1. Measurement in K-5

2. List the ways you have used measurement in the past two days2 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 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 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 of units 5 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 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 7

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

9. Box Sort 9 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 10

11. Measurement Determine the attribute to be measured Object Attribute …11 11

12. Attribute Sort
Mass
Length
Capacity 12 12

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

14. Measurement Determine the attribute to be measured Object Attribute
How would I Unit
measure it? 14 14

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

16. Exploring Linear Measurement
Task 1:
Measure the length of your assigned tape strip using multiple index cards 16 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 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 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 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 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 23

24. Measurement Objectives
Grade
Objectives K 1 2
Identify the measurement objectives for each grade 24 24

25. Units for Length
Name the standard units for the metric and customary systems
Customary
Metric
Inch
millimeter
Foot
centimeter
Yard
decimeter
Mile
meter
kilometer 25 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 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 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 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 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 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 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 35

36. NAEP Question

37. NAEP Question Percentage of students and their responses
Percent Responding
How long is this line segment?
Grade 3
Grade 7
3 cm 4 1
5 cm* 14 49
6 cm 31 37
8 cm 30 9
11 cm 6 2
I don’t know. 15 37 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! 38 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 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 40

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

42. Measurement Objectives
Grade
Objectives 2 3 4 5
Identify the
objectives in the SCS that focus on standard measurement 42 42

43. Make a New Tool
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

44. Tape Measures Measure each strip of tape and record your measurements.
Length in feet (ft)
Length in yards (yd) A B C D 44 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 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 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 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 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 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 50

51. Reflecting on Measurement
Measurements are used by adults frequently each day, yet this is an area of mathematics in which many students are not successful
Making connections: How are the ideas in measurement linked with objectives in geometry? 51 51

52. Reflecting on Measurement
What objectives in measurement have we not discussed?
Rethinking instruction through the lens of “big ideas” may help increase student understanding and achievement
How do the objectives for your grade level fit under the “big ideas”? 52 52

53. Big Ideas in Measurement
The measurement of a specific numerical attribute tells how many units
The process of measurement is similar for all attributes, but the measurement system and tool vary according to the attribute
An object can be described and categorized in multiple ways (attributes) 53 53

54. Big Ideas in Measurement
Measurements are accurate to the extent that the appropriate unit/tool is used properly
Work with a partner to place the objectives for your grade level beneath the big ideas listed in your handout 54 54

55. DPI Mathematics Staff Everly Broadway, Leanne Barefoot Robin Barbour
Carmella Fair
Chief Consultant
Mary H. Russell
Johannah Maynor
Partners for Mathematics Learning is a Mathematics-Science Partnership Project funded by the NC Department of Public Instruction. Permission is granted for the use of these materials in professional development in North Carolina Partner school districts.
Partners
for Mathematics Learning

56. PML Consultants Amanda Baucom Julia Cazin Anna Corbett Gail Cotton
Ryan Dougherty
Tery Gunter
Kathy Harris
Joyce Hodges
Karen McCain
Vicki Moss
Kayonna Pitchford
Ron Powell
Susan Riddle
Judith Rucker
Shana Runge
Kitty Rutherford
Penny Shockley
Pat Sickles
Nancy Teague
Bob Vorbroker
Jan Wessell
Carol Williams
Stacy Wozny

57. Partners Writers Ana Floyd Jeane Joyner Rendy King Katherine Mawhinney
Gemma Mojica
Elizabeth Murray
Wendy Rich
Catherine Stein
Please give appropriate credit to the Partners for Mathematics Learning project when using these materials. Permission is granted for their use in professional development in North Carolina Partner school districts.
Jeane Joyner, Project Director
Partners
for Mathematics Learning

58. Measurement 58