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Measurement in K-5
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List the ways you have used measurement in the past two days
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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
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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
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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
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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
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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
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Process of Measurement (Step 1)
Select the attribute of something (e.g., an object) you wish to measure 8 8
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Box Sort 9 9
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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
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Measurement Determine the attribute to be measured Object Attribute …
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Attribute Sort Mass Length Capacity 12 12
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Process of Measurement (Step 2)
Understand the relationship of units to systems and to the processes of measuring Choose appropriate units 13 13
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Measurement Determine the attribute to be measured Object Attribute
How would I Unit measure it? 14 14
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Measurement In what types of measurement activities do students in grades K-2 participate? Why are these activities appropriate? 15 15
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Exploring Linear Measurement
Task 1: Measure the length of your assigned tape strip using multiple index cards 16 16
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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
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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
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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
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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
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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?
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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
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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
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Measurement Objectives
Grade Objectives K 1 2 Identify the measurement objectives for each grade 24 24
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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
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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?
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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?
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“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
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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
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Beyond the Classroom Would you want children to find benchmarks for a mile? Why or why not? How would you do this?
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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
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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
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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
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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
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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
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NAEP Question
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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
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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
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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
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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
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Estimation Strategies
Use of benchmarks Chunking Subdivisions Partitioning Iterate Units Caution: Use Ranges of Estimates 41 41
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Measurement Objectives
Grade Objectives 2 3 4 5 Identify the objectives in the SCS that focus on standard measurement 42 42
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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