Measurement in K-5

1. Measurement in K-5

2. Measurement List the ways you have used measurement in the past two days 2

3. Measurement In spite of how regularly we use measurement, results of local, state, national, and international assessments indicate that students of all ages are significantly deficient in their knowledge of measurement concepts and skills. Why do you think this is the case? What makes measurement difficult for students? 3

4. Measurement Measurement is a complex topic: Many kinds of units Some units have the same name (fluid ounces and ounces in a pound) Two measurement systems U.S. Customary and Metric Measurements are approximations Requires lots of practice and experience 4

5. Big Ideas in Measurement An object can be described and categorized in multiple ways (attributes) The measurement of a specific numerical attribute tells the number ofunits 5

6. Big Ideas in Measurement The process of measurement is similar for all attributes, but the measurement system and tool vary according to the attribute Measurements are accurate to the extent that the appropriate unit/tool is used properly 6

7. Process of Measurement Select an attribute of something you wish to measure Choose an appropriate unit of measurement Determine the number of units, usually by using a measuring tool 7

8. Processof Measurement(Step 1) Select the attribute of something (e.g., an object) you wish to measure 8

9. Box Sort 9

10. Attributes Characteristics: ways that materials, objects, or ideas can be sorted Which of the attributes named are measurable? • Blue • Rectangular prism • With a lid • Long & skinny 10

11. Measurement Determine the attribute to be measured 11

12. Attribute Sort Mass Length Capacity 12

13. Processof Measurement(Step 2) Understand the relationship of units to systems and to the processes of measuring Choose appropriate units 13

14. Measurement Determine the attribute to be measured 14

15. Measurement In what types of measurement activities do students in grades K-2 participate? Why are these activities appropriate? 15

16. Exploring Linear Measurement Task 1: Measure the length of your assigned tape strip using multiple index cards 16

17. Non-Standard Measurement How would students start measuring? How would they count the number of cards? How would students deal with the end measurement? 17

18. Exploring Linear Measurement Task 2: Measure the same length of tape using one piece of notebook paper How is measuring with one piece of paper different from measuring with the multiple index cards? What difficulties might students have? 18

19. Measurement Components Unit– the single quantity used to measure an attribute; the type of unit depends on the type of attribute being measured Unit Iteration – the units must be repeated, or iterated, in order to determine the measure of an object 19

20. Exploring Linear Measurement • Compare the two measurements _____ length in index cards _____ length in paper Compensatory Principle – the principle states that the bigger the unit, the smaller the number of that unit needed

21. Compensatory Principle • What is the distance across the room walking heel to toe? • What is the same distance measured in giant steps? What are other examples to illustrate the compensatory principle that would be appropriate for students at different grade levels?

22. Exploring Linear Measurement Task 3: Compare the measure of your masking tape strip to the length of another group’s strip of masking tape using the string provided 22

23. Measurement Components Transitivity – two objects can be compared in terms of a measurable quality using a third object Conservation– objects maintain their same size and shape when they are rearranged, transformed, or divided in various ways 23

24. Measurement Objectives Identify the measurement objectives for each grade 24

25. Units for Length Name the standard units for the metric and customary systems 25

26. Show An Inch… • Hold up your fingers to show an inch • Hold up your hands to show a foot • Hold up your arms to show a yard How close were you? How were you able to approximate each measurement?

27. Show A Centimeter… • Hold up your fingers to show a centimeter • How would you show a meter? How close were you? How were you able to approximate each measurement?

28. “Measurement Sense” Measurement sense demands that students are familiar with commonly used measurement units (their size and what they measure) For example, a square tile can be used to identify items that are about an inch in length 28

29. Benchmarks A benchmark is a familiar item that becomes a referent or way to remember the size of the unit Students must begin with items they are familiar with, objects they see and use on a daily basis 29

30. Beyond the Classroom • Would you want children to find benchmarks for a mile? Why or why not? • How would you do this?

31. Benchmark Benefits Help students develop a working familiarity with various measurement units Enable students to estimate measurements more accurately Give students some sense of how the customary and metric measurements relate to one another 31

32. Revisiting Linear Measurement What if you… Measured the length of your assigned tape strip in feet using one ruler What if you used one yard stick? 32

33. Standard Measurement How would you (or students) start measuring? How would you (or students) count the number of units? How would you (or students) deal with the end measurement? 33

34. Measurement Components Unit–single quantity used to measure an attribute Unit Iteration – the units are repeated, or iterated, in order to determine the measure How are the difficulties students have with unit iteration the same with standard/non-standard units? 34

35. Big Ideas in Measurement The process of measurement is similar for all attributes, but the measurement system and tool vary according to the attribute Measurements are accurate to the extent that the appropriate unit/tool is used properly 35

36. NAEP Question

37. NAEP Question Percentage of students and their responses 37

38. Measuring Instruments Helping students understand and improve their use of linear measuring tools: Make rulers Mark ruler divisions Use broken rulers Practice, Practice, Practice! 4 5 6 7 38

39. Estimation What difficulties do students have with estimation? *Students often make poor estimates because they are not familiar enough with the various units of measurement 39

40. Make an Estimate About how long is the marker? What strategies did you use to decide? Skills improve if students have many, many opportunities to practice using the same units again and again establishing referent measures or benchmarks 40

41. Estimation Strategies Use of benchmarks Chunking Subdivisions Partitioning Iterate Units Caution: Use Ranges of Estimates 41

42. Measurement Objectives Identify the objectives in the SCS that focus on standard measurement 42

43. At each table combine three of your foot rulers to make a “yard stick” Work together to re-measure four of the masking tape strips Make a New Tool

44. Tape Measures Measure each strip of tape and record your measurements. 44

45. Measurement Conversions Refer back to the giant steps and heel-to toe steps Record the measurement of the room ___ Giant Steps = ___ Heel-to-toe Steps 9 feet = ____ yards 150 centimeters = ____ meters ____ feet = 24 inches 45

46. Measurement Conversions Compensatory Principle Smaller Units Larger Units (number of units is fewer) Larger Units Smaller Units (number of units is greater) Strategy of Partitioning - dividing larger units into equivalent, smaller units 46

47. Measurement Conversions Miguel’s bedroom is 15 feet wide. How many yards is this? A. 45 yards C. 5 yards B. 18 yards D. 3 yards If a new pencil is 19 centimeters long, about how many pencils will equal one meter? A. 5 pencils C. 19 pencils B. 10 pencils D. 38 pencils 47

48. Measurement Conversions Miguel’s bedroom is 15 feet wide. How many yards is this? A. 45 yards C. 5 yards B. 18 yards D. 3 yards If a new pencil is 19 centimeters long, about how many pencils will equal one meter? A. 5 pencils C. 19 pencils B. 10 pencils D. 38 pencils 48

49. Mass vs. Weight Read article by Dr. Anita Bowman Highlight key ideas that help clarify your thinking about these concepts What experiences will help students distinguish these ideas? 49

50. Mass vs. Weight What objectives in the Standard Course of Study focus on mass and weight? What activities do students need at your grade level to experience the concepts of mass and weight as different attributes? 50