DOCSLIB.ORG

Measurement Progression Document

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Measurement Progression Document K–12 Mathematics Measurement Standards/Cluster Math Other Content Areas K.MD.B: Classify objects and count the • Practice sorting collections of objects • Identify similarities and differences number of objects in each category extending to more than one way to sort between objects • Use descriptive words to describe how • Use attributes to sort a collection of collections have been sorted objects Kindergarten 1.MD.A: Measure lengths indirectly and • Use measurement vocabulary to first estimate, • Order objects by length in terms by iterating length units describe, and then compare measurable of the length of another object attributes • Determine the length of an object 1st Grade 1st • Measure items with different sizes of nonstan as a whole number of length dard units units 2.MD.A: Measure and estimate lengths • Use appropriate tools and terminology for • Measure the length of an object in standard units measurement using rulers, yardsticks, meter sticks, • Describe how different unit measurements measuring tapes, and other relate to each other and the size of the unit measuring tools 2nd Grade 2nd chosen • Estimate distance, volume, weight, • Estimate before measuring etc 3.MD.A: Solve problems involving • Choose appropriate units of measure for word • Measure liquids using liters measurement and estimation of problems • Measure mass using grams and intervals of time, liquid volumes, and • Understand the concept of mass in relationship kilograms masses of objects to weight and the concept of measuring in • Understand units of metric capacity by 3rd Grade 3rd volume looking at packaging • Solve word problems about metric capacity and mass 4.MD.A: Solve problems involving • Express measurement equivalents in a larger • Use both metric and standard measure measurement and conversion of unit in terms of a smaller unit in a two-column ment vocabulary measurements from a larger unit to a table • Understand the relationship between smaller unit. • Represent measurement quantities using units within one system of measurement 4th Grade diagrams such as money or distance • Visualize benchmark measurements 5.MD.A: Convert like measurement • Solve word problems involving conversion of • Discuss both customary and standard units within a given measurement metric or customary units measurements within the same system system • Use the vocabulary associated with the metric of measurement using appropriate and customary conversions. units 5 eth Grad 5 eth Except where otherwise noted, this work is licensed under a Creative Commons Attribution 4.0 International License. All logos are property of their respective owners. K–12 Mathematics Measurement Standards/Cluster Math Other Content Areas 6.RP.2: Understand the concept of a • Understand rate as a ratio that compares • Calculate and understand unit rates unit rate a/b associated with a ratio a:b two quantities with different units of (miles per gallon, cost per hour, days with b≠0, and use rate language in the measure per month) context of a ratio relationship • Understand that unit rates are the ratio of two measurements or quantities in which 6th Grade 6th the second term means “one” • Interpret rate language • Solve unit rate problems 7.RP.1: Compute unit rates associated • Use precise mathematical language when • Read and create scale drawings with ratios of fractions, including ratios presenting solutions to scale drawings using • Calculate actual measures from of length, areas and other quantities appropriate measurement units scale drawings (ie floor plans) 7th Grade 7th measured in like or different units. • Redraw a picture or diagram using a different using appropriate measurement scale units. • Calculate measurements of objects using right • Find distance by drawing and e 8.G.7: Apply the Pythagorean Theorem to determine unknown side lengths in triangles measuring two sides of a right right triangles in real-world and triangle mathematical problems in two and 8th Grad 8th three dimensions. N.Q.A: Reason quantitatively and use • Determine and/or explain why a specific scale • Connect measurement concepts to units to solve problems. was chosen for a graph science and other contexts to show • Explain the meaning of different quantities in a h School h understanding of significant digits and problem and its solution scientific notation Hig • Select and properly use an existing quantity for a real-world context • The standards identified are representative of the focus at each grade level to demonstrate the devel- opmental nature of our Learning Standards • The math skills listed are applicable within the context of the identified standards but do not offer a comprehensive list of skills they describe • The other content areas are examples to provide possible uses of the math skills within the listed standards Except where otherwise noted, this work is licensed under a Creative Commons Attribution 4.0 International License. All logos are property of their respective owners..
Load more

Recommended publications
  • Metric System Units of Length
    Math 0300 METRIC SYSTEM UNITS OF LENGTH Þ To convert units of length in the metric system of measurement The basic unit of length in the metric system is the meter. All units of length in the metric system are derived from the meter. The prefix “centi-“means one hundredth. 1 centimeter=1 one-hundredth of a meter kilo- = 1000 1 kilometer (km) = 1000 meters (m) hecto- = 100 1 hectometer (hm) = 100 m deca- = 10 1 decameter (dam) = 10 m 1 meter (m) = 1 m deci- = 0.1 1 decimeter (dm) = 0.1 m centi- = 0.01 1 centimeter (cm) = 0.01 m milli- = 0.001 1 millimeter (mm) = 0.001 m Conversion between units of length in the metric system involves moving the decimal point to the right or to the left. Listing the units in order from largest to smallest will indicate how many places to move the decimal point and in which direction. Example 1: To convert 4200 cm to meters, write the units in order from largest to smallest. km hm dam m dm cm mm Converting cm to m requires moving 4 2 . 0 0 2 positions to the left. Move the decimal point the same number of places and in the same direction (to the left). So 4200 cm = 42.00 m A metric measurement involving two units is customarily written in terms of one unit. Convert the smaller unit to the larger unit and then add. Example 2: To convert 8 km 32 m to kilometers First convert 32 m to kilometers. km hm dam m dm cm mm Converting m to km requires moving 0 .
    [Show full text]
  • How Are Units of Measurement Related to One Another?
    UNIT 1 Measurement How are Units of Measurement Related to One Another? I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind... Lord Kelvin (1824-1907), developer of the absolute scale of temperature measurement Engage: Is Your Locker Big Enough for Your Lunch and Your Galoshes? A. Construct a list of ten units of measurement. Explain the numeric relationship among any three of the ten units you have listed. Before Studying this Unit After Studying this Unit Unit 1 Page 1 Copyright © 2012 Montana Partners This project was largely funded by an ESEA, Title II Part B Mathematics and Science Partnership grant through the Montana Office of Public Instruction. High School Chemistry: An Inquiry Approach 1. Use the measuring instrument provided to you by your teacher to measure your locker (or other rectangular three-dimensional object, if assigned) in meters. Table 1: Locker Measurements Measurement (in meters) Uncertainty in Measurement (in meters) Width Height Depth (optional) Area of Locker Door or Volume of Locker Show Your Work! Pool class data as instructed by your teacher. Table 2: Class Data Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Width Height Depth Area of Locker Door or Volume of Locker Unit 1 Page 2 Copyright © 2012 Montana Partners This project was largely funded by an ESEA, Title II Part B Mathematics and Science Partnership grant through the Montana Office of Public Instruction.
    [Show full text]
  • Measuring in Metric Units BEFORE Now WHY? You Used Metric Units
    Measuring in Metric Units BEFORE Now WHY? You used metric units. You’ll measure and estimate So you can estimate the mass using metric units. of a bike, as in Ex. 20. Themetric system is a decimal system of measurement. The metric Word Watch system has units for length, mass, and capacity. metric system, p. 80 Length Themeter (m) is the basic unit of length in the metric system. length: meter, millimeter, centimeter, kilometer, Three other metric units of length are themillimeter (mm) , p. 80 centimeter (cm) , andkilometer (km) . mass: gram, milligram, kilogram, p. 81 You can use the following benchmarks to estimate length. capacity: liter, milliliter, kiloliter, p. 82 1 millimeter 1 centimeter 1 meter thickness of width of a large height of the a dime paper clip back of a chair 1 kilometer combined length of 9 football fields EXAMPLE 1 Using Metric Units of Length Estimate the length of the bandage by imagining paper clips laid next to it. Then measure the bandage with a metric ruler to check your estimate. 1 Estimate using paper clips. About 5 large paper clips fit next to the bandage, so it is about 5 centimeters long. ch O at ut! W 2 Measure using a ruler. A typical metric ruler allows you to measure Each centimeter is divided only to the nearest tenth of into tenths, so the bandage cm 12345 a centimeter. is 4.8 centimeters long. 80 Chapter 2 Decimal Operations Mass Mass is the amount of matter that an object has. The gram (g) is the basic metric unit of mass.
    [Show full text]
  • MEMS Metrology Metrology What Is a Measurement Measurable
    Metrology • What is metrology? – It is the science of weights and measures • Refers primarily to the measurements of length, MEMS Metrology wetight, time, etc. • Mensuration- A branch of applied geometry – It measure the area and volume of solids from Dr. Bruce K. Gale lengths and angles Fundamentals of Micromachining • It also includes other engineering measurements for the establishment of a flat, plane reference surface What is a Measurement Measurable Parameters • A measurement is an act of assigning a • What do we want to • Pressure specific value to a physical variable measure? • Forces • The physical variable becomes the • Length or distance •Stress measured variable •Mass •Strain • Temperature • Measurements provide a basis for • Friction judgements about • Elemental composition • Resistance •Viscosity – Process information • Roughness • Diplacements or – Quality assurance •Depth distortions – Process control • Intensity •Time •etc. Components of a Measuring Measurement Systems and Tools System • Measurement systems are important tools for the quantification of the physical variable • Measurement systems extend the abilities of the human senses, while they can detect and recognize different degrees of physical variables • For scientific and engineering measurement, the selection of equipment, techniques and interpretation of the measured data are important How Important are Importance of Metrology Measurements? • In human relationships, things must be • Measurement is the language of science counted and measured • It helps us
    [Show full text]
  • Laser Power Measurement: Time Is Money
    Laser power measurement: Time is money SEAN BERGMAN Rapid, accurate laser power measurements meet high-throughput needs In nearly every any laser application, it’s necessary to measure laser output power to be able to obtain optimum results. For industrial applications, making power measurements often requires interrupting production and this creates a tradeoff. Specifically, is the cost of stopping or slowing production for laser measurement outweighed by the benefits that making the measurement will deliver? To make this determination, it’s useful to ask some specific questions. These include: How sensitive is my process to variations in laser power? How fast does my laser output typically change, and therefore, how frequently do I need make a laser measurement to keep my process within specification? [Native Advertisement] What is my production throughput? How much bad product will I make, and how much does this scrap cost me, when I delay making a laser measurement for a given amount of time? How long does it take to make the laser measurement, and what is the total cost of this measurement in terms of production downtime or manpower? For high-speed industrial processes based on high-power lasers, the answers to these questions often show that it is not possible to achieve a good tradeoff between measurement frequency and cost. This is because traditional thermopile laser power sensors are relatively slow, so making frequent measurements results in high production downtime. Alternatively, making infrequent measurements can result in high scrap rates. Thermopile power sensors Although they are relatively slow, thermopiles have long been used for measuring high-power lasers because high-speed photodiode detectors saturate at low power levels.
    [Show full text]
  • 3.1 Dimensional Analysis
    3.1 DIMENSIONAL ANALYSIS Introduction (For the Teacher).............................................................................................1 Answers to Activities 3.1.1-3.1.7........................................................................................8 3.1.1 Using appropriate unit measures..................................................................................9 3.1.2 Understanding Fundamental Quantities....................................................................14 3.1.3 Understanding unit definitions (SI vs Non-sI Units)................................................17 3.1.4 Discovering Key Relationships Using Fundamental Units (Equations)...................20 3.1.5 Using Dimensional Analysis for Standardizing Units...............................................24 3.1.6 Simplifying Calculations: The Line Method.............................................................26 3.1.7 Solving Problems with Dimensional Analysis ..........................................................29 INTRODUCTION (FOR THE TEACHER) Many teachers tell their students to solve “word problems” by “thinking logically” and checking their answers to see if they “look reasonable”. Although such advice sounds good, it doesn’t translate into good problem solving. What does it mean to “think logically?” How many people ever get an intuitive feel for a coluomb , joule, volt or ampere? How can any student confidently solve problems and evaluate solutions intuitively when the problems involve abstract concepts such as moles, calories,
    [Show full text]
  • Measurement of Length: How Can We Teach It Better? Easurement of Length Is Taught Repeatedly in the South (Kamii and Clark 1997)
    Measurement of Length: How Can We Teach It Better? easurement of length is taught repeatedly in the South (Kamii and Clark 1997). Each child starting in kindergarten and continuing in was given a sheet of paper (11 by 17 inches) with an Mgrades 1, 2, and beyond. However, during inverted T photocopied on it (see fig. 1). Although the past twenty-five years, according to the National the vertical line appeared longer—the result of a Assessment of Educational Progress (NAEP), the perceptual illusion—both lines were 8 inches long. outcome of this instruction has been disappoint- This task was designed to find out how the child ing. As can be seen in table 1, only 14 percent of went about comparing two lines that could not be the third graders and half (49 percent) of the sev- compared directly. Because the lines could not be enth graders gave the correct answer—5 cm—to moved and placed side by side, the child had to use a question on the 1985–1986 NAEP (Lindquist an object such as a ruler or a strip of paper to make and Kouba 1989). Similar items included in other an indirect comparison. NAEPs before and after this one have produced The interview procedure consisted of the follow- similar findings. ing four steps: What is so hard about measurement of length? 1. Perceptual judgment. Presenting the child Table 1 is informative because it reveals the incor- with the figure of the inverted T (fig. 1), the inter- rect answers the students gave. Thirty-seven per- viewer asked, “Do you think this line (line A) is as cent of the seventh graders gave the answer 6 cm, long as this line (line B), or is this one (A) longer, evidently determined by counting the numerals 3, or is this one (B) longer?” The purpose of these 4, 5, 6, 7, and 8.
    [Show full text]
  • Units and Magnitudes (Lecture Notes)
    physics 8.701 topic 2 Frank Wilczek Units and Magnitudes (lecture notes) This lecture has two parts. The first part is mainly a practical guide to the measurement units that dominate the particle physics literature, and culture. The second part is a quasi-philosophical discussion of deep issues around unit systems, including a comparison of atomic, particle ("strong") and Planck units. For a more extended, profound treatment of the second part issues, see arxiv.org/pdf/0708.4361v1.pdf . Because special relativity and quantum mechanics permeate modern particle physics, it is useful to employ units so that c = ħ = 1. In other words, we report velocities as multiples the speed of light c, and actions (or equivalently angular momenta) as multiples of the rationalized Planck's constant ħ, which is the original Planck constant h divided by 2π. 27 August 2013 physics 8.701 topic 2 Frank Wilczek In classical physics one usually keeps separate units for mass, length and time. I invite you to think about why! (I'll give you my take on it later.) To bring out the "dimensional" features of particle physics units without excess baggage, it is helpful to keep track of powers of mass M, length L, and time T without regard to magnitudes, in the form When these are both set equal to 1, the M, L, T system collapses to just one independent dimension. So we can - and usually do - consider everything as having the units of some power of mass. Thus for energy we have while for momentum 27 August 2013 physics 8.701 topic 2 Frank Wilczek and for length so that energy and momentum have the units of mass, while length has the units of inverse mass.
    [Show full text]
  • Accurate Measurement of Small Execution Times – Getting Around Measurement Errors Carlos Moreno, Sebastian Fischmeister
    1 Accurate Measurement of Small Execution Times – Getting Around Measurement Errors Carlos Moreno, Sebastian Fischmeister Abstract—Engineers and researchers often require accurate example, a typical mitigation approach consists of executing measurements of small execution times or duration of events in F multiple times, as shown below: a program. Errors in the measurement facility can introduce time start = get_current_time() important challenges, especially when measuring small intervals. Repeat N times: Mitigating approaches commonly used exhibit several issues; in Execute F particular, they only reduce the effect of the error, and never time end = get_current_time() eliminate it. In this letter, we propose a technique to effectively // execution time = (end - start) / N eliminate measurement errors and obtain a robust statistical The execution time that we obtain is subject to the mea- estimate of execution time or duration of events in a program. surement error divided by N; by choosing a large enough The technique is simple to implement, yet it entirely eliminates N, we can make this error arbitrarily low. However, this the systematic (non-random) component of the measurement error, as opposed to simply reduce it. Experimental results approach has several potential issues: (1) repeating N times confirm the effectiveness of the proposed method. can in turn introduce an additional unknown overhead, if coded as a for loop. Furthermore, this is subject to uncertainty in I. MOTIVATION that the compiler may or may not implement loop unrolling, meaning that the user could be unaware of whether this Software engineers and researchers often require accurate overhead is present; (2) the efficiency of the error reduction measurements of small execution times or duration of events in process is low; that is, we require a large N (thus, potentially a program.
    [Show full text]
  • Metrology and Measurement Laboratory Manual
    JSS MAHAVIDYAPEETHA JSS SCIENCE & TECHNOLOGY UNIVERSITY (JSSS&TU) FORMERLY SRI JAYACHAMARAJENDRA COLLEGE OF ENGINEERING MYSURU-570006 DEPARTMENT OF MECHANICAL ENGINEERING Metrology and Measurement Laboratory Manual IV Semester B.E. Mechanical Engineering USN :_______________________________________ Name:_______________________________________ Roll No: __________ Sem _ _________ Sec ________ Course Name __________________ ______________ JSS MAHAVIDYAPEETHA Course Code _______________________________ JSSSTU, MYSURU Department of Mechanical Engineering DEPARTMENT OF MECHANICAL ENGINEERING VISION OF THE DEPARTMENT Department of mechanical engineering is committed to prepare graduates, post graduates and research scholars by providing them the best outcome based teaching-learning experience and scholarship enriched with professional ethics. MISSION OF THE DEPARTMENT M-1: Prepare globally acceptable graduates, post graduates and research scholars for their lifelong learning in Mechanical Engineering, Maintenance Engineering and Engineering Management. M-2: Develop futuristic perspective in Research towards Science, Mechanical Engineering Maintenance Engineering and Engineering Management. M-3: Establish collaborations with Industrial and Research organizations to form strategic and meaningful partnerships. PROGRAM SPECIFIC OUTCOMES (PSOs) PSO1 Apply modern tools and skills in design and manufacturing to solve real world problems. PSO2 Apply managerial concepts and principles of management and drive global economic growth. PSO3 Apply thermal,
    [Show full text]
  • Measurement of the Percentage of Root Filling in Oval-Shaped Canals Obturated with Thermafil Obturators and Beefill 2In1: in Vitro Study
    J Clin Exp Dent. 2015;7(2):e299-303. Obturation of long oval canals Journal section: Operative Dentistry and Endodontics d oi:10.4317/jced. 52177 Publication Types: Research http://dx.doi.org/10.4317/jced.52177 Measurement of the percentage of root filling in oval-shaped canals obturated with Thermafil Obturators and Beefill 2in1: In vitro study Vicente Faus-Llácer 1, Nicolás Collado-Castellanos 2, Teresa Alegre-Domingo 3, María Dolz-Solsona 2, Vicente Faus-Matoses 3 1 DDS, Professor. Department of Dental Pathology, Conservative Dentistry and Endodontic, Department of Stomatology, Faculty of Medicine and Odontology, University of Valencia 2 Postgraduate Degree. Department of Dental Pathology, Conservative Dentistry and Endodontic, Department of Stomatology, Faculty of Medicine and Odontology, University of Valencia 3 Associate Professor. Department of Dental Pathology, Conservative Dentistry and Endodontic, Department of Stomatology, Valencia University Medical and Dental School Correspondence: Deparment of Dental Patology Conservative Dentistry and Endodontics Odontology Clinic, Gascó Oliag 1 46021, Valencia, Spain Faus-Llácer V, Collado-Castellanos N, Alegre-Domingo T, Dolz-Solsona [email protected] M, Faus-Matoses V. Measurement of the percentage of root filling in oval-shaped canals obturated with Thermafil Obturators and Beefill 2in1: In vitro study. J Clin Exp Dent. 2015;7(2):e299-303. http://www.medicinaoral.com/odo/volumenes/v7i2/jcedv7i2p299.pdf Received: 08/11/2014 Accepted: 15/12/2014 Article Number: 52177 http://www.medicinaoral.com/odo/indice.htm © Medicina Oral S. L. C.I.F. B 96689336 - eISSN: 1989-5488 eMail: [email protected] Indexed in: Pubmed Pubmed Central® (PMC) Scopus DOI® System Abstract Background: The aim of the study was to measure the percentage of root canal fillings in long oval canals obturated with thermoplasticized gutta-percha techniques, Beefill 2in1® andThermafil Obturators®.
    [Show full text]
  • Introduction to Dimensional Analysis
    Introduction to Dimensional Analysis Dimensional analysis is a math tool used to change units. With this method, it is easy to change very complex units provided you know the necessary conversion definitions. This method is also referred to as unit conversion, factor analysis, unit analysis, DA, factor-label method, unit multipliers or unit fractions. Here are some basic concepts that are used in dimensional analysis: Any whole number can be written as a fraction. A number can be changed to a fraction and still keep its value by placing 1 as the denominator. 4 Ex. 4 1 The value of a quantity is not changed when it is multiplied by 1. When a number is multiplied by 1, the value of the number remains unchanged. Ex. 12(1) = 12 One (1) can be written as a fraction in many ways. As long as the numerator of the fraction equals the denominator of the fraction, the fraction is equal to one. 1 2 7 45 1 1 2 7 45 Unit fractions are also fractions that equal 1. The difference is these fractions are in units. Any definition involving units can be made into a unit fraction. 12 inches = 1 foot 12 inches 1 foot 1 1 foot 12 inches The unit labels are crucial to forming unit fractions. If the labels are removed, the statement is no longer true. Since unit fractions equal 1, it is possible to multiply a quantity by a unit fraction and not change the value. Unit labels cancel in the same way that common factors reduce to 1 in fraction multiplication.
    [Show full text]