The topic of a points formula for Kings of War has reared its head again. It comes up from time to time and the truth is that there is no fixed formula where you type in the statlines and special rules and it gives you the points cost. We actually use a lot of comparisons between existing units, and a ratio for the points cost for a troop vs a regiment vs a horde (e.g. an infantry troop is worth 70% of the points cost of its regiment). I discuss it in the *ahem shameless plug* Clash of Kings book.
One of my first tasks when joining the Rules Committee was to try and come up with such a formula. I work in data modelling and have plenty of experience with complex spreadsheets, so I gave it my best shot.
I tried for a month in my spare time (obviously not every minute of my spare time, but it was a significant timesink and about as much work as I’d spend on a typical data model at work!). In the end I had something that… kinda worked… I guess… if you squint hard enough… The only special rules it could handle were Crushing Strength and Piercing, and it wasn’t particularly great when a unit had both good ranged and melee attacks. When it came to other special rules… that’s the point where I gave up.
There are plenty of ideas about how the formula could work. Sadly I’ve long since lost the copy I worked on, but I do remember how mine worked. I’m going to break a few of the high level calculations down and illustrate the problems I ran in to.
Note: If anyone doesn’t realise, I use the asterisk character (*) to show multiply by and a forward slash (/) to show divide by.
The calculation essentially came up with an arbitrary “score” for the unit. If I remember rightly, the basic Kingdoms of Men Shieldwall regiment had a score of 11.34632 (ok, the decimals are made up but it was eleven point something), and a unit that was twice as good as a Shieldwall would be worth 22.86924.
If we assume that we want the Shieldwall to be 100 points in-game, then we divide 100 by 11.34632 to give us a points multiplier of 8.81. Then we can take any score pumped out by the formula, multiply it by 8.81, and we get the points value for a score of that unit score.
(Points Value) = (Unit Score) * 8.81
Calculating the Unit Score
The unit score consisted of three calculated elements; the offensive value, the defensive value and the speed multiplier;
(Unit Score) = (Speed Multiplier) * ( (Offensive Score) + (Defensive Score) )
Let’s take the right hand part first; (Offensive Score) + (Defensive Score). I came up with separate scores for how much damage the unit can deal and how much damage the unit can take. These are first added together. They were essentially a total of the average damage that the unit could deal and the average damage that a unit would take, based on how prevalent crushing strength, piercing and various Defence values are in the game.
The other part of this equation is the speed multiplier. The faster a unit is in Kings of War, the better it is all round. We assume that the basic speed in the game is 5, so anything that is speed 5 is considered the norm. If something has a speed of 4 then it is worth less than an otherwise identical speed 5 unit, so its total score needs to be brought down a touch. In this case the multiplier for speed 4 might be 0.8. If we wrote a unit that was identical to the shieldwall, but had speed 4 instead, then we would multiply the shieldwall’s score of 11.3 by 0.8 to give us a unit score of 9.0. This would then correspond to a points value of 80 points.
On the flipside, if something was faster than speed 5 then it needed a positive speed multiplier, such as 1.2 for a speed 6. The whole speed multiplier table might look like this:
So a unit that was speed 9 would multiply its total offensive and defensive score by 1.8, to give its total unit score.
Already we’re seeing an issue.
How do you determine what those multipliers should be?
The ones above are just an educated guess. It means that any Speed 7 units are balanced with each other, but how do you know that 1.4 is a good multiplier for speed 7 rather than 1.3 or 1.35 or even 2.0? They might be balanced with other speed 7 units, but would they be paying too much or too little compared to units of other speeds?
To take it to extremes, if we set the multiplier for Speed 6 to be 1.5, that wouldn’t be balanced in my opinion. I would never pay 50% more points for a speed 6 unit that was otherwise identical to a speed 5 unit.
The issue with this table is that it relies on human intuition, which is what the formula is intending to get away from. We could look back to existing unit types, find similar or identical units with slightly different speeds and try to figure out what the ratio between them is, but that again assumes that the original points value, the one derived from human intuition, is correct. There’s no way to be certain of that and it kind of undermines the entire point of the formula if one of its main calculations is based on human intuition.
Special Rules Multiplier
The missing part of the Unit Score calculation was something that I didn’t even attempt – a multiplier for the unit’s special rules. Some special rules, such as Crushing Strength have a measurable effect on a units performance and can be included in the offensive or defensive score calculation. Others, such as Nimble, don’t have a direct impact on the offensive/defensive scores, but actually impact on everything. Fly for example, gets exponentially better the faster, stronger and tougher a unit is. Fly on a troop of Orc Ax would be fairly lacklustre compared to the same thing on a dragon. I wouldn’t pay 30 points for Fly on a unit of Orc Ax since the speed holds them back so much, but 30 points for fly on say a heavy cavalry unit? Hell yes!
The unit score calculation should therefore be something like:
(Unit Score) = (Speed Multiplier) * ( (Offensive Score) + (Defensive Score) ) * (Special Rules Multiplier)
Each special rule would have to have its own formula for determining its multiplier. A very simple one might be Inspiring which had a fixed multiplier of say 1.2. The better a unit is, the better Inspiring is since not only does it inspire itself, but it’s able to stick around longer if it’s an otherwise better unit.
A special rule might not be a fixed multiplier either. Nimble and Fly could be exponentially better and have to be done more like the speed multiplier above, where the higher the Speed and Offensive/Defensive scores, the larger the multiplier is.
Nimble provides another issue – it not only needs to multiply the overall score of the unit, but the score for its shooting output since nimble units ignore the moving & shooting modifier.
We’ve not touched on how a special rule loses its worth the more common it is. Ogres have Brutal on nearly every single unit, however that +1 from brutal is only ever applied once per combat. It doesn’t matter if one unit or three units are in a combat with Brutal; the effect is the same – it’s still a single +1 modifier. I’d happily pay the 15 points for the Brutal artefact in an army that doesn’t have the rule, but I would not pay 15 points for every single Ogre unit to have it. The same applies for pathfinder; there’s only so much terrain on the board for you to benefit from. At some point you’ve filled every available forest with your units, so it’s wasted on all your other units.
On TOP of all this, we come back to the same issue that plagues the speed multiplier. Whatever that calculation is for the special rule, it ultimately comes from human intuition. If that baseline human intuition is wrong then the calculation is also wrong. Units with the same special rule might be balanced with each other, but they wouldn’t be balanced with units without the special rule. If we had the multiplier for Brutal be 1.5, then any units with Brutal would be balanced against other units with Brutal, but I sure as hell wouldn’t pay 50% more points for Brutal. Equally if we had the multiplier for Yellow Bellied be 0.5 then they would cost half of their equivalent units without yellow bellied! That would be ridiculous!
Extremes, obviously, but illustrating the point!
Formulas don’t work
The whole point of using a points formula is to remove human intuition and mistake. You could sit there for weeks and months deriving rules and multipliers for every single special rule in the game. Ultimately, at some point in the equation, there’s going to be a baseline number that’s derived from human intuition. That basic cost for a special rule, that basic assumption for how many De6 units are in army lists so how valuable your Crushing Strength(4) is, they all come from human intuition and are susceptible to error.
If someone wants to go ahead and write an amazing formula that spits out perfect points values according to all the units we’ve entered in the game, then please do so. I don’t personally think it’s a productive use of time, unless you’re doing it purely for academic reasons, but if it works then we will use it.
One of the guys illustrating that we don’t use a formula, therefore the game is “grossly” unbalanced, used the example of a Knight Horde that he calculated to be 10 points less than it should be. Regardless of the calculation he used (which was wrong), even if something it’s 10 points undercosted, that’s not enough to swing the game. An imbalance of 3.9% is nothing. Nearly every single unit is going to be ever so slightly under or overcosted, if just because we round points values off to the nearest 5. Overall it’s going to work out to a roughly even cost, and even if you were to take only units that are undercosted, as long as that slight imbalance is not enough to override player skill, we’re not bothered.
Perfect balance is impossible. We’ve got it pretty damned close without a formula, and those problematic units that we under or overcosted significantly, we’ll address in annual tournament pack updates.


The Russian School of Mathematics works with many students and parents around the world to curb the problem of mathematical instability. RSM Parent Portal was founded by Inessa Rifkin and founder Iren Khavinson in 1997. The main purpose of this program was to assist in primary maths.
The program helps children improve students’ marks in maths and go to K-12 in all schools, public and private schools. As you know, Mathematics education is a challenging subject for several students around the world. Solving different formulas for each problem proves that it is not easy to understand in a general study. High school students are ready to take the standard exams such as the SAT, SAT II, and AP exams.
RSM Parent Portal has spent ten years developing a unique curriculum to achieve this goal. Instead of providing a quick fix, our unique curriculum and learning approach allows students to build a deeper and lasting understanding. This program uses a lot of tests, examples, and real learning materials to help keep a clear memory of the mathematical problem they are solving.
The Russian school of mathematics originally started in Boston in Inessa’s founding room of the founder. The small startup has helped thousands (15,000) students worldwide and enrolled in the program. Students do not grow up in their comfort zone, so we make sure they are always equally challenged (and rightly so).
Students become accustomed to and enjoy the idea that problems require concentration, thinking, and persistence. The school does this by constantly involving our students in complex and unusual situations, where they have to push the limits of their knowledge to find a solution.
The school has various facilities and an online program for serving others from different parts of the world. RSM is located in New York, California, Kentucky, Illinois, Washington, Connecticut, New Hampshire, and New Jersey. Now, RSM is one of the oldest and most effective after-school plans in the United States. Our graduates have achieved impressive results in school, general exams, college, and beyond. Their program has appeared several times in the Boston Globe and appeared in the New York Times.
How do you log in to the RSM Student Portal?
So now we let you people know how to access the biggest platform of learning Mathematics globally by following these steps are as follows:
- For better reach, visit the link.
- Enter your login details, provided at the time of registration or by the RSM official on the RSM website.
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- You can now log in to the page and select the service you want to receive.
Note the official website page is www.russianschool.com, with no other links provided by the school.


Links Academy offers Functional Skills in English and Mathematics from Entry 1 to Level 2. Suitable for learners of all ages, they’re also a mandatory part of all Apprenticeship frameworks in England.
Problem solving is at the heart of Functional Skills, they require the learner to apply their knowledge and understanding in a range of familiar and unfamiliar situations. Functional Skills are a mandatory element in apprenticeships as well as being stand-alone qualifications in their own right at Entry Level 1-3, Level 1 and Level 2. Level 1 Functional Skills are equivalent to a GCSE Grade E-D, and Level 2 Functional Skills are equivalent to GCSE Grade C-A*.


FIXED INCOME STATISTICS
Average Price is a price of bond's interest- rate sensitivity based on the average of the price over which a bond's cash flows accrue to the bondholder.
Source: Thompson, Siegel & Walmsley LLC
Average Maturity is computed by weighting the maturity of each security in the portfolio by the market value of the security, then averaging these weighted figures.
Average Duration is a time measure of a bond's interest-rate sensitivity, based on the weighted average of the time periods over which a bond's cash flows accrue to the bondholder.


Thursday, April 18, 2013
According to a recent theory the Universe could be a dodecahedron. It is surprising that Plato used a dodecahedron as the quintessence to describe the cosmos. Plato (c. 427 BC – c. 347 BC) also stated that time had a beginning; it came together with the universe in one instant of creation.
Plato held the view that mathematical objects really existed so that they are discovered by mathematicians (in the same way that new continents are discovered by explorers) rather than invented. Plato believed that mathematics provided the best training for thinking about science and philosophy. The five regular solids are named Platonic Solids today after Plato.
Of the 5 solids, the tetrahedron has the smallest volume for its surface area and the icosahedron the largest; they therefore show the properties of dryness and wetness respectively and so correspond to Fire and Water. The cube, standing firmly on its base, corresponds to the stable Earth but the octahedron which rotates freely when held by two opposite vertices, corresponds to the mobile Air. The dodecahedron corresponds to the Universe because the zodiac has 12 signs (the constellations of stars that the sun passes through in the course of one year) corresponding to the 12 faces of the dodecahedron.
“To earth, then, let us assign the cubic form, for earth is the most immovable of the four and the most plastic of all bodies, and that which has the most stable bases must of necessity be of such a nature. Now, of the triangles which we assumed at first, that which has two equal sides is by nature more firmly based than that which has unequal sides, and of the compound figures which are formed out of either, the plane equilateral quadrangle has necessarily a more stable basis than the equilateral triangle, both in the whole and in the parts. Wherefore, in assigning this figure to earth, we adhere to probability, and to water we assign that one of the remaining forms which is the least movable, and the most movable of them to fire, and to air that which is intermediate. Also we assign the smallest body to fire, and the greatest to water, and the intermediate in size to air, and, again, the acutest body to fire, and the next in acuteness to air, and the third to water. Of all these elements, that which has the fewest bases must necessarily be the most movable, for it must be the acutest and most penetrating in every way, and also the lightest as being composed of the smallest number of similar particles, and the second body has similar properties in a second degree, and the third body, in the third degree. Let it be agreed, then, both according to strict reason and according to probability, that the pyramid is the solid which is the original element and seed of fire, and let us assign the element which was next in the order of generation to air, and the third to water.We must imagine all these to be so small that no single particle of any of the four kinds is seen by us on account of their smallness, but when many of them are collected together, their aggregates are seen. And the ratios of their numbers, motions, and other properties, everywhere God, as far as necessity allowed or gave consent, has exactly perfected and harmonized in due proportion.“
Plato: Timaeus (55d-56c) p 1181
The posters visualize the five solids in space creating a surreal depiction of Plato’s Universe.


Microsoft KB Archive/36735
Article ID: 36735
Article Last Modified on 11/21/2006
This article was previously published under Q36735
Microsoft QuickBASIC Version 1.00 for the Apple Macintosh does not use Standard Apple Numeric Environment (SANE). Microsoft QuickBASIC (b) uses its own IEEE standard binary floating-point routines, which are faster than using SANE. Microsoft QuickBASIC (d) uses a decimal math package that is slower but more accurate for business calculations (such as making dollars and cents add up exactly).
SANE is the set of methods that provides a basis for floating-point calculations in Apple computers. SANE meets all requirements for extended-precision, floating-point arithmetic as prescribed by the IEEE Standard 754 and ensures that all floating-point operations are performed consistently and return accurate results. This information about SANE is from the "Technical Introduction to the Macintosh Family," by Apple Computer, Inc. (Published by Addison-Wesley, 1987).
For more information about SANE, please refer to the "Apple Numerics Manual", which should be available from Apple Computer, Inc. or Apple Dealers.
(The "Apple Numerics Manual" used to be available from the Apple Programmer's and Developer's Association (APDA), but Apple Computer, Inc. has taken over the functions of APDA for offering official Macintosh technical manuals and developer-oriented products through mail-order.)
Additional query words: MQuickB


Ph.D. in Applied Mathematics, May 2012, New Jersey Institute of Technology, USA
Dissertation: Instabilities in Newtonian films and nematic liquid crystal droplets.
Advisors: Dr. Lou Kondic and
Dr. Linda J. Cummings
M.S. in Applied Mathematics, National Chung Cheng University, Taiwan
Thesis: Numerical methods for the nonlinear Schrodinger equation
Advisor: Dr. Ming-Chih Lai
B.S. in Mathematics, National Chung Cheng University, Taiwan
2012.12--2014.07 Research Associate, Loughborough University, UK
2012.06--2012.12 Marie Curie Experienced Researcher, Loughborough University, UK
Coherent structures in non-local dispersive active-dissipative systems T.-S. Lin, M. Pradas, S. Kalliadasis, D. T. Papageorgiou and D. Tseluiko,
Modeling flow of nematic liquid crystal down an incline
M. A. Lam, L. J. Cummings, T.-S. Lin and L. Kondic, J. Eng. Math., in press.
Numerical study of a non-local weakly nonlinear model for a liquid film sheared by a turbulent gas T.-S. Lin, D. Tseluiko and S. Kalliadasis, Procedia IUTAM, 11, 98 (2014).


The purpose of the study was to investigate the secondary level students’ learning difficulties in mathematics in the areas of Geometry, Arithmetic and Algebra. All math teachers and students of public secondary schools of nine towns of Lahore was the population of this study. The sample of 60 mathematics teachers and 300 students was selected through simple random sampling. Researcher adapted two questionnaires with 21 items each, one for the teachers and other for the students with reliability values 0.966 and 0.941 respectively. Findings of the study revealed that teachers highlight students as feeling difficulty in learning Geometry, Arithmetic and Algebra. Similarly, students also pointed out that they face difficulty in learning Geometry, Arithmetic and Algebra.


You’ll come across a vast assortment of z methods for preschoolers
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How to generate a PHP Random Number?
How to generate a PHP Random Number? This is simple tutorial to generate random number in php using PHP rand function. This PHP rand function can be used to generate a random number from a minimum and maximum number limit or we can generate a complete random number. Here is the syntax of PHP rand function and example code for using PHP rand function, and generating random number from PHP rand function.
Syntax of php rand function
Generate a random number without setting any limits.
[/php] If you want to set a upper & lower limit for generating a random number then use
$max variables. Where
$min is the minimum number and
$max is the maximum upper limit for generating random number.
[php] rand($min, $max)
You can use minimum and maximum values for generating a php random number between two values one is lower value and the other one is upper value.
For example if you want to generate a number between 100 to 1000, then we can php rand function to do this by using below code.
It generates a number in between 100 and 1000, but not less than 100 and not greater than 1000.
[php] rand(100, 1000)
In the same way if you want to generate a five digit number, then use this below code.
Then random number will be in between 10000 and 99999, so that it is always generates a five digit number.
[php] rand(10000, 99999)


Do you ever need to measure out a specific quantity of liquid, but don’t know how many ounces are in a cup? Don’t worry, you’re not alone! This is a common question that many people have. In this blog post, we will provide a comprehensive guide on how many ounces are in a cup. We will also discuss other common liquid measurements, such as tablespoons and milliliters. Stay tuned for more information!
Table of Contents
What is an Ounce?
An ounce is a unit of measurement for weight and mass. It is equal to 28.34 grams, or about 0.96 ounces avoirdupois (the standard unit of measurement for weight). The common ounce you are familiar with is actually the international avoirdupois ounce. This is the type of ounce that is used in the United States.
There are other types of ounces, however. The troy ounce, for example, is used to measure precious metals like gold and silver. It is equal to 31.103 grams, or about 0.91 troy ounces. There is also the apothecaries’ ounce which is used to measure medicine. It is equal to 28.35 grams, or about 0.96 apothecaries’ ounces.
How Many Ounces in a Cup?
The short answer is: There are eight fluid ounces in a cup.
How many grams in a cup?
This is a question that I get asked a lot. The answer, unfortunately, is not as simple as you might think.
There are actually two different types of cups that you need to take into account when asking this question – the metric cup and the imperial cup. A metric cup holds 250ml (or approximately 0.26 quarts) of liquid, while an imperial cup holds 284.131ml (or approximately 0.30 quarts).
This means that there are different conversion factors for each type of cup. Using the metric cup, we know that there are 250 grams in a cup. However, using the imperial cup, we know that there are only 227.3045 grams in a cup.
How many ounces in a cup and a half?
A cup and a half is equal to 24 fluid ounces. So, if you’re looking to know how many ounces are in a cup and a half, simply multiply 24 by the number of cups and a half you have. For example, two cups and a half would be equal to 48 fluid ounces. Easy peasy!
How many ounces in a cup dry?
This is a question that often comes up, especially when baking. The answer is actually quite simple – there are eight ounces in a cup dry. So, if you need to measure out a cup of flour for your recipe, you would use eight ounces of flour.
How many ounces in a cup of butter?
This is a question that I am often asked, and it can be a bit tricky to answer. The reason being is that there are actually two different types of cups when it comes to measuring ingredients – dry measure cups and liquid measure cups.
Dry measure cups are typically used for measuring things like flour, sugar, and other baking ingredients, and they are designed to hold a precise amount. One cup of flour, for example, will always weigh the same no matter how it is packed into the measuring cup.
Liquid measure cups, on the other hand, are used for measuring liquids like milk, water, and oil. They are not as precise as dry measure cups, and the amount of liquid they can hold will depend on how full they are.
How many ounces in a cup of cheese?
This is a question that often comes up, especially when cooking or baking. The answer can actually vary depending on the type of cheese. For example, shredded cheese generally weighs less than cubed cheese.
In general, however, there are about eight ounces in a cup of cheese. This means that there are two cups in a pound of cheese. So, if a recipe calls for one pound of shredded cheese, you would need to use two cups.
How many ounces in a cup of coffee?
This is a question that many coffee drinkers have. The answer is actually quite simple. There are eight ounces in a cup of coffee. This means that there are two tablespoons in a cup of coffee. Thus, if you want to make a stronger cup of coffee, you can simply add more coffee grounds to your brew. If you want a weaker cup of coffee, you can add less coffee grounds. It’s really that simple!
How many ounces in a cup of flour?
There are a few different ways to answer this question, as the conversion rate can depend on whether you’re measuring by weight or volume.
Generally speaking, there are about eight ounces in a cup of flour. However, if you’re measuring by weight, the conversion rate is slightly different. In this case, there are approximately four and a half ounces in a cup of flour.
No matter how you measure it, a cup of flour is generally equivalent to eight ounces. However, if you’re measuring by weight, the conversion rate is slightly different. In this case, there are approximately four and a half ounces in a cup of flour. This means that there are slightly more than eight ounces in a cup of flour when measuring by weight.
How many ounces in a cup of rice?
This is a question that many people ask, especially when they are first learning to cook. The answer is actually quite simple – there are eight ounces in a cup of rice.
Now, this doesn’t mean that you should just go and measure out eight ounces of rice every time you want to make a cup. The amount of water that you use will also affect the final outcome.
For example, if you use too much water, your rice will be mushy. On the other hand, if you use too little water, your rice will be hard and dry.
So how do you know how much water to use? A good rule of thumb is to add enough water so that it comes up to about an inch above the level of the rice.
Once you’ve added the water, give it a stir and then put a lid on the pot. Bring the pot to a boil over high heat.
Once it reaches a boiling point, reduce the heat to low and let it simmer for about 20 minutes. After 20 minutes, turn off the heat and let the pot sit for another five minutes.
How many ounces in a cup of shredded cheese?
The answer may surprise you – there is no definitive answer! The amount of cheese in a cup can vary depending on the type of cheese and how tightly it is packed.
For example, one cup of loosely packed shredded cheddar cheese can weigh anywhere from four to six ounces. So if you’re looking for an exact measurement, it’s best to go by weight rather than volume.
How many ounces in a cup of water?
This is a question that often comes up, particularly when people are trying to measure out precise amounts of water for cooking or baking.
There are actually two different types of measurements for cups – the U.S. customary cup and the metric cup. A U.S. customary cup is equivalent to 0.23 liters, while a metric cup is equivalent to 0.25 liters.
How many ounces in a gallon?
There are 128 ounces in a gallon. This means that there are 16 ounces in a pint, 32 ounces in a quart, and 64 ounces in a half-gallon.
When converting from gallons to other units, it is important to remember this relationship. For example, if you want to know how many pints are in a gallon, you would divide 128 by 16 to get the answer: eight pints.
Similarly, if you want to know how many quarts are in a gallon, you would divide 128 by 32 to get the answer: four quarts. Finally, if you want to know how many half-gallons are in a gallon, you would divide 128 by 64 to get the answer: two half-gallons.
Knowing how many ounces are in a gallon is important for many reasons. For instance, when you are baking, it is often necessary to measure ingredients by the ounce.
Therefore, if a recipe calls for one gallon of milk, you would need to use 128 ounces of milk. Similarly, if you are making a pot of soup that calls for one gallon of broth, you would need to use 128 ounces of broth.
In addition, many people like to drink water throughout the day and may want to know how many ounces they should aim to drink in order to reach their daily recommended intake. For example, if you need to drink eight cups of water per day, and there are eight ounces in a cup, then you would need to drink 64 ounces of water per day.
There are many other applications for knowing how many ounces are in a gallon. For instance, if you are filling up a gas tank that holds 15 gallons, you would need to use 1920 ounces of gasoline.
Similarly, if you are buying laundry detergent by the gallon, you would need to use 128 ounces of detergent. Ultimately, whether you are baking, cooking, or simply trying to stay hydrated, it is important to know how many ounces are in a gallon. After all, this conversion is one of the most basic and essential conversions there is.
How many ounces in a pound?
There are 16 ounces in a pound. This means that there are 28 grams in an ounce, and 45359237 grams in a pound.
To convert from pounds to ounces, divide the number of pounds by 16. For example, if someone weighs 120 pounds, they would have 120/16 = 75 ounces.
Conversely, to convert from ounces to pounds, multiply the number of ounces by 16. So, if someone has 75 ounces of something, they have 75*16 = 1200 grams.
Is 16 oz same as 1 pound?
No, 16 oz is not the same as one pound. One pound equals 16 ounces, but that doesn’t mean that every 16 ounce object weighs one pound. The weight of an object depends on its density, which is the amount of mass per unit of volume. So, an object with a higher density will weigh more than an object with a lower density, even if they have the same volume.
For example, one pound of feathers will take up a lot more space than one pound of lead. But since lead is much more dense than feathers, it actually weighs less. So 16 ounces of feathers will weigh more than 16 ounces of lead, even though they both have the same volume.
This is why it’s important to know the density of an object when you’re trying to determine its weight. The denser an object is, the more mass it has for a given volume. And that means it will weigh more than a less dense object of the same size.
How many fl oz are in a pound?
This is a question that many people have. The answer may surprise you. There are actually 16 fluid ounces in a pound. This means that there are 128 tablespoons in a pound or 768 teaspoons. So, if you ever need to know how many tablespoons or teaspoons are in a pound, now you know!
How much does 16 oz of milk weigh?
This is a question that I get asked a lot, and it’s one that doesn’t have a straightforward answer. The weight of milk depends on a few factors, including the type of milk (whole, skim, etc.), the fat content, and whether or not the milk has been homogenized.
Generally speaking, 16 oz of whole milk will weigh between one and two pounds. Skim milk is typically lighter, with 16 oz usually weighing around one pound. Homogenized milk falls somewhere in the middle, with a weight of 16 oz usually being around one and a half pounds.
Which is heavier a gallon of milk or water?
Many people believe that a gallon of milk is heavier than a gallon of water, but this is not actually the case. A gallon of water weighs about eight and a half pounds, while a gallon of milk only weighs about eight pounds.
So, while milk is certainly denser than water, it is not actually heavier. This misconception likely arises from the fact that milk is often sold in heavier containers than water.
A gallon of milk is typically sold in a plastic jug that weighs about two pounds, while a gallon of water is usually sold in a one-pound bottle. So, when you compare the weight of the container to the weight of the liquid, it appears as though milk is heavier.
Of course, this is all relative. A gallon of milk is still much lighter than a gallon of gasoline, which weighs about six and a half pounds. And a gallon of milk is also lighter than a gallon of honey, which weighs about 12 pounds. So, if you’re ever in need of some extra weight for your car or your pantry, milk is not the way to go. Water is still the heaviest liquid you can find.
How much does one gallon of jet fuel weigh?
This is a question that many people ask, especially those who are interested in aviation. The answer may surprise you – jet fuel weighs less than water! A gallon of jet fuel weighs about six and a half pounds, while a gallon of water weighs close to eight pounds. This means that jet fuel is actually lighter than water.
The reason jet fuel is so light is because it is a type of aviation gasoline. Aviation gasoline is made up of lighter hydrocarbons than regular gasoline. This makes it easier for planes to take off and fly.
How much does 8 oz of water weigh?
The short answer is that one ounce of water weighs about 28.35 grams. So, to answer the question, eight ounces of water weigh about 226.80 grams. Of course, this assumes that we’re talking about pure water. If you’re measuring something like seawater, which is saltwater, then the weight will be slightly higher.
In conclusion, there are 16 ounces in a cup. This is a simple conversion to remember and is very useful when you’re baking or cooking. Now that you know how many ounces are in a cup, you can measure out your ingredients with ease! Thanks for reading and happy cooking!


Does or will Sage support the Visual Python module?
asked 2012-01-08 10:03:14 -0500
This post is a wiki. Anyone with karma >750 is welcome to improve it.
Does or will Sage support the Visual Python (http://vpython.org/) module?
I use it to create 3D examples for several of my courses including Calculus III, Differential Equations, Modern Algebra, Combinatorics and my students use it for projects in both Modern Algebra and Scientific Computation.
Adam Hausknecht, Department of Mathematics, UMass Dartmouth


About FOSSEE Animations
The FOSSEE Animations Project works on making seemingly complex Science and Mathematics topics feel natural and approachable through animations.
The animations are created by students across the country. The students work with a mentor in creating a library of visualizations.
FOSSEE Animations is a part of the FOSSEE
project at the Indian Institute of Technology, Bombay
. The FOSSEE project is funded by the National Mission on Education through ICT, MHRD, Government of India.
All animations are made with open-source toolkits and are freely available under a Creative Commons Attribution-ShareAlike 4.0 International License. The animations themselves are open-source. You may find them here
Anyone can contribute to this project! You may read the Guidelines page
for detailed instructions on how you can contribute.
Math Internships and Workshops (on Visualizing Math with Open-Source toolkits) are conducted throughout the year. Visit our Outreach
page for more details on the same.
Internships are from selected topics in Mathematics, like Real Analysis, Linear Algebra and Calculus. Our focus lies primarily on an undergraduate level of Mathematics. To view our repository on Mathematics topics, visit math.animations.fossee.in
We also conduct workshops in colleges and universities across India. You can write to us at firstname.lastname@example.org
to request a workshop at your college.


Stability of solutions of differential equations and its application in economic models
|Author:||Bc. Filip Ravinger|
|Year:||2005 - summer|
|Leaders:|| doc. RNDr. Miroslav Zelený Ph.D.
|Work type:|| Bachelors
|Awards and prizes:|
|Abstract:||Differential equations represent one of possible methods for modelling dynamic systems. This paper seeks to illustrate how the apparatus of differential equations can be applied in economic modelling and to emphasise their importance in description of real-world processes. Qualitative analysis of the solutions of systems of differential equations is primarily focused on. The central notion of the paper is the notion of stability of solutions, which is interpreted in economic application as stability of given system of simultaneously acting economic factors.
The first chapter examines in detail the mathematical tools that are used to accurately construct the dynamic model. The
grounds of the theory of systems of differential equations is explained. This knowledge and the particular techniques are then utilised in the second chapter, where the model of Walrasian competitive equilibrium is studied. The main issue is the question of stability of the equilibrium price adjustment process. Mathematically correct exposition is one of the aims of the paper.


Logic Cards Yellow is the second edition of Logic Cards with all new challenges – a set of logic, geometry, and mathematical tasks to tease your brain. It comes with an augmented reality app, that shows you animated solutions for each challenge. The challenges have various difficulty levels to choose from. The pack fits in your pocket and you can take it anywhere with you. It’s educational, it’s math, it’s smart, and it’s a maze of IQ boosting fun! Enjoy yourself! Logic Cards Yellow includes 53 cards with number, logic or geometry challenges in 5 difficulty levels, instructions, answers and a solutions app.


Italians are known for their food, their women, and alas, their cars. Now we can add math to their list of talents, based on this simple equation: One Ferrari F430 + 20 horsepower - 220 pounds = the new Ferrari 430 Scuderia. Basically a street-legal version of the F430 Challenge racer, the 430 Scuderia includes ceramic brakes, a revised transmission, some minor aero tweaks, and numerous weight-saving measures intended to show how directly Ferrari's F1 program benefits its road cars. As if we didn't know.
Get the Best Deal on a Ferrari F430
Build and Price


Q: What courses should be taken during the first year?
Analytical, computational and technological skills have become increasingly important in many disciplines and professional careers. We therefore encourage students to improve and further develop those skills, independent of their intended majors, by taking courses in Mathematics and Computer Science in their first year in college.
To enroll in an introductory mathematics course, students (with the exception of those with advanced-placement credit in calculus) must take the Mathematics Placement Test given during preregistration. Based on placement test scores, students are place into Precalculus, Calculus, or Honors Calculus. Students are encouraged to enroll in the course according to their placement . Students may challenge their placement by taking a backup placement test once.
Two Calculus tracks are open to students with appropriate scores in the Mathematics Placement Test: the regular track MATH 120-MATH 121, and the Honors track MATH 124-MATH 125. Both tracks start in the Fall. Students who do not place into Calculus, but place into Precalculus (MATH 119), can start with MATH 119, to prepared for Calculus and continue with MATH 120 the following year.
The regular track is the less theoretical Calculus sequence (MATH 120-MATH 121). It is geared toward students interested in the natural and social sciences, as well as Computer Science. Many of those studetns will not continue with upper level mathematics classes. Students in this sequence who plan to continue to study mathematics in the future are encourage to take MATH 121 in the Spring semester of their first year.
Honors Calculus (MATH 124-MATH 125) is the more theoretical track and prepares students for intermediate and upper level mathematics classes. It is therefore recommended that students with a strong mathematical background, who intend to take higher-level mathematics classes in the future, start with MATH 124-MATH 125. Those students are usually interested in Mathematics, Physics, Computer Science, and Economics.
Students with a sufficiently high score on the AP (AB) Calculus test receive credit for MATH 120. This credit fulfills the prerequisite for MATH 121, but not for MATH 125. It is recommended that these students start with MATH 124 and continue into MATH 125 if they are interested in taking higher-level mathematics classes in the future.
Students with a sufficiently high score on the AP (AB/BC) Calculus test receive credit for MATH 121 and may continue with MATH 130. In the exceptional circumstances, first-year students without credit for MATH 121 may enroll in MATH 130 with permission fo the instructor.
Q: What courses should first year students steer clear of?
Most mathematics courses have to be taken in a particular sequence. Students are not allowed to register for courses without fulfilling the necessary prerequsities first. For this reason, a mathematics major cannot be completed in less than three years.
Q. Does the deparment offer a First-Year Intensive course?
The department offers 2 FYI courses: 1) Diving into Mathematics Research (MATH 110); 2) Diving into Computer Science Research (CSci 110). It is a 5th class for all students, and it is spread over the course of the year with 0.5 credits per semester. It gives first-year students a unique opportunity to work with faculty and peers on interesting current research projects and to become a part of an intellectual and social community of students with similar interests. Both courses are by permission only and there is a limited number of spaces. With few exceptions, only students with a strong background in Mathematics who register for Honor Calculus or have credit for Calculus with be allowed to join in the class. Students interested in Mathematics research should contact Professor Gideon Maschler (firstname.lastname@example.org). Students interested in Computer or Computational Science should contact Professor Natalia Sternberg (email@example.com).
Q: Where should students or faculty go for more information?


A simple game of touching the numbers on the screen in the right order, i.e. 1, 2, 3, 4, etc.
The faster you do it, the higher the score.
Its a pretty straightforward, yet challenging game, just press real quick (and accurately). You just press the buttons in numeric order - 1, followed by, 2, 3, and so on. The more buttons you press correctly by the time the game ends, the higher your score. If you press correctly consecutively, you will get higher scores.


Monday, October 15, 2012
Third World Farmer
After looking at various games, I chose Third World Farmer. I think this game gives the student the opportunity to problem solve and by the choices made, they will either succeed or fail. I have played this game five times and I have to admit I was horrible at first! But, each time I am getting better and better! This game really forces the student to understand world problems and to use cognitive skills.
Using Third World Farmer, I would have my students keep of log of how much money they have, what they spend for the year and how much they made, repeating this every year. The objective would be for the students to understand adding and subtracting figures in a non-traditional math way (solving equations). This would ready them for their own life, learning how to manage money. They would have to present the log that they have kept and explain to the class what money they used and what they made each year and if they had enough left over for the following year and the outside factors that affected this.
I could also use this game as a history/geography lesson. The objective would be to understand and discuss how resources affects life in third world countries. They will also be able to compare and contrast our own life with those in a third world, like Africa. Working in small groups, students can compare and contrast their own life to that of Africa's. Then, as a class, we can discuss the results before having the students write their findings. Talking in a small group (where some may feel more comfortable talking) and then in a larger class group will give the students plenty of ideas and time to ask questions before having to work on their own and write their conclusions.


- The size of a single person escape pod
- Maybe the size of a small shuttle
- A cruiser (maybe 100m)
- Massive (a kilometre or so)
Here's the image.
It was proposed that maybe the form was the size of a tablet "Take two of these an call me in the morning" (+David VC), and certainly that was a size option I hadn't added to the mix.
At this point, I've had 53 votes in the following pattern
Generally, that gives high votes around the small shuttle or cruiser size. I can see that, the level of detailing might need to be higher in a larger form, the bulbous forms at one end (which might be fuel pods) and the structural scaffolding seem to imply upper and lower limits around that point.
I'm seeing the various vote levels as exponential size categories, each one ten times longer than the one before.
- 10 - 20cm
- 1 - 2m
- 10 - 20m
- 100 - 200m
- 1km - 2km
With that in mind I'm thinking of throwing some formulas down to determine an average size for this thing. The mean average of the 53 votes is 3.35849. Because our votes are in an exponential progression of "10 to the x", we'd need to apply this mean average as an exponent. This gives us a figure around 2282.91. The base size is 10-20 cm (lets call it 15)...and that gives us an overall length of 342.43 metres.
A preliminary render of this piece of technology in the Darkhive might look like this. I think it's actually a bit big for the scale democratically chosen by the people (maybe twice as big as it needs to be), but I'll sort that out in the next render. There would also need to be some kind of damaged roof section where the ship/artefact crashed into the hive (unless it mystically teleported into it's current location).
I'll throw in a few more overgrown rubble piles and maybe a shanty town that scavenges stuff from this wreckage to trade with other communities.
Here's a wireframe of that model (before I've made the scale modifications).
Time to modify some scales before we go much further.


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Affiliate Marketing: What Do you Mean by High Converting Affiliate Programs
A high converting affiliate programs are programs that have a very high ratio of sales compare to the number of visits that the website have. For example, if the website got 100 people visiting it and there is one sale, the website's conversion is 1%.
It will of course be better if for every 100 people, there are 10 sales which will means that the conversion is higher and you earn more commissions. You have to know that conversion is really all about how much work that you have to put in to get the commissions.
For example, you pay $5 on a pay per click advertising campaign and you are able to generate 200 visitors to the merchant's website which claims to have a 30% conversion. If the merchant is selling the product for $57 and you will get a 75% commission for every sale, the number will look like this:
200 Visitors at 30% will be equal to 60sales. For every sale you make, you will make a commission of 75% on $57 = $42.75. Total sales that you will have are $42.75 multiply by 60 which will be a total of $2565. You will make a net profit of $2565-$5 = $2560.
Imagine how much different it will make to your income if you are able to choose a affiliate program that has high conversion. Since you will be putting in the same effort, why not choose one that has got higher conversion so that you will be able to earn more.
This are the reason why you must choose programs with high conversion rate and it will also be good if you can find one affiliate programs that offers high commission percentage as well.


Congratulations to Mr. Alvarado, our Project Lead the Way: STEM teacher! Mr. Alvarado received a Quality Science and Math (QSM) Grant. The grant was given to teachers who were looking for a way to purchase instructional materials and equipment for their math, science or STEM class. Through the grant, Mr. Alvarado was able to purchase a new 3-D printer and other instructional materials for students in grades 5 - 8. Bravo, Mr. Alvarado!
Mr. Alvarado Wins QSM Grant
DEC 16, 2022


Incredible GCSE Success for Inspiration TrustBack
Inspiration Trust wants to say a gigantic well done to all of its pupils, teachers, and parents/carers today, as after two years of unprecedented disruption surrounding the pandemic, incredible GCSE results have been achieved!
Hethersett Academy has seen stratospheric results with 90% 9-4 grades in Maths and English, with 1 in 3 grades being 9-7 and an impressive 10 pupils achieving straight nines! Across all GCSES, the percentage of 9-4 grades is 92%!
The Ofsted ‘Outstanding’ school saw stand-out success in English, Computing, Geography, History, Music, Spanish and Textiles, where 49.7%, 50%, 66.7%, 54.8%, 55.6%, 54% and 55% of grades were 9-7 respectively.
The school is also celebrating an impressive increase in the percentage of 9-5 grades vs. 2019 with Sciences up from 48% to 78%, History up from 50% to 80.8%, Geography from 63.9% to 96.4%, Food and Nutrition from 57% to 71.2% and Art from 29% to 81.6%.
Wayland Academy are delighted to have achieved the school’s best ever results with 81% of grades 9-4 across Maths and English, seeing a 35% increase in English grades and 20% increase in Maths grades vs. 2019. The community school, which is located in the heart of Watton prides itself on its strong culture of raising aspirations, and helping pupils to achieve their very best and this year’s results showcases this exponentially.
Similar success is also being enjoyed by everyone over at Cromer Academy too, who are celebrating their knock-out GCSE results with 80% of grades at 9-4 across Maths and English with 16 pupils moving on to Sir Isaac Newton Sixth Form or Jane Austen College Sixth Form.
The school has seen a significant improvement in results vs. 2019 in all areas, with standout subjects being Art, History and Languages, with success also seen across Sport and Music too. With the challenges that have surrounded teaching and learning due to the pandemic and the return to exams following their hiatus, the staff are extremely proud of what their pupils have achieved.
There is lots for everyone at Jane Austen College and Thetford Academy to be proud of too. Jane Austen College saw 73% of grades at 9-4 in Maths and English while Thetford Academy has seen 60% of Maths and English grades at 9-4, with significant improvements seen in a wide range of subjects. 100% of grades in Biology, Chemistry, Physics and French were at grade 4 or above. 20% of all GCSE grades were at grade 7 or above, which includes 54 grade 9s - double the number that was seen in 2019!
Everyone is also very proud of all the students at East Point Academy, King Edward VII Academy, Great Yarmouth Charter Academy and Hewett Academy. Lots of hard work and dedication has gone into this set of GCSEs following all the disruptions to teaching and learning that occurred as a result of the pandemic, and lots of fantastic results were achieved.
East Point Academy is celebrating yet another year of excellent GCSE results with 60% 9-4 grades across Maths and English, with one Y11 student attaining a truly fantastic set of results - seven Grade 9's and two Grade 8's! King Edward VII Academy has also been going from strength-to-strength, with several exceptional individual performances, as well as many students who have exceeded their expected grades by a significant amount despite the challenges that have been thrown at them. One standout student achieved 7 GCSEs at Grade 7, two at Grade 8 and one at Grade 9!
Great Yarmouth Charter Academy is not only delighted to see so many celebrating success but so many students continuing their education in sixth forms within the Inspiration Trust, including the new Sir Isaac Newton East Sixth Form opening on the school’s site this September. Hewett Academy is proud of all its students, each coming with their own personal journey and demonstrating immense resilience to pre and post-pandemic challenges. A special mention must go to this year’s Head Student, who has received an amazing set of results to finish the year. From joining the school in Year 7 with average primary school SATs scores she has gone on to make phenomenal progress with grade 9 in Art and Graphics, grade 8 in Science and French and grade 7 in English and Maths.


Just how to Go Into a Mathematics Competition
The International Mathematics Contest is an online competition based on internationally acclaimed mathematics curriculum from all over the world. Involvement in the contest is totally free. All you require to do to sign up with the competition is to submit an online registration form. Once your account has actually been activated, you can then submit your entrance. You will certainly also get a rating record that offers your kid’s average rating, complete rating, rank, percentile, the percent of factors earned by the leading 4 winning entries and gives the student’s grasp of math. To register for the International Math Contest, simply enter your postal code to find the competitors in your location. For instance, if you live in Ohio, you could register for the competition there. You will be offered with instructions on exactly how to enter your entrance. Once you have entered, you will get email reminders throughout the competition duration. Your kid has a great chance to win this contest due to the fact that the standards for winning are relatively simple to satisfy. Along with having a high percentile of winning, the champion will certainly be able to offer their rating online and take home a free reward. There are a variety of rewards readily available such as notebooks and also also trips to Math Olympics in New York City. The contest is very interactive for your youngsters. They can discover via their ratings and take on various other trainees around the globe that have achieved the very same degree of accomplishment. Your kid can likewise utilize their expertise of the competition to discover more about the topic that they are researching. This expertise can assist them make better qualities in college in math. There are no age restrictions on taking part in this competition for your youngster. It is open to anybody of any age from pre-school kids to grownups. All they need is a Web link and a computer system. You may locate it easier to register your youngster for the competition when compared to signing them up for normal math competitors. There are a variety of mathematics contests that you can enter for your kid. A few of these include: Other kids’s math contests include; The most effective part concerning mathematics competitions is that your youngster does not need to spend cash for entrance right into the competitions. All they require to do is a click away! There are additionally some competitions that you can sign up with locally via your neighborhood town library. Libraries frequently organize mathematics competitions with a wide variety of prizes. These rewards can include unique books, electronics, or even money. The contest can be for a variety of subjects. You will certainly need to take a look at the various competitions in order to determine the subject that your kid wants finding out. As soon as your kid has actually picked their math competition, you should attempt and also urge them to go into in as most of the contests as they can to ensure that they have the possibility to satisfy the judges.


There are three teachers in Year 5: Mr Archer (Great Portland Street), Mrs Webb and Miss Radley (Monument), Mrs Chapman (Hammersmith).
Do you have any ideas for this page? Why not let your Teacher know!
Have you seen the Kids’ Zone? Play games and visit some cool websites. You can vote for your favourites.
In Monument, we have been working on place value, reading and writing 6 digit numbers.
We used numicon to support our learning, it was fun to use physical resources to create our numbers. We had to think about the value of each digit and then we had to compare each number we made!
Click here for more information.


MLB Opening Day makes Black Lives Matter center stage, July 23, 2020
It’s just another reminder, the Jesuits run it.
Black Lives Matter = 56; Society of Jesus = 56; Washington D.C. = 56
Remember, this year concludes with the 116th World Series.
African American = 116
Today is July 23rd, or 23/7, the numbers that are the prime factors of 42.
2x3x7 = 42
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Mrs. Sepulveda's 6th Grade Math and Science Class
Welcome to the 2022-2023 school year at Mountain View Middle School! Our classroom is not only in C-7 but we have a Google Classroom as well. Within our Google Classroom, students and parents will be able to view the daily agenda, assignments, videos, presentations, and additional materials. When students are absent, Google Classroom should be accessed to find out what they missed. Be sure to check out the links on this page to help with assignments and projects as well as fun sites for practicing various math skills.
Please look at the links to the units for math and/or the science links.
If you have any questions, please feel free to email me at any time!
Mrs. Ana Maria Sepulveda


VECTOR AND TENSOR ANALYSIS WITH APPLICATIONS.
Edition. Translated and Edited by Richard A. Silverman.
Publications, Inc.- New York. - 1968
Copyright © 1968 by Richard A. Silverman.
All rights reserved under Pan American and Inter-
national Copyright Conventions
Published in Canada by General Publishing Company.
Ltd., 30 Lesmill Road, Don Mills, Toronto. Ontario.
Published in the United Kingdom by Constable and
This Dover edition, first published in 1979. is an unabridged
and corrected republication of the work
originally published in 1968 by Prentice-Hall, Inc.
International Standard Book Number. 0-486-63833-2
Library of Congress Catalog Card Number: 79-87809
Manufactured in the United States of America
Dover Publications, Inc.
180 Varick Street New York 10014
The present book is a freely revised and restyled version
of the third edition of the Russian original (Moscow,
1966). As in other volumes of this series, I have not
hesitated to introduce a number of pedagogical and
mathematical improvements that occurred to me in the
course of doing the translation. I have also added a brief
Bibliography, confined to books in English dealing with
approximately the same topics, at about the same level.
In their prefaces to the three Russian editions, the au-
thors, acknowledge the help of the following colleagues:
Professors Y. P. Blank, V. L. German, G. I Drinfeld,
A D. Myshkis, N. I. Akhiezer, P. K Rashevsky, V, A.
Marchenko and N.V. Yefimov.
VECTOR AND TENSOR ANALYSIS WITH APPLICATIONS
A.I. Borisenko and I.E.Tarapov
". . . the exposition is clear and the choice of topics is excellent . . ."
Prof. R.E. Williamson
Univ of Sussex, Brighton, England
This concise introduction to a basic branch of applied mathematics is indispensable to mathematicians, physicists and engineers. Eminently readable,
it covers the elements of vector and tensor analysis, with applications of the theory to specific physics and engineering problems. It lays particular
stress on the applications of the theory to fluid dynamics.
The authors begin with a definition of vectors and a discussion of algebraic operations on vectors. The vector concept is then generalized in a natural
way, leading to the concept of a tensor. Chapter Three considers algebraic operations on tensors. Next, the authors turn to a systematic study of the
differential and integral calculus of vector and tensor functions of space and lime. Finally, vector and tensor analysis is considered from both a
rudimentary standpoint, and in its fuller ramifications, concluding the volume.
The strength of the book lies in the completely worked out problems and solutions at the end of each chapter. In addition, each chapter incorporates
abundant exercise material. Intended primarily for advanced undergraduates and graduate students of math, physics and engineering, the work is
self-contained and accessible to any student with a good background in calculus.
Vector and Tensor Analysis With Applications is one of a series of SELECTED RUSSIAN PUBLICATIONS IN THE MATHEMATICAL SCIENCES, several of which have
already been published by Dover. The authors are distinguished Russian mathematicians and specialists in gas dynamics and numerical analysis Richard
A Silverman, editor of the series as well as editor and translator of this volume, has revised and improved the original edition and added a bibliography.
" . . a concise, clear and comprehensive treatment…"
Prof. Henry C. Booker
University of California, San Diego


Present key algebra concepts with vibrant examples and clear definitions: Vocabulary, Properties, How to Solve an Equation, Order of Operations, Graphing, and Formulas. Includes Algebra basics header. 7 pieces, up to 25 inches wide. Includes a Discovery Guide with creative activities that teach and delight!
NewPath Learning 93-6505 Algebra Skills Bulletin Board Chart Set (Pack of 7)
The 7-chart set covers Algebra Skills concepts. Each 18” x 12” chart is double-sided and laminated. One side provides an illustrated overview of the topic, while the reverse features “write-on/wipe-off” graphic organizers, problem-based questions and other review activities. Algebra Skills Bulletin Board Chart Set of 7 includes the following charts: Algebra Skills Solving equations Systems of Equations Multi-step Equations Inequalities Introduction to Algebra Properties of Addition and Multiplication.
Carson Dellosa School Pop Properties of Operations Mini Bulletin Board Set (110332)
Introduce the properties of operations with the 13-piece School Pop properties of operations mini bulletin board set. This math set explains the properties, displays clear examples, and features cheerful colors and patterns to make the pieces stand out for easy reference. --Ideal for small spaces, curriculum-based mini bulletin board sets allow you to use valuable wall space for presenting standards-based concepts without sacrificing an inviting classroom atmosphere. These essential sets will appeal to your students, offering daily reinforcement that enhances the learning process. Be sure to look for coordinating products to create a cohesive classroom theme! Curriculum-based bulletin board sets offer a time-saving solution for helping students build essential skills through visual reinforcement. The 13-piece School Pop Properties of Operations mini bulletin board set provides an easy reference for essential math properties. Content-rich decor enhances the learning process by reinforcing the lessons necessary for academic success.
Carson Dellosa Mark Twain Math Vocabulary Words Borders (408005)
This eight-strip border set features four math vocabulary words with definitions on each strip for a total of 32 words that can be used as a border, cut apart into flash cards, or displayed together on a wall.
Learning Resources Answer Buzzers, Set of 4 Assorted Colored Buzzers, Ages 3+
Game show buzzers let you turn any lesson into a game and get students actively engaged as you assess them. Four different colors and fun sounds include a horn honx, boxing bell, doorbell and "boing" sound. Buzzers also enable students to work on their own while allowing them to signal to a teacher when they need help. Buzzers require three AAA batteries (sold separately) and are designed for children ages 3 and up.
The new Common Core Fractions bulletin board takes each fraction concept from the third- through fifth-grade standards and explains it in clear, step-by-step directions. Each explanation is accompanied by helpful illustrations. The fractions posters are a useful addition to any upper elementary classroom. Includes 7 pieces; 5 large charge and 2 half-board charts. The new Common Core bulletin board set line provides curriculum displays for the trendy Common Core classroom. Bright, inviting designs allow teachers to use valuable wall space to support the Common Core standards without sacrificing an inviting classroom atmosphere. Topics covered include Common Core Anchors and Domains, Math Strategies, Fractions, Nonfiction Text Features, and Writing Modes. The resource guide included with each bulletin board set provides teachers with additional support and activities to make learning go even further.
McDonald Publishing Math Basics Teaching Poster Set
We've taken our best-selling basic math concepts and combined them into one set that's sure to become a teacher favorite. The concepts include the order of operations, math symbols, math formulas, and what good mathematicians do. Package includes 4 posters, 4 reproducible activity sheets, and a helpful Teacher's guide.
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Algebra Basics Bulletin Board Set by TREND T-8256
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Colorful examples and clear definitions make it easy to introduce key algebra concepts: Vocabulary, Properties, How to Solve An Equation, Order of Operations, Graphing, and Formulas.
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Origami 6 : I. Mathematics
A unique collection of papers illustrating the connections between origami and a wide range of fields. The papers compiled in this two-part set were presented at the 6th International Meeting on Origami in Science, Mathematics and Education (10-13 August 2014, Tokyo, Japan). They display the creative melding of origami (or, more broadly, folding) with fields ranging from cell biology to space exploration, from education to kinematics, from abstract mathematical laws to the artistic and aesthetics of sculptural design.
This two-part book contains papers accessible to a wide audience, including those interested in art, design, history, and education and researchers interested in the connections between origami and science, technology, engineering, and mathematics. This Part 1 contains papers on various aspects of mathematics of origami: coloring, constructability, rigid foldability, and design algorithms.
Download Origami 6 : I. Mathematics (9781470418755).pdf, available at pdfstock.com for free.
- Koryo Miura, Toshikazu Kawaskai, Tomohiro Tachi, Ryuhei Uehara, Robert J. Lang
- Paperback | 368 pages
- 178 x 254 x 25.4mm | 725.75g
- Publication date
- 03 Jan 2016
- American Mathematical Society
- Publication City/Country
- Providence, United States
- Bestsellers rank


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Cecilia Kilhamn works as a senior lecturer in teacher education and in-service teacher training at the Department of Education, Gothenburg University. Her main interest is Mathematics Education in primary and elementary school. In her dissertation from 2011 she studied teaching and learning of the concept of negative numbers and student’s development of number sense, using a longitudinal research approach including both interviews and video observations. In the thesis the importance of mathematical language including the use of metaphors were particularly highlighted. Cecilia’s research interest concerns different ways of teaching specific mathematical contents, particularly processes that connect teaching with learning. Her masters’ thesis from 2003 described an experimental study teaching the function concept in grade 3 and 5 using “function boxes”. Cecilia has also supervised many Learning Studies, where the use of Variation theory is a main feature. In addition to her research interests and teaching duties at the university Cecilia writes material for teachers, for example papers in the teacher journal Nämnaren, and material for in service teacher training run by the National Agency for Education (Matematiklyftet).
Between 2011 and 2014 Cecilia worked in an international research project concerning the teaching and learning of early algebra. The project was funded by Nordiska Samarbetsnämnden för Humanistisk och Samhällsvetenskaplig forskning (NOS-HS) and is a collaboration between research teams at Gothenburg University in Sweden; Åbo Academy in Vasa, Finland; University of Agder in Norge, and; University of California Los Angeles (UCLA). The project, VIDEOMAT, is a comparative video study with a specific focus on “the introduction of variables in expressions” in grades 6 and 7. A second research interest is the use of video recorded classroom instruction in teacher education and professional development.
Kilhamn, C. (2011). Making sense of negative numbers. Gothenburg Studies in Educational Sciences 304, Göteborg, Sweden: Acta Unversittatis Gothenburgensis
Lundberg, A. L. V., & Kilhamn, C. (accepted). Transposition of Knowledge: Encountering Proportionality in an Algebra Task. International Journal of Science and Mathematics Education. doi:10.1007/s10763-016-9781-3
Kilhamn, C. (2014). When does a variable vary? Identifying mathematical content knowledge for teaching variables. Nordisk matematikkdidaktikk - Nordic Studies in Mathematics Education. 19 (3-4) s. 83-100.
Nyman, R. & Kilhamn, C. (2014). Enhancing Engagement in Algebra: Didactical Strategies implemented and Discussed by Teachers. Scandinavian Journal of Educational Research (published online oct. 2014)
Kilhamn, C. ; Hillman, T. (2014). Structural and Pedagogical Diversity in Swedish Grade Six Algebra Classrooms, Proceedings of the ninth annual conference of the Swedish Society for Mathematics Education Research (MADIF9). Umeå: SMDF
Partanen, A-M.; Cecilia Kilhamn (2014). Distribution of lesson rime in introductory algebra classes from four countries. In: Röj-Linberg, A-S., Burman, L., Kurtén-Finnäs, B. & Linnanmäki, K. (Eds.) Spaces of learning: past, present and future. Proceedings of the FMSERA 30th annual symposium in Vaasa, November 6-8, 2013, ( Report 36/2014 ) s. 236-237
Kilhamn, C. (2013). Hidden differences in teachers' approach to algebra - a comparative case study of two lessons, Proceedings of the 8th Congress of the European Society for Research in Mathematics Education. CERME8, Antalya Turky, 6-10 february 2013.
Lundberg, A. L. ; Kilhamn, C. (2013). The Lemon Squash Task, Watson, A. Ohtani, M. Ainley, J. Bolite Frant, J. Doorman, M. Kieran, C. Leung, A. Margolinas, C. Sullivan, P. Thompson, D. R. Yang, Y.. (Eds.). (2013). Task Design in Mathematics Education. Proceedings of ICMI Study 22. Oxford. 1 s. 359-368.
Drageryd, K. ; Erdtman, M. ; Kilhamn, C. (2013). Comparing and ordering fractions - a learning study, WALS, international Conference 2013 in Gothenburg, Sweden. Lesson and learning study as teacher research. September 6-9, 2013. s. 111.
Kilhamn, C. (2012). The role of justification in small group discussions on patterning, Smith (Ed.), Proceedings of the British Society for Research into Learning Mathematics. 32 (3) s. 109-114.
Kilhamn, C. (2009a). Addition and Subtraction of Negative Numbers Using Extensions of the Metaphor "Arithmetic is Motion Along a Path". In C. Winsløw (Ed.), Nordic Research in Mathematics Education. Proceedings from NORMA08 in Copenhagen, April 21- April 25, 2008 (pp. 17-23). Rotterdam: Sense Publishers.
Kilhamn, C. (2009b). Making sense of negative numbers through metaphorical reasoning. In C. Bergsten, B. Grevholm & T. Lingefjärd (Eds.), Perspectives on mathematical knowledge. Proceedings of MADIF6 (pp. 30-35). Linköping: SMDF.
Kilhamn, C. (2009c). The notion of number sense in relation to negative numbers. In M. Tzekaki, M. Kaldrimidou & H. Sakonidis (Eds.), Proceedings of the 33rd conference of the international group for the psychology of mathematics education (Vol. 3, pp. 329-336). Tessaloniki: PME.
Kilhamn, C. & Röj-Lindberg, A-S. (2013). Seeking hidden dimensions of algebra teaching through video analysis. In B. Grevholm, P. S. Hundeland, K. Juter, K. Kislenko & P.-E. Persson (Eds.), Nordic research in mathematics education, past, present and future (pp. 299-326). Oslo: Cappelen Damm Akademisk.


Keno, as a game, has managed to attain incredible popularity. It has become even more popular since its inclusion in online casinos. The game is fairly simple and does not involve much strategic thinking to enjoy. It also offers great payouts, which makes it incredibly worthwhile to play.
Keno is played by many players in live casinos. It allows players ample of time to crunch their numbers so that they can be used wisely on the Keno cards. The game is usually played for leisure, but there are substantial monetary gains to be achieved as well.
Rules for playing Keno online
The inclusion of the game in online casinos has somewhat changed the game. Such online casinos allow players to play Keno at a pace that is quicker than any real casino. Players can play more number of games within short time duration. They can easily control the intervals between two successive games, as well as the time needed to play a single game. All of it is at the discretion of the players involved.
The game involves a Keno “board” that accommodates numbers between 1 and 80. Players are allowed to mark their individual card with up to a set of fifteen different numbers of their choice. Once the players have compiled their numbers, the program on the board generates a set of twenty different numbers randomly. The objective of the game is to match as many numbers as possible from the compiled set of numbers on a Keno card with the numbers drawn by the board. The payouts are made according to the quantity of numbers matched.
The board accompanies a pay table that informs each player about the amount of money they have won. The table is available ti players in plain sight so that they can see how many numbers they have been able to match and how much money they have been able to win.
Strategy of playing the Keno game
The game involves little to no strategic angle at all. Hence, it becomes very interesting to figure out how to play the game better. Since there is very little mathematical calculation can be done to predict the winning numbers, players have to depend solely on their chances of luck. They have to track numbers and past results, and then guess their number choices on the basis of the likelihood of them appearing in the winning combination. Honestly, it is all chance, which is as good an approach to a casino game as any.
Alternatively, players can also manage their money and budgets wisely in order to get the best out of playing this game. This will largely depend on the number of games that one intends to play as well as the total money that they intend to wager in all of these games. This will help them to determine the amount of money to wager on each game or bet. The aim here would be to recover the total money in wagers by the end of the game. Any winnings would automatically be a bonus!
Helpful tips to playing Keno in online casinos
Discussed here are some useful tips that will help you to enjoy the game thoroughly in an online casino. They will also help you to improve you chances of winning more money.
- It is always recommended that you become well-accustomed to the functioning of the game. You must understand that you are given the option of choosing up to fifteen different numbers. This means that you have to place fifteen different bets on a single game. At the same time, this also allows you the opportunity to win up to fifteen different bets in a single game if the numbers match.
- Although you have the option of playing at a fast pace, you should avoid playing any faster than you actually want to. Take your time in compiling the numbers of your choice, and only go forward with the game when you are good and ready.
- If you have the habit of tracking past winning numbers for the compilation of your own set of numbers, locate the place where those numbers are displayed. This will help you with your tracking during a game.
- Budget you wagers appropriately. Figure out how many games you wish to play and ensure that you have adequate money to wager on those games. This will not only help you place your bets wisely, but also ensure that you do not exceed your budget when playing the game. After all, money management is of prime importance when wagering money on live online casinos.


Easy to use, myRandom is a random number generator. Based on a given range, it generates a random number (or a set of random numbers) for you! You can use it to raffle gifts, on events, promotions and much more!
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