Time and Measurement

1. Time and Measurement Grades 3 -5 Instructor Dr. Sandra Trotman (NSU, FL)

2. Welcome & Introductions • Participants will engage in an ice breaker activity (e.g., role playing) • Instructor will: • review objectives, and ground rules. • Discuss the Pre test and Post test • Administer the Pre test

3. Show What you Know! • Participants will be given a 5 item review exercise on measurement. • This exercise will be used to assess participants’ understanding of the teaching and learning of measurement as it applies to the use of customary and metric units, estimation, selecting and using measuring tools, length, time, perimeter and area.

4. Overview • Designed to assist Grades 3 – 5 teachers as they exercise the task of aligning the Next Generation Sunshine State Standards with the mathematics content • Workshop is divided into 3 modules that are designed to engage participants in active explorations, individualized and cooperative learning settings; researching; and integrating technology and literature/Language Arts in the math curricula. • Emphasis placed on developing each math concept from concrete to abstract representations

5. Three Training Modules • Module 55 Tell time nearest minute, quarter hour, and elapsed time, strategies, error problems, solving real-world problems • Customary and Metric Units of Measure: compare, contrast, and convert units of measure within the same dimension; measure fractional parts of linear units such as ½, ¼, and 1/10 • Perimeter and Area: Selecting and using appropriate measuring tools: estimation and precision of measurement, measuring tools to estimate and solve real-world area problems

6. Identifying the NGSSS Criteria for establishing desired performance based on the Next Generation Sunshine State standards: Content Strand: Measurement • MA.3.G.5.2 Measure objects using fractional parts of linear units such as ½, ¼, and 1/10. • MA.3.G.5.3 Tell time to the nearest minute and to the nearest quarter hour, and determine the amount of time elapsed. • MA.5.G.5.2 Compare, contrast, and convert units of measure within the same dimension (length, mass, or time) to solve problems. • MA.5.G.5.3 Solve problems requiring attention to approximation, selection of appropriate measuring tools, and precision of measurement. • MA.4.G.3.3 Select and use appropriate units, both customary and metric, strategies, and measuring tools to estimate and solve real-world area problems.

7. Module 55 Objectives Participants will : • Complete a 5 item measurement Pre test • Examine the grades 3 – 5 NGSSS related to telling time and Measurement • Discuss research ideas related to the importance of measurement in the elementary math curriculum • Demonstrate understanding of the connection between being able to calculate or find given times and real-life situations. • Identify and/or propose effective strategies for teaching time to the nearest minute, nearest quarter hour, elapsed time, and developing the related vocabulary. • Connect Math and Language Arts by providing activities for students to develop their vocabulary skills while simultaneously developing conceptual understandings. (e.g., Create different graphic organizers) • Examine common errors/difficulties encountered by students when telling or finding times. • Explore web-based educational resources designed to reinforce learning of concepts of time.

8. Why Teach Measurement? • It provides many applications to everyday life. • It can be used to help learn other mathematics. • It can be related to other areas of the school curriculum. • It involves the students in active learning. • It can be approached through problem solving.

9. How to teach Measurement • Provide opportunities for children to measure frequently and often, preferably on real problems • Provide activity –oriented measurement situations – learn by doing/experimenting • Provide instruction that help student to make connection between subject areas -emphasize the important ideas of measurement

10. Telling Time Module 55 Next Generation Sunshine State Standards • MA.3.G.5.3 Tell time to the nearest minute and to the nearest quarter hour, and determine the amount of time elapsed. • MA.5.G.5.3 Solve problems requiring attention to approximation, selection of appropriate measuring tools, and precision of measurement.

11. Discussion • Why is it important to be able to tell time? • What would happen if people never knew what time it was?

12. Developing Math Language Strategies: Vocabulary development time, half hour, hour, quarter hour, five minute interval, analog, digital clock, tell time, minutes • Using Venn Diagrams • Word Search • Picture book • Catering for diverse learners Strategies!

13. Students struggle learning time? • It requires the application of indirect scales. • Clocks cannot be placed next to an hour to measure time • Measuring time is complex because it requires • (i) knowledge and skill of reading an analog clock; • (ii) understanding of points in the duration of time periods • Use of a particular vocabulary (confusing); e.g., 45 minutes after 6:00 can be referred to as 6:45 or 15 minutes before 7:00, a quarter until/of/before 7:00.

14. Which Tool? • Time is measured in seconds, minutes, hours, and days…you may measure in years. • For each kind of measurement, you will use a different tool OR part of the same tool. • The length of time it takes a car to roll from the top of a ramp to the bottom… Stop watch • Time from sunrise to sunset … Clock • Time it takes a seed to sprout after being planted … Calendar

15. Paper folding Activity • Participants will engage in making clocks to be used in problem solving activities.

16. Critical Thinking Discuss how you will model the strategy(ies) for solving the following problem. • Suppose you wanted to know what time it was 4 hours ago and it is now 1 p.m. • It is now 5:25 p.m. What time will it be in 1 hour 35 minutes?

17. Telling time To the nearest 1/4, ½, ¾ and minute

18. Elapsed Time • What do you understand by the term elapsed time? • When might you need to use elapsed time during a school day?

19. Elapsed Time Defined • This is the amount of time that passes from the start to the end of an action. • The hour hand goes around an analog clock twice a day: once for the morning or before noon (a.m.), and once for after noon (p.m.)

20. From time to time Getting a drink of water from the fountain will have a short elapsed time measured in seconds. Riding in a car from Ft. Lauderdale to Orlando will have a long elapsed time measured in hours.

21. Calendar • A Calendar can be used to find elapsed time.

22. The Grouchy Ladybug by: Eric Carle Connecting Literature and Math Purpose: read to determine the elapsed time during a day.

23. Problem Solving Skills MA.3.G.5.3 Indentifying Extra or missing information • A problem is missing information when you cannot solve it unless you have more information. • A problem has extra information when it gives more information than needed to solve it.

24. Developing Problem Solving Skills

25. Activity 9. Reading CalendarsIdentifying common errors Task: Student X is asked to determine the number of days between two dates, some of which are in the same month and some of which fall in different months. • Participants will examine the student’s work sample by • Scoring the student’s paper. • Identifying all strengths the student exhibits • Identifying all challenges the student encounters. Begin with the first incorrect problem and determine the error pattern. • Finally, participants in small groups will describe at least 2 activities that may be used to help this student develop mastery of concept/skill.

26. Module 56 Length

27. Block 56 NGSS Standards Criteria for establishing desired performance based on the Next Generation Sunshine State Standards • MA.3.G.5.2 Measure objects using fractional parts of linear units such as ½, ¼, and 1/10. • MA.5.G.5.2 Compare, contrast, and convert units of measure within the same dimension (length, mass, or time) to solve problems.

28. Length • Aligning the Next Generation Sunshine State Standards • Customary Length • Measure to the nearest ¼, ½, 1/10 inch • Metric Length • Centimeters, Decimeters, and Meter • Problem Solving strategies – e.g., • Teach with Tech • Errors/misconceptions held by students

29. All measurements require units 16 ounces = 1 pound (lb) 4 quart = 1 gallon 1 minute = 60 seconds 12 inches (in)

30. Fostering Communication in Mathematics • Journal Activity: You have a child in your class who physically cannot handle a ruler. What would you do in this situation? Describe at least 2 solutions.

31. Measuring to the nearest ¼, ½ or an inch Question: How best can we help students develop understanding of the concept of measurement using a ruler? • Use a ruler to measure the line segment below to the nearest ½, ¼ and 1/10 of an inch.

32. A Dictionary of Units of MeasurementHow Many? • DistanceIn all traditional measuring systems, short distance units are based on the dimensions of the human body. • The inch represents the width of a thumb; in fact, in many languages, the word for "inch" is also the word for "thumb." • The foot (12 inches) was originally the length of a human foot, although it has evolved to be longer than most people's feet. • The yard (3 feet) seems to have gotten its start in England as the name of a 3-foot measuring stick, but it is also understood to be the distance from the tip of the nose to the end of the middle finger of the outstretched hand. • Finally, if you stretch your arms out to the sides as far as possible, your total "arm span," from one fingertip to the other, is a fathom (6 feet).

33. Developing estimation Skills • Participants will develop a PowerPoint or Podcast presentation on the use of accurate and estimate measurements • Participants will view a video clip on estimation by clicking on the url: http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/2_Estimation_of_Length/index.html

34. Accurate vs. Estimated Measurements

35. The role of Research in informing curriculum & instruction • Measurement in PreK-2 Mathematics by Douglas H. Clements & Michelle Stephan • Excerpt: In international comparisons, U.S. students’ score lower in measurement and geometry than in other topics (National Center for Education Statistics, 1996). • We need much stronger measurement instruction in the early years.

36. Primary Teachers’ Perceptions of Their Knowledge and Understanding of Measurement • Current literature suggests that teachers’ content knowledge effects student learning and is improved by professional development (e.g., Hill & Ball, 2004). • In particular, studies have shown that students do not understand the attribute being measured or the units that are used for measurement (Outhred & McPhail, 2000; Outhred et al., 2003). Such evidence raises questions about the effectiveness of the instruction students are receiving within these content areas. • Michelle O’Keefe & Janette Bobis, University of Sydney

37. Using Technology

38. Using Technology • Tools: Spreadsheet, Encyclopedia or Internet • Purpose: To determine elapsed time Distribute Activity Sheet: Mathspreadsheet Alternative activities: Participants use a spreadsheet to organize a schedule for a football player. They then find the elapsed time. Participants will research time zones throughout the world, why different time zones were created, and the number of time zones in the world. Discuss what would happen if all clocks worldwide read 9 a.m.?

39. Module 57 Perimeter and Area

40. Perimeters • Aligning the Next Generation Sunshine State Standards • Model Perimeter • Measure Perimeter • Find Perimeter • Modeling and finding Areas • Problem Solving strategies – e.g., searching for patterns • Teach with Tech • Errors/misconceptions held by students

41. Areas • Aligning the Next Generation Sunshine State Standards • Modeling and finding Areas • Relate Perimeter and Area • Problem Solving strategies – e.g., • Teach with Tech • Errors/misconceptions held by students

45. Thank you for participating in this session Remember to submit all suggestions.

46. Resources • Big Idea 3. (2011). Orlando, FL: Houghton Mifflin Harcourt. • Bragg, P., & Outhred, L (n.d.). A measure of rulers- the importance of units in a measure. Retrieved from http://www.emis.de/proceedings/PME28/RR/RR169_Bragg.pdf or Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 2004, 2, 159–166. • Bragg, P., & Outhred, L. (2000). What is taught versus what is learnt: The case of linear measurement. Proceedings of the Twenty-Fourth Annual Conference of the International Group for the Psychology of Mathematics Education. Japan: Program Committee. • A Dictionary of Units of Measurement. http://www.unc.edu/~rowlett/units/ • Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2009). Helping children learn mathematics, 9th ed. Hoboken, NY: John Wiley & Sons, Inc. • Carle, E. (1977). The Grouchy Ladybug. New York: HarperCollins Publishers