Published at Saturday, October 05th, 2019 - 05:18:36 AM. Kids Worksheet. By Yolanda Charrier.
If you do want to produce your own worksheets and do not have the Microsoft software, you can download free tools like OpenOffice or use an online word processor or spreadsheet such as the free Google Docs which help you do similar tasks. You just need to create a table with as many rows and columns as you need and then type in some numbers before printing it off for your children to practice - depending on the level of complexity choose single digits or multiple digits. If you are not sure what level to start at, aim low, start with easy numbers and see how your child goes, the self-esteem boost they will get from acing the first worksheet will give them confidence for more difficult math problems.
Most of even beginning algebra depends on being able to do two things--one, doing multiplication quickly and accurately in your head, two, knowing how to add, subtract, multiply, and divide fractions. You might remember a concept in algebra called factoring. Factoring means breaking up into parts that are multiplied together to give you the whole. You can factor numbers. For instance, 6 factors into 2 and 3--2x3 =6. In elementary algebra we learn to factor expressions such as x^2+4x+4. This particular expression is easily factor-able into (x+2)^2. If this does not make any sense to you, do not worry about it. Just trust me, if you do not know your multiplication tables, you can not factor. If you can not factor, you will not do well at all in algebra, geometry, or trigonometry.
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Chuck It! is a fun and fast paced game that builds fluency and problem solving skills. This game is quick and easy to prep and will become a part of your classroom routine in no time! This is a great cooperative way to warm up for a Math lesson, end a lesson when you still have a few minutes before the bell, or to use for an entire Math Lesson to build those fluency skills in addition, subtraction, multiplication, and division! I have used this game for years in 3rd, 5th, and 7th grade classrooms! The children beg to play!!!


Calc 4.4b The Average (Mean) Value of a Function
H.S. Math Instructor
9 years ago
The Average (Mean) Value of a Function
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The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:
Answer: Option D
Let the speed of two trains be 7x and 8x km/hr.
Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.


A Purely Visual Guide to Completing the Square
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A course focusing on the fundamental techniques and applications of linear algebra including vector and matrix algebra, vector representation of lines and planes, projections, Gaussian elimination, eigenvectors and complex numbers. 160.102, alongside 160.101, forms a foundation for further study in mathematics. It is essential for students intending to study Mathematics, Physics, Food Technology or Engineering, or for anyone who wants a strong mathematical component to their degree.
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Problem. Decide if a proportional relationship is present in each of the following situations. If so, describe the relationship and use it to solve the problem.
a. In one small office within a corporation, 6 out of 9 management positions are held by women. If that rate holds throughout the corporation, how many of the 180 management positions are held by women?
b. One inch is the same length as 2.54 cm. About how many inches is 75 cm?
c. If the length of a side of a triangle is 3 in. and its area is 9 sq. in., what is the length of the corresponding side of a similar triangle whose area is 36 sq. in.?
d. The scale on a road map is 1 inch = 20 miles. How many miles are there between two cities 11.5 inches apart on a map?


"Count, Colour, Cut & Combine!"
Your WHOLE class will be ENGAGED in a coin counting colouring quest!
Every student gets a different worksheet
representing a small piece of the bigger picture. Students tally the total for each money amount shown (betwee $0.05 and $0.99) then use their answers to colour-by-number their section of the mystery mosaic. When the work is done, the coloured sheets are put together to reveal the large pixel Olympic Rings image. It will look great hanging up in the hallway or on your classroom wall.
This mosaic is geared toward the grade 2 Ontario curriculum for the Number Sense and Numeration Strand:
◾ Represent, compare, and order whole numbers to 100, including money amounts
to 100¢, using a variety of tools (e.g., ten frames, base ten materials, coin manipulatives, number lines, hundreds charts and hundreds carpets)
◾ Estimate, count, and represent (using the ¢ symbol) the value of a collection of coins with a maximum value of one dollar.
◾Both .pdf format, and editable .docx format
◾Class set of 24 unique worksheets. There are 12 money amounts shown on every worksheet.
◾Master Answer Key provided for easy assessment.
◾Coloured mosaic image as a guide to help you assemble the big picture!
This would make great supply teacher work too!
If you like this product, be sure the check out the whole Collaborative Math Mosaic directory, sorted by topic!
Leave the picture a secret or show it for motivation… it’s your call.
Encourage students to check their answers by finding them in the randomized list on their worksheets before they colour each square. This will increase the accuracy of the final picture!
All my "Colouring by..." worksheets use standard pencil-crayon colours found in the Crayola 24 pack. For best results, use the exact colour name match, and stick to one colouring medium. Perhaps a class set of pencil crayons would be a fun math department investment!
I’d love and appreciate any feedback, suggestions, and frontline stories you can share!!
@CalfordMath on Facebook & Twitter
/CalfordMath on Pinterest


This resource, from the National Countil of Teachers of Mathematics, shares Activities with Rigor and Coherence (ARC) for a range of grade levels from kindergarten through high school. Each ARC is a series of lessons that addresses a mathematical topic and demonstrates the vision of Principles to Actions: Ensuring Mathematical Success for All.
ARCs scaffold effective teaching and support enactment of the eight Mathematics Teaching Practices articulated in Principles to Actions as well as the instructional guidance set forth in 5 Practices for Orchestrating Productive Mathematics Discussions. ARCs also include community features that offer opportunities for social interaction. Engage in online discussions with other math educators, post a comment, and give feedback with ratings and reviews.


Search Results for "number ninja"
Rainbow Price: $19.99
Practice the ancient art of Mathjitsu, Kar-add-e, Tai-sub-tract. And please, make sure to do it with friends. In this ninja-styled game, your mission is to navigate your ninja through the treacherous game board by using the four basic math operations. A Ninja Recruit will have an easier time with the riddles, but may not move as fast across the board. A Ninja Mathster - I mean Master - will have the addition of multiplication and division dice to roll with, giving a mobility edge, but the challenges are harder. Once you make it to one of the four "Number Ninja challenge cards", you must answer a math riddle in order to unlock a piece of the Golden Dragon. In one card, Yamamoto's aunt may have kites to sell, or Fujimoto is taking pictures of animals in his back yard, requiring you to use a mix of math operations to solve the problem. Who cares if Oshima is counting tiger stripes? You do. It could mean the difference between victory and defeat! ~ Stephen
Rainbow Price: $14.99
When children are young, we teach them to recognize sequences, shapes, and patterns as prerequisites to math – important skills to build upon. This book from The Critical Thinking Company incorporates some fun puzzles to work with children at the fifth to seventh grade level to really get them thinking about math functions. Five different types of puzzles make the math exploration challenging – Pattern Predictor, Equality Explorer, Sequence Sleuth, Number Ninja, and Function Finder. There are eight of each type for a total of 40 puzzles that become progressively more difficult. Pattern Predictor asks the student to look at a pattern of shapes and predict where the pattern will be in future stages. Equality Explorer is like Balance Benders (also by Critical Thinking Press) where the student sees a series of balances with shapes on one side and a number on the other – the student has to figure out the value of each shape in order to equal the number on the other side (balancing equations). Sequence Sleuth shows a sequence of patterns, objects, letters, etc. and asks a series of questions in which the student is to determine future stages in the sequence based upon what they can already see. Number Ninja lays out a series of operations and tells you a starting or ending number. Based on the operations you have to determine the missing start or finish number. The fifth type of puzzle is the Function Finder in which the student is to determine what functions are being employed given the example presented – look for a pattern and understand it. An example of this last puzzle would be 6♦7=43, 8♦3=25, 9♦10=91, 2♦5=11. Based on the mystery function offered here, what would the answers be to 5♦9 and 16♦3? The mystery functions would be multiply and add one, so the answers would be 46 and 49, consecutively.
Hints for solving the puzzles and solutions are offered at the back of the book. These are very helpful when you get stuck.
I know this book says that it is for 5th – 7th grade, but I feel like the number-brain exercises in these puzzles would be good for even high school and adults. I have completely enjoyed working the puzzles in this book. Like other Critical Thinking products, this book is reproducible for classroom and family use. ~ Donna


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A modern calculator is needed for all kinds of research. Our collection of tools allows you to perform calculations with fractions, calculate logarithms and trigonometric functions, solve quadratic equations, and much more. No matter your math problem, your calculator is now always close at hand.
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Significant figures are essential in various situations. Here, we determine the rules of sig figs and how we can apply them in the real world.
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Least common denominator calculator, or LCD calculator, determines the lowest common denominator of integers, mixed numbers, and fractions.
The modulo calculator finds the remainder of the division of two rational/irrational positive/negative numbers. You can also find out how to find modulus manually.
This volume calculator uses a density formula ρ = m/V to find densities of different substances and objects. It calculates the third one for two given values - density, mass, or volume of a substance.
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Online hex calculator performs hex math operations and conversions. Hex addition, hex subtraction, hex multiplication, hex division became fast & easy
The tank volume calculator finds the total volume of various tank shapes in gallons, liters, and cubic meters. It calculates the liquid volume of partially filled tanks.
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PEMDAS calculator solves mathematical expressions with the order of operations - brackets, exponents, multiplication, division, addition, and subtraction.
Kinetic energy calculator easily finds kinetic energy, mass or velocity with the kinetic energy formula KE = 1/2 mv². Easy to use KE calculator.
Cube root calculator finds the principal (real) cube root of positive and negative numbers and the imaginary cube roots of the given number.
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Adding and subtracting integers calculator allows adding and subtracting positive and negative integers and decimals, demonstrating the solution algorithm.
The significant figure rounder rounds numbers to the required quantity of significant figures. It works with a standard number format, e-notation, and scientific notation.
Free online velocity calculator solves for v, u, a or t using velocity formula. Calculate the final velocity (v) using the equation v = u + at.
Easy to use force calculator helps determine the unknown variable in the force equation (F = ma). Force = mass × acceleration.
These calculators find the distance between two points on a 2D plane, in a 3D space, as well as along the surface of the Earth with Lambert’s formulas.
The percent to fraction calculator converts the given percentages into fractions. If the percent value exceeds 100, the calculator performs percent to mixed number conversion.
Pythagorean theorem calculator finds the unknown side length of a right triangle. It also calculates angles, area, perimeter, and altitude to hypotenuse.
The percentage decrease calculator finds a percentage decrease from the starting value to the final value and identifies whether the change is an increase or a decrease.
The ratio calculator finds a missing ratio number based on the given proportion. The calculator can also scale ratios, enlarging or shrinking them.
Quadratic Equation Calculator is a free tool that provides a detailed solution to quadratic equations by supplying the values of a, b and c.


This section of the Grill can set up to 32 guests. We can seat up to 14 people per table. It is an excellent space for small intimate groups.
Groups larger than this will be seated on a number of tables next to each other. The maximum set up of this room is made up of 2 tables of 6 guests and 4 tables of 5 guests.


Can mathematics provide fundamental contributions to biology? The example of topology
- Harald Jockusch (Entwicklungsbiologie und Molekulare Pathologie, Universität Bielefeld)
Contributions of mathematics to biology can be of very different kinds: supportive, as in data analysis (statistics, approximations); challenging, by suggesting quantitative models that can be falsified; inspiring, by suggesting novel qualitative features that remain to be discovered in "real life". I will discuss this topic from the subjective viewpoint of a biologist, using examples from developmental biology and morphogenesis and their interpretation by topology.


We discuss the advantages of using Julia for solving multiscale problems involving partial differential equations (PDEs). Multiscale problems are problems where the coefficients of a PDE oscillate rapidly on a microscopic length scale, but solutions are sought on a much larger, macroscopic domain. Solving multiscale problems requires both a theoretic result, i.e., a homogenization result yielding effective coefficients, as well as numerical solutions of the PDE at the microscopic and the macroscopic length scales.
Numerical homogenization of PDEs with stochastic coefficients is especially computationally expensive. Under certain assumptions, effective coefficients can be found, but their calculation involves subtle numerical problems. The computational cost is huge due to the generally large number of stochastic dimensions.
Multiscale problems arise in many applications, e.g., in uncertainty quantification, in the rational design of nanoscale sensors, and in the rational design of materials.
Our code for the numerical stochastic homogenization of elliptic problems is implemented in Julia. Since multiscale problems pose new numerical problems, it is in any case necessary to develop new numerical codes. Julia is a dynamic language inspired by the Lisp family of languages, it is open-source, and it provides native-code compilation, access to highly optimized linear-algebra routines, support for parallel computing, and a powerful macro system. We describe our experience in using Julia and discuss the advantages of Julia’s features in this problem domain.


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Tracey is contemplating the purchase of 100 shares of a stock selling for 15 per share. The stock pays no dividends. Her broker says that the stock will be worth 20 per share in 2 years. What is the annual rate of return on this investment?


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1995 jayco eagle 310 fs ssMultiplication Worksheets: Multiplication Grids. Grid problem multiplication worksheets for introducing multiplication and discovering patterns in multiplication problems (Answer keys to these sheets make a great multiplication fact chart!) Improve your math knowledge with free questions in "Multiplication tables for 2, 3, 4, 5, and 10" and thousands of other math skills. Save time with these multiplication worksheets for grade 3 student. Our product collection below includes various worksheets, coloring pages, mystery pictures, and other activities on multiplying numbers. You'll find these products helpful, fun and delightful for your students. Choose the perfect material for your clas
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This guide to a fifth grade math curriculum is a reference tool for Time4Learning parents. Time4Learning is an online learning system for homeschool education, enrichment, tutoring, or for sharpening summer skills. We provide 5th grade math worksheets and 5th grade math games in a total curriculum. 1 12 Multiplication Table. Showing top 8 worksheets in the category - 1 12 Multiplication Table. Some of the worksheets displayed are Five minute timed drill with 100, Multiplication work multiplication facts tables in, Multiplication work, Grade 3 multiplication work, Multiplication table, Blank multiplication table, Grade 3 multiplication work, Multiplication table.
Dl 44 application pdfIXL Math Workbook, Grade 3. Your child will love to practice math with this fun, vibrant workbook! Created by IXL, a trusted leader in math education, this workbook covers the must-know skills for third graders, from multiplication and fractions to geometry and measurement. Practice multiplication facts for 5. This is the first in the series of multiplication facts (or times table) for numbers up to 10. It is important that the kids know multiplication facts of all single digit numbers from memory at the end of this grade, as it forms the base for multi digit multiplication in the next grade.Multiplication Worksheets: Bullseye Multiplication. Get on target with those multiplication math facts! These fun multiplication worksheets provide some additional kinesthetics over and above your usual math fact practice. If you are looking for a fun or interesting practice worksheet, or just need to change things up a bit, these unique ...


The volume recorded in February this year was 25 percent higher than the volume recorded in February 2019 (5.24 million gallons).
Sales in February this year was slightly lower than sales in January (6.83 million gallons). However, this could be atrributed to the fact that February is a shorter month and January and there were fewer stations reporting in February. In January, there were 286 stations reporting. In February, there were 282 stations.
Nonethless, the daily average volume sold in February was 227,193 gallons while the daily average volume sold in January was 220,405 gallons.
On a cumulative basis, E15 sales in Minnesota in the first two months of the year was 13.42 million gallons.
In 2019, a record 78.52 million gallons of E15 was sold in Minnesota, 32 percent higher than the volume sold in 2018 (59.4 million gallons).


Table of Contents :
Top Suggestions Short Division Worksheet Math :
Short Division Worksheet Math Children use their math skills to solve real life problems in this division worksheet learners will find the answers to multi step word problems using addition subtraction and long division Whichever way you write the remainder you can use the short division method bus stop method to help you solve the answer a bakery bakes doughnuts in a day doughnuts are put in boxes of 4 Here you will find a video and a quiz about multiplication and division try them out and then test your knowledge with a short quiz before have a go at this worksheet from maths whizz.
Short Division Worksheet Math Kids will get the phonics practice they need with these short u long u worksheets this one features a unicorn a duck and some bugs to help kids understand all the different sounds the letter u can Math facts in a flash is exactly what its simple title sounds like straightforward web based practice designed to strengthen students fluency in basic math concepts like addition subtraction Working parenthood was hard enough before covid 19 and now it s an all out crisis but as we exit the pandemic we don t.
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Division Worksheets Free Math Worksheets
Welcome To The Division Worksheets Page At Math Drills Please Give Us Your Undivided Attention While We Introduce This Page Our Worksheets For Division Help You To Teach Students The Very Important Concept Of Division If Students Have A Good Recall Of Multiplication Facts The Division Facts Should Be A Breeze To Teach If You Want Your Students To Experience Success In Learning
Short Division Worksheets Free Printables Education
This Short Series Of Pages Asks Your Child To Divide Numbers By Five 10 Or 15 Ease Into Division With This Worksheet That Shows The Relationship Between Multiplication And Division Children Become Familiar With Key Division Symbols And Terms In This Division Fundamentals Worksheet
Short Division Worksheets Maths Resource Twinkl
These Worksheets Aim To Teach Your Children The Principles Of Short Division And Help Them Put It Into Practice It Also Includes Some Long Division Exercises For Students Of More Advanced Ability It Also Includes An Answer Sheet For Easy Marking This Worksheet Is An Excellent Way To Refresh Your Child S Knowledge Of Division But The More They Practice Short Division The Better Give Them Simple Problems To Solve Off The Top Of Their Heads Showing You Re Truly Engaged In Their Learning
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These Short Division Worksheets Are Configured In A Horizontal Problem Format The Numbers For The Divisors May Range From 2 Through 9 For These Division Worksheets The Number Of Digits In The Quotients May Be Varied From 1 To 3 Digits For These Division Worksheets You May Also Select How May Digits Will Be In The Dividend As Well The Short Division Problems May Be Configured With No Remainders All Remainders Or Mixed Remainders The Answer Key Can Be Displayed With A Remainder Or As A
Ks2 Short Division Practice Worksheet Classroom Resource
These Teacher Made Ks2 Maths Worksheets Are Designed To Help Students Hone Their Short Division Skills And Reinforce Your Teachingplete With 16 X Differentiated Short Division Sums Squares For Working And A Full Answer Sheet These Worksheets Are A Great Way Of Gauging The Progress Of Your Pupils And Highlighting Any Areas That Need Further Attention These Division Worksheets Have Been Made With Year 5 Children In Mind But They D Also Work For Ted Lks2 Pupils Or Older Children InFree Printable Division Worksheets Math Fun Worksheets
Understand Division As The Inverse Of Multiplication Using Our Picture Division Exercises Quick Links To The Topics Listed Below For Free Printable Division Worksheets Division Tables Long Division Without Remainder Long Division With Remainder Horizontal Number Division Division ActivitiesDivision Worksheets Free And Printable
The Division Worksheets Motivate Kids Of Grade 3 Grade 4 And Grade 5 And Help Them See The Real Life Benefits Division Skills Can Bring Them And Help Build Those Skills Included Here Are Division Times Tables And Charts Various Division Models Division Facts Divisibility Rules Timed Division Drills Worksheets With Grid Assistance Basic And Advanced Division Multiplication And DivisionShort Division By 2 Digits Worksheets Kiddy Math
Short Division By 2 Digits Displaying Top 8 Worksheets Found For This Concept Some Of The Worksheets For This Concept Are Short Division 2 Digit By 1 Digit Maths Work From Mathematics Division Witho Ut Remainder 2 Digit By 1 Digit S1 Division Work Long Division Division Short Division 3s 4s 6s No Remainders Booster Dividing Whole Numbers By Two Digit Divisors
Short Division 3 Digit By 1 Digit Worksheets Free
In These Worksheets Children Will Practice Short Division Division By A Single Digit Numeber With No Remainder I E Answer Is A Whole Number Times Tables Are Very Important For Short Division The Dividend In All These Questions Is A 3 Digit Number
Division Worksheets For Grades 3 4 And 5 Homeschool Math
These Are Free Printable Division Worksheets Randomly Generated For Grades 3 5 Topics Include Division Facts Mental Division Long Division Division With Remainders Order Of Operations Equations And Factoring
Short Division Worksheet Math. The worksheet is an assortment of 4 intriguing pursuits that will enhance your kid's knowledge and abilities. The worksheets are offered in developmentally appropriate versions for kids of different ages. Adding and subtracting integers worksheets in many ranges including a number of choices for parentheses use.
You can begin with the uppercase cursives and after that move forward with the lowercase cursives. Handwriting for kids will also be rather simple to develop in such a fashion. If you're an adult and wish to increase your handwriting, it can be accomplished. As a result, in the event that you really wish to enhance handwriting of your kid, hurry to explore the advantages of an intelligent learning tool now!
Consider how you wish to compose your private faith statement. Sometimes letters have to be adjusted to fit in a particular space. When a letter does not have any verticals like a capital A or V, the very first diagonal stroke is regarded as the stem. The connected and slanted letters will be quite simple to form once the many shapes re learnt well. Even something as easy as guessing the beginning letter of long words can assist your child improve his phonics abilities. Short Division Worksheet Math.
There isn't anything like a superb story, and nothing like being the person who started a renowned urban legend. Deciding upon the ideal approach route Cursive writing is basically joined-up handwriting. Practice reading by yourself as often as possible.
Research urban legends to obtain a concept of what's out there prior to making a new one. You are still not sure the radicals have the proper idea. Naturally, you won't use the majority of your ideas. If you've got an idea for a tool please inform us. That means you can begin right where you are no matter how little you might feel you've got to give. You are also quite suspicious of any revolutionary shift. In earlier times you've stated that the move of independence may be too early.
Each lesson in handwriting should start on a fresh new page, so the little one becomes enough room to practice. Every handwriting lesson should begin with the alphabets. Handwriting learning is just one of the most important learning needs of a kid. Learning how to read isn't just challenging, but fun too.
The use of grids The use of grids is vital in earning your child learn to Improve handwriting. Also, bear in mind that maybe your very first try at brainstorming may not bring anything relevant, but don't stop trying. Once you are able to work, you might be surprised how much you get done. Take into consideration how you feel about yourself. Getting able to modify the tracking helps fit more letters in a little space or spread out letters if they're too tight. Perhaps you must enlist the aid of another man to encourage or help you keep focused.
Short Division Worksheet Math. Try to remember, you always have to care for your child with amazing care, compassion and affection to be able to help him learn. You may also ask your kid's teacher for extra worksheets. Your son or daughter is not going to just learn a different sort of font but in addition learn how to write elegantly because cursive writing is quite beautiful to check out. As a result, if a kid is already suffering from ADHD his handwriting will definitely be affected. Accordingly, to be able to accomplish this, if children are taught to form different shapes in a suitable fashion, it is going to enable them to compose the letters in a really smooth and easy method. Although it can be cute every time a youngster says he runned on the playground, students want to understand how to use past tense so as to speak and write correctly. Let say, you would like to boost your son's or daughter's handwriting, it is but obvious that you want to give your son or daughter plenty of practice, as they say, practice makes perfect.
Without phonics skills, it's almost impossible, especially for kids, to learn how to read new words. Techniques to Handle Attention Issues It is extremely essential that should you discover your kid is inattentive to his learning especially when it has to do with reading and writing issues you must begin working on various ways and to improve it. Use a student's name in every sentence so there's a single sentence for each kid. Because he or she learns at his own rate, there is some variability in the age when a child is ready to learn to read. Teaching your kid to form the alphabets is quite a complicated practice.
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Conduct a quantitative analysis of a data sample provided by the instructor; write a hypothesisUsing the NoNameSchoolData, answer the following questions:1. What is the average English MCAS scaled score for girls in grades 4-5?2. What is the standard deviation?3. What scaled score is 1 standard deviation below the mean for these students? Students who score at this level are in what percentile for their group?4. What scaled score is 1 standard deviation above the mean for these students? Students who score at this level are in what percentile for their group?5. Taking the answers to #3 and 4, what percent of students have a score between these 2 limits?6. Repeat questions 1-5 for boys in grades 4-5.7. Which cohort (boys or girls) had the highest mean English MCAS score? Is the difference significant (p < .05)?8. What is the correlation between the boys English MCAS scores and their behavior (grades 4-5)?9. What is the correlation between the boys English MCAS scores and their attendance (grades 4-5)?10. Describe the relationship between race and English MCAS performance levels in grade 4-5.11. Based on what you found in #10, write a hypothesis which offers an explanation for the results and might be tested with data found in this spreadsheet. Test your hypothesis; what is the result?Questions on Probability1. Imagine rolling one die (with the numbers 1,2,3,4,5,6 on each side) 60 times in a row.• What is the probability that you would roll a 6 with all these tosses?• If you were to graph the data, on the graph below, what would the line look like?Results(number of times each number appears)1 2 3 4 5 6Number on the die• Is this a normal curve? Why not?2. The average height of all the students at UMass Boston is 65 inches. The standard deviation is 3 inches. Use the Normal Curve Calculator to find the answers below.• What is the probability of finding a student on the campus who is 60” tall or shorter?• What is the probability that all the students are six feet tall or shorter?• What is the probability of finding students that are more than 6 feet tall?• What is the probability of finding students that are 65 inches or shorter?• What is the probability of finding students that are 65 inches or taller?3. What proportion of all the students will be between 62 and 68 inches tall?4. What proportion of all the students will be between 59 and 71 inches tall?Descriptive Statistics Questions on NoNameSchool Data1. What is the mean of the 7th grade boys’ scaled Math MCAS score? Is this larger or smaller than the girls’ average?2. What was the median behavioral referrals for 7th grade boys last year? How does this compare to the girls’ median? Why is the median the best choice for comparing behavioral referrals (rather than the mean or mode)?3. What is the mode for 7th grade boys racial identity? How about the girls? Why do we use mode for racial categories instead of mean or median? Name another variable on this spreadsheet that would be appropriate for the mode.4. Question (honor system): were you able to calculate these answers using the spreadsheet formulas or did you calculate these manually?5. What is the variance for the 7th grade boys scaled Math MCAS scores last year? How does this compare to the girls’ variance?6. What is the standard deviation for the 7th grade boys scaled Math MCAS scores last year? How does this compare to the girls’ standard deviation?Challenge question: Calculate the z-scores on the boys’ Math MCAS results for 2012. Compare the mean z-scores by racial category (Asian, black, Hispanic, white). What does this tell you?Questions on the NoNameSchoolData spreadsheet:1. Is this quantitative or qualitative data? Why?2. Which of the 4 categories of school data are presented here?3. Would it be possible to add school processes data? Give examples. What are some examples that might not fit in this spreadsheet?4. Would it be possible to add perception data? Give examples. What are some examples that might not fit in this spreadsheet?Take the spreadsheet and perform the following exercises. You can answer questions 13– 19 on the same document as questions 1 – 4.You should turn in 2 documents for this assignment: written answers to questions 1 – 4 and 13 – 19 and then also the revised spreadsheet following steps 5 – 12 below.Excel PracticeSkills to address:5. Narrow the race column so it doesn’t take up so much space6. Widen the Behavioral Referrals column so the column heading is more readable7. Change the alignment of the column headers to 60 degrees8. Give the ID numbers a left margin alignment9. Change the page orientation to landscape (is it possible to get columns A-T all on one page?)10. Freeze the pane so the top row and left column do not move11. Hide columns K, L, M, N12. Highlight row 25 in yellow.13. How many students scored at the Proficient or Advanced level on the 2012 Math MCAS?14. How many students in grade 8 scored at the Proficient or Advanced level on the 2012 Math MCAS?15. How many Hispanic students in grade 8 scored at the Proficient or Advanced level on the 2012 Math MCAS?16. How does this last number compare with Black, Asian and White students?17. What can you learn about gender differences, by race, for students in grade 8 on the 2012 Math MCAS?18. What is the mean Math scaled score for Black 8th grade girls? What is the median? What is the mode?19. What is the S.D.?


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Displays various statistical information for each question. This report is useful for gaining a better understanding of the distribution of respondents’ answers and how they relate to the entire population.
The Item Statistics report displays the following statistics for each question:
Question: sample size and number excluded
Summary Statistics: mean, variance, standard deviation and standard error
Descriptive Statistics: skewness, kurtosis, T value, mean absolute deviation
Percentiles: 25th and 75th percentiles, median and inter quartile range
Values: minimum, maximum and range
Confidence Intervals: upper and lower bound estimates for a 95% and for a 99% confidence interval


Ok, there’s a new trailer for Avengers: Age of Ultron. A new trailer means a new analysis. I am going to pick the scene that shows the Avengers jumping out of a jeep during some type of fight in a snow covered forest. Why are they in the forest? Who are they fighting? Why are some of them riding in a jeep? I have no idea about these questions. All I can do is analyze the motion of these superheroes. That’s what I’m going to do.
Let me start by looking at the motion of Black Widow during this scene. The camera does pan a bit, so I will use Tracker Video Analysis (free and awesome) to compensate for this background motion. Here is the same scene with a stationary camera.
The one other thing I need is a scale. Thor and Black Widow are fairly close to each other so I will use the size of Thor (Chris Hemsworth is 1.9 meters tall). With that, I get the following for the horizontal motion of Black Widow.
It’s clear that the end of the scene is in slow motion. I bet they used the iPhone 6 to record this part of the movie. If I assume the first part of the motion is in real-time, I can fit a linear function to the position-time graph and get the horizontal velocity with a value of 8.88 m/s (about 20 mph).
When a person is off the ground, there is essentially only one force on that person – the gravitational force. Since this force is in the vertical direction, there is zero force in the horizontal direction. And this is why the horizontal velocity is constant. Now, going back to the data I can look at the slope of the later part of the function. This says the horizontal speed is 1.41 m/s. However, this isn’t in “seconds” but some slowed down time unit (I will call it s‘). Since I know the horizontal speed should be constant, I can set the before and after speeds equal to each other.
This means the slow motion part of the video is 6.3 times slower than real-speed (assuming the beginning is in real speed).
Now let’s look at the vertical motion. It isn’t as pretty for three reasons. First, it’s accelerating in the vertical direction – so no straight lines. Second, there is that time in frame rate in the slow motion part. Third, the Black Widow doesn’t move up and down that much. This means that any smaller error in marking a point looks more dramatic.
There is one way I can fix the problem with the changing time – don’t plot time. I could just plot the trajectory of Black Widow (y vs x instead of y vs t). Since the trajectory doesn’t show the time, you don’t have problems with the slow motion vs. regular motion. However, dealing with a trajectory equation is a little bit more difficult that y vs. time. Let me fix it another way.


This unit provides students with the opportunity to measure various objects and use their data to determine area, volume, radius, diameter, and density. They will use Math rulers, protractors, and Vernier Calipers to make their measurements rounding to four different scales. They will measure the radius and diameter of a cylinder and use Pi to calculate the area of various cylindrical objects. Students will measure the circumference and determine the surface area of a sphere and using the thickness of the wall of a hollow sphere, determine the volume inside the sphere as well. The mathematical skills emphasized in Intermediate Level Measurement are measuring, collecting data, and calculating for volume, area, and density.
This collection is available as downloadable PDFs, but portions of the content are found in wiki format (see WIKI Learning Experiences and Resources) which can be edited or built up with other materials on the same topic by members of the Curriki community.
More About CABOCES
Welcome to the Math, Science, and Technology Department (MST) of Cattaraugus Allegany Board of Cooperative Educational Services (CA BOCES). As a department of Instructional Support Services (ISS), we provide Math, Science, and Technology kits along with support services to meet the needs of the individual districts in our area.
The BOCES Teaching and Learning Center at Allegany provides hands-on math, science, and technology kits to over twenty area school districts in Cattaraugus and Allegany counties. Our department provides forty-three different varieties of kit topics. The kits cover topics in math, life science, physical science, chemistry, and earth science. Each kit contains a teacher's manual, student activity book, materials inventory list, instructional video, and materials needed to complete each learning experience. Each kit aligns with the New York State standards and prepares students for the New York State assessments.
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80 N Fourth St, Third Floor
Allegany, NY 14706
Phone: (716)-376-8272; Fax: (716)-372-0621


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This p0st section brings along 38 picture of Kindergarten, some of them are including Ks2 Maths Starters. Math Worksheets For 1st Grade Google Search Math Pinterest 14. Ks2 Maths Worksheets Awesome Math 1000 About Javales Math Worksheets. Ks2 Worksheets Maths Counting Money Pinterest Year Pdf Free To 2.
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I need two comments, each part is around 100 words comment.
There are a few actions that would be taken in the preliminary investigation of the time series to inform the choice of the forecasting method. Time series incorporates the number of observations collected over a successive period of time. By observing a variable or sets of variables for a specific period of time and record the behavior of the variables, then a trend is established against time. One of the actions that would be undertaken is to identify the values and how they change over time. A large amount of series data is dependent on past values. Current trends provide information about the behavior of variables (Ho & Ting, 2015). Variables such as exchange rates are lagged values that could be regressed over one or many lagged values in order to predict the future and current values of the variable. Missing data can be filled with past data, which can be calculated by taking averages.The second action would be to identify time periods.Time periods can be yearly, monthly, weekly, and daily. When forecasting future data with past data, lag operators could be used in forecasting methods to quantify future, present, and past values that are linked to one another. Further, the univariate time series is a progression of the measurements of the same variables obtained over time. Often, the measurement is made at regular intervals. A major defining characteristic of a time series is that ordering matters. The importance of ordering in time series is that a change in order could also change the meaning of the data due to the dependency. As such, identifying the time periods between values or variables is essential in determining the right forecasting method to use.
The classical decomposition is a simple procedure that forms the starting point for most other methods of time series decomposition. Two forms of classical decompositions can be used; multiplicative decomposition and additive decomposition. The additive decomposition method would be preferred when the seasonal variations of variables are relatively constant in the period under consideration. In additive decomposition method, the variance of data does not change over different values of the time series. The trend line is a straight line, the additive approach is a straight line, and the seasonality has the same amplitude and frequency. The individual values are differentiated and added together to model the data. A real-life example that would call for the use of additive decomposition is a business that experiences seasonal variations in sales over specific periods. For example, a business that sells umbrellas is likely to experience a boom in sales during the June-August period. An additive decomposition method would be the most appropriate for the business given that the seasonal variation is about the same magnitude across time.
The multiplicative method would be preferred when variation increases over the period under consideration. In this method, seasonal components and the trend are multiplied and then added to the error component. Unlike the additive method, the multiplicative method results to a curved line. A real-life situation that would call for the application of multiplicative decomposition is the forecast of the quarterly earnings of a business. The quarterly earnings data varies significantly based on a range of factors including the strategies of the business, the life-cycle stage, external factors such as regulatory forces and competition. Multiplicative decomposition would be the most appropriate because the seasonality has a decreasing or increasing amplitude and frequency over time.
Question 1: Suppose that you are given a time series and are asked to forecast the values of the time series during one or more of the future periods. Explain a few of the actions that you will undertake as your preliminary investigation of the given time series before you decide which particular forecasting method you should use.
Being able to forecast data based on trends and patterns is one of the most powerful tools available in data analytics today. Although there are a variety of methods prior to working with dataset, if I was provided with the opportunity to forecast the values of a given time series during one of more future periods, I would perform the following actions:
- First, I would review the dataset at a high-level to understand the different components, and the message that the data is intending to deliver. I would particularly look for trends in the data, to get a better sense of this message. In addition, I would want to know the overall data structure, as well as the format of the data within the columns.
- Next, I would start to manipulate and tidy up the data. I would use a variety of packages such as “dplyr” and “tidyr” to ensure that my data is well-organized and clean for analysis. This would include ensuring that there are no rows or columns with missing values.
- Finally, I would validate whether the data is ready for a time series analysis. I would ensure there is enough historical data to work with, in the first place. In addition, I would want to know which specific questions the dataset, once analyzed through a time series, can help with answering.
Once I have completed performing the above actions, I would have a better understanding of the data. I would then choose the appropriate method for forecasting, which would include either of Moving Average, Regression Analysis, or Exponential Smoothing.
Question 2: In many applications, a time series decomposition (i.e., time series filtering) is used to separate or decompose a time series XtXt into its trend, seasonal, and irregular components. In some of these applications, the decomposition relationship is assumed to be additive; while in other applications the decomposition relationship is assumed to be multiplicative. Explain in what situations you would prefer to use an additive decomposition method, and in what situations you would prefer to use a multiplicative method in your time series decomposition. Furthermore, mention a specific example of a real-life time series that is of interest to some enterprise, and for which you would prescribe a multiplicative decomposition. Note: an additive decomposition of XtXt is a decomposition of the form: Xt=Trendt+Seasonalt+IrregulartXt=Trendt+Seasonalt+Irregulart; and a multiplicative decomposition is a decomposition of the form: Xt=Trendt×Seasonalt×IrregulartXt=Trendt×Seasonalt×Irregulart.
In the case of a time series analysis, I would choose between various models depending on whether there is seasonality or not, and whether or not a trend is noticed. If there was no seasonality and no trend, I would choose either the Single Moving Average or the Single Exponential Smoothing models. However, if there was a trend despite no seasonality, I would pick one of the Double Moving Average or Double Exponential Smoothing models. On the other hand, if seasonality was present, but no trend, the Seasonal Additive and Seasonal Multiplicative models would be chosen. If seasonality was present with a trend, I would choose either one of the Holt-Winters Additive or Holt-Winters Multiplicative models.
Diving deeper in to the Seasonal and Multiplicative models, if I was presented with a time series dataset, for which the dependent variable that changed very slightly over a period of time, and stayed constant for the most part, I would choose the Seasonal Additive Model. On the other hand, if there was a noticeable trend being present over the entire time series, then it would make sense to use the Seasonal Multiplicative Model.
One of the most common real-life examples for time-series analysis is the stock market. If there are specific stocks, which increase over time, those stocks become more favourable, and in turn, start to get followed. To understand this relationship more closely, a time series analysis would be used. Given that the change in stock price is seen as a trend over time, the Multiplicative model would be ideal.
As a result of the different criteria being presented, I would choose the appropriate models for my time series analysis. By doing so, I would be able to better analyze the relationship of a given independent variable as it changes over time.


Chantelle Charline December 1, 2020 Worksheet
No matter what materials you choose, it is most important that you supervise your child constantly so that mistakes get caught rather than practiced. I learned this particular lesson the hard way. When my daughter was young, she did something that needed ”attention.” I no longer remember what it was that she did, but I told her to write the sentence ”I will not disobey my parents again” 50 times. I should have known better, but I didn’t check on her at the beginning and then I got busy. So, sometime later, she brought me 50 sentences of ”I will not disobey my parents agen.” She had just practiced misspelling ”again” as ”agen” — 50 times! I’m not certain that we ever really got that fixed.
Have you ever noticed how many K-12 math content websites are devoted to math worksheets? There seems to be an increase in websites that cater to desperate teachers and parents by offering fast, free ”worksheet generation”, ”10 free fractions worksheets,” etc. Now, as a former teacher I am not saying that one should never use math worksheets; however, I do believe that many teachers are using a very superficial method of instruction that relies too much on low-level math worksheets and hands-off instructional approaches. Worksheet lessons move from reading the directions aloud, to doing sample problems as a group, to completing the worksheet independently (or at home with parents), day in and day out.
The math worksheets are specially designed for kids and adults. They are very helpful in improving mathematical aptitude and skills. They can be easily used by school students as well as college goers. They are available from elementary to advanced level. You can also buy customized worksheets. Customized sheets can be planned according to the level of your school going child. You can find several types of sheets online and offline. You can choose among multiplication, Addition, Subtraction, Division, Geometry, Decimal, Shapes and Space worksheets. These sheets help the users to practice mathematical problems. Solving these problems become much easier with the help of mathematical worksheets.
Another advantage of these math worksheets is that kids and parents will be able to keep them to serve as their references for review. Since worksheets are easy to correct, students will be able to identify the items and areas that they had mistakes so that they will be able to correct those deficiencies. Keeping record is really a good thing; As a parent, you will be able to go back through them and assess their strong and weak areas. Keeping track you will be able to track your child’s progress as empirical evidence.
Of course, there is a place for math worksheets. After some instruction has occurred, math worksheets can provide extended practice and support development in fluency, provided the teacher is engaged with students as they work. Teachers who are effective at grouping students can use math worksheets as a springboard for discussions, discovery, and communication. So the next time you do a search for curriculum materials, skip the worksheets. Instead, consider resources that provide interactive experiences or consider sites that provide students with challenging problems. These sites will more likely engage students, foster discussion, and build a true understanding of the purpose and joy of learning math.
At the grassroots level, teachers in schools are given a packed curriculum for the year. Schools try to teach the students a number of procedures without delving much into its finer details. Hence, the student is left in a confounding position as to when a particular procedure must be used. The key ingredient to understanding math is constant practice and math assignment help. Unfortunately, this is not a common scenario among the popular math classes.
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Let X be a one-dimensional metric space and ℍ be the Hawaiian earring.(1) Each homomorphism from π1(ℍ) to π1(X) is induced from a continuous map up to the base-point-change isomorphism on π1(X).(2) Let X be a one-dimensional Peano continuum. Then X has the same homotopy type as that of ℍ if and only if π1(X) is isomorphic to π1(ℍ), if and only if X has a unique point at which X is not semi-locally simply connected. (3) Let X and Y be one-dimensional Peano continua which are not semi-locally simply connected at any point. Then, X and Y are homeomorphic if and only if π1(X) and π1(Y) are isomorphic. Moreover, each isomorphism from π1(X) to π1(Y) is induced by a homeomorphism from X to Y up to the base-point-change-isomorphism.
ASJC Scopus subject areas


Instructor: Philip Pearce
Email: ppearce [at] mit .edu
Office: Room 2-231B
Lectures: M W 1:00 - 2:30 pm in 2-146
Office Hours: M 4:00 - 5:00pm in 2-231
General mathematical principles of continuum systems. From microscopic to macroscopic descriptions in the form of linear or nonlinear (partial) differential equations. Exact solutions, dimensional analysis, calculus of variations and singular perturbation methods. Stability, waves and pattern formation in continuum systems. Subject matter illustrated using natural fluid and solid systems found, for example, in geophysics and biology.
Prerequisites: 18.03 or 18.034; Physics II (GIR)
Text Book: Although there are no textbooks which follow the precise spirit of this course, there are literally hundreds of textbooks where the topics we will cover are discussed. For most lectures, typed notes can be downloaded from the course webpage. Additional material will be handed out in class. One book that will be useful frequently is: D. J. Acheson, Elementary Fluid Dynamics, Oxford University Press (1990).
[04.24.2017] The midterm is now online here.
[04.05.2017] Problem set 4 is now online (here).
[03.15.2017] Problem set 3 is now online (here).
[03.01.2017] Problem set 2 is now online (here).
[02.15.2017] IMPORTANT NOTICE: Due to President's Day on Monday 02/20, the next lecture will take place on TUESDAY 02/21.
[02.15.2017] Problem set 1 is now online (here).
[02.13.2017] Lecture 2 is cancelled because MIT is shut due to the snow. We will catch up on the topics of Lecture 2 in Lecture 3.
[02.08.2017] I've added a summary of what we covered in the first lecture to the Schedule page. I will add to this throughout the semester so you always know what we covered and which part of the online notes it is from. I'll also give the sections of the online notes relevant to the next lecture, in case you want to read ahead.
[02.01.2017] Welcome to the spring semester!


min() -- return the smaller of its two arguments
Return the minimum of its two argument.
for a=1 to 1000
for a=1 to 9
print a,": ",m(a)
For each iteration of the loop, the lower of two random number is recorded. The result is printed at the end.


wake frequency of thermowell
Wake Frequency Calculations for Thermowells, Bizfluent
The information required for the completion of wake frequency calculations include the interior diameter of the thermowell, the height of the thermowell and the thickness of the walls of the thermowell. Calculations are completed for periods of dynamic and static movement within the pipeline.
Wake frequency calculation WIKA Polska
Wake frequency calculation per ASME PTC 19.3 TW2016 for standard bar stock thermowells as an engineering service Recommendations for structural changes to the thermowell where the permissible stress limits are exceeded can be derived Description The wake frequency calculation per ASME PTC 19.3 TW2016 is used for solid drilled bar
Wake Frequency for Thermowell, Automation & Control
Most of the time there is no need to do any wake frequency calculation for the thermowell inside the vessel. ASME PTC 19.3 TW2010, gives the following conditions when wake frequency calculation is not required.
Technical Description Wake Frequency Calculations –
frequency is no more than 80% of the thermowell harmonic frequency. A great deal of discussion has taken place as to whether Murdock''s formulae are an over simplification of the problem of wake frequency analysis. However, the standards have yet to adopt an improved me thod. It is therefore reasonable, but not
LUDWIG SCHNEIDER Wakeup frequency calculation
The wakeup frequency calculation of the thermowell can be used as a static and dynamic response relative to the operating temperature and pressure.Mathematical proof of strength.
THERMOWELL CALCULATIONS TO THE NEW ASME PTC
The thermowell design has PASSED the wake frequency calculation “These well design calculations are based on the ASME power test code PTC 19.3 formulas. The results of these calculations should only be used as a guide for thermowell design. Temperature Controls does not guarantee the performance of a specific
White Paper: Thermowell calculations Emerson Electric
thermowell to be conservative. For an acceptable thermowell design, the ratio of the Strouhal frequency and the natural frequency “shall not exceed” 0.8. The final step is an evaluation of the thermowell length based on the steady state stress. This determines the maximum length the thermowell can be in order to handle the bending stress.


|Location:||MSRI: Simons Auditorium|
Fractional order operators appear naturally in several geometric contexts that range from the study of minimal surfaces with boundary to conformal geometry.
In this talk I will describe a geometric evolution equation that can be understood as a fractional analog to the Mean Curvature Flow. I will establish some analogies with the classical evolution
and I will particularly focus on the graphical case.
This is joint work with Enrico Valdinoci.No Notes/Supplements Uploaded No Video Files Uploaded


We begin by defining the optimization problem. Our objective is to maximize or minimize the sum of objective terms by selecting optimal feasible levels of the independent variables. The set of process limits or constraints define the feasible region. For example, upper and lower limits on the independent variables are constraints on the problems. Additionally, there are dependent variables that aid in defining the objective terms and/or constraints. These dependent variables are functions …show more content…
Generate optimal parameter and bound sensitivities to identify areas of model improvement
J.D. Terry, Ken Tyner, Bill Docter, John Righi
In sensitivity analysis, we determine the optimal sensitivity to parameter changes. These parameters may include prices, process limits, variable bounds, and other problem constants. While shadow values directly quantify the total objective incentive to constraint changes; this invention also analyzes incremental improvements in each objective term and other process variables.
In both linear and nonlinear optimization analyses, skilled users may perform sensitivity analysis for individual parameters (see Fiacco 1976; Ganesh and Biegler 1987). This invention improves this by expanding the practice to the systematic sensitivity of all process limits. Furthermore, this invention obtains an advantage by leveraging clever side-by-side layouts to improve individual sensitivity analyses using cross comparisons for more well-rounded analyses.
By understanding how problem constants affect the final solution, the user is better equipped to improve the model and the system. These improvements become an intuitive consequence of this module. Moreover, these improvements and the cross comparisons of numerous potential improvements, cause additional insights into the system to be apparent to the


Balancing the Books
Last Tuesday, we came up with the idea of guessing how many books can be placed at the edge 1/10 of the table before they topple down. We realize it takes a little bit more than half the books to be on the table before the pile goes down.
First we estimate that it takes 6 books before toppling down.We carry out an experiment. It actually took 5 books, just as the hint suggested. So it can't be above 5 books to be placed on the edge 1/10 of the table.
My friend and I found this an interesting puzzle
We used exercise books. Maybe you can try using a thicker book to see whether it works or not. Have fun !
Find the Balancing the Books puzzle on our puzzle hub.


When I heard the learn’d astronomer,
When the proofs, the figures, were ranged in columns before me,
When I was shown the charts and diagrams, to add, divide, and measure them,
When I sitting heard the astronomer where he lectured with much applause in the lecture-room,
How soon unaccountable I became tired and sick,
Till rising and gliding out I wander’d off by myself,
In the mystical moist night-air, and from time to time,
Look’d up in perfect silence at the stars.
I first encountered this poem in high school English, and I come across it again every few years. I can't explain entirely the rage it summons in me.
But maybe this is the point I wish to make. A friend mentioned the Randall-Sundrum model of the universe and I went to that wikipedia page to try to learn what that was. Pretty soon I was desperately linkhopping- I have a basic education in relativity and differential geometry, but pretty basic, and even the vocabulary I did learn at some point, it's been a decade since and I needed to refresh my memory.
So I clicked on anti-de-Sitter space and from there to Lorentzian manifold and from there to Riemannian manifold, and I want to point out something about these four articles.
The article on Randall-Sumdrum model begins "In physics" The article on Anti-de-Sitter Space begins "In mathematics and physics." The articles on Lorentzian Manifold and Riemannian Manifold begin "In differential geometry." There's that tricksy slippage between physics and mathematics Whitman is writing about. Are the learn'd astronomer's "proofs, the figures," his "charts and diagrams" a meaningful and interesting representation of the actual stars, or are they just lifeless mathematical models that lack the "mystical" potency of observing the stars with the naked untrained eye? Aside from answering this question, though, the distinction is, I think, actually important to doing physics. Because if you theorize that spacetime takes a certain shape that can be modeled by a particular manifold, and then your measurements in an experiment don't match the manifold, you have to consider two different possibilities: One, that spacetime doesn't match your theorized model, and two, that your measurements were inaccurate. But if you're a mathematician working with a manifold and it doesn't match your expectations, only your math is wrong.
So this distinction Whitman writes on matters. There are the mathematical models of the stars, and there are the actual stars themselves, and if you forget this you end up confusing the manifold with the spacetime. A physicist needs both to do their work.
Nonetheless, I feel a great rage when I read Whitman's poem, a rage at the idea that the untrained eye bestows a more exciting and therefore truer reality than the subtle delver into the measureable mysteries of the cosmos can attain through experimentation and analysis. This may be dogmatic scientism on my part, but if so, let it be!