YEAR 5 MATHEMATICS CHALLENGE
A challenge for young mathematicians to solve puzzles at six stations.
Working in pairs the Year 5 mathematicians will work through five problems during an eight minute period at each station. The activities during the could event could involve work with:
Pentominoes Tangrams Railway timetables Ordering playing cards Dice Mystery numbers Domino jigsaw Shopping lists Mazes Code breaking Sequences Broken calculators Make 24 Logic puzzles Cross numbers
AND THE ANSWER IS ...
In the final round all young mathematicians participate in a multiple choice quiz involving up to 10 questions.
No preparation is required and all instructions for the activities during the afternoon will be clearly explained.
Number of children from each school: Four
Entry fee: FREE
Duration of event, including tea: 2 hours 15 minutes


Place the simplified Chinese numbers in the grid so that every row, every column, and each of the nine 3x3 square contains only one occurrence of all the Chinese numbers from one to nine.
You should be able to solve any puzzle here without writing anything down, and they all have only one solution. If you feel you can't go, you can click the 'give me a hint' button, and any errors you have made will be highlighted in red, or if you've made no mistakes, a green square will show where you can go next. If you try to place a number where it already exists on that row, column, or small square, both occurrences will be highlighted in red.
To play this one again, simply click 'refresh' on your browser, or try a different one with the links above.


A day does not go by without a technology vendor waving banners about securing data in the cloud with strong encryption. File sync and cloud storage controller vendors are the new kids on the block that tout the benefits of using strong encryption algorithms such as AES-256 and RSA to secure data in the cloud. A strong encryption algorithm is one of the key mechanisms for securing data in the cloud. The encryption process can take place either on the client side, on the gateway, or in the cloud itself. An encryption algorithm derives strength from its sophisticated mathematical operations and a strong a random number generator which is the foundation for producing strong cryptographic keys. A weak random number generator can produce keys that are predictable and thus easy to guess.
We know that a cryptographic algorithm can take any plain data and a key and run it through mathematical operations to create cipher data. However, these sophisticated mathematical operations can be rendered useless if one uses keys that can be easily guessed. Making keys longer is one way to make your keys stronger but if those long keys are using bits that are predictable then the keys are of low quality and your data in the cloud is at risk.
The generation of bits (key material) for the keys is one of the most important factors in determining the strength of your encryption process. The generation of your key material is based on your system’s Pseudo-Random Number Generator (PRNG). Time and time again, security experts have highlighted the folly of having your keys being generated based on a weak PRNG. One of the foundations of strong cryptography is a strong PRNG. A well designed PRNG provides your cryptographic engine with truly random bits for your keys, where every new key that is generated is different from the previous ones and there is no consistent pattern in the key material.
Unfortunately, there are some cases where a PRNG is intentionally weakened to make the encryption scheme vulnerable for intruders. Any user that is looking to move data to the cloud should request its cloud solution provider to certify that it is using a strong PRNG to encrypt data. Since PRNGs are the weakest link in any encryption scheme, we encourage all users to request their respective vendors to certify that their PRNGs indeed produce highly random data. If a cloud vendor dances around this topic or provides vague answers then you know there is something wrong with their encryption scheme.


By Haripriya Mehta, Co-founder of MehtA+
When the CEO of Math Kangaroo USA, Ms. Joanna asked if MehtA+ would be interested in sponsoring 3000+ digital kits for the 2021 Math Kangaroo competition, without a moment of hesitation, I said yes.
My brother (and the other co-founder of MehtA+) and I had participated in Math Kangaroo since elementary school. I had placed in the top 10 nationally twice and my brother received 1st place internationally twice in high school with a perfect score besides placing top 10 nationally several other times! And while winning and receiving an award, a certificate and a medal were exciting, there was much greater joy in learning and strengthening our mathematical and logic skills as we prepared for and took the Math Kangaroo test. The skills we learned during Math Kangaroo preparation helped me succeed at MIT and my brother at Stanford where we majored in electrical engineering and computer science.
Even so, we wanted our digital kits to be special for the top 10 winners in grades 1–5, which they would be receiving in addition to a certificate from Math Kangaroo. After all, it had been a difficult year with the ongoing pandemic and we wanted to create something that students would be looking forward to. We didn’t have any budget because all of the instructors in our organization are current university students or recent alumni. But, inspired by Math Kangaroo’s volunteers such as Ms. Grazyna, a longtime volunteer of my hometown’s Math Kangaroo chapter, who have dedicated their lives to facilitating this math competition, MehtA+ instructors were absolutely ready to volunteer their time to design a memorable prize!
Designing a prize was definitely a challenging feat. MehtA+’s target demographic for camps, workshops, tutoring and consulting services are middle and high school students so we were not sure what elementary-aged students would like. We also did not want it to be a completely digital prize because it is often more exciting to play with a physical prize. More importantly, we had heard from a lot of grownups that they did not want their students to be looking at their computer screens any more than they needed to, since students had been looking at screens non-stop throughout the virtual school year.
Then, one fine morning, as I was cleaning my room, inspiration struck. A little kangaroo stuffed animal fell out of my bookshelf. This was a kangaroo I had won in Math Kangaroo as an elementary student. I remember how much I had cherished it and kept it ever since. This is what the elementary students would love. MehtA+ instructors could teach elementary school students how to create their own paper model of a kangaroo, while learning principles of mechanical engineering and design.
I enjoyed the MehtA+ Digital Kit. It was fun to assemble and is a great decoration for my study area!
I hurriedly called our Product Lead and instructor, Ms. Marwa who had completed her undergraduate studies in mechanical engineering at MIT, if she could design such a kit. She gladly agreed despite her busy schedule — she was reaching out to labs for her PhD program in Mechanical Engineering at MIT, which she was to begin a couple of months later. She was also fasting as it was Ramadan!
Ms. Marwa first took the Math Kangaroo logo and vectorized it. She exported the file to DXF format so she could create a 3-D model of the kangaroo by extruding the image in CAD software. She then created the unfolded pattern of the 3-D model. However, it turned out that the design of the 3-D model was larger than A4 paper (normal printer paper)! A design larger than A4 paper would mess with the integrity of the paper structure because there would be individual cutouts split between multiple papers rather than having one continuous pattern. Ms. Marwa spent several more hours trying to modify the structure so that it would fit on an A4 paper and it was easy for students to assemble.
It was important for us that the students could create the kangaroo using materials easily accessible to them. The kit was designed in such a way that students could print out the design on printer paper or cardstock and only needed household items to create it — scissors, Q-tips, and glue/tape was sufficient.
Ms. Marwa also recorded videos that taught students how to fold the kangaroo cutout as well as how to create similar cutouts using software that mechanical engineers use — TinkerCad and Pepakura. We figured that this was a great opportunity for younger students to strengthen their motor skills and practice cutting and coloring. For older students, this was a great way to understand the applications of mathematical concepts that they had learned in preparation for the Math Kangaroo.
Growing up, none of our instructors had this kind of exposure to the applications of the theory we learned in school. While there were many 3-D cutouts of different animals found on the web, no one explained to the students how these cutouts were made using mechanical engineering software. We always strive to introduce new concepts to students, while they are having fun!
The kit was a huge success. 2nd grader Gideon B. from RSM Winchester created, colored and sent us a picture of his beautiful 3-D paper kangaroo. One 4th grade student remarked, “I enjoyed the MehtA+ Digital Kit. It was fun to assemble and is a great decoration for my study area!”
We are excited to announce that we will be sponsoring Math Kangaroo USA again in 2022. For students in grades 1–12, please don’t forget to register for Math Kangaroo by December 15, 2021. Who knows, you might be receiving one of our prizes next year!


Operations Research For BMS 6th Semester(Mumbai Univ.) Full Course By Madhusudan Sohani
₹2,650.00 – ₹4,875.00
- This Course covers full course of BMS Mumbai University for 6th Semester As per latest course
- 1 printed handout of 32 pages
- Over 85 numerical problems have been solved with full explanation
- One video is devoted to solving April 2017 QP fully
- Numerical questions are kept approximately at the level as contained in standard text-books on the subject. Some more difficult problems have been included for brighter students
- About 85 to 90 numerical questions have been solved.


I am a 6th Grade Math teacher. . I teach six - 6th grade math classes. My 1st 2 periods will be honors classes. I will be introducing 7th grade math to these students. They also will be working on a year long Community Service Project.
I was honored to be chosen the "Teacher of the Year" for 2010-2011 for La Vega Intermediate!
My conference period is from 12:30-1:15.
School phone # is 254-799-5553.


Kuga Varieties: Fiber Varieties over a Symmetric Space Whose Fibers Are Abelian Varieties
Higher Education Press
260 x 185mm
On OrderTo be dispatched within 4 weeks
Mathematics is the queen of sciences. She is pure， noble and attractive， and also has a distinct character in comparison with subjects in sciences such as physics： its permanent relevance and eternal validness ofits theories and theorems. Whatever was once proved will stay true forever. Mathematics is a vast subject， and many new concepts， theories and results spring up like mushrooms after spring rain. Similarly， there is also a large number of new mathematics books appearing in libraries and on bookshelves. Probably due to the usefulness of mathematics and its foundational nature， there seems to be more books in mathematics than in other subjects. On the other hand， only a limited number， or even a few， of them stand out and are appreciated and used by many people. The best test on the quality of books is the test of time. In this series ofbooks Classical Topics in Mathe'matics， we have selected books written by leading experts on topics which are well-tested by time. We believe that in spite of the passage of time， their power and value have not diminished， and hence they bear the trademark of the classical mathematics.


Creativebug offers online video arts and crafts workshops and techniques. Learn how to paint, knit, crochet, sew, screen print, and more.
EdX offers free interactive online classes from the world’s best universities like MITx, HarvardX, BerkeleyX, and UTx. Topics include biology, business, chemistry, computer science, economics, finance, electronics, engineering, food and nutrition, history, law, literature, math, medicine, music, philosophy, physics, science, statistics and more.
Khan Academy is a not-for-profit with the goal of changing education for the better by providing a free world-class education for anyone anywhere. All of the site’s resources are available to anyone. It doesn’t matter if you are a student, teacher, home-schooler, principal, or an adult returning to the classroom after 20 years. Khan Academy’s materials and resources are available to you completely free of charge.
With over 100 instructional videos each, plus interactive drills and quizzes, ProCitizen provides the civics, vocabulary, plus reading and writing practice that new citizens need to succeed on the citizenship test.


Given a -cube of points in a space of dimensions, i.e. all the points in the square of , , , etcetera, is it possible to put every point from this region somewhere in the infinite -dimensional plane, so no two points will be put in the same place (a.k.a one-to-one correspondence), and that in the new arrangement, every point will be "isolated", i.e. there will exist a neighborhood of that point which contains no other points?This is the more impressive wording I thought of:
Given a space of -dimensionality, is there a way to take all the points from that space and map them back into that space, so no two points will be put in the same place (a.k.a one-to-one correspondence), so that in the new arrangement, every point will be "isolated", i.e. there will exist a neighborhood of that point which contains no other points?We will refer to this theorem as , where is a free variable that represents the dimensionality of the space.
easy direction: . Whatever mapping was good enough to satisfy
in , we can use it for on one axis of and put zeroes into all the
other coordinates. More formally:
We take the set of points on which satisfies . We build a mapping from it to the set on , defined as the set of all members of for which the first coordinate is a member of and all the other coordinates are zero--a trivial one-to-one mapping. If all the points in were isolated, all the points in are isolated, and satisfies . The full mapping is : From to (bound to exist since they are both ), from to isolated points in (we assume its existence by assuming ), and from isolated points in to isolated points in (which is the mapping we described in this paragraph).
Now the hard part: . One might think that finding a mapping for , where , will be ��easier�� since there are more dimensions to play with and there’s more room for all the points and their luxurious, empty neighborhoods. However we shall prove that given a mapping that satisfies , we can construct a mapping that satisfies , e.g. relocates these points to the straight Real Avenue while still making sure everyone’s got elbow room.
A digression. We must understand, that in our efforts to map a set of points to another set of points with certain restrictions, it doesn’t really matter from which set we are trying to map--as long as that set’s power is . This is because the only restriction we have to obey, namely the empty neighborhoods around each point, is concerned only with the range of the mapping. Since there are one-to-one mappings between any two sets with cardinality, we do not have to bother to show the whole mapping from the original domain, , to the final set of isolated points, we just need to show that they are of the same cardinality, , and set theory guarantees us there’s a one-to-one mapping between them.
Back to proving . For this proof we shall use a function based on the Alternating Digits function. If you are not familiar with it, these are the essentials: we’ll call our function , its domain is , and it is onto its range of . It is continuous. It is not one-to-one, but, and this is important, each point in its range has not more than points from the domain leading to it.
We are assuming . There is a one-to-one mapping from all the points in to a subset of such that all the points are isolated. Or, as we noted in our digression, we can say that we have a set of isolated points in which is of cardinality. In the course of this proof we will build an set on , and prove that is satisfies by contradiction: we will prove that if it does not satisfy our original set did not satisfy .
Enough with the foreplay and let’s prove it. We define as all the members of which satisfy . Of course is of cardinality, as we have a function from it onto another set (namely, onto ). All the points in are isolated--to prove it we will assume the opposite. Assume there’s a point in which is not isolated, i.e. it does not have a neighborhood in which there are no other points from , i.e. for every neighborhood of there are some points from in it. Now the trick is, we can build a sequence, made entirely from members of , which converges to . We will call this sequence . To recap: We have a sequence of numbers from which converges to our point which also belongs to , and most importantly, all the members of are different from , or in other words does not appear in the sequence.
Now to show that our original set does not satisfy the empty neighborhood condition. Observe the point . It is a member of . And now we will show it is not isolated. We will build another sequence: . Since all members of are members of , all members of are members of . And since the function is continuous, the limit of is . Only one thing left to settle in order to show the contradiction and complete the proof. We want to show that for every neighborhood of , there is a member of different from inside it. The sequence almost gives us that, but not quite! While it was true for that all its members were different from its limit , it is not necessarily true that all the members of are different from its limit, ! Why is that? That is because the function f is not one-to-one. Even though there is no member of which is equal to , there might be members of which lead to the same point in as , i.e. there might be a point for which , or maybe infinitely many points like that.
Fortunately, there’s a workaround. Remember in our introduction to , we noted that for every point in its range, there are a finite amount of points in its domain which lead to it? So it follows, that we can take our series , and form a sub-sequence by omitting those values which are equal to ; and since we now know there is merely a finite number of them, this is possible.
So there we have it: A sequence of numbers from converging to a member but all different from it. Thus will never be alone and isolated, as it will always have the members of getting infinitesimally close to it. So the points in are not isolated, i.e. if does not satisfy does not satisfy , from which follows that if satisfies satisfies , from which finally follows , QED.
There exists a set of real numbers in the open segment , such that the cardinality of is and all the points in are isolated.Our next mission is to prove that . Again, one easy direction and one harder direction.
direction, . We are assuming the existence of the set of
cardinality, and that all the points in are isolated. It doesn’t even matter
that all the points in are between 0 and 1, since the proof comes without it:
Since the cardinality of is , we can map into it, and this mapping
will satisfy since all the points are isolated. We have proved .
Now we will prove . Assume there’s a one-to-one mapping from to a subset of such that all the points in are isolated. Now we will create , a set which will satisfy . We define as all the numbers expressible as , where is a member of . This is a kind of a compression function, and we shall refer to it as in this proof. The domain of is , and its range is . It is a one-to-one, continuous, strictly increasing function.
Now to prove that satisfies . We know that every point in is isolated. Let’s take a point in , call it . We know is isolated, so we can say there exists a positive real number such that in the open segment , the only member of is . What this gives us, is that the point is isolated: There are no other members of in the open segment . Since f is a strictly increasing function, we know that is smaller than and that is bigger than , and it is impossible for any member of to ��squeeze�� between them, because that would mean there would be a corresponding member of between and , which would violate our original assumption. Therefore is isolated.
Since we did not have any requirements from , we can apply this argument to all the points in , and deduce that all points in are isolated. Therefore,
The well-definedness of is not totally trivial. One might suspect that the set in question does not have a maximum. Let me reassure you that it does have a maximum for every , but even if it didn't, the proof would work the same if returned the supremum of that set (which can be shown to be equal to the maximum.)
Do you understand what we’re getting at? Let’s say we use the sequence of as . will contain all the points in that have a clear neighborhood of at least 0.5 radius around them. will contain all the points in with at least 0.25 clear around them. will contain all the points with 0.125 clear around them. Now there are some vital things we have to prove about .
for the sake of convenience we shall define . Assume that
has at least members. Therefore we can find two members, we will notate the
smaller one and the bigger one , that have at least members in
the open segment between them. We will notate these members as according to size, e.g. is the smallest member, is next
etcetera. Now observe:
Because b is an increasing finite sequence, we can add absolute values:
Now, because we know that all these are members of , we know that the distance between each pair of them is at least .
But the distance between two points on cannot be 1! Contradiction, is finite for every and bounded by , QED.
There does not exist a set of real numbers in , such that is and all the points in are isolated;
There does not exist a set of real numbers, such that is and all the points in are isolated;
There does not exist a set of points in -dimensional space, such that is and all the points in are isolated;
We have proved that Eyal's Protein Conejcture is false: It is impossible to rearrange all the points in a -dimensional space and map them back into that space, without putting two points in the same place, and that in the new arrangement every point will be isolated.
All content in this website is copyright © 1986-2011 Ram Rachum.


iMAGINE STEAM Festival
The iMAGINE Upstate festival, which has occurred in Greenville over the past 4 years, is coming to Greenwood. The festival will feature interactive exhibits and shows emphasizing Science, Technology, Engineering, Arts and Math (STEAM) to Greenwood Uptown and Uptown Market on Saturday, March 16, 2019.
The purpose of iMAGINE STEAM Festival, fueled by the Greenwood Arts Center, is to ignite the interest of Pre-K through 12th-grade students (and their families) in STEAM subjects by providing up-close engagement with the latest technologies and giving them exposure to high-skill industries.
iMAGINE partners with corporations, schools, nonprofits, and volunteers to make STEAM come to life through hands-on exhibits and interactive stage shows.
Date & Time
March 16, 2019
10:00AM - 2:00PM
The Arts Center of Greenwood 120 Main St Greenwood 29646 SC US http://www.greenvillebusinessmag.com/businesses/sc-greenwood-the-arts-center-of-greenwood


Contrary to popular belief, you don’t actually need a college degree to get a job in engineering. What you do need is an excellent grasp of math.
To improve your algebra, statistics, and calculus, the Mathematics for Engineers Prep Bundle offers more than 60 hours of hands-on lessons. The training is worth $1,195, but you can get it today for only $28.99.
Math is a stumbling block for many students of engineering. Practical minds don’t always respond well to learning from textbooks, but there are other ways to improve your number-crunching skills.
Developed specifically for aspiring engineers, this bundle of courses helps you master practical mathematics and develop a strong sense of intuition. You learn through hands-on video lessons which take you from the basics of calculus and algebra to advanced topics like matrices and wave representations.
Because the courses are focused on engineering, the lessons are based around real-world problems. Along with video tutorials to watch and absorb, you’ll try your hand at various activities. This means you’ll gain knowledge and confidence that you can actually apply at work.
The training is delivered by experienced pros, including aerospace and robotics engineer, Mark Misin. All the courses have great reviews from students, and you get lifetime on-demand access.
You would normally pay $1,195 for all nine courses, but you can get the bundle now for just $28.99.
Hearst Newspapers participates in various affiliate marketing programs, which means we may get paid commissions on editorially chosen products purchased through our links to retailer sites.


The problems with parallelism in the preconditioner have led to searches for other preconditioners. Often simple diagonal scaling is an adequate preconditioner and this is trivially parallelizable. For results on a Connection Machine, see . Often this approach leads to a significant increase in iteration steps. Still another approach is to use polynomial preconditioning: , i.e. , for some suitable jth degree polynomial. This preconditioner can be implemented by forming only matrix--vector products, which, depending on the structure of A, are easier to parallelize . For one often selects a Chebychev polynomial, which requires some information on the spectrum of A.
Finally we point out the possibility of using the truncated Neumann series for the approximate inverse of A, or parts of L and U. Madsen et al.  discuss approximate inversion of A, which from the implementation point of view is equivalent to polynomial preconditioning. In  the use of truncated Neumann series for removing some of the recurrences in the triangular solves is discussed. This approach leads to only fine-grained parallelism (vectorization).


Xenia Sports – London
Under-fire Arsenal boss Mikel Arteta has bamboozled supporters by turning to maths and statistics in an attempt to explain their poor Premier League form.
The Gunners lost 2-1 at Everton on Saturday and sit 15th in the table having not won a league game since November 1.
Arteta’s side has taken just two points from their last seven fixtures and only the current bottom three have a worse goal return than the 12 managed by Arsenal in their 14 league outings so far this season.
While those numbers make for poor reading, Arteta turned to his own sums to prove how unfortunate his team has been.
But fans were left scratching their heads as, during an answer in his press conference previewing Tuesday’s Carabao Cup quarter-final clash with Manchester City, the Spaniard failed to show his working out.
“Last year we won the game against Everton with a 25 percent chance of winning, you win 3-2,” he said.
“Last weekend, it was a 67 percent chance of winning, any Premier League game in history, and a nine percent chance of losing, and you lose.
“Three percent against Burnley and you lose, seven percent against Spurs and you lose.
“There is something else apart from that. It is not just the performance on the pitch, it is something else that needs to go our way and at the moment it doesn’t.
“Saying that it doesn’t care because you lose and the only thing that cares is that you lose a football match and this is what we hear.”
One thing is for certain, the pressure will continue to mount on Arteta unless he can work out an equation to address results on the pitch heading into the festive fixtures.


Year 6 2020 - 2021
Welcome to our Year 6 Page
Mrs Rogers is the teacher in Class 6R and Mr Paterson is the teacher in Class 6P.
|Mrs Rogers||Mr Paterson|
We follow the objectives set in the National Curriculum. Below are links to these documents for the core subjects (mathematics, English and science).
- Mathematics: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/335158/PRIMARY_national_curriculum_-_Mathematics_220714.pdf
- English: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/335186/PRIMARY_national_curriculum_-_English_220714.pdf
- Science: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/425618/PRIMARY_national_curriculum_-_Science.pdf
Click here to download the topic letter for Autumn 1.
Here are some guides to help you access some of the educational websites listed on this page.
- Mathletics guide: https://secure.schoolspider.co.uk/uploads/518/grade/444899_grade_file.doc
- Oxford Owl guide: https://secure.schoolspider.co.uk/uploads/518/grade/444906_grade_file.pptx
- Espresso guide: https://secure.schoolspider.co.uk/uploads/518/grade/444894_grade_file.doc
Support for Home Learning during Coronavirus Pandemic:
On this page, you will find home learning resources, links to websites and a suggested timetable that have been put together to support families having to work with children at home due to school closure. We have also included links to National Curriculum documents for core subjects and half-termly overviews so you have an idea of what is covered in school. Please make sure you scroll through the whole page to see what is included. During this time of school closure, we ask that you check the school website regularly for any important updates or information. We will continue to add to the home learning resources for each year group over this time.
Below are some links to websites that have various resources and interactive games to help with your child’s learning. These are a great way to consolidate what we have learnt in school. Children have been given usernames and passwords for Oxford Owl, Mathletics and Times Tables Rock Stars.
Oxford Owl: https://www.oxfordowl.co.uk
Times Tables Rock Stars: https://ttrockstars.com
Topmarks Education: https://www.topmarks.co.uk
Twinkl (free subscription, enter the code UKTWINKLHELPS): www.twinkl.co.uk/offer
BBC Bitesize Revision: https://www.bbc.co.uk/bitesize/levels/zbr9wmn
Maths Frame: https://mathsframe.co.uk/
- Master the Curriculum: https://masterthecurriculum.co.uk/categories/?year=year-6
- Espresso (username student 22144 password mauldeth): https://www.discoveryeducation.co.uk/
- Hamilton (free English and maths home learning packs updated weekly): https://www.hamilton-trust.org.uk/blog/learning-home-packs/
- Scratch App (free download): https://scratch.mit.edu/
- Number Fun Portal: https://parent.numberfunportal.com
- White Rose Maths (free home learning resources with videos and worksheets): https://whiterosemaths.com/homelearning/
- Literacy Company: http://www.theliteracycompany.co.uk/free-resources/
- NRICH (free online mathematics resources for ages 3 to 18 set up by the Faculties of Mathematics and Education at the University of Cambridge): https://nrich.maths.org/primary
- Robin Hood Academy (weekly home learning packs): https://www.robinhoodmat.co.uk/learning-projects/
- The World of David Walliams (free audio story everyday at 11am): https://www.worldofdavidwalliams.com/elevenses/?fbclid=IwAR1RqmHrK6WyzTDnvyvgkdg6_6Q76wfr3xW6O8E5Zs9qG60K6OLmce4dKg8
- The Maths Factor (free maths website created by Carol Vorderman): http://www.themathsfactor.com
Files to Download
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Gideon Math and Reading - Colleyville
Gideon Math & Reading Programs in Colleyville, TX offers tutoring services for students who struggle with math and reading skills. Their programs focus on building confidence and academic mastery through structured, step-by-step booklets. They offer both in-person and online support, and their tutors are qualified to work with students of all ages, including those with learning differences or special needs. With flexible scheduling options and a student-to-teacher ratio of 2:1 or 4:1, Gideon Math & Reading Center aims to help students make excellent strides in their academic progress. They have received positive reviews from parents who have seen significant improvements in their children's skills and confidence levels.


What is STREAM ?
STREAM is hands-on experimental learning that has a real world application with practical knowledge of a concept. STREAM stands for Science, Technology, Engineering, Arts & Mathematics.
Why STEM in Preschool ?
- STEM are a part of Child’s daily Life.
- Children have a natural curiosity for STEM.
- It is extremly important to include STEM subjects in pre primary education.
- STEM encourages child to wonder.
- STEM teaches how to observe, ask questions and investigate.
- STEM includes knowledge about the world around us.
- STEM scaffolds student learning.


forgive my ignorance, but why is 127 a special number for gear teeth?
in combination with a 5 tooth gear? Surely it is the ratio that matters. This must be some kind of standard that I know nothing about
Yes, all imperial units have been redefined in terms of SI ones. Inches and feet, pounds weight and force, acceleration. Everything.There are EXACTLY 2.54 cm in one inch. 254 / 2 = 127. So a 127 (or a 254) gear provides for a perfect metric imperial conversion.
A 254 gear is too big. 127 is the smallest gear that can serve this perfect function.
127 is also a prime number, so no further factorization is possible. Surely there are other tooth counts that generate the same _exact_ ratio. But I guess this is the simplest / standard one
That was painful. Especially for an old guy with one good eye......
But I totally and completely deserved that. Kudos to you for very kindly and gently getting me to do it.
Truth be known, I never did finish. I've probably tried 6 times now. Each time I thought I was gunna make it, that part in the shadow kicked me so hard I lost count!
I'm still laughing.


AACC Workshops Help You Overcome Math Anxiety
Friday, March 4, 2016
Posted by: Megan Mann
Don’t Let Math Fears Keep You from Achieving Academic Goals
Don’t let your math difficulties get in the way of your academic future. This spring, Anne Arundel Community College (AACC) is offering several workshops focusing on ways people can overcome their math anxieties. The two-hour workshops are free to both current students and people considering attending or returning to college.
Some of the topics covered include:
- Discovering how your past math performance may be impacting your present reaction to math.
- Conquering math anxiety, math avoidance and math procrastination.
- Adopting new approaches for solving word problems and using formulas.
- Using effective memory strategies to help retain what you learn.
- Starting the habit of checking your math work to minimize careless errors.
- Reducing math test anxiety so you can relax and demonstrate what you know.
No pre-registration is necessary. Workshops are scheduled on the Arnold campus, 101 College Parkway, unless otherwise noted:
- 7-9 p.m. Tuesday, March 8, in the Careers Center building (CRSC) Room 107.
- 2-4 p.m. Tuesday, March 22, in the Careers Center building (CRSC) Room 107.
- 4-6 p.m. Thursday, March 24, at Glen Burnie Town Center Room 103, 101 Crain Highway N, Glen Burnie.
- 4-6 p.m. Monday, April 4, in the Careers Center building (CRSC) Room 107.
For information about the workshops, contact Nancy L. Chell, associate professor of mathematics, at firstname.lastname@example.org or visit http://www.aacc.edu/math and click on “Overcoming Math Anxiety Spring 2016.” If you are unable to attend a workshop, visit http://bridge2success.aacc.edu to get started.
About Anne Arundel Community College
Anne Arundel Community College is an award-winning, fully accredited public two-year institution serving approximately 50,000 students each year through classes offered at more than 50 sites in Anne Arundel County or online. AACC offers national and regional studies leading to a degree, certificate, industry credential, transfer to a four-year institution or career enhancement, personal enrichment and lifelong learning.
Laurie Farrell, assistant director, public relations and marketing
Susan Gross, public relations specialist


FYEE 2017 Session Index
Sunday, August 6
Monday, August 7
Tuesday, August 8
Session T2B: Student Success & Development - Focus on Mathematics
Time: Tuesday August 8, 10:00 AM - 11:15 AM, Bill France B
This page contains a list of all papers in this session.
High School ACT Math Scores: Why and How Do We Use Them?
Modification and Assessment of a First-Year Engineering Course to Improve Students' Calculus Readiness
Noah Salzman, Gary Hunt
Math Problem Solving Sessions for Freshman Engineering Success
Robert Rabb, Kevin Bower, Ally Martin, Emily Book
Using a Math Tutorial Program to Decrease the Number of Failed Grades the First Semester helping the College achieve a 91% First Year Retention Rate


The notion of structure is present in most conceptions or approaches recognized in school algebra (Molina and Cañadas, 2018). Within the framework of generalized arithmetic, the term structure refers to a system comprised of a set of mathematical objects, one or more operations, as well as certain properties and relations of and between said objects and operations (Castro, Rico and Romero, 1997).
In the functional conception of algebra, the term structure is equal to regularity or pattern of the values of the two related variables (Torres, Cañadas, Moreno & Gómez, under review). In the study of patterns, this term is used less precisely which makes it difficult at times to distinguish between the notion of pattern and the notion of structure. We consider the former one as broader and containing the latter. It is our understanding that the notion of structure refers to identifying the pattern through particular cases, and the expression or application of the same for general cases.
Based on the conception of algebra as a tool to express general methods that solve classes of problems, the term structure is used to refer to the semantic structure of the problem, which allows distinguishing meanings assigned to the operations in the verbal problems (Molina and Cañadas, 2018).


Hello young pupils. I am Prof. Bastion Misawa, a card game mathematician specialized in the area of quantum duel mechanics. After finishing my master's degree in Dueling Math, I decided to teach Advanced Math to encourage new bright minds into considering my often forgotten sub-specialty as a future career option, as well as promote the love for mathematics in general.
I am always available if my students or colleagues have any problem they believe I could help out in, specially if its solution could lead to a new mathematical breakthrough! Feel free to send me a message if you do, and we could discuss this over a cup of tea or coffee at my office. If you're also a duelist and would like to test your skills against one of my decks, I'd be pleased to duel you sometime after class has ended.


PTE Academic Test Centers issue a score report for every candidate who finishes the test successfully. Usually, this report card will be ready within 2 to 72 hours after the exam is finished.
1. Score report information
The PTE score report provides an overall score which is then broken down into two main categories: communicative skills and enabling skills. Your communicative skills consist of four contributors namely Listening, Reading, Speaking and Writing. Your enabling skills composed of Grammar, Oral fluency, Pronunciation, Spelling, Vocabulary and Written Discourse. Watch our youtube video on how to calculate your PTE overall score.
2. How to calculate the overall
In order to get 20 points for immigration to Australia, you need to have an average score of 79 with no skills less than 79. Let’s see how a computer calculates the overall score of your PTE test score.
First, they add up all the scores of enabling skills. Then, the sum is divided by 6 which is the number of added items. This number which is the average sum of the enabling skills becomes the fifth contributing factor along with the other four communicative skills in calculating the overall of the PTE score. In other words, your enabling skills can indirectly help you boost your average. For instance, I had a student who had no skills less than 79, but his average was 78. This meant that he could only claim 10 points instead of 20 because his average was not 79. Therefore, enabling skills can be decisive if your communicative skills scores are on the borderline.
The overall scores are usually rounded up, and once the average is above 88, it will be rounded up to 90 and the average of the enabling skills is automatically disregarded as you can see here in my PTE report card.
3. Sample calculations
So let’s put this hypothesis to test by calculating the average of a few score reports. So first up is this one: So I add up the enabling skills and then divide it by 6 and the result is 37.5. This will be the fifth contributor for calculating the overall score and the sum of the communicative skills plus the enabling skills average will be 189.5. This sum divided by 5 will be 37.9 which will be rounded up to 38.
4. Baffling ones
Now some baffling cases that really don’t add up and I have found no explanations for them.
So here as you can see even without using a calculator you can see that the average of the communicative skills is 74ish and if you add up the 6 enabling skills, you would have 453 and divide it by six you would get 75.5. Now if you add this figure to the above sum and divide it by 5, you will get an overage of 74.5. But as you can see here the overall score by the computer is 72. Hello! You make me think twice about asking for a rescore of my PTE test result Mr computer.
Need more information?
For learning the tricks of how to ace the PTE academic test, and for doing a free scored PTE mock test and practicing real PTE materials on our PTE practice platform, visit our website at www.thepte.com, where you can also book a free online PTE coaching with one of our Melbourne-based expert PTE trainers via the zoom app.


Suppose that we managed to assign some signs to quadrisecants of a knot (i.e., lines cutting it 4 points) so that their total number, counted with signs, does not change under knot isotopy. What kind of invariant is it, and how to assign such signs? While the answer in this case is known, it motivates more general attempts to count (with signs) various geometric objects inscribed into a knot or a plane curve. In all cases invariants are easily seen to be of finite type. I will explain a general setting to produce such invariants (using evaluation maps of configuration spaces and homology intersections) and will formulate some results and conjectures. No prior knowledge of these themes will be assumed.


In India, Pakistan, Bangladesh, and Nepal, they don’t group numbers by three decimals like we do, but by two. That is, while we have thousand (1,000), million (1,000,000), billion (1,000,000,000), etc., they have lakh (1,00,000), crore (1,00,00,000), etc. Sometimes there are two decimals between each comma, sometimes three. Somebody with 10 million rupees would have 1 crore rupees, or 1,00,00,000 rupees. I had assumed that three decimals was universal, and that language followed accordingly, but in retrospect there’s no reason why that should be so. →
but 3 shall be the number and the number shall be 3
5 is right out
Comments are closed.


Non-probability sampling is a sampling technique where the samples are gathered in a process that does not give all the individuals in the population equal chances of being selected.
Aug 31, 2009 Combining Probability and Non-Probability Sampling Methods: Model-Aided Sampling and the O*NET Data 1519 views; 59 pdf downloads A probability sampling method is any method of sampling that utilizes some form of random selection. In order to have a random selection met sampling method – both probability and non- ficulties assembling sampling frames for probability sampling survey.caltech.edu/alvarez.pdf on September 29,. Purposive sampling is a type of non-probability sampling where the sites that are assessed are defined by the assessment Team and based on the purpose of Stratified random sampling and cluster sampling are still probability sampling methods. • Non-probability methods trade generalizability for logistics. • Probability
In quota sampling, you select people nonrandomly according to some fixed quota. There are two types of quota sampling: proportional and non proportional. In proportional quota sampling you want to represent the major characteristics of the population by sampling a proportional amount of each. For instance, if you know the population has 40% Non-Probability Sampling - Explorable.com Non-probability sampling is a sampling technique where the samples are gathered in a process that does not give all the individuals in the population equal chances of being selected. Non-Probability Sampling - Research-Methodology In non-probability sampling (also known as non-random sampling) not all members of the population has a chance of participating in the study. This is contrary to probability sampling, where each member of the population has a known, non-zero chance of being selected to participate in the study SAMPLING TECHNIQUES INTRODUCTION Probability sampling (a term due to Deming, [Deming]) is a sampling porcess that utilizes some form of random selection. In probability sampling, each unit is drawn with known probability, [Yamane, p3] or has a nonzero chance of being selected in the sample. [Raj, p10] Such samples are usually selected with the help of random numbers.
Nonprobability sampling describes any method for collecting survey data which does not utilize a full probability sampling design. Nonprobability samples are Dec 22, 2015 In nonprobability sampling, randomization is not important in selecting a sample from the population of interest. Rather, subjective methods are Non-probability sampling involves non-random selection based on convenience or other criteria, Jan 7, 2016 Proportional Quota Sampling – The "proportional" in the name is because the population of interest is represented almost exactly by the Through a Monte Carlo study simulating conditions of probability and nonprobability sampling procedures, the study demonstrates consequences of using Jan 29, 2018 Key words: Data integration; inverse sampling; non-probability sample; selection bias. 1 Introduction. Probability sampling is a scientific tool for Sep 16, 2014 Sampling. Non-Probability. Samples. Convenience. Snow ball. Probability Samples. Simple. Random. Systematic. Stratified. Cluster. Purposive
Probability Sampling: Definition, Methods and Examples Probability sampling is defined as a method of sampling that utilizes forms of random selection method. This sampling method is based on the fact that every member in the population has an equal chance of getting selected. Learn more with probability sampling example, methods, advantages and disadvantages. H. T. SCHREUDER ,T.G.GREGOIRE and J. P. WEYER non-probability samples, probability samples, sampling protocols 1. Introduction Environmental and ecological data are important for our understanding of the struc-ture and functions of our ecosystems. When environmental or ecological data are obtained by sampling but the design and other aspects of the sampling protocol are The Methods of Probability Sampling & When to Use Each ... Probability Sampling vs. Non-Probability Sampling. In statistics, sampling is when researchers determine a representative segment of a larger population that is then used to conduct a study. Sampling comes in two forms — probability sampling and non-probability sampling. Probability sampling uses random sampling techniques to create a sample. Sampling - University of Kent


The purpose of this program is for the kids to have more practices with the 4 basic math operations: Addition, Subtraction, Multiplication, and Division. This program comes with a scratch paper, where the kids can do their calculation before they enter the answer into the box.
Calc 3D Pro Calculator for statistic, function plottting, vectors, matrices, complex numbers, coordinates, intersections. For objects like point, line, plane and sphere distances, intersections, volume, area of squeres, area of a triangle can be calculated.
Prime Number Spiral The Prime Number Spiral (a.k.a. the Ulam Spiral) is formed by marking the prime numbers in a spiral arrangement of the natural numbers. This is software is for exploring the Prime Number Spiral.
Geometry Master Geometry Master 3.0 is a Geometry Tutor that enhances Geometrical, Spatial and Drawing skills. The program comes with many excellent drawing tools.
GraphSight GraphSight is a feature-rich 2D math graphing utility with easy navigation, perfectly suited for use by high-school and college math students. The program is capable of plotting Cartesian, polar, table defined, as well as specialty graphs.
Linear Algebra Performs computations associated with matrices: Solves systems of linear equations, finds sum, difference, product, determinant, trace, inverse, adjoint, transpose, eigenvalues, eigenvectors, LU factors, QR factors, tests for definiteness, etc.
CalculPro CalculPro will help your elementary school students practice mental arithmetic or to do fractions. Choose addition, subtraction, multiplication, division or fractions for an exercise.


UW-Madison math professor says the numbers prove it: Aaron Rodgers is better than Tom Brady
A professor at the University of Wisconsin-Madison has mathematically concluded what Packer national already knows: Aaron Rodgers is a better quarterback than Tom Brady.
UW-Madison math professor Jordan Ellenberg — author of the bestseller “How Not to Be Wrong" — will make his numbers-crunching case for Rodgers in a pregame feature during the national broadcast Sunday of the match-up between the Green Bay Packers and Brady's team, the New England Patriots.
A crew from NBC Sports filmed Ellenberg in a vintage Bascom Hall classroom, crunching the numbers. The crew also spent a couple of days in Green Bay, asking Green Bay fans whether Brady or Rodgers is the greatest.
Some pundits would argue Brady's better because he's been to eight Super Bowls, winning five of them, and he's won the NFL MVP award three times.
Rodgers was Super Bowl MVP in 2010, leading the Packers to victory over the Pittsburgh Steelers. He has two league MVP titles.
Don't be surprised if a professor from New England sets up a different mathematical equation.
A separate production crew is setting out later this week to talk to a professor from Boston College about who wins according to his math in a Rodgers/Brady match-up.
You can catch Ellenberg on NBC Sports at 6 p.m. Sunday.


Trinajstić Nenad, F.C.A.
- October, 26, 1936, in Zagreb
- August 27, 2021, in Zagreb
Trinajstić Nenad, F.C.A.
- Fellow of the Croatian Academy of Sciences and Arts
- Doctor of Science
- scientific adviser, retired – Ruđer Bošković Institute
- full professor, retired – Faculty of Science, University of Zagreb
Functions in Academy:
- member of the Presidency – Croatian Academy of Sciences and Arts (12/17/2015 – 12/31/2018)
- deputy secretary – Department of Mathematical, Physical and Chemical Sciences (01/01/2011 – 12/31/2014)
- member of the Presidency – Croatian Academy of Sciences and Arts (01/01/2004 – 12/31/2010)
Membership in Academy:
- full member – Department of Mathematical, Physical and Chemical Sciences (06/18/1992 -8/27/2021)
Professor Nenad Trinajstić was born on October 26, 1936 in Zagreb, where he finished elementary school (1951) and high school (1956). He graduated from the Department of Chemical Technology of the Technological Faculty in Zagreb in 1960. He won his master’s degree in 1966; his master-thesis supervisor was Professor Milan Randic. He got his doctor’s degree from the Faculty of Science and Mathematics of the University of Zagreb in 1967. His doctoral thesis, entitled “Electronic Structure of Some Polyatomic Molecules”, was the first Croatian dissertation in quantum chemistry.
After receiving his BSc. Chem. Techn. degree, he was employed by the Pliva Research Institute (1960–1961). He moved to the Rugjer Boskovic Institute (RBI) in early 1962, where he spent all his working life. For many years he was the head of the Theoretical Chemistry Group in the Department of Physical Chemistry. He retired at the end of 2001. In 1992 he was elected for a full membership of the Croatian Academy of Sciences and Arts. He was also a member of the International Academy of Mathematical Chemistry from its foundation in 2005, the same year he became emeritus scientist at the Rudjer Boskovic Institute.
He published more than 500 scientific papers, few hundreds of professional articles, and 12 books, among which is the most famous Chemical Graph Theory (CRC Press, 2nd ed. 1992). He is one of the most cited Croatian chemists, with h-factor 59.
His professional interest was in the fields of quantum-chemical and mathematical methods in chemistry. In mathematical chemistry, he worked on the development and application of graph theory and topology to chemistry of conjugated systems. He was also involved in the development of molecular descriptors known as topological indices (Zagreb indices, Harary index, various distance indices, detour index, etc.) and in the development of quantitative relations between the structure, properties and activities of organic molecules and biomolecules. His contributions
in the fields of chemical graph theory and the graph-based computer chemistry made him well known as one of the pioneers in these branches of mathematical chemistry.
Professor Trinajstić will be fondly remembered by all his friends and colleagues.


Geometric Constraint Solving
Product design for manufacture is an activity driven by descriptive information. Increasingly, design includes the use of design constraints that impose conditions on the shape of the product. That is, the designer states specific constraints without telling the system in detail how to satisfy them. It is the task of the underlying constraint solver to derive a plan by which to solve the constraint system.
Constraint solving will be presented in two parts. In the first part, the architecture of a simple planar constraint solver is described that anyone can implement. We then discuss ways in which to extend the solver, both regards geometric coverage as well as more complex constraints patterns.
The second part addresses spatial constraint solving focusing in particular on the algebraic side and some of the techniques that are known for solving the equations.
Before joining the Purdue faculty, Professor Hoffmann taught at the University of Waterloo, Canada. He has also been visiting professor at the Christian-Albrechts University in Kiel, West Germany (1980), and at Cornell University (1984-1986). His research focuses on geometric and solid modeling, its applications to manufacturing and science, and the simulation of physical systems. The research includes, in particular, research on geometric constraint solving and the semantics of generative, feature-based design. Professor Hoffmann is the author of Group-Theoretic Algorithms and Graph Isomorphism, Lecture Notes in Computer Science, 136, Springer-Verlag and of Geometric and Solid Modeling: An Introduction, published by Morgan Kaufmann, Inc. Professor Hoffmann has recieved national media attention for his work simulating the 9/11 Pentagon attack.
He is on the editorial boards of


Probability Math Puzzles Apk
Free download Probability Math Puzzles Apk 3.7 for Windows with direct link
About The Game
This app offers over 80 probability math puzzles in three levels. I've included a math parser so that you can type equations as answers: if the answer is 0.49^2, for example, you can enter 0.49^2 or 0.49*0.49 without having to work out the multiplication yourself. Some of the puzzles are very challenging, even for ... read more...
How to Install Probability Math Puzzles for Windows PC?
You can install and play Probability Math Puzzles on Windows PC. Installing Probability Math Puzzles on a Windows operating system requires the installation of an Android Emulator like Bluestacks. Bluestacks Emulator application makes it possible for you to download Probability Math Puzzles on you Windows operating system.
Probability Math Puzzles for Windows PC [ view more photos ]
STEP 1: Download and Install BlueStacks
BlueStacks is absolutely free to download. You can get the installation file on their website at https://www.bluestacks.com. Once you've downloaded your copy, simply install it on your computer and open the program.
STEP 3: Download the Probability Math Puzzles Apk
The next thing you want to do is to download the Probability Math Puzzles Apk. BlueStacks would need the APK file so that it can proceed to run the app onto your computer. You can download the Probability Math Puzzles Apk for Windows at the top of this page.
STEP 4: Run the APK file on BlueStacks
After successfully downloading the Probability Math Puzzles Game APK, right-click on the file and run it with BlueStacks. BlueStacks will automatically translate that file into the useable app onto your computer. When the process is finished, you should find a shortcut of the Probability Math Puzzles Game on home screen of BlueStacks. And voila! You now have the Probability Math Puzzles Game for Windows PC.
How to install Probability Math Puzzles for Mac?
1. To install Probability Math Puzzles for Mac using Apk file, you first need go to the official BlueStacks website, and download the installer for Mac.
2. Download the APK installer file of Probability Math Puzzles at top of this page.
3. In most cases, installation of Probability Math Puzzles on Mac starts automatically. If it not, you can also drag the Probability Math Puzzles Apk file and drop it to Bluestacks Emulator to install the game.
Game Additional Information
Updated: 28 Oct 2020
Apk Size: 3.4 MB
Current Version: 3.7
Rating: 4.8/5 - 6,596 votes
Game ID: atorch.statspuzzles
Whats New: New puzzle, improved hints, and a link to the app's repo for those who want to suggest new puzzles or peek at answers! read more...
(*) is required


Wha is Abel Prize and How got in 2024
The Abel Prize is an annual award honoring outstanding mathematicians.
Often referred to as the "Nobel Prize of Mathematics".
Here's a breakdown of its key features:
Recognition: Awarded by the King of Norway, it acknowledges exceptional contributions to the field of mathematics.
Establishment: Created in 2002, it commemorates the 200th anniversary of the birth of Norwegian mathematician Niels Henrik Abel.
Monetary Award: It carries a significant monetary prize of 7.5 million Norwegian kroner (roughly equivalent to $1 million USD).
Selection Process: A committee of distinguished mathematicians selects the winner after a rigorous nomination process.
The winner of the Abel Prize for 2024 is Michel Talagrand.
He is a French mathematician who was awarded the prize for his groundbreaking contributions to probability theory and functional analysis, with outstanding applications in mathematical physics and statistics.


The PASC17 Conference, co-sponsored by the Association for Computing Machinery and the Swiss National Supercomputing Centre, is an interdisciplinary conference in HPC focused on domain science, applied mathematics and computer science. Don’t miss out on the opportunity to gather with your peers and engage in thought-provoking technical sessions and interactive discussions in the charming setting of Lugano, Switzerland, from June 26-28. We are accepting submissions for papers, minisymposia and posters. Visit our website for additional information and to sign up to receive further announcements. Follow us on Twitter @PASC_Conference.
“Russian Supercomputing Days” (Sep. 25-26, 2017, Moscow, Russia) is the largest international HPC event in Russia. Conference topics of interest cover all aspects of supercomputing technologies: parallel and distributed computing, new software and hardware computing solutions, new algorithms, big problems, supercomputing education, and much more. Conference agenda include rich research and industrial sessions, PhD showcase, exhibition, workshops, and master classes.


How much do you know your IQ level?
I always loved trying the quiz test in from TICKLE
And guess what my IQ score is 122!! :o)
This is the comment:
Congratulations, mimi!Your IQ score is 122
This number is based on a scientific formula that compares how many questions you answered correctly on the Classic IQ Test relative to others.
Your Intellectual Type is Precision Processor. This means you're exceptionally good at discovering quick solutions to problems, especially ones that involve math or logic. You're also resourceful and able to think on your feet. And that's just some of what we know about you from your test results.


Hey, this is Presh Talwalkar. This problem was part of a written interview test for Amazon in India. A drawer contains twelve identical black socks and twelve identical white socks. If you pick two socks at random: what is the probability of getting a matching pair? Can you figure it out? Give this problem a try and when you’re ready keep watching the video for the solution. Many people think when you pick two socks they will either match or they will not match. Since the number of black and white socks are equal, the probability of matching should be 50%. But this tempting answer is wrong! The probability of making a pair is actually slightly less than 50%. Let’s calculate and figure out why? There are 12 white socks and 12 black socks. By symmetry the probability of picking a black pair of socks equals the probability of picking a white pair of socks. So let’s calculate the probability of picking a black pair of socks. There is a 12 over 24 chance the first sock is black. This is because there are 12 black socks out of 24 socks total. 12 over 24 simplifies to be 1/2. Now what’s the chance of picking a black sock on the second draw? For the second sock the chance will be 11 out of 23, because there are 11 black socks remaining out of a total of 23 socks remaining. The asymmetry is because we are sampling without replacement. So what does this all mean? It means, the probability of picking a black pair is 1/2 times 11 over 23. This will also be the probability of picking a white pair by symmetry. So, we can put this all together to get the odds of picking a pair of matching socks. The probability of picking a matching pair will equal the probability of picking a black pair plus the probability of picking a white pair. Each of these is equal to 1/2 times 11 over 23. And therefore the probability of picking a pair of matching socks will be 11 over 23, which is approximately 47.8%. This is slightly less than 1/2. Did you figure it out? Thanks for watching this video. Please subscribe to my channel. I make videos on math. You can catch me on my blog mindyourdecisions. If you like this video you can support me on patreon… …and you can check out my books which are listed in the video description. You can also follow me on social media either at mindyourdecisions or at preshtalwalkar depending on the site.


Independent calculation of strip foundations from A to Z
Calculation of strip foundations is a complex and rather laborious process that should be trusted exclusively by professionals who have a state license to carry out such work. However, with the independent erection of low-rise buildings, it is quite possible to do on your own, making the necessary calculations on your own, because the work of a design specialist is very expensive. In this publication, the methodology for calculating the foundation of the strip type, set out in SP 20.13330.2011 and SP 22.13330.2011, will be considered in detail..
Brief characteristics and design features
This type of base is a single structure in the form of a tape, located under all the load-bearing walls of the building..
In terms of depth, strip foundations can be:
- buried below the freezing point of the soil;
- shallow (MZLF) with an average depth of 0.5 m;
Depth is considered to be the height of the supporting structure from the level of the planning to its “base”.
Structurally, belt-type bases can be:
The construction of a monolithic foundation is a strip made of monolithic reinforced concrete. Prefabricated foundations are erected from concrete blocks, bricks or rubble stone. In modern construction, monolithic foundations are most often erected, which allow to evenly distribute the load on the ground, preventing their destruction. Prefabricated foundations are less reliable, although they require less investment in construction.
Calculation of the strip foundation: a method for determining the bearing capacity of the soil
All calculations are performed after receiving the project in hands with a specification for the building and fastening materials used, necessary for the construction and finishing of the structure..
The calculation of the foundation parameters by this method is performed in three stages:
- Collecting loads on a strip foundation.
- Determination of parameters (width of the tape and “base”, height, depth) of the foundation.
- Calculation of the possible draft.
Another step that is not indicated in the methodology, but may be necessary when performing calculations of the strip foundation, is the performance of work to correct the data obtained. Let’s consider each stage in more detail.
Primary data collection
When determining the load on the base, it is necessary to take into account:
- the mass of the structure;
- estimated weight of the strip foundation;
- the mass of the filling of the building (equipment, people, furniture, etc.);
- snow and wind load factor.
The mass of the building is calculated by summing the weight of all building materials used in the construction of the house, taking into account the characteristics of the materials used. For simplicity of calculations, we recommend that you familiarize yourself with the table, which shows the loads on the foundation from walls, floors and roofs made of various building materials..
Use the following table to determine snow loads in a specific region:
For residents of Ukraine, this table will look like this:
Depending on the roof structure (slope angle), tabular data may require the use of a correction factor:
- up to 25 ° – the coefficient is 1;
- 60 ° and more – the coefficient is not taken into account.
To calculate the snow load on the foundation, you need to: determine your region on the map, the weight of the snow cover per 1 m2 of the roof, the coefficient taking into account the slope angle, and then multiply the roof area by the obtained data.
When using classical architectural solutions of low-rise construction, wind loads on the base of the structure can be ignored..
Calculation of the height of the strip foundation
The height of the foundation strip is the sum of the parameters, which include the following data:
- the depth of the laying, taking into account the type of soil, the level of groundwater and freezing of the soil in a particular region;
- basement height.
To determine the recommended depth of the strip foundation, depending on the soil, use the table:
To counteract the forces of heaving, it is necessary to deepen the base below the freezing point by 15-20 cm.
For example, consider the calculation of the estimated height of the base, provided that the depth of soil freezing in the region is 1.5 m; estimated height of the basement – 0.5 m.
Calculations of the base height are as follows: 1.5 + 0.5 + 20 cm (recommended laying depth below the freezing point) = 2.2 m.
Calculation of the width of the “foot” of the strip foundation
The calculation of this parameter depends on the material used in the construction of the “box”, the length and thickness of the bearing walls. A simplified version of calculating the width of the tape – using the averaged data shown in the table below:
For more accurate calculations of the width of the “sole” of the tape, you can use the formula:
- 1.3 – load safety factor;
- P is the total mass of the building with the foundation in kg;
- L is the length of the foundation tape in cm;
- Ro – soil resistivity.
Knowing the parameters of the tape, you can easily calculate the volume of the tape base. This is done as follows: it is necessary to multiply the length of the tape by its width and height.
It should be understood that the foundation structure may not have a constant cross-section. In some cases, the section of the strip foundation can be made in the form of a parallelepiped with an inclined outer surface for better resistance to heaving forces. T-shaped cross-section with an extended “base” (tape with an extended base) is erected in order to save material.
To determine the mass of the supporting structure, the volume of the tape must be multiplied by its specific gravity, taking into account the materials used for its construction.
Calculation of the soil load
How to calculate the strip foundation for the load created by the structure on the soil? This is easy to do: you need to divide the total mass of the structure (the weight of the house, the filling of the building, the snow load) by the base area in cm2.
To find the area of the supporting structure, you need to multiply its length by its width.
The obtained data are compared with the soil resistivity R0 kg / cm², on which the construction of the building is planned..
|Soil type||Soil resistance (R0 kg / cm²)|
|Clay soil with gravel||4.0|
|Soil with coarse sand||6.0|
|Soil with sand of medium fraction||5.0|
|Soil with river sand of fine fraction||4.0|
|Bulk compacted soil||1.5|
An example of calculating a foundation for bearing capacity
Let us assume that the total mass of the structure (walls, roof, foundation, filling), taking into account snow and wind loads, is 400 thousand kg. The base area is 100 thousand cm2 (the length of the tape is 4 thousand cm; the width is 25 cm.) To obtain data on the specific load of the building per cm2 of soil, it is necessary to divide the total mass of the house by the area of the base. 400000 kg / 100000 cm2 = 4.
We determine the type of soil on which the construction is supposed to be based on the table in order to obtain data on its bearing capacity. Then everything is simple: we compare the calculated indicator and the bearing capacity of the soil. It is necessary that the following condition be met: P ≦ Ro where P is the total mass of the structure, Ro is the resistivity of the soil. If the data in the table is greater than or equal to the calculated ones, then there is no need to make adjustments.
If the condition is not met, then for correction, the width of the sole increases by 10 cm and the calculations of the mass and dimensions of the foundation are repeated. This is done until the condition P ≦ Ro is satisfied.
Calculation of materials
In order to know exactly how much concrete mixture is required when erecting the base of the house, you need to calculate the volume of the foundation tape. How to calculate the cubic capacity of a strip foundation? It is necessary to multiply the indicators of the foundation tape obtained during the calculations, namely the length, width and height of the base. For example: the length of the tape is 40 m, the width is 25 cm, the height is 2.2 m. Multiplying the obtained data, we get the value 22 m3. When ordering concrete, be guided by this figure, plus 10% of the stock.
To calculate the order of the number of reinforcement you need to know:
- The minimum permissible diameter of the longitudinal rods, depending on the cross-sectional area of the tape.
- The number of armored belts with the minimum permissible number of rows of longitudinal rods.
- Cross bar diameter.
- Step of transverse reinforcement bars.
- Overlap length of rods.
- Reinforcement cage weight.
All calculations are made on the basis of the normative data given in SP 52-101-2003. To simplify calculations, you can use the services of an online calculator.


Wednesday, March 14, 2012
Approximately 3.14 Reasons to Eat Pie
Today, March 14 (written as 3/14 or sometimes 3.14 in this part of the world) is Pi Day, a celebration of everyone's favorite irrational number, π. Now, I recognize that Pi and pie are homophones and not the same word. But, it is the case that the ratio of a pie's circumference to its diameter is Pi. To this dessert blogger, that's as good a reason as any to seek out a slice of pie. Our family already finished off a fabulous apple crumb pie that my wife made over the weekend, so we'll have to find another source today. We might go over to Redbones, a local southern-style barbecue joint, which has a very decent pecan pie. How will you be celebrating Pi Day?


[Notation: The obvious notational choice for proportion or probability is p. The standard convention is to use Roman letters for sample quantities and the corresponding Greek letter for population quantities. Some books do just that. However, the Greek letter has its own special place in mathematics. Therefore, instead of using pfor sample proportion and for population proportion, many authors use p for population proportion and p with a hat (caret) on it, (called p-hat), as the sample proportion. The use of "hat" notation for differentiating between sample and population quantities is quite common.]
There's really nothing new to learn to compare two proportions because we know how to compare means. Proportions are just means! The proportion having a particular characteristic is the number of individuals with the characteristic divided by total number of individuals. Suppose we create a variable that equals 1 if the subject has the characteristic and 0 if not. The proportion of individuals with the characteristic is the mean of this variable because the sum of these 0s and 1s is the number of individuals with the characteristic.
While it's never done this way (I don't know why not*), two proportions could be compared by using Student's t test for independent samples with the new 0/1 variable as the response.
An approximate 95-% confidence interval for the difference between two population proportions (p1-p2) based on two independent samples of size n1 and n2 with sample proportions and is given by
Even though this looks different from other formulas we've seen, it's nearly identical to the formula for the "equal variances not assumed" version of Student's t test for independent samples. The only difference is that the SDs are calculated with n in the denominator instead of n-1.
An approximate 95-% confidence interval for a single population proportion based on a sample of size n with sample proportion is
Comparing Two Proportions
There is a choice of test statistics for testing the null hypothesis H0: p1=p2 (the population proportions are equal) against H1: p1p2 (the population proportions are not equal). The test is performed by calculating one of these statistics and comparing its value to the percentiles of the standard normal distribution to obtain the observed significance level. If this P value is sufficiently small, the null hypothesis is rejected.
Which statistic should be used? Many statisticians have offered arguments for preferring one statistic over the others but, in practice, most researchers use the one that is provided by their statistical software or that is easiest to calculate by hand.
All of the statistics can be justified by large sample statistical theory. They all reject H0 100(1-)% of the time when H0is true. (However, they don't always agree on the same set of data.) Since they all reject H0 with the same frequency when it is true, you might think of using the test that is more likely to reject H0 when it is false, but none has been shown to be more likely than the others to reject H0 when it is false for all alternatives to H0.
The first statistic is
The second is
where is the proportion of individuals having the characteristic when the two samples are lumped together.
A third statistic is
The test statistic z1 is consistent with the corresponding confidence interval, that is, z1 rejects H0 at level if and only if the 100(1-)% confidence interval does not contain 0.
The test statistic z2 is equivalent to the chi- square goodness-of-fit test, also called (correctly) a test of homogeneity of proportions and (incorrectly, for this application) a test of independence.
The test statistic z3 is equivalent to the chi- square test with Yates's continuity correction. It was developed to approximate another test statistic (Fisher's exact test) that was difficult to compute by hand. Computers easily perform this calculation, so this statistic is now obsolete. Nevertheless, most statistical program packages continue to report it as part of their analysis of proportions.
Common sense suggests using z1 because it avoids conflicts with the corresponding confidence interval. However, in practice, the chi-square test for homogeneity of proportions (equivalent to z2) is used because that's what statistical software packages report. I don't know any that report z1. However, z2 (in the form of the chi-square test) has the advantage of generalizing to tests of the equality of more than two proportions.
When testing the null hypothesis H0: the population proportion equals some specified value p0 against H1: the population proportion does not equal p0, there is, once again, a choice of test statistics.
all of which are compared to the percentiles of the standard normal distribution.
Again, z1 gives tests that are consistent with the corresponding confidence intervals, z2 is equivalent to the chi-square goodness-of-fit test, and z3 gives one-sided P- values that usually have better agreement with exact P-values obtained, in this case, by using the binomial distribution.
These techniques are based on large sample theory. Rough rules of thumb say they may be applied when there are at least five occurrences of each outcome in each sample and, in the case of a single sample, provided confidence intervals lie entirely in the range (0,1).


Math Professor Pulls Off The Coolest April Fool’s Day Prank On Class
If more professors were like this man above, the attendance rate would be almost at 100 percent. This professor decided to not so much pull a fast one on his students but a cool prank for April Fool's Day.
This type of prank he decided to pull on his class took a lot of skill, practice and time to get it down. He had to do double the work to freak out his students with this trick he came up with all on his own. The math professor has you believe he's written on the projector screen and attempts to fix his mess. The class got a real kick out of his almost 3 minute performance. April Fool's Day isn't just for the fools, it's also for the smart that get fooled too.
In the spirit of April Fool's Day today, give this math professor some props for his tricky skills!


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Mathematics and mathematical thinking include basic operations reading and interpreting data from charts and tables predicting outcomes based on data and combinatorics modular arithmetic may 2012 this issue of students explorations in mathematics introduces students to modular arithmetic and its applications. Student solution manual for mathematical statistics with application 7th edition the quantitative literacy project that formed the basis of the data analysis strand in the curriculum standards of the national council of teachers of mathematics he also led the task force that developed the ap statistics program for which he served as . The national council of teachers of mathematics nctm has identified five imperatives or needs for all students nctm 1998 45 46 become mathematical problem solvers. Institutions nctm institutional subscriptions to one or more of our journals provide your institution faculty and students with up to date information on research development and the ongoing effort to improve the teaching and learning of mathematics. Student workbook for book 1 of the principles of mathematics biblical worldview curriculum for junior high math is a real life tool that points us to god and helps us explore his creation yet it often comes across as dry facts and meaningless rules here at last is a curriculum that has a biblical worldview integrated throughout the text and
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- Choosing an Agent
- Covering Your Costs
- The DIY Mover
- Moving Into Storage
- Removal Experts
Self-storage units come in various sizes from a small unit of 20 feet to upwards of a 200 feet. Self storage companies usually only quote floor space (width x length) when describing the different sizes of unit they have available and don’t generally give a cubic feet capacity unless asked.
So a 70 ft2 unit may be 10 feet in length by 7 feet wide = 70 ft2
To convert to cubic feet value of your storage room or unit simply add the height to the equation (length x width x height).
The height of a self storage unit is normally about 8 feet, so the total cubic capacity of a 70 ft2 unit would be:
|10ft||7ft||8ft||560 cubic ft|
1 foot = 0.3048 metres
1 metre = 3.2808399 feet (3 feet 3⅜ inches)
Please remember that all house contents are different so the above unit size requirements are approximations only. Always check with your storage company.