strategies for Teaching and Learning Overview Standards

34. Coherence and Focus – Unit 3 What are students coming with from Unit 2? A developing understanding of number and quantity, and some ideas about addition and subtraction. They will also have measured and compared measurements with non-standard units in First Grade.

35. Coherence and Focus- Unit 3 Where does this understanding lead students? Look in your unit and find the Enduring Understandings.

36. Coherence and Focus – Unit 3 View across grade bands K-6 th  Understanding the fundamental properties of measurement of time, length, mass  Geometric measurement- Understanding angles and angle measure  Geometric measurement- area, perimeter, volume  Fraction understanding, operations with fractions. 8 th -12 th  Everything!

37. Navigating Unit Three The only way to gain deep understanding is to work through each task. No one else can understand for you. Make note of where, when, and what the big ideas are. Make note of where, when, and what the pitfalls might be. Look for additional tools/ideas you want to use Determine any changes which might need to be made to make this work for your students. Share, ask, and collaborate on the wiki. http://ccgpsmathematicsk-5.wikispaces.com/Home

38. Revision-ish Unit 3 Page 57- clocks, not clacks Page 61- the arrows are slightly off. Need to shift to the left to accurately depict the concept. Fortunately, this is a teacher knowledge page.

39. Questions from the Wiki

40. What’s the big idea? Time and distance can be measured. Measurement can be done using standard and non-standard units. Units can be compared, and different units are useful in different situations. Line plots show “how many” on a numeric scale.

41. Examples & Explanations Standards addressed in Unit 3 MCC2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. MCC2.MD.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

42. Examples & Explanations Standards addressed in Unit 3 MCC2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters. MCC2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

43. Examples & Explanations Standards addressed in Unit 3 MCC2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. MCC2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., and represent whole-number sums and differences within 100 on a number line diagram.

44. Examples & Explanations Standards addressed in Unit 3 MCC2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. MCC2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

45. Examples & Explanations Standards addressed in Unit 3 MCC2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put- together, take-apart, and compare problems using information presented in a bar graph.

46. Examples & Explanations Resources which work with Unit 3: Connecting cubes, color tiles Measurement tools Models Sketches Constructions Thinking…

47. Examples and Explanations What understandings do students need in order to think about measurement? Exposure to and use of measurement vocabulary Exposure to different ideas and ways of measuring Non-examples Hands-on grappling

48. Examples & Explanations Measurement thinking: Expansiveness of thought Understanding of idea of repeated units Understanding of how to use tools Reasoning and articulating thought, both verbally and in journals

49. Examples & Explanations

57. Where is it going?

58. Examples & Explanations

59. http://www.learner.org/courses/learningmat h/measurement/ http://www.learner.org/courses/learningmat h/measurement/

60. How to develop all of these? Hold number talks regularly, expand them to include geometric ideas that support development of understanding. http://bit.ly/OYVpKNhttp://bit.ly/OYVpKN Not sure about the geometry yourself? VandeWalle, “Teaching Student-Centered Mathematics- K-3” Clements and Sarama- “Learning and Teaching Early Math”

61. Examples & Explanations Standards: Illustrative Mathematics- MD.9, 10 http://illustrativemathematics.org/standards/k8# SEDL- MD.5- http://secc.sedl.org/common_core_videos/http://secc.sedl.org/common_core_videos/ Tools: Tools for the Common Core: http://commoncoretools.me/2012/04/02/general-questions-about-the- standards/ On the wiki: Discussion threads Unpacked standards from other states. Proceed with caution.

62. Assessment

63. Formative- tasting while you cook. Summative- the completed dish.

64. Navigating Unit Three The only way to gain deep understanding is to work through each task. No one else can understand for you. Make note of where, when, and what the big ideas are. Make note of where, when, and what the pitfalls might be. Look for additional tools/ideas you want to use Determine any changes which might need to be made to make this work for your students. Share, ask, and collaborate on the wiki. http://ccgpsmathematicsk-5.wikispaces.com/Home

65. Just remember:

66. Resource List The following list is provided as a sample of available resources and is for informational purposes only. It is your responsibility to investigate them to determine their value and appropriateness for your district. GaDOE does not endorse or recommend the purchase of or use of any particular resource.

67. Have you visited the wiki yet? http://ccgpsmathematicsk-5.wikispaces.com

68. Very Second Grade Wiki- http://ccgpsmathematicsk- 5.wikispaces.com/http://ccgpsmathematicsk- 5.wikispaces.com/ Inside math- http://bit.ly/Q5Wb8fhttp://bit.ly/Q5Wb8f Edutopia- http://bit.ly/o1qaKfhttp://bit.ly/o1qaKf Teaching channel- http://bit.ly/LZ5DJRhttp://bit.ly/LZ5DJR Blogs/websites  http://www.projectapproach.org/grades_1_to_4.php http://www.projectapproach.org/grades_1_to_4.php  http://classblogmeister.com/blog.php?blogger_id=1337 http://classblogmeister.com/blog.php?blogger_id=1337  http://confessionsofahomeschooler.blogspot.com/ http://confessionsofahomeschooler.blogspot.com/

69. Resources Books  Van De Walle and Lovin, Teaching Student- Centered Mathematics, K-3  Clements and Sarama, Learning and Teaching Early Math  Parrish, Number Talks  Shumway, Number Sense Routines  Wedekind, Math Exchanges

70. Resources Common Core Resources  SEDL videos - https://www.georgiastandards.org/Common- Core/Pages/Math.aspx or http://secc.sedl.org/common_core_videos/https://www.georgiastandards.org/Common- Core/Pages/Math.aspxhttp://secc.sedl.org/common_core_videos/  Illustrative Mathematics - http://www.illustrativemathematics.org/http://www.illustrativemathematics.org/  Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/http://www.ccsstoolbox.com/  Arizona DOE - http://www.azed.gov/standards- practices/mathematics-standards/http://www.azed.gov/standards- practices/mathematics-standards/  Inside Mathematics- http://www.insidemathematics.org/http://www.insidemathematics.org/  Common Core Standards - http://www.corestandards.org/http://www.corestandards.org/  Tools for the Common Core Standards - http://commoncoretools.me/http://commoncoretools.me/  Phil Daro talks about the Common Core Mathematics Standards - http://serpmedia.org/daro-talks/index.html http://serpmedia.org/daro-talks/index.html

71. Resources Professional Learning Resources  Inside Mathematics- http://www.insidemathematics.org/http://www.insidemathematics.org/  Edutopia – http://www.edutopia.orghttp://www.edutopia.org  Teaching Channel - http://www.teachingchannel.orghttp://www.teachingchannel.org  Annenberg Learner - http://www.learner.org/http://www.learner.org/ Assessment Resources  MARS - http://www.nottingham.ac.uk/~ttzedweb/MARS/http://www.nottingham.ac.uk/~ttzedweb/MARS/  MAP - http://www.map.mathshell.org.uk/materials/index.phphttp://www.map.mathshell.org.uk/materials/index.php  PARCC - http://www.parcconline.org/parcc-stateshttp://www.parcconline.org/parcc-states

72. As you start your day tomorrow…

73. Thank You! Please visit http://ccgpsmathematicsK-5.wikispaces.com/ to provide us with your feedback!http://ccgpsmathematicsK-5.wikispaces.com/ Turtle Gunn Toms Program Specialist (K-5) tgunn@doe.k12.ga.us These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Join the listserve! join-mathematics-k-5@list.doe.k12.ga.us Follow on Twitter! Follow @turtletoms (yep, I’m tweeting math resources in a very informal manner)