Common Units Facilitator Instructions
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Stage 1: the Number Sequence
1 stage 1: the number sequence Big Idea: Quantity Quantity is the big idea that describes amounts, or sizes. It is a fundamental idea that refers to quantitative properties; the size of things (magnitude), and the number of things (multitude). Why is Quantity Important? Quantity means that numbers represent amounts. If students do not possess an understanding of Quantity, their knowledge of foundational mathematics will be undermined. Understanding Quantity helps students develop number conceptualization. In or- der for children to understand quantity, they need foundational experiences with counting, identifying numbers, sequencing, and comparing. Counting, and using numerals to quantify collections, form the developmental progression of experiences in Stage 1. Children who understand number concepts know that numbers are used to describe quantities and relationships’ between quantities. For example, the sequence of numbers is determined by each number’s magnitude, a concept that not all children understand. Without this underpinning of understanding, a child may perform rote responses, which will not stand the test of further, rigorous application. The developmental progression of experiences in Stage 1 help students actively grow a strong number knowledge base. Stage 1 Learning Progression Concept Standard Example Description Children complete short sequences of visual displays of quantities beginning with 1. Subsequently, the sequence shows gaps which the students need to fill in. The sequencing 1.1: Sequencing K.CC.2 1, 2, 3, 4, ? tasks ask students to show that they have quantity and number names in order of magnitude and to associate quantities with numerals. 1.2: Identifying Find the Students see the visual tool with a numeral beneath it. -
Using Concrete Scales: a Practical Framework for Effective Visual Depiction of Complex Measures Fanny Chevalier, Romain Vuillemot, Guia Gali
Using Concrete Scales: A Practical Framework for Effective Visual Depiction of Complex Measures Fanny Chevalier, Romain Vuillemot, Guia Gali To cite this version: Fanny Chevalier, Romain Vuillemot, Guia Gali. Using Concrete Scales: A Practical Framework for Effective Visual Depiction of Complex Measures. IEEE Transactions on Visualization and Computer Graphics, Institute of Electrical and Electronics Engineers, 2013, 19 (12), pp.2426-2435. 10.1109/TVCG.2013.210. hal-00851733v1 HAL Id: hal-00851733 https://hal.inria.fr/hal-00851733v1 Submitted on 8 Jan 2014 (v1), last revised 8 Jan 2014 (v2) HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Using Concrete Scales: A Practical Framework for Effective Visual Depiction of Complex Measures Fanny Chevalier, Romain Vuillemot, and Guia Gali a b c Fig. 1. Illustrates popular representations of complex measures: (a) US Debt (Oto Godfrey, Demonocracy.info, 2011) explains the gravity of a 115 trillion dollar debt by progressively stacking 100 dollar bills next to familiar objects like an average-sized human, sports fields, or iconic New York city buildings [15] (b) Sugar stacks (adapted from SugarStacks.com) compares caloric counts contained in various foods and drinks using sugar cubes [32] and (c) How much water is on Earth? (Jack Cook, Woods Hole Oceanographic Institution and Howard Perlman, USGS, 2010) shows the volume of oceans and rivers as spheres whose sizes can be compared to that of Earth [38]. -
Basic Statistics Range, Mean, Median, Mode, Variance, Standard Deviation
Kirkup Chapter 1 Lecture Notes SEF Workshop presentation = Science Fair Data Analysis_Sohl.pptx EDA = Exploratory Data Analysis Aim of an Experiment = Experiments should have a goal. Make note of interesting issues for later. Be careful not to get side-tracked. Designing an Experiment = Put effort where it makes sense, do preliminary fractional error analysis to determine where you need to improve. Units analysis and equation checking Units website Writing down values: scientific notation and SI prefixes http://en.wikipedia.org/wiki/Metric_prefix Significant Figures Histograms in Excel Bin size – reasonable round numbers 15-16 not 14.8-16.1 Bin size – reasonable quantity: Rule of Thumb = # bins = √ where n is the number of data points. Basic Statistics range, mean, median, mode, variance, standard deviation Population, Sample Cool trick for small sample sizes. Estimate this works for n<12 or so. √ Random Error vs. Systematic Error Metric prefixes m n [n 1] Prefix Symbol 1000 10 Decimal Short scale Long scale Since 8 24 yotta Y 1000 10 1000000000000000000000000septillion quadrillion 1991 7 21 zetta Z 1000 10 1000000000000000000000sextillion trilliard 1991 6 18 exa E 1000 10 1000000000000000000quintillion trillion 1975 5 15 peta P 1000 10 1000000000000000quadrillion billiard 1975 4 12 tera T 1000 10 1000000000000trillion billion 1960 3 9 giga G 1000 10 1000000000billion milliard 1960 2 6 mega M 1000 10 1000000 million 1960 1 3 kilo k 1000 10 1000 thousand 1795 2/3 2 hecto h 1000 10 100 hundred 1795 1/3 1 deca da 1000 10 10 ten 1795 0 0 1000 -
Order-Of-Magnitude Physics: Understanding the World with Dimensional Analysis, Educated Guesswork, and White Lies Peter Goldreic
Order-of-Magnitude Physics: Understanding the World with Dimensional Analysis, Educated Guesswork, and White Lies Peter Goldreich, California Institute of Technology Sanjoy Mahajan, University of Cambridge Sterl Phinney, California Institute of Technology Draft of 1 August 1999 c 1999 Send comments to [email protected] ii Contents 1 Wetting Your Feet 1 1.1 Warmup problems 1 1.2 Scaling analyses 13 1.3 What you have learned 21 2 Dimensional Analysis 23 2.1 Newton’s law 23 2.2 Pendula 27 2.3 Drag in fluids 31 2.4 What you have learned 41 3 Materials I 43 3.1 Sizes 43 3.2 Energies 51 3.3 Elastic properties 53 3.4 Application to white dwarfs 58 3.5 What you have learned 62 4 Materials II 63 4.1 Thermal expansion 63 4.2 Phase changes 65 4.3 Specific heat 73 4.4 Thermal diffusivity of liquids and solids 77 4.5 Diffusivity and viscosity of gases 79 4.6 Thermal conductivity 80 4.7 What you have learned 83 5 Waves 85 5.1 Dispersion relations 85 5.2 Deep water 88 5.3 Shallow water 106 5.4 Combining deep- and shallow-water gravity waves 108 5.5 Combining deep- and shallow-water ripples 108 5.6 Combining all the analyses 109 5.7 What we did 109 Bibliography 110 1 1 Wetting Your Feet Most technical education emphasizes exact answers. If you are a physicist, you solve for the energy levels of the hydrogen atom to six decimal places. If you are a chemist, you measure reaction rates and concentrations to two or three decimal places. -
Metric Prefixes and Exponents That You Need to Know
Remember, the metric system is built upon base units (grams, liters, meters, etc.) and prefixes which represent orders of magnitude (powers of 10) of those base units. In other words, a single “prefix unit” (such as milligram) is equal to some order of magnitude of the base unit (such as gram). Below are the metric prefixes that you are responsible for and examples of unit equations and conversion factors of each. It does not matter what metric base unit the prefixes are being applied to, they always act in the same way. Metric prefixes and exponents that you need to know. Each of these 1 Tfl 1×1012 fl tera T = 1x1012 1 Tfl = 1x1012 fl or 1x1012 fl = 1 Tfl or have positive 1×1012 fl 1 Tfl exponents because each prefix is larger than the 1 GB 110× 9 B giga G = 1x109 1 GB = 1x109 B or 1x109 B = 1 GB or base unit 1×109 B 1 GB (increasing orders of magnitude). 6 Remember, the 1 MΩ 1×10 Ω mega M = 1x106 1 MΩ = 1x106 Ω or 1x106 Ω = 1 MΩ or power of 10 is 1×106 Ω 1 MΩ always written with the base unit 1 kJ 110× 3 J whether it is on kilo k = 1x103 1 kJ = 1x103 J or 1x103 J = 1 kJ or the top or the 3 1×10 J 1 kJ bottom of the Larger than the base unit base the than Larger ratio. 1 daV 1×101 V deka da = 1x101 1 daV = 1x101 V or 1x101 V = 1 daV or 1×101 V 1 daV -- BASE UNIT -- (meter, liter, gram, second, etc.) 1 dL 110× -1 L deci d = 1x10-1 1 dL = 1x10-1 L or 1x10-1 L = 1 dL or Each of these 1×10-1 L 1 dL have negative exponents because 1 cPa 1×10-2 Pa each prefix is centi c = 1x10-2 1 cPa = 1x10-2 Pa or 1x10-2 Pa = 1 cPa or smaller than the -2 1×10 Pa 1 cPa base unit (decreasing orders 1 mA 110× -3 A of magnitude). -
Lesson 2: Scale of Objects Student Materials
Lesson 2: Scale of Objects Student Materials Contents • Visualizing the Nanoscale: Student Reading • Scale Diagram: Dominant Objects, Tools, Models, and Forces at Various Different Scales • Number Line/Card Sort Activity: Student Instructions & Worksheet • Cards for Number Line/Card Sort Activity: Objects & Units • Cutting it Down Activity: Student Instructions & Worksheet • Scale of Objects Activity: Student Instructions & Worksheet • Scale of Small Objects: Student Quiz 2-S1 Visualizing the Nanoscale: Student Reading How Small is a Nanometer? The meter (m) is the basic unit of length in the metric system, and a nanometer is one billionth of a meter. It's easy for us to visualize a meter; that’s about 3 feet. But a billionth of that? It’s a scale so different from what we're used to that it's difficult to imagine. What Are Common Size Units, and Where is the Nanoscale Relative to Them? Table 1 below shows some common size units and their various notations (exponential, number, English) and examples of objects that illustrate about how big each unit is. Table 1. Common size units and examples. Unit Magnitude as an Magnitude as a English About how exponent (m) number (m) Expression big? Meter 100 1 One A bit bigger than a yardstick Centimeter 10-2 0.01 One Hundredth Width of a fingernail Millimeter 10-3 0.001 One Thickness of a Thousandth dime Micrometer 10-6 0.000001 One Millionth A single cell Nanometer 10-9 0.000000001 One Billionth 10 hydrogen atoms lined up Angstrom 10-10 0.0000000001 A large atom Nanoscience is the study and development of materials and structures in the range of 1 nm (10-9 m) to 100 nanometers (100 x 10-9 = 10-7 m) and the unique properties that arise at that scale. -
On Number Numbness
6 On Num1:>er Numbness May, 1982 THE renowned cosmogonist Professor Bignumska, lecturing on the future ofthe universe, hadjust stated that in about a billion years, according to her calculations, the earth would fall into the sun in a fiery death. In the back ofthe auditorium a tremulous voice piped up: "Excuse me, Professor, but h-h-how long did you say it would be?" Professor Bignumska calmly replied, "About a billion years." A sigh ofreliefwas heard. "Whew! For a minute there, I thought you'd said a million years." John F. Kennedy enjoyed relating the following anecdote about a famous French soldier, Marshal Lyautey. One day the marshal asked his gardener to plant a row of trees of a certain rare variety in his garden the next morning. The gardener said he would gladly do so, but he cautioned the marshal that trees of this size take a century to grow to full size. "In that case," replied Lyautey, "plant them this afternoon." In both of these stories, a time in the distant future is related to a time closer at hand in a startling manner. In the second story, we think to ourselves: Over a century, what possible difference could a day make? And yet we are charmed by the marshal's sense ofurgency. Every day counts, he seems to be saying, and particularly so when there are thousands and thousands of them. I have always loved this story, but the other one, when I first heard it a few thousand days ago, struck me as uproarious. The idea that one could take such large numbers so personally, that one could sense doomsday so much more clearly ifit were a mere million years away rather than a far-off billion years-hilarious! Who could possibly have such a gut-level reaction to the difference between two huge numbers? Recently, though, there have been some even funnier big-number "jokes" in newspaper headlines-jokes such as "Defense spending over the next four years will be $1 trillion" or "Defense Department overrun over the next four years estimated at $750 billion". -
Time and Frequency Users' Manual
,>'.)*• r>rJfl HKra mitt* >\ « i If I * I IT I . Ip I * .aference nbs Publi- cations / % ^m \ NBS TECHNICAL NOTE 695 U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards Time and Frequency Users' Manual 100 .U5753 No. 695 1977 NATIONAL BUREAU OF STANDARDS 1 The National Bureau of Standards was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology and facilitate their effective application for public benefit To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, a technical (3) basis for equity in trade, and (4) technical services to pro- mote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research the Institute for Applied Technology, the Institute for Computer Sciences and Technology, the Office for Information Programs, and the Office of Experimental Technology Incentives Program. THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consist- ent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essen- tial services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of the Office of Measurement Services, and the following center and divisions: Applied Mathematics -
NSF Sensational 60
Cover credits Background: © 2010 JupiterImages Corporation Inset credits (left to right): Courtesy Woods Hole Oceanographic Institution; Gemini Observatory; Nicolle Rager Fuller, National Science Foundation; Zee Evans, National Science Foundation; Nicolle Rager Fuller, National Science Foundation; Zina Deretsky, National Science Foundation, adapted from map by Chris Harrison, Human-Computer Interaction Institute, Carnegie Mellon University; Tobias Hertel, Insti- tute for Physical Chemistry, University of Würzburg Design by: Adrian Apodaca, National Science Foundation 1 Introduction The National Science Foundation (NSF) is an independent federal agency that supports fundamental research and education across all fields of science and engineering. Congress passed legislation creating the NSF in 1950 and President Harry S. Truman signed that legislation on May 10, 1950, creating a government agency that funds research in the basic sciences, engineering, mathematics and technology. NSF is the federal agency responsible for nonmedical research in all fields of science, engineering, education and technology. NSF funding is approved through the federal budget process. In fiscal year (FY) 2010, its budget is about $6.9 billion. NSF has an independent governing body called the National Science Board (NSB) that oversees and helps direct NSF programs and activities. NSF funds reach all 50 states through grants to nearly 2,000 universities and institutions. NSF is the funding source for approximately 20 percent of all federally supported basic research conducted by America’s colleges and universities. Each year, NSF receives over 45,000 competitive requests for funding, and makes over 11,500 new funding awards. NSF also awards over $400 million in professional and service contracts yearly. NSF has a total workforce of about 1,700 at its Arlington, Va., headquarters, including approximately 1,200 career employees, 150 scientists from research institutions on temporary duty, 200 contract workers and the staff of the NSB office and the Office of the Inspector General. -
Chapter 3: Numbers in the Real World Lecture Notes Math 1030 Section B
Chapter 3: Numbers in the Real World Lecture notes Math 1030 Section B Section B.1: Writing Large and Small Numbers Large and small numbers Working with large and small numbers is much easier when we write them in a special format called scientific notation. Scientific notation Scientific notation is a format in which a number is expressed as a number between 1 and 10 multiplied by a power of 10. Ex.1 one billion = 109 (ten to the ninth power) 6 billion = 6 × 109 420 = 4.2 × 102 0.5 = 5 × 10−1 Ex.2 Numbers in Scientific Notation. Rewrite each of the following statement using scientific notation. (1) The U.S. federal debt is about $9, 100, 000, 000, 000. (2) The diameter of a hydrogen nucleus is about 0.000000000000001 meter. Approximations with Scientific Notation Approximations with scientific notation We can use scientific notation to approximate answers without a calculator. Ex.3 Approximate 5795 × 326. 1 Chapter 3: Numbers in the Real World Lecture notes Math 1030 Section B Ex.4 Checking Answers with Approximations. You and a friend are doing a rough calculation of how much garbage New York City residents produce every day. You estimate that, on average, each of the 8 million residents produces 1.8 pounds or 0.0009 ton of garbage each day. Thus the total amount of garbage is 8, 000, 000 person × 0.0009 ton. Your friend quickly presses the calculator buttons and tells you that the answer is 225 tons. Without using your calculator, determine whether this answer is reasonable. -
Orders of Magnitude (Length) - Wikipedia
03/08/2018 Orders of magnitude (length) - Wikipedia Orders of magnitude (length) The following are examples of orders of magnitude for different lengths. Contents Overview Detailed list Subatomic Atomic to cellular Cellular to human scale Human to astronomical scale Astronomical less than 10 yoctometres 10 yoctometres 100 yoctometres 1 zeptometre 10 zeptometres 100 zeptometres 1 attometre 10 attometres 100 attometres 1 femtometre 10 femtometres 100 femtometres 1 picometre 10 picometres 100 picometres 1 nanometre 10 nanometres 100 nanometres 1 micrometre 10 micrometres 100 micrometres 1 millimetre 1 centimetre 1 decimetre Conversions Wavelengths Human-defined scales and structures Nature Astronomical 1 metre Conversions https://en.wikipedia.org/wiki/Orders_of_magnitude_(length) 1/44 03/08/2018 Orders of magnitude (length) - Wikipedia Human-defined scales and structures Sports Nature Astronomical 1 decametre Conversions Human-defined scales and structures Sports Nature Astronomical 1 hectometre Conversions Human-defined scales and structures Sports Nature Astronomical 1 kilometre Conversions Human-defined scales and structures Geographical Astronomical 10 kilometres Conversions Sports Human-defined scales and structures Geographical Astronomical 100 kilometres Conversions Human-defined scales and structures Geographical Astronomical 1 megametre Conversions Human-defined scales and structures Sports Geographical Astronomical 10 megametres Conversions Human-defined scales and structures Geographical Astronomical 100 megametres 1 gigametre -
Chapter 1 - the Numbers of Science
Chapter 1 - The Numbers of Science 1.1 Orders of Magnitude and Scientific Notation What does it mean when we say something increases by an order of magnitude? Does it mean the value doubles, triples, or eve quadruples? When we say something has increased by and order of magnitude, we mean that it has changed by a factor of 10. If something increased by two orders of magnitude, it increased by 10 x 10 = 102 =100.. And increase of three orders of magnitude would be 10 x 10 x 10 = 103 = 1000, etc. Activity 1.1 How much stronger ws the 2011 Japan earthquake than the 2001 Nisqually earthquake? One of the ways seismologists measure the magnitude of an earthquake is with the Richter scale. First developed by Charles Richter in 1935, while studying earthquakes in California, the Richter scale has become the predominant way we talk about the magnitude of an earthquake. The 2011 earthquake in Japan measured 9:0 on the Richter scale, while the 2001 Nisqually earthquake registered at 6.8 magnitude. Clearly, the earthquake in Japan was stronger, but how much stronger? Each increase of 1 on the Richter scale corresponds to an increase of 10 in the intensity of the earthquake. See Table 1. Table 1: Earthquake Magnitude and Relative Increase Magnitude Relative increase in energy over a magnitude 1 earthquake 1 1 2 10 3 100 4 1000 5 10,000 6 100,000 7 1,000,000 8 10,000,000 9 100,000,000 1. With a partner, compare the difference in strength between the earthquake in japan the the Nisqually earthquake.