- What is a good ACT score?
- What mode should my calculator be in?
- Is the TI 83 Plus allowed on the act?
- How do you put a function into a calculator?
- Which four subjects are always tested on the act?
- What’s a good ACT score 2020?
- Is Act easier than SAT?
- How do I pass the ACT math test?
- What does M+ mean on a calculator?
- Can you use a TI 84 on the ACT?
- What math is tested on the act?
- Is a 30 ACT score good?
- How much is Algebra 2 on the act?
What is a good ACT score?
The average ACT score is 20.8.
This is the composite score, which combines all four sections: English, reading, math, and science.
So if you earn a composite score of 21, you’re right in the middle of the pack.
Generally, a score of 24 or higher is good..
What mode should my calculator be in?
If you are working with radian values such as p/2, p/3, or 5p/6, you MUST have your calculator set in Radian mode to evaluate trig functions of those values. Likewise, if you are working with angle measures in degrees, you MUST have your calculator set in Degree mode to perform calculations that involve trig functions.
Is the TI 83 Plus allowed on the act?
Graphing Calculators TI-83 and TI-84 models are approved. Many schools have used these calculators in the classroom for years, so students are familiar with them.
How do you put a function into a calculator?
To enter functions in the calculator, perform the following steps:Press [MODE] and put the calculator in Function mode. To highlight an item in the Mode menu, use the. … Press ! to access the Y= editor. See the second screen.Enter your function. If necessary, press [CLEAR] to erase a previous function entry.
Which four subjects are always tested on the act?
The ACT includes the following ACT sections: English, Reading, Math and Science, as well as an optional Writing Test. Some schools may require the Writing Test, so be sure to ask before you register for the ACT.
What’s a good ACT score 2020?
What Is a Good ACT Score for 2020 Overall?PercentileEnglishReading99th (Best)35-3635-3690th (Excellent)303175th (Good)2425*50th (Average)19*20*3 more rows•Dec 6, 2019
Is Act easier than SAT?
There are many other differences between the SAT and the ACT. English on the SAT focuses on writing style, while the ACT may ask more questions about the grammar and sentence structure. … So when “Is the ACT easier than the SAT?” is asked, there is really no true answer.
How do I pass the ACT math test?
10 Must-Know ACT Math TipsChoose the correct solution to each question and fill in the corresponding bubble on your answer sheet.Do not continue to spend time on questions if you get stuck. Solve as many questions as you can before returning to any if time permits.You may use a calculator on this test for any question you choose.
What does M+ mean on a calculator?
Memory and clear functions for this standard calculator are listed below. mc = Memory Clear. m+ = Memory Plus. m- = Memory Minus. mr = Memory Recall.
Can you use a TI 84 on the ACT?
The TI-84 Plus graphing calculator is allowed during the entire portion of the math section of the ACT. * The questions get more difficult as the problem number increases, so you should aim to do questions #1-20 in 30 seconds each, #20-40 in 60 seconds each, and #40- 60 in 90 seconds each, on average.
What math is tested on the act?
The ACT Math Test usually breaks down into 6 questions types: pre-algebra, elementary algebra, and intermediate algebra questions; plane geometry and coordinate geometry questions; and some trigonometry questions.
Is a 30 ACT score good?
Yes, a score of 30 is excellent. It places you in the top 93rd percentile nationally out of the 2 million test takers of the ACT entrance exam. The score indicates you’ve done a significantly above above average job answering the questions on the English, Math, Reading and Science sections of the test.
How much is Algebra 2 on the act?
The content breakdown for ACT math is: Pre-Algebra (20-25%) Elementary Algebra (15-20%) Intermediate Algebra (15-20%) Coordinate Geometry (15-20%)


Millimeter is used for measuring very small objects. This means that equals() receives a copy of object t2 with name otherTime. The number of marks equals the object's measurement in millimeters. Lengths between 10−11 and 10−10 m (10 pm and 100 pm). A meter stick is a little over 3 feet long, because a meter is approximately 3.2 feet. In 2010, a California Buca di Beppo set a world record by preparing a 13,780-lb bowl of spaghetti, served in a swimming pool. These objects, measured in microns, are in the realm of what is referred to as the microscale. 100 nm — larger than 90% of the particles of wood smoke, 120 nm — greatest particle size that can fit through a, 300 nm — greatest particle size that can fit through a, 15 cm = 1.5 dm — approximate size of largest. While millimeters are measurement of length (a thousandth part of a meter) , milliliters are measurement of volume, the thousandth part of liter. Examples include measuring the thickness or length of debit card, length of cloth, or distance between two cities. Here's the question i'm stuck on: "A milligram measures the mass of an object. What is the solutions to y plus 3 squared minus 81? For example, 0.01 mm means you can get reasonably accurate measurements up to 0.01 mm. Example; 1 mm: The thickness of a Canadian dime: 1 cm: Diameter of a AAA battery, or the … Electrospray versus Nebulization for Aerosolization and Filter Testing with Bacteriophage Particles. Estimation of larger distances in centimeters is done using larger objects. Any object can be measured in millimeters-- here are 6 objects. Use a vernier caliper to make measurements to the nearest 1/10 of a millimeter. 1. The prefix is mega-, so a megameter is a million meters. Example 5. — Stephen Battaglio Staff Writer, Los Angeles Times, "Hollywood’s Fort Knox is Iron Mountain.Its latest restored treasure: Bee Gees footage," 9 Dec. 2020 In a bioRxiv preprint last … Getting top hits by using scripted metric … These objects, measured in microns, are in the realm of what is referred to as the microscale. Besides, the reference material is water that always has a density of 1 gram per cubic centimeter or 1 gram per millimeter. It is an object that you can think of to help you estimate the length of an unknown object. Metric rulers are base 10. 0.621371192 miles . If a function needs to store or change data in an object’s member variables, the object must be passed to it by reference. 7. mm. Most credit cards (and other … Metric Length. If an object is the length of a ruler or smaller, then it makes sense to use centimeters to … 3 Gm — Total length of "wiring" in the human brain. 5p (gbp) a dime (usd) a pea. 10-6 m (1 micron) 10-5 m (10 microns) 10-4 m (100 microns) 10-3 m (1 mm) bacteria red blood cells your hair parasitic mite a grain of salt Figure 3. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. How long will the footprints on the moon last? Usually insects like fleas, red ants have lengths of the order of millimeters. Example 1: What if we zoomed in 1000 times again, so that the bacteria were as big as the box? thickness of a finger nail. The height of the object is the distance between the top and the bottom. The Amazing Smallness of Our World . Using the centimeter measurement to quickly calculate the bulk of the object’s length in millimeters just saves time. The microscale. All rights reserved. If you wish, either in class or at home, have students create their own meter sticks by cutting out ten paper decimeter strips including the tab (see attached Blackline … We can measure how long things are, or how tall, or how far apart they are. (average; restaurant and supermarket applications) (based on FMA Omcan Italian Made TR50 Counter Top Pasta Machine Extruder 13317) An average strand of restaurant-grade spaghetti measures 1.7 mm in thickness. Here are some examples of nanoscale objects, plus the length of common objects expressed in nanometers. If it’s easier for you, you can also measure one centimeter past the end of your object and then subtract the number of millimeters in between. Millimeter is abbreviated as mm. 2. Eyepiece Lens Field Number (engraved on the eyepiece) FN. Each printable PDF includes an answer key and there are measurement worksheets of centimeter and millimeter positions as well as length measurements of objects placed either the start or the middle positions of the ruler. This means millimeter waves are longer than infrared waves or x-rays, for example, but shorter than radio waves or microwaves. 10 millimeter (mm) = 1 centimeter (cm) 10 centimeter cm = 1 decimeter (dm) 10 decimeter (dm) = 1 meter (m) 1 dekameter (dam) = 10 meters (m) 1 hectometer (hm) = 10 dekameter (dam) 1 kilometer (km) = 10 hectometer (hm) Examples of Millimeter. A meter stick closely compares to a yard stick. The width of a penny. km. Most rulers come with two measurement metrics, centimeters, and inches and are made usually in … In this lesson, we solve problems where the length of objects is measured to the nearest centimeter. The firm notes on its Web site that the process can create objects with high precision at scales of less than a thousandth of a millimeter. Sea level rise, annual (global average over the last decade) src. In this lesson, we solve problems where the length of objects is measured to the nearest millimeter. If the New Metric dialog box is displayed, click the Empty Metric icon. Microscope Field of View. See Different Pearl Sizes 2mm - 16mm, and compare them to common household items like Batteries, Matches, Coins, Toothpicks, Dice, Paperclips, Buttons and more! thinkness of a ring ( the inside to out side) meter. In this lesson, we solve problems where the length of objects is measured to the nearest millimeter. The millimeter-wave region of the electromagnetic spectrum is usually considered to be the range of wavelengths from 10 millimeters (0.4 inches) to 1 millimeter (0.04 inches). Video Examples: How Many Cubic … An example of an object the size of a Centimeter (cm) is the fingernail. The Amazing Smallness of Our World . Furthermore, the specific gravity can tell us if the object will sink or float in reference material. I was in The Corps right as Vietnam was ending and the rule against laying hands on recruits was not yet in place. Feel Free to edit this page and all related pages; Keep the page organized following the current layout; Only Content entirely related to the ABAP Objects can be inserted here; Always add the reference link for your text; Any copyrights violation will not be allowed "ABAP Objects is indicated for … Millimeter wave scanners produce their waves with a series of small, disc-like transmitters stacked on one another like vertebrae in a spine. Step 1: The reading is closer to 729 mm than to 728 mm. 1 1. Or about the thickness of 10 sheets of paper on top of each other. b. Repeat the task above to find five common objects that are close to each of these units: 1 centimeter, 1 decimeter, and 1 meter. Your fingernails grow at the rate of about 1 nanometer per second. You don't actually need to count every single millimeter mark along the ruler – you can use the numbered centimeter marks as a shortcut. Twitter Facebook … These unique features make Virtual Nerd a viable alternative to private tutoring. It is used to measure small objects, for example, notebooks, pencils, and bottles. Length: Millimeter (mm), Decimeter (dm), Centimeter (cm), Meter (m), and Kilometer (km) are used to measure how long or wide or tall an object is. 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This is a probability experiment – and like a lot of physics and maths, it’s a thought experiment. In other words, it’s an idealised situation, which it would be very hard to replicate in the real world. For a real-world experiment with some striking similarities, go to the NAG board – but stay here first, and find out what it’s all about.
[VIDEO WITH GRAPHIC AND/OR COMPUTER GALTON BOARD – Video 4V]
In a Galton board, we have an imaginary ball, and imaginary pins in an imaginary board – ok. It’s a thought experiment, so please just keep the ‘imaginary’ thing in your mind. If we keep on saying everything is imaginary, it’s going to get really wordy and annoying.
A Galton board is a board with pins in it, in a criss-crossing pattern. When you drop a ball in at the top, there is a 50-50 chance that it will go in either direction at each pin. Let’s unpack that.
[graphic of Galton board for next para to point to; one pin highlighted]
Let’s look at this pin – it could be any pin, but let’s choose this one. There are two ways the ball could go here – to the left of the pin, or to the right. There is a fifty-fifty chance of it going either way.
At the pin the ball hits in the next row, the odds are the same. And so on all the way down the board until the ball reaches the bottom. By adding up the probabilities at each level of pins, we can come to a probability for the ball landing in each marked pocket at the bottom of the board.
Try out the Galton board here. [link to Galton board interactive]
The Galton board reflects some basic statistical concepts of uncertainties in measurements. You can play games with it just like tossing a coin (Game 1), or tossing a coin lots of times and seeing how confident you are about predicting what will happen (Game 2).
Once you’ve got an idea of how the Galton board works, we can make it more interesting by changing both the board and the games.


Do you know exactly how to calculate the odds connected with winning the lotto, as well as the Florida Lotto? You may calculate each set associated with chances for each different lottery activity you enjoy. With the aid involving a small hand held car loans calculator or with typically the free finance calculator on the computer, you just grow this numbers together together with add one division course of action when “the order” of your chosen statistics will be not required for the particular lottery game.
Just what you “need in order to know” is the number associated with full balls that typically the winning amounts are attracted from….. is it 59, 56, 40, 49, or maybe 39? If there is usually a secondary getting with regard to the single extra soccer ball, such as the “red ball” along with Powerball or perhaps the Mega Millions’ “gold ball” you need for you to know the amount of balls can be in this group such as well. Are there forty-nine as well as 39?
It isn’t going to matter if it can be the Sarasota, Ohio, Colorado, PENNSYLVANIA as well as NJ Lotto. This strategy or even mixture gives you the real probabilities. Florida Lottery is 6/53. New York Lotto is 6/59. The Kansas Lottery, Ma Lottery, Wisconsin Lotto, along with the State of Washington Lottery carry some sort of 6/49 lotto numbers rate. Illinois Lottery carries a good 6/52.
After getting this details correctly in front associated with you along with your calculator within hand, you can start out functioning the formulas. Anyone need to decide on 5 regular balls and one additional ball correctly matched to the winning drawn quantities to win the multi-million dollar jackpot that best among us dream about succeeding someday.
From the first instance there are 56 balls in the first collection and 46 balls from the secondary group. In buy to get the Lotto jackpot you need to go with all these balls (5 and up. 1) exactly, although not necessarily in purchase. The Los angeles Lottery’s Super Parte As well as is 47/27. The big carol is usually spinning with the primary part of the getting. You have a 1/56 chance to match your number to this initial ball.
Along with one ball removed as soon as the first range has been sketched, you now have a 1/55 possibility of matching an additional a single of your numbers in order to the second ball pulled. With each drawn number a ball is eliminated lowering the number involving remaining paintballs by simply the total of one.
Chances of you correctly complementing the number on often the third golf ball to become drawn is now 1/54 from the total range of paintballs remaining within the drum. While using third ball removed from the particular drum and sitting with the other two winning numbers, your odds of accurately complementing the fourth golf ball is reduced to 1/53.
As you can notice if a ball is unveiled from drum the odds are decreased by one particular. You started with the 1/56 chance, subsequently having each new being successful amount it is reduced in order to 1/55, 1/54, 1/53, in addition to with the fifth soccer ball you could have the odds of 1/52 accurately matching this specific fifth succeeding number. That is the first part of the formula of how to help calculate your current odds associated with winning the lottery, like the Sarasota Lottery.
Nowadays take these five odds representing the five receiving numbers (1/56, 1/55, 1/54, 1/53, and 1/52). Often the “1” on top of the fraction represents the one and only possibility to effectively match the driven number.
Now you have your car loans calculator and increase in numbers all leading numbers (1x1x1x1x1) equal a person (1). Up coming you multiply the many bottom level numbers (56x55x54x53x52). Correctly entered and multiplied anyone uncover the total is 458, 377, 920. The fresh small part becomes 1/458, 377, 920. This is the 458 mil to one particular chance to win. In the event that you where required to pick often the numbers to be able just like they are drawn, then these would be often the odds against you to win this Get 5/56 ball lottery match.
The good thing is or even unfortunately, that you are not necessarily required to pick this quantities in the exact order these are drawn. Often the second step on the formulation will lessen the odds, which will allows you to match these five winning figures in any order. Within this action you may multiply the number connected with paintballs drawn — 5 (1x2x3x4x5). With calculator inside hand the truth is that the total equals 120.
To be able to give you the ideal to choose the five matching numbers in any purchase, you create all these prospects by dividing 120/417, 451, 320. You definitely need to have a calculator for this a person. 120/458, 377, 920 reduces your odds of winning this lotto to one-fourth, 819, 816. These happen to be over 3. five mil to one odds in opposition to you of winning this Pick 5/56 ball lotto game.
If this were being this Mega Millions Lotto, you should add the “gold ball” to these a few winning attracted balls in order to win the Multi-Million Dollar Jackpot. The only gold ball is measured as a 1/46 opportunity of corresponding it accurately, and since that you are pulling just one number it has to be an exact match. Again, you only have that “1” possibility to do it right. Now you need for you to multiply 3, 819, 816 by way of 46.
Grab your own personal finance calculator and do often the copie. Your final odds against you winning the Mega Thousands Jackpot happen to be calculated to be 175, 711, 536 as well as clearly explained 175 million, 711 1000, 5 hundred thirty six thirty-six to one (175, 711, 536 to 1). You know how to estimate the odds associated with receiving the Mega Millions Lotto.
The Powerball Lottery measurements are based on a new 1/59 for the first five bright balls and 1/39 for any “red” energy ball. In your first set of multipliers is 59x58x57x56x55. This party totals six hundred, 766, 320. Now partition 600, 766, 360 by simply 120 (1x2x3x4x5). Your new overall will be 5, 006, 386. There is a 1/39 likelihood to hook the “red” ball. 39 x five, 006, 386 gives a person the real odds regarding earning the Powerball Jackpot feature, specifically 195, 249, 054 to at least one.
Another 5 plus one Lottery that appears to be in order to be everywhere in the United Says is the “Hot Lotto” which has a 39/19 count. It truly is played within 15 distinct States. POWER Lottery, Delaware Lottery, Idaho Lottery, Grand rapids Lottery, Kansas Lottery, Maine Lottery, Minnesota Lottery, Montana Lottery, New Hampshire Lottery, New South america Lottery, North Dakota Lottery, Oklahoma Lotto, South Dakota Lottery, Vermont Lottery, and the West Va Lotto. The final odds involving receiving the minimum $1 Million Jackpot is twelve, 939, 383 to you.
A Pick 6/52 baseball Lottery game mixture looks like this: (1/52, 1/51, 1/50, 1/49, 1/48, 1/47) for a total of 14, 658, 134, 4 hundred split by 720 (1x2x3x4x5x6) for that odds of 1/20, 358, 520. Your likelihood to win this 6/52 Lottery is over 13. 5 million to one particular to win, such because the Illinois Estrazione.
Typically the Hoosier Lottery the fact that utilizes Indiana State’s nickname, has a 6/48. prediksi togel is 6/47, Illinois Lotto and Missouri Lotto are usually 6/44, Maryland Lottery is 6/43, and Rojo Lottery is 6/42. Compare this to the Lakewood ranch Lotto.
Some sort of Pick 5/39 soccer ball Lotto game solution looks like this: (1/39, 1/38, 1/37, 1/36, 1/35) with regard to a total regarding 69, 090, 840 split by way of 120 (1x2x3x4x5) for that chances of 1/575, 757 regarding winning the Jackpot such as the Illinois Little Lotto. Additional States with the same 5/39 lottery numbers include the particular NC Lottery, Georgia plus Florida Lottery Dream 5, and Tennessee Lottery’s Get 5. Virginia Lottery’s Money 5 carries a 5/34 range.
Now, basically that better to select a Lotto game together with lower chances against you?


Math Worksheets Grade 1 Multiplication
You may vary the numbers of problems on the worksheet from 15 to 27.
Math worksheets grade 1 multiplication. 1st grade math multiplication worksheets printable it is simple to make a first grade math worksheet. Learning multiplication facts will be both educational and entertaining with these review workbooks facts books and math centers. Grade 5 multiplication worksheets multiply by 10 100 or 1 000 with missing factors. Multiply in columns up to 2x4 digits and 3x3 digits.
Free math worksheets for grade 1. 1 3 or 5 minute drill multiplication worksheets a multiplication math drill is a worksheet with all of the single digit problems for multiplication on one page. These multiplication worksheets are appropriate for kindergarten 1st grade 2nd grade 3rd grade 4th grade and 5th grade. Multiplying in parts distributive property.
Mixed 4 operations word problems. Each of our worksheets come with an answer key for your reference and students can complete them with or without the help of a multiplication chart just choose the grade level and skill that s right for your class and then click to download. They are randomly generated printable from your browser and include the answer key. This is our most popular page due to the wide variety of worksheets for multiplication available.
These multiplication worksheets may be configured for 2 3 or 4 digit multiplicands being multiplied by multiples of ten that you choose from a table. Also a first grader can do it. 4th grade multiplication worksheets free pdf workbook 5th grade multiplication worksheets free pdf workbook multiply your students mastery in multiplication with systematic practice using these innovative worksheets. 20 printable multiplication worksheets.
Given that there are lots of skills that are needed in order to accomplish a positive outcome you will locate that it is practical to discover the worksheet that best fits your youngster s skills. Multiplication grade 1 math resources. Multiply 1 digit by 3 digit numbers mentally.


"[E]very copy is unique, irreplaceable, but (since the Library is total) there are always several hundred thousand imperfect facsimiles..." --Jorge Luis Borges, The Library of Babel
I don't know how this happens. Every couple of years, I fall into some book or conversation that purports to open windows onto the workings of human consciousness. I'm not sure that I like the subject exactly, and I may even hate it. For me, it's like that itch you notice it bugging for your attention for a long time, and when you break the urge and gouge up your skin in hopeful relief, you don't really feel any better. The deep fundamentals of mathematical and cognitive philosophy have a habit of annoying the fuck out of me, partly it's the language, and partly goofy notation, but mostly it's because my brain aches when it's knotted around in order to try and contemplate itself. As a rule, I just try to avoid them, but Oxford mathematician Roger Penrose has been taunting me from my bookshelf for seven years now with Shadows of the Mind. The basis of the book is an attempt to use Gödel's incompleteness theorem to show that consciousness can't be a product of a consistent formal mathematical/logical system, and from there move to some bizarre quantum theory of consciousness. I'm going to mostly concentrate on the first part here.
Wikipedia has a pretty decent discussion of incompleteness, stating it (not in the mathematician's own words) as,
"For any consistent formal, computably enumerable theory that proves basic arithmetical truths, an arithmetical statement that is true, but not provable in the theory, can be constructed. That is, any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete."Basically, any set of theories which manages to conclude that "this set of theories can not be proven" contradicts itself, and is therefore inconsistent. (Also, everything I tell you is a lie.) Sounds reasonable, but the philosophical consequences of it get a little funky. In its least mind-bending application, Gödel's statement says that there are any number of mathematical truths that can't be proven by a system of rules. It also suggests that there will always be more axioms (unprovable starting points) to add, and any algorithm that operates by a mathematical set of rules--a computer program, say--will not be able to deduce any of those new axioms, including (and especially) the one that says it can't reach them all. Penrose takes this to mean that no Turing machine (i.e., a computer that operates according to a set of rules) will ever achieve the status of a human thought (or for that matter, human language). Why? Because humans can infer truths such as Gödel's theorem, that's why. Cognition can't, therefore, be a mathematically consistent process, and we'll never be able to fake that sort of thing using a computer.
This bothers me. It's not the idea that formal systems must be incomplete, it's that notions of inconsistency must be so rare and intolerable. In those increasingly rare times I act like an engineer, I'm constantly working in the realm of consistent enough. Engineering math works that way: it's good only over some range of underlying values, and only to the extent that the assumptions are valid. You can never quite capture every aspect of a physical phenomenon into a theoretical model and still have the model compute. The natural world quickly leads you past solutions that are analytic (that is, that can be solved by symbolic math), and even as you turn to numerical methods of problem-solving (that is, chunking the model up into approximate pieces, and keeping track of them all with a computer), you still need to limit your interpretation of the world in terms of mathematical logic that is possible to manipulate, and this always proves smaller than the world itself. Even revolutionary models like quantum mechanics rely on constructing equations in such a way that they can be partially solved, with just sufficient accuracy to get their points across. That's practical math for you, and I don't know if it's a correct extension of Gödel's theorem to say that as you specify a system more accurately, then your logic must become necessarily less consistent, but it's in the same vein. Actually, it's starting to sound more like quantum uncertainty than anything else, and that may well be somewhere close to where Penrose is heading*. I'll see over the next several days. (Even if he's not going there, some amazing conceptual beasties still lurk just beneath the Planck length.)
Computers are algorithmical by definition, but are they in practice? What is the relationship between the universe and math anyway? You can see how basic ideas such as natural numbers (one rock, two trees, three eggs, hrair bunnies) and basic arithmetic (addition, multiplication, etc.) are readily correlated to observable properties of the Universe, but I'm going to take a step beyond that correlation and assert that computations and ideas don't merely represent physical objects, they are in fact physical objects. Your conception of the number 3, say (or of Gödel's theorem), is a pattern of electrical impulses, probably a dynamic one, stored in or circulated around the knot of nerve cells in your head, which, when the power's turned on, can interact with many of the other nervous sparks, some old, and some freshly arrived from the senses, and churn around in fantastically complicated ways. Likewise, the concept of a 3 can be stored in that pile of blocks over there, as many beads on an abacus, so many divisions of a slide rule, or so much charge distributed over so many transistors. Algorithms are things too, objects on a tape, capacitated electrical charges, whatever. The ideas behind them are contained in all those networks of neurons, which are also things, and in the coded instructions for neurons that we leave everywhere for ourselves (such as these electromagnetic doohickeys that I'm directing at you right now, not to mention the modulated acoustics and the blobs of ink of produced by generations of philosophers and fools. There is no Platonic spirit realm of pure ideas--we approximate all of them over and over again, never quite the same but usually close enough, in accordance with a common outline of a wiring scheme and all of our own ubiquitous clues. Algorithms are arrangements of somethings too--Turing machines are worthwhile conceptual aids, but their instructions can clutter up the shadowy cave as much as anything else. Actual computers, just like brains, are really only algorithmic enough.
I'm not really going too far past Penrose here. His point is that thinking can not be based on sound algorithms. I'm saying that I don't think computers are algorithmic either, nor is the universe, not quite.
[Part II will discuss some ways to make computers that are more like brains.]
*Or not. I'm told that despite the profundity regarding the incompleteness theorem, his physics of consciousness are not widely accepted.


For practical purposes, if the Reynolds number is less than 2000, the flow is laminar. The accepted transition Reynolds number for flow in a circular pipe is Red,crit = 2300. For laminar flow, the head loss is proportional to velocity rather than velocity squared. Thus the friction factor is inversely proportional to velocity.
The Darcy friction factor for laminar (slow) flows is a consequence of Poiseuille’s law that and it is given by following equations:
- Re < 2000
- ‘low’ velocity
- Fluid particles move in straight lines
- Layers of water flow over one another at different speeds with virtually no mixing between layers.
- The flow velocity profile for laminar flow in circular pipes is parabolic in shape, with a maximum flow at the center of the pipe and a minimum flow at the pipe walls.
- The average flow velocity is approximately one-half of the maximum velocity.
- Simple mathematical analysis is possible.
- Rare in practice in water systems.


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Quantitative Reasoning through Social Justice
Math for the People is a new approach to teaching Quantitative Literacy to students outside of traditional STEM fields. By leading with social justice topics, Math for the People seeks to introduce students first to the problems we want to solve, and then introduce the mathematics we can use to understand them. The textbook is intended for a college freshman level course in quantitative literacy at a two or four-year postsecondary institution. This course would fulfill a terminal mathematics requirement for students whose degree programs do not require any further mathematics.
The text will be structured in stand-alone modules, each related to a single social justice topic. Each module will begin with an overview of the topic, historical context, and a discussion of current questions and concerns related to the topic. This section may include particular case studies related to the topic, articles discussing the topic, and other resources. This section will followed by discussion prompts for faculty to use in helping students explore the issue.
The mathematical content will follow. Each topic will be paired with 2-4 mathematical topics which will help the reader to ask questions and build understanding about the social justice topic being discussed. These mathematical topic sections will be connected directly to the social justice topic. The same mathematical topic may be repeated in multiple places throughout the text (for example, a section on exponential growth may be included in the module on climate change as well as the module on predatory lending – in each section, the topics would be couched in examples related to the social justice topic).


Romancing Google And Demystifying PageRank
What is PageRank? PageRank is one of the important factors that determine Search Engine Results Page (SERP). It is a numerical value assigned by Google that shows the importance of a web page. When one page links to another, it is actually casting a vote for the other page. It goes to say that a page with more relevant inbound links enjoys a higher page rank. For simplicity sake, PageRank is referred to PR in this article. Applying the Mathematical Concept of PageRank Google calculates the PR of a web page using this equation: PR(A)=(1-d) + d[PR(t1)/C(t1) +.
+ PR(tn)/C(tn)] 't1.tn' are pages linking to Page A 'C' is the number of outbound links of the linking page 'd' is a damping factor set at 0.85 This is the original equation Google published when it developed PR. Whether Google uses a variation of it, only God knows. This equation, though, is essential to an understanding of PR.
Don't be scared by the above equation. For a fuller explanation of this equation with working examples read The Google Page Rank Algorithm and How it Works by Ian Rogers. The purpose of this present article is to apply the Mathematical concept of PR to your web page ranking strategy. Yes, you can organize your linking strategy to achieve high PR for your important web pages. Inbound Linking Strategy Many people assume that the Toolbar PR values of PR1 to PR10 are set on a logarithmic scale. Nobody outside Google knows for sure, but there is a very good reason for this assumption. That being the case, moving from a lower page rank to the next higher one gets increasingly difficult. So, moving from PR3 to PR4 is more difficult compared to moving from PR1 to PR2. For illustration refer to the table below. Toolbar PageRank (log base 10).
Real PageRank 0.0 - 10 1.100 - 1,000 2.
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M. De Domenico, A. Solé-Ribalta, E. Cozzo, M. Kivelä, Y. Moreno, M. A. Porter, S. Gómez, A. Arenas
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems are very rich. Achieving a deep understanding of such systems necessitates generalizing “traditional” network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multilayer complex systems. In this paper, we introduce a tensorial framework to study multilayer networks, and we discuss the generalization of several important network descriptors and dynamical processes—including degree centrality, clustering coefficients, eigenvector centrality, modularity, von Neumann entropy, and diffusion—for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multilayer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems.
Phys. Rev. X 3, 041022


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Update: A friend suggested a rewording of this post for tone.
Tomorrow I will post the first of a new series of articles where I will dissect the math of other designers' prototypes (or even published games). I will do this with an eye towards promoting understanding of how mechanics interact with regard to determining winning strategies.
Why am I doing this? First, there is the selfish desire to expand my audience beyond those interested in my own attempts to have a game published. Second, I believe that designers can and should help each other make their games better. In my time spent with the NYC Board Game Designers Playtest Group (as well as a couple of times attending Spielbany), I have received great help with aspects of my designs at which I am unskilled. As an example, Dan Cassar was the one who came up with this board layout (vastly improving on the original).
In return, I have helped other designers with the aspects of game design at which I am strongest: the understanding and manipulation of incentives on player behavior and spotting mathematical weak points that lead to strategic imbalances. It was always gratifying to break a game and be thanked for doing so, and to be asked to play the next version to see if the problem was fixed.
I hope that this new series will help other designers to spot similar patterns in their own games. If you are interested in having your game featured, please email me at email@example.com


The Myths of Solving Math Problems in 2021
Math problems tend to be a bit of a problem for a lot of people out there. For many, math is a little less than a subject that is intent upon making everyone’s life harder. The truth is that math is often misunderstood like completing ‘write my essay’ tasks. It is believed that solving math problems is not something that has to be the kind of a mammoth task that it comes to be for most of us.
Here are some of the most common myths associated with solving math problems so that you can work on the relationship that you have with the subject and be able to approach it with much less hostility in the future. Don’t run at the first sight of a problem. You can solve it if you have the right attitude towards math in general.
Myth # 1: Math Problems are Only for Math Geniuses
While it is true that there are math geeks who seem to have it so easy while the rest of us toil and sweat over a problem, it is not true that only geniuses can solve math problems. If understood properly, scholastic math can be for anyone to comprehend and get through with flying colors. The reason that people think they cannot do math generally lies in the way that it is traditionally taught. Which leads us to the second myth.
Myth # 2: Math Problems are not Relevant to Everyday Life
Somewhere along the line when you were learning algebra and matrices, the math may seem to have drifted away from the practical life that you lead. It was not math that drifted away, it was the way that you solve problems. You lost touch with it because you have been taught to just follow a bunch of instructions and solve some problems to get a good grade. You may be surprised to know that math is relevant to your everyday life if you have understood it instead of just performing a few steps in completing ‘write my paper’ tasks.
Myth # 3: Math Problems are Boring and Dull by Nature
I admit that most people get bored while solving a problem but again, that is not because of the fact that there is something inherently boring about these problems, rather the experience of dullness lies in the way these problems have been understood and conceptualized. Find a way to understand the crux and practical application of a problem and you will find that you are interested in solving it!
Myth # 4: Math Problems are Meant to be Learnt but not Understood
The technique that many students get by their tests and exams is rooted in a misconception that math cannot be understood by laypeople and that to pass exams, the bitter pill has to be swallowed somehow by making sure that methods and all steps of these methods are memorized and practiced. We need to have better techniques for practical understanding and relevance. Every problem is an interesting puzzle that is waiting to be figured out…
Myth # 5: There is One Method to Solve a Problem
Many students seem to harbor the belief that each problem has only one designated method because that is how they have learned it at school. Different chapters have different methods to teach and exercises that belong to one chapter cannot be related to other exercises belonging to different chapters. Nothing could be farther from the truth. There are many ways to solve the problem. Be daring and creative. Find the best method that suits you. Your aim is just to solve and reach the answer!
If all the problems are too problematic for you and the traditional teaching methods have left you fearing the subject itself, you can always get help from online essay writing service who can provide you access to math experts who can assist you in your assignments for a nominal fee.


Do you dream of hitting the jackpot? The allure of the Canadian Lotto Max lottery draws millions to try their luck, hoping for that life-changing win. But how do you increase your chances in this game of chance?
Enter the lucky Lotto Max numbers generator, a tool designed to assist you in selecting numbers that might just lead to your fortune. In this article, we’ll unravel the workings of this generator, explore the intricacies of Lotto Max, and delve into strategies for picking those winning numbers.
Ready to uncover the secrets behind the numbers that could change your destiny? Let’s dive in!
Your 7 Lotto Max lucky numbers:
How does the Lotto Max number generator work?
The Lotto Max number generator works like a magician conjuring numbers from 1 to 50. It’s a tool designed to assist eager players in their quest for the jackpot by selecting 7 random numbers. But how does this Lotto Max generator actually operate?
When you initiate the generator, it swiftly leaps into action. It sifts through countless possibilities within the 1 to 50 range. It’s like having a lightning-fast mathematician at your service, sorting and sifting through numbers at a mind-boggling speed.
Each number the generator spits out is truly random. It doesn’t favor any specific number or sequence. It’s as though each number has an equal chance of being chosen, making the entire process fair and unbiased.
However, while this generator offers a helping hand in number selection, it’s crucial to understand that it doesn’t possess the power to foresee the future. Its predictions aren’t guarantees of winning the jackpot. Instead, it’s a tool rooted in statistical analysis, aiming to enhance the odds of success.
In essence, the Lotto Max number generator is like a trusty assistant in your quest for that elusive jackpot. It relies on math, patterns, and randomness to offer a set of numbers, leaving the final outcome to chance and fate. So, while it can’t promise a win, it might just tip the scales in your favor.
Understanding the Lotto Max lottery
The Lotto Max lottery stands tall as one of Canada's most thrilling games of chance, captivating millions with its promise of life-altering winnings. But what exactly is Lotto Max, and how does it captivate the dreams of so many hopefuls?
Lotto Max is a national lottery game where players aim to select 7 numbers from a pool of 1 to 50. This task might seem simple, but it holds the key to unlocking substantial prizes, including the grand jackpot that could change a fortunate winner's life forever.
The excitement surrounding Lotto Max stems from its bi-weekly draws, held every Tuesday and Friday. During these draws, 7 main numbers and 1 bonus number are randomly drawn from the pool of 50. Players eagerly anticipate these moments, hoping their chosen numbers align perfectly with those selected in the draw.
The jackpot is the ultimate prize, won by matching all 7 main numbers drawn. However, even if a player doesn’t hit the jackpot, there are secondary prizes for matching fewer numbers. This multi-tiered structure means there are various opportunities to win, adding to the allure of the game.
Players can purchase their tickets at authorized retailers or through online platforms, allowing widespread access to anyone dreaming of a chance at the coveted winnings. Each ticket carries a unique set of numbers, and players can choose their own or opt for the quick pick method, where numbers are randomly generated for them.
One of the fascinating aspects of Lotto Max is that a portion of the proceeds from ticket sales goes back to supporting various causes and initiatives across Canada. This adds a charitable element to the game, making each ticket purchased contribute to the betterment of communities.
Lotto Max payout structure
At the top of the pyramid sits the grand jackpot, the ultimate prize. To claim this colossal bounty, a player must match all 7 main numbers drawn during the bi-weekly Lotto Max event. This is the golden ticket to life-changing wealth, captivating the dreams of every hopeful player.
However, even if hitting all 7 numbers seems elusive, fear not! Lotto Max offers additional prize tiers for matching fewer numbers.
- 7/7: This is the grand jackpot where a player matches all 7 main numbers drawn. The chance of winning is 1 in 33,294,800, and the prize typically comprises 87.25% of the total prize pool.
- 6/7 + Bonus: Matching 6 main numbers along with the bonus number carries a 1 in 4,756,400 chance of happening. The prize allotted for this tier is usually 2.5% of the total prize pool.
- 6/7: Matching 6 out of the 7 main numbers drawn offers a 1 in 113,248 probability of winning and usually constitutes 2.5% of the prize pool.
- 5/7 + Bonus: If a player matches 5 main numbers plus the bonus number, the chance is 1 in 37,749, and the prize accounts for about 1.5% of the total prize pool.
- 5/7: Matching 5 out of the 7 main numbers drawn happens with a probability of 1 in 1,841 and usually holds 3.5% of the prize pool.
- 4/7 + Bonus: Matching 4 main numbers along with the bonus number carries a 1 in 1,105 chance of occurring and usually awards a 2.75% share of the prize pool.
- 4/7: Matching 4 out of the 7 main numbers typically grants a fixed prize of $20 with a 1 in 82.9 chance of winning.
- 3/7 + Bonus: Matching 3 main numbers along with the bonus number also usually grants a fixed prize of $20 with a 1 in 82.9 chance of winning.
- 3/7: Matching 3 out of the 7 main numbers typically rewards players with a free play and has a probability of 1 in 8.5.
Choosing your lucky Lotto Max numbers
Selecting the right numbers for your Lotto Max ticket is like crafting your own destiny within the game of chance. Here's a guide on how to choose your lucky Lotto Max numbers and enhance your shot at those enticing prizes.
Trust your instincts
When it comes to picking numbers, trust your gut feelings. Whether it's birthdays, anniversaries, or numbers that hold personal significance, go with what feels right to you. Your intuition might just guide you towards the winning combination.
Mixing highs and lows
Consider diversifying your number choices. Lotto Max draws from a pool of 1 to 50, so include a mix of high and low numbers. This balanced approach can add versatility to your selection strategy.
Spread the odds with even and odd
Balance is key. Include both even and odd numbers in your chosen combination. This method broadens your possibilities and avoids skewing your selection toward one type of number.
Mind the frequency
Take a look at the historical frequency of numbers drawn in Lotto Max. While there's no guaranteed pattern, knowing which numbers have appeared more frequently in the past might influence your choices.
Stay clear of common patterns
Avoid falling into the trap of common number patterns, like consecutive sequences. Opting for diverse, non-patterned numbers can set your ticket apart from the rest and reduce the chance of sharing the prize.
Embrace randomness with quick picks
For those who prefer a touch of randomness, consider using the Quick Pick option. The Lotto Max number generator can swiftly generate a set of numbers for you. It's a fuss-free way to let chance play its part in your number selection.
Change it up each time
If you're a frequent player, consider changing your number combination regularly. Consistently sticking to the same numbers might mean missing out on potential opportunities. Keep the game dynamic and fresh by mixing up your choices.
Join a pool for more fun
Consider joining a Lotto Max pool with friends or colleagues. Pooling resources allows you to play more combinations without breaking the bank. Plus, it turns the game into a shared adventure with higher chances of winning.
In the world of Lotto Max, choosing your lucky numbers is a personal journey. Whether you trust your instincts, analyze patterns, or opt for randomness, the key is to enjoy the process and savor the excitement of what those chosen numbers might bring. Remember, each draw is a new opportunity to turn your selected digits into a winning ticket.
The most common Lotto Max numbers
In the world of lottery games like Lotto Max, players often wonder if certain numbers appear more frequently than others. While lottery draws are based on chance, analyzing historical data can offer insights into the most commonly drawn numbers.
Here, we delve into the trends and unveil the most popular Lotto Max numbers based on past occurrences.
The number 1 stands tall as one of the most frequently drawn numbers in Lotto Max history. It’s been a recurring guest in many past draws, capturing the attention of players seeking patterns in number selection.
Considered a symbol of luck, the number 7 often graces the drawn combinations. Its appearance in previous draws has made it a popular choice for many hopeful players.
Surprisingly, the number 9 has made consistent appearances in past Lotto Max draws, earning its place among the commonly drawn numbers.
The number 18 has proven itself as a reliable contender, frequently making its way onto drawn combinations, catching the eyes of keen observers.
In the lineup of commonly drawn numbers, 24 has showcased its frequency in past Lotto Max draws, becoming a noteworthy inclusion for players strategizing their selections.
With its regular appearances in past draws, the number 36 has established itself as a consistent performer, sparking interest among players seeking recurring patterns.
Number 44 has earned its place among the frequently drawn numbers, often finding its way into past winning combinations, inviting speculation and consideration from players.
While these numbers have shown a tendency to appear more frequently in past draws, it's essential to remember that lottery games are inherently random. Each draw operates independently, and past occurrences don’t guarantee future outcomes.
However, for those who enjoy analyzing trends and patterns, these commonly drawn numbers might offer inspiration in crafting their next Lotto Max selection.
In the world of Lotto Max, where chance reigns supreme, the quest for those winning numbers continues. Whether players choose to follow historical trends or trust their instincts, the excitement of the game lies in the anticipation of every draw and the possibility that these popular numbers might just lead to a life-changing win.
Biggest historical Lotto Max winnings
Lotto Max has been a beacon of hope for countless dreamers, offering life-altering fortunes to the fortunate few who clinch the coveted jackpot. Let's delve into the history books and explore some of the most monumental wins that have left an indelible mark on the Lotto Max legacy.
$70 million Jackpot: a Canadian record
In 2019, Lotto Max crowned its largest jackpot winner, a remarkable $70 million prize. This historic win set a new record for Canadian lotteries, igniting excitement and fervor across the nation.
A syndicate’s triumph
Notable wins often involve syndicates, where groups of players pool their resources. In 2018, a syndicate from Quebec secured a staggering $60 million jackpot, showcasing the power of collective play.
Ontario's $60 million Jackpot
In 2020, Ontario witnessed a life-changing win with a $60 million jackpot. The winning ticket belonged to a lucky individual who stepped into the realms of unimaginable wealth.
British Columbia’s fortunate winner
British Columbia saw its own share of Lotto Max fortune with a jaw-dropping $50 million jackpot. The lucky ticket holder joined the ranks of the game’s biggest winners, transforming their life in an instant.
A $50 million windfall in Quebec
Quebec has celebrated multiple significant Lotto Max wins. In one instance, a $50 million jackpot made its way into the hands of an incredibly fortunate player, reshaping their future.
These monumental wins stand as testaments to the life-changing potential of Lotto Max. They've brought joy and transformation to the lives of those fortunate enough to match the elusive winning numbers.
Each win not only reshapes the winner's destiny but also adds to the allure and excitement of Lotto Max, fueling the dreams of countless hopefuls aiming for their shot at a life-altering jackpot.
As Lotto Max continues to capture imaginations and create millionaires, these historical wins serve as inspiring chapters in the ever-evolving saga of the Canadian lottery, reminding players that amid chance and luck, life-changing fortunes await the chosen few.
Pros and cons of using lucky Lotto Max numbers generator
The lucky Lotto Max numbers generator stands as a tool designed to aid players in selecting their numbers for the game. While it offers convenience and a systematic approach to number selection, there are both pros and cons to consider before entrusting your fate to this digital assistant.
- Speed and convenience: The generator operates swiftly, instantly providing a set of numbers. It eliminates the time-consuming task of manually selecting numbers, making it a quick and hassle-free option for players.
- Statistical analysis: It employs algorithms to analyze number patterns and statistics. This method aims to offer numbers based on mathematical probabilities, potentially increasing the odds of choosing a winning combination.
- Diversity in selection: By generating random numbers, the generator can introduce a variety of combinations that players might not consider themselves, adding diversity to their number choices.
- No guarantee of success: While the generator uses statistical analysis, it doesn’t guarantee a win. Lottery draws are inherently random, and past success with the generator doesn’t ensure future wins.
- Over-reliance on algorithms: Relying solely on the Lotto Max generator might lead to overdependence on mathematical algorithms. Players might overlook their own intuition or preferred numbers, limiting their personal engagement with the game.
- Reduction in emotional connection: Picking Lotto Max numbers manually can foster an emotional connection and anticipation, making the lottery experience more personal and engaging. Relying on a generator might dampen this emotional aspect of the game for some players.
The lucky Lotto Max numbers generator offers speed and statistical analysis, yet it lacks personal connection and guarantees. Players must weigh the convenience against potential drawbacks before entrusting their fate to algorithms.
Whether opting for the generator's efficiency or the personal touch of hand-picking numbers, the essence of Lotto Max remains unchanged: the thrill of anticipation and the hope of hitting the jackpot.
Each ticket holds a chance, whether guided by math or sentiment, and every draw sparks excitement, knowing that fate might just unveil life-changing fortunes.
So, whether using the generator or choosing numbers by hand, embrace the excitement, play responsibly, and let the Lotto Max adventure unfold!


Mathematics Software Packages on Athena.
These packages vary widely in their capabilities. Which is best for you depends on what you are trying to do. The packages annotated with Recommended are the ones that you are most likely to get help on.
On this page:
Matlab, located in the matlab locker, is a powerful mathematics (and especially matrix) manipulation program, which works numerically with up to double precision floating point accuracy. Matlab has a number of packages directly applicable to engineers, such as plot bode curves, optimize filters, find filter coefficients, and DSP. A graphic interface (simulink) can be used to put together and simulate complicated dynamical systems. SIPB puts out a useful "Inessential Matlab" document. See also the documentation on the Mathworks web site: http://www.mathworks.com/access/helpdesk/help/helpdesk.shtml
Xess, in the xess locker, is a scientific spreadsheet, which contains a number of mathematical, statistical, and logical functions, and can draw (moderately simple) graphs.
Maple, in the maple locker, is a symbolic math program (with a somewhat cranky interface). Some further information on Maple is available at http://web.mit.edu/maple/www/maple.html
Mathematica, in the math locker, is a programming environment for performing both symbolic and numerical calculations as well as displaying and formatting the output. It can process algebra, calculus, graphics, sounds, and more, and includes a large set of add-on packages to customize if for specific tasks such as discrete math, statistics, linear algebra, and number theory. In addition to the built in help, there's extensive documentation on the Wolfram web site
xcalc (no locker need be attached) is a simple scientific calculator.
bc (no locker need be attached) is a simple calculator with a text interface.
SAS, in the SAS locker, is an integrated application for data access, management, analysis, and presentation. Available only on Suns.
The mathlibrary locker has been set up to make it easier for "one stop shopping" for mathematical routines for use on Athena. The Mathlibrary presently includes:
- lapack, a library of Fortran subroutines for linear algebra recipes
- the software from the book "Numerical Recipes, the Art of Scientific Computing"
- a collection of C++ code from the netlib server
- NA-digest, an archive of the NA-NET news digest
Full details on the locker are in mathlibrary/README. Much of this stuff is from circa 1997, and seems to have fallen into disrepair. If you are in need of a particular solution, do ask.
last updated: 02/24/2004


Grace O'Neil is a graduate student in Raffaele Ferrari’s and Paul O’Gorman’s groups. She is interested in atmospheric dynamics and climate change. O'Neil received her BA in Mathematics and Physics from the University of Pennsylvania in 2019 and her MA in Mathematics from Columbia University in 2020.
Program in Atmospheres, Oceans and Climate
Massachusetts Institute of Technology
77 Massachusetts Avenue | Room 54-1614 | Cambridge, MA 02139


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We spend a lot of time in FE, and we used to in schools when I was in them, trying to put English and maths front and centre. Jonny and I argued that co teaching and collaboration should happen across disciplines in colleges. If Pythagoras is being taught in the vocational area, maths staff need to share how they would teach it and a consistent approach to be taken across the college. We carefully craft policies for every eventuality and we may even have a maths marking policy and code, but what do we do in our day to day tasks to support the development of maths?
I remember maths stairs being a necessity, an equation revealed or a fact to be recalled as you ascend. Yet when the same students answers maths problems in hair and beauty there was no consistent maths marking to help build connections to the maths qualification they were studying. SPaG policies and marking codes are almost a given, common currency transferable between institutions. If you arrive at a new school or college you can guess 'SP' probably means spelling mistake in work maybe even '//' is new paragraph. This currency of whole college and school marking has become the norm for English. Some have moved away and things will always shift though.
In researching this blog post I lost hours on an image search of whole school marking policy. Lots of // and SP and P. All familiar to me. One post I read said that the marking policy must be printed in size A1 in the classroom so that all teachers adhere to it! I remember in my NQT re-marking a set of books that I had marked in the wrong shade of green and I was terrified my mentor would tell me off. They didn't; but they did point out that my students were using the wrong coloured pens for reflections. I'm not proposing maths teachers head down this route, but a more unified marking code may help bring maths out in other areas more to be celebrated.
The EEF found that there was little difference of impact of teacher using coded Vs non-coded marking, as long as students knew what the codes meant. https://educationendowmentfoundation.org.uk/evidence-summaries/evidence-reviews/written-marking/. They suggested that time can be saved for teacher in using coded marking. Maybe this is why SPaG took off, everyone has or had one, each with a nuance for their institution.
What I can't let go of though is a maths code. I know in primary I have seen some use of maths marking codes in my local area. I haven't seen it in secondary (granted not visited very secondary school around and would love to be shown successful examples). In colleges I haven't seen it either. Again if you are successfully using a maths marking code please share your experiences, I am keen to learn.
I often say we are the double glazing sales people of education as maths teachers. Everyone needs windows but they are reluctant to pay (put the effort in) for them. I know this is a generalisation, though, but I hope that you get my meaning. We are on the back foot from the beginning. We talk a lot about embedding maths in other subjects. Julia Smith (https://twitter.com/tessmaths) (on our podcast e-m-booth.site) suggests that my embedding maths we are pushing it down and squeezing it in. Julia suggests we should be enhancing out maths in other subjects. I think she is on to something.
In vocational subjects that tokenistic embedding of maths can happen.
"When we look at graphs of data maths will be embedded in this unit of work."
Great, graphs, perfect! What I always say is, ask that next question. What does the data tell you? What would happen if the outliers were removed from the sample? What percentage of success can you assume from this data? Whenever I talk about embedding (or enhancing) maths I want staff to ask that extra question. Conversely, those not taking a tokenistic approach maybe actually teaching units that involve serious calculations. Think about the calculations needed in electrical engineering or motor vehicle or catering. These calculations will be being taught in colleges, but then we may encounter another conflict. The methods chosen might not be the methods used by the maths department. Who has checked for consistency of message? Who is looking out for the interests of the students here? Imagine being taught ratio one way by your vocational tutor (I have 4 ratio methods that my students regularly come to class with from school!) and the next day being taught it another way by your maths tutor? This could easily happen. Consistency is key.
Move over SPaG MATH is on the scene.
M - clear method used
A - accuracy in the stages of calculation
T - task met
H - Work is set out in a clear, legible manner.
Anytime there is maths being used in work, this code can be applied. In vocational subjects that have maths, in study skills sessions that cover maths, in maths lessons. There can be a consistent message. Adding in here for progression from functional skills to GCSE, consistent message is also key to supporting students in feeling settled. This MATH message suggested is also consistent to GCSE and functional skills marking codes as well.
GCSE and functional skills maths have coded marking too. M for method is common currency as is A for accuracy. The setting out of work is key skill we, as maths teachers, push. The examiner wants to award marks (trust me I examine for an awarding body) but only if they can follow the working out. High standards of the setting out of work is not only a great study skill; it is important when submitting work to be marked externally, which probably isn't just happening in students' maths subject but in their vocational subject also.
The time saved by teachers in marking using a code, as the EEF (ref above) found, is worth considering. Time saving, wherever found, should be explored. The MATH marking code, as I suggest, may save time and deliver a more consistent student experience. I would also include the movement to a coded policy could enhance the student experience further as it moves away from tick and flick.
A tick at the end of the work doesn't tell a student what was good. Likewise a X at the end doesn't explain what or where they went wrong. I would love feedback to be given to inform students on every piece of work but we have to be mindful of teacher workload. I'm not going to stray into the difficulties in students receiving quality feedback, that might be another blog. A coded policy may be a handy bridge between tick and flick to full feedback, whilst also bringing focus on maths across all subject areas too.
In this example, the method and answer are correct but the setting out of work is wrong. There is no 24 x 37 = 888 but task met has been awarded as we can imply that is what was meant by the student. The method chosen hasn't been accurately applied, the 24 should have been where 88 is and 888 should arrive on the left hand side. I have indicated where the high standards also applies with the formation of 2 in 28. This may seem harsh to non maths specialists but these are the margins that can cause grades to change. Exam papers are scanned into a computer system to be externally marked for GCSE. Clarity is a key skill required. Opinions on this are all valid but these are the facts and the job of the maths teacher is to prepare students for their final exam, as it stands.
This is a paint mixing example from motor vehicle. Here the method is sound but there are errors in following through with numbers so A is not awarded. It is nearly set out and so H is awarded but the task hasn't been met as the final answer is incorrect and T isn't given. I can vision student reflecting on this and seeing that they have made mistakes within their working out using this code and seeking further guidance, or a teacher initiated discussion around the errors. The code is not the end of the journey but hopefully a consistent and speedy way to promote maths and high standards across colleges.
In this example the method is sound, there is accuracy throughout until the final stage which has meant the final answer is incorrect. H wasn't awarded as there is a mis-alignment of the expanded bracket and the =44.
I think M sits well, is there a sound method being used? A, is the student accurate in their application of the chosen method? T, have they answered the question that the teacher set them correctly? H, does the work read easily?
I have tried, unsuccessfully at a college previously, to embed this marking code. The college had a whole college numeracy marking code and didn't want to change. That code wasn't used by staff, it wasn't reviewed, it wasn't on A1 printouts on the walls (maybe that's where it fell down?) And it was a full page long. It had numeracy, processing, shape all included. For example, of drawing shapes must be done with a ruler. That awarded the  mark on the code. 0 indicated correct order of digits. You get the idea. It was lengthy and not shared regularly, most importantly it wasn't led from the front. Was it a policy to grab if OfSTED asked if they had one maybe?
What I'm suggesting here is a brief whole college marking code. Wherever calculations are used they are marked the same way. Consistency of message aligned to GCSE and functional skills maths marking codes. But it must be led, it can't be assumed others will follow it, maths needs pushing to the top of the agenda! If college resit results are to improve, something has to change. If you have a SPaG marking code do you have a maths one too? I would love to know more, is it commonly used, is it equally used as much as SPaG?
And if you don't maybe you might consider applying my MATH example?
Context whole links included to be more accessible rather than hyperlinked behind a word of text. I am a consultant to colleges on their teaching and learning, EdTech and embedding of maths; whilst still teaching GCSE maths in an FE college.


The first quilt that I am entering in Amy's Blogger's Quilt Festival is my Pi Quilt in the lap quilt division.
Both my husband and myself are engineers so for his birthday I knew that wanted to make a special math type quilt for him, thus design for the Pi Quilt was born. I wanted to paper piece the numbers and could not find a pattern of numbers I liked so I set off to make my own.
The resultant quilt contains 49 digits of Pi (including the period) with the numbers formed from over 700 individual pieces of fabric (and yes, about half way through I realized how insane this was!) I sashed the numbers in Kona white and added some borders with the Architextures line from Carolyn Friedlander.
For the quilting, I added a swirled vine pattern to the sashing to make the numbers stand out and a sharp line meandering pattern to the borders.
For any other math lovers / nerds / engineers out there (or a quilter with one of those in their lives), I have the pattern for the Pi Quilt listed for free in craftsy. The pattern works with any 3" x 5" numbers, but I also have my paper pieced numbers pattern (including three different sizes of numbers) listed on craftsy and etsy.
Quilt Measurements: 51.5" x 61.5"
Design by: Me (Meadow Mist Designs)
Quilted by…Me on my home machine, my old Singer.
Category – Throw Quilt
Link Number: ___
Thank you so much for taking a look at my quilt! I hope you stay awhile and have a look around the rest of my blog :) My second quilt entry, the Broken Pink Herringbone Quilt, can be found here.
Linking up toAmy's Creative Side, the Blogger's Quilt Festival, and the Throw Quilt Division


This past weekend I had the wonderful opportunity to attend the Annual Conference of the Association of Mathematics Teachers of New York State. Yes - me and Math. This conference gave me the opportunity to gain some skills in the "new" math (yes, I did number bonds!) and gather some terrific resources, including websites and apps. Below is a list of links that I think will provide you with some cool new FREE tools. If you'd like to use the apps, please let me know and I can load them on either our ipads or ideapads. Email me or come see me for details on how to reserve these items and load the apps. Many of the websites also have app versions. Check 'em out!
Cool Tech Tools for MathDesmos Graphing Calculator - Lesson idea : Graph your name! Includes an activity bank.
Hotmath - FREE math textbooks, review exercises, lessons and more.
Kahoot - Create, play and share fun learning games for any subject, for all ages, for free!
Quizizz - Multiplayer quizzes for any age.
Braingenie - AWESOME tool for students to build deep mastery and sharpen problem-solving skills. Students learn, practice and compete in real-time.
Plickers - "simple tool that lets teachers collect real-time formative assessment data without the need for student devices"
Flubaroo - Simple, free way to create and grade assignments online.
Khan Academy - "Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content."
Edpuzzle - Import, edit, create interactive video lessons. Super tool for the flipped classroom. I'm going to try this one myself!
Blendspace - Use Blendspace to create lessons and assessments that include a variety of digital resources.
Rekenrek and Number Rack apps - Excellent manipulative number line tool for younger elementary students.
13 Rules That Expire - Article by the National Council of Mathematics Teachers on math rules that eventually expire


15 July 2017 update: Maryam Mirzakhani, an Iranian-born mathematician who was the first woman to win the coveted Fields Medal, has died in a US hospital after a battle with cancer. She was 40.
Mirzakhani’s friend Firouz Naderi announced her death on Saturday on Instagram, and her relatives confirmed the death to the Mehr agency in Iran.
“A light was turned off today. It breaks my heart … gone far too soon,” wrote Naderi, a former director of Solar Systems Exploration at NASA.
“A genius? Yes. But also a daughter, a mother and a wife,” he added in a subsequent post.
Mirzakhani, a professor at Stanford University in California, died after the cancer she had been battling for four years spread to her bone marrow, Iranian media said. – Geo
A mathematician of Indian-origin has won the prestigious Fields Medal, known as the ‘Nobel Prize for mathematics’.
Manjul Bhargava, a Canadian-American professor of mathematics at Princeton University, was among four winners of the celebrated award.
Iranian-born Maryam Mirzakhani, who works in the US, has become the first ever female winner of the Fields Medal.
The medals will be presented in Seoul at the International Congress of Mathematicians, held every four years.
The other winners of the prize are Prof Martin Hairer from the University of Warwick, UK, and Dr Artur Avila, a Brazilian mathematician who earned his PhD in dynamical systems at the age of 21.
Mr Bhargava “is awarded a Fields Medal for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves,” according to the award citation.
The IMU website says Mr Bhargava’s work in number theory has had “a profound influence” on the field.
“A mathematician of extraordinary creativity, he has a taste for simple problems of timeless beauty, which he has solved by developing elegant and powerful new methods that offer deep insights.”
Born in 1974 in Canada, he grew up primarily in the US and spent some time in India. He has been teaching at Princeton since 2003.
The Fields Medal, established by Canadian mathematician John Fields, is regarded as akin to a Nobel Prize for maths and comes with a 15,000 Canadian dollar cash prize.


Associate Professor, Systems Engineering
Department of Electrical Engineering and Computer Sciences
Department of Civil and Environmental Engineering
Ph.D. Aeronautics and Astronautics, Stanford University, 2003
M.Sc. Aeronautics and Astronautics, Stanford University, 1999
Eng. Deg., Applied Math. Ecole Polytechnique, France, 1998
Research interests: Mobile internet applications (location based services), participatory sensing, inverse modeling and data assimilation, control, estimation and optimization of distributed parameter systems.