SAS and R programs:
| I find interest in every research
problem I am working on. That is why my research interest is closely
related to my research experience.
My research interests can be roughly partitioned into the following categories:
(1) using auxiliary information in statistical estimation;
(2) missing and censored data;
(3) survey data analysis (large, complex surveys).
Using auxiliary information in statistical estimation was my first research topic. I started working on this topic during my diploma work (1995-1996). When I graduated Tomsk State University (TSU), Russian Federation, I enrolled in the TSU-post-graduate program of the Department of Applied Mathematics and Cybernetics and continued working on auxiliary information problems. The original problem I focused on was "probability estimation when probabilities of some other events are known". This was relatively artificial for me. I did not see real-life problems behind the underlying mathematics. I started thinking that the additional probabilities cannot be known exactly in real-life. Instead, these probabilities could have been obtained from previous experiments. Using this practical correction, I was able to find some interesting formulas, and surprisingly for myself, I realized that I did not have strong background in statistics. My mathematical knowledge did not cover a variety of statistical methods developed for data analysis. At that time, I decided to take additional education in statistics. After I defended my dissertation for candidate of technical sciences (2002), I left for the USA and enrolled as a PhD student of the Department of Statistics at the University of Kentucky.
My interest in missing and censored data evolved out of the approaches I used in "using auxiliary information ..." that can be successfully applied to this new area. After proper development of these techniques my co-authors and I proposed an alternative method for estimating parameters in the presence of missing data. New method is distribution-free and does not require using imputations in any form. This approach can be safely applied for sufficiently large sample sizes if the missing data mechanism does not affect on the mean and variance-covariance structures. This assumption holds for larger set of problems than the assumption of ignorable missing data does. Applying the proposed approach to random dropout, the well-know Kaplan-Maier estimator was obtained. Working on change score estimation interesting results were found.
Since January 2004 I have been the statistician to the "Intimate Partner Violence Surveillance Project" (funded by Centers for Decease Control and Prevention) at the Kentucky Injure Prevention and Research Center. During five years (1999-2003) simple random samples of about two thousand Kentucky women each year were interviewed about intimate partner violence. The analysis of these surveys is my responsibility. The results of these analyses are presented in a number of technical reports, peer reviewed articles, training materials and violence prevention initiatives.
Separately, I should say, I like programming. People with Russian education in applied mathematics usually become programmers. I do not have problems with new programming languages. It is easy to learn them, if you know how they are supposed to work. Three years ago, my favorite languages were C++ (I used STL) and Visual Basic for Applications. But now, because of my strong interest in statistics, I program on SAS and R. I do take great pleasure solving programming problems. This work is both challenging and exciting. For example, working on survey analysis, I like to write IML-based SAS-macros from time to time. It is not required, but it makes routing work much more interesting.


Earlier than we talk about Powerball methods and statistics, lets take a look at some fundamental details about Powerball: Powerball is an American lottery game through which tickets are offered for a shared jackpot pool. Every participant of the game should buy a ticket. On buying the ticket, the shopper has to pick 5 numbers from 1 by 59 and one Powerball number (written in crimson) inside 1 by 39. When the draw is made, tickets which match no less than three white balls and/or the crimson Powerball are winners. 파워볼
Two time Powerball millionaire Terry Fisher means that one ought to examine the sample in previous attracts to enhance the percentages of profitable sooner or later.
In a Powerball system of 10 numbers, the one option to assure that one all of them 5 number you will have will likely be collectively is play a complete of 252 games. On the opposite hand solely 54 games are required for a four-from-four system of 10 numbers. This ensures that the 4 numbers you will have chosen will come out collectively.
However in actuality, you will have 5 Powerball numbers and also you need all of them. As talked about, the wining situation of a Powerball draw is that three consecutive numbers. However each game has 5 number and should you assure that your 4 numbers are collectively, then you will need to have one in six probability of getting all 5 of your numbers collectively. This in essence implies that you’ll find yourself saving nearly 80% of the associated fee.
Nevertheless, in 270 games of a four-from-four with 10 numbers can have 5 units. Examine this with 10 numbers in 252 games. So, the previous means that you can play 50 in case your set of 10 numbers are all totally different which clearly improves your possibilities of profitable small prizes.
The factor of statistics in Powerball may be illustrated by a set of 10 numbers containing 5 odd numbers and 5 even numbers is significantly higher guess then all even or all odd numbers.
It is because previous attracts present that nearly two third of all Powerball outcomes are two odd numbers plus three even number OR vice verse i.e. three odd numbers plus two even number.


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Students typically learn to add and subtract fractions and mixed numbers in upper elementary school. The denominators must be the same when adding or subtracting fractions, so students must first learn to find the “least common denominator.” The least common denominator (LCD) is the smallest number that both denominators will divide into evenly. Although denominators in math books are kept fairly simple at first, the numbers students are expected to work with begin to increase in sixth and seventh grades, making it more challenging to determine the LCD. As a middle-school math teacher, I know it is important to show students methods that work for both large and small denominators. If a student doesn’t know how to find a common denominator, he is headed for confusion in future math classes.
Even in middle school, some students still confuse numerators and denominators. Give them a memory trick: “down” and “denominator” both begin with the letter “d.” The denominator is “down” on the bottom, under the fraction bar.
You can always simply multiply the denominators together to find a common denominator. The trouble with this method is that the result is often not the least common denominator, so the denominator may be too large to work with comfortably.
If the fractions you’re adding are 5/6 and 1/3, you can multiply the denominators, 6 and 3, and find a common denominator of 18. That number can be used; however, it will require reducing the final answer. It’s best to find the least common denominator – in this case, 6.
Match Least Common Multiples
This is the predominant method used – especially in elementary school – to find the LCD.
To find a number’s multiples, multiply the number by 1, 2, 3, and so on.
The multiples of 4 are 4, 8, 12, 16, 20, 24, 28 …
To find the least common denominator (LCD) for two or more fractions, list the denominators’ non-zero multiples until you find a match. That match is the least common denominator.
Find the LCD for 1/6 and 1/8:
Multiples of 6: 6, 12, 18, 24…
Multiples of 8: 8, 16, 24…
The lowest number that’s a multiple of both 6 and 8 is 24; therefore, the LCD for 1/6 and 1/8 is 24.
Practice finding least common multiples/denominators with the entire class by putting IXL’s least common denominator program on an overhead device. Create a customized practice sheet for finding the LCD/LCM at Math Worksheet Site.com.
Use the Greatest Common Factor
Multiply the denominators together and then divide by their greatest common factor (the greatest common factor or GCF is the largest number that will divide into the denominators evenly).
Find the least common denominator for 1/12 and 2/9.
Multiply the denominators: 12 x 9 = 108.
Divide 108 by 3, the GCF of the two denominators: 108/3 = 36.
The least common denominator for 1/12 and 2/9 is 36.
Another form of this method is to divide one of the denominators by its GCF and then multiply the other denominator by that quotient.
12 divided by the GCF, 3, is 4.
9 times 4 is 36.
Choose the denominators you wish to use and create a customized worksheet at Math Teacher’s Assistant.
Large Numbers: Use Prime Factorization
Students need to understand how to find the prime factorization of a number in order to use this method for finding the least common denominator. This method is definitely the way to go when working with larger denominators. Click here for tips on how to teach prime factorization.
- Factor each denominator into primes.
- Count the number of times each prime number appears in each factorization.
- Take the largest of these counts for each number and write it down.
- The least common denominator is the product of those prime numbers you have written.
Find the least common denominator for 1/5, 1/9 and 1/12.
9: 3, 3
12: 2, 2, 3
The most 2 appears on any factor list is two times (for the denominator 12); the most 3 appears is two times (for the denominator 9); the most 5 appears is one time (for the denominator 5).
Multiply: 2 x 2 x 3 x 3 x 5 = 180
The least common denominator for 1/5, 1/9 and 1/12 is 180.
Create your own practice sheet at WorksheetWorks.com to practice using prime factorization to find least common denominators. Download this free worksheet and answer key from MathX.net for practice working with large denominators.
To read more education articles by this author, click here.
Image credit: Wikimedia Commons public domain


Welcome to my webpage! I am an Assistant Professor of Mathematics at Virginia Commonwealth University. My mathematical interests include Analysis, Partial Differential Equations, Stochastic Analysis and Calculus of Variations with application to Materials Science Problems. I got my Master's degree in Mathematics from Kyiv National University, Ukraine. My PhD in Applied Mathematics is from Penn State University. I worked as Golomb Assistant Professor at Purdue University, and as a Courant Instructor/Assistant Professor at Courant Institute of Mathematical Sceinces, New York University, prior to my current position.
Department of Mathematics and Applied Mathematics
Virginia Commonwealth University
1015 Floyd ave., Richmond, VA, 23284


Mathematics education is changing all across the world. Early primary school math test questions are now probing deeper into cognitive and pattern reasoning skills than simple arithmetic, particularly in Hong Kong, Japan, and China.This shift is the result of a growing amount of evidence indicating that early maths skills predict subsequent performance in school and in life. A recent study, for example, discovered that children who had a strong foundation in arithmetic at the age of five were more likely to go on to achieve good scores in other areas, such as reading and science.There is also a rising understanding of the value of mathematics in the global economy. In a world where employment are rapidly being outsourced to lower-cost countries, countries with high maths education are better positioned to compete. Hong Kong, Japan, and China are pioneering this new approach to mathematics instruction. These countries have a long history of prioritising memorization and rote learning. They are, however, beginning to recognise the value of greater comprehension and problem-solving abilities.As a result, their early primary school math test questions are increasingly measuring cognitive and pattern reasoning skills rather than plain arithmetic. This is a huge adjustment that will undoubtedly benefit their pupils’ future success.


Interesting information about mathematics are a few of the a lot more significant and exciting factors that we study when we are young.
At a young age, we are basically taught mathematics at the same time as other parts of science that we are able to take with us into adulthood. So, the trick is to choose a topic that interests you and study it properly adequate to know it at an early age.
What are some exciting information about mathematics? Properly, here are some information about it: The Greek alphabet consists of twenty-eight letters. That is certainly not to say that Greek is definitely the only language which has this a lot of letters. We all know that the alphabet is according to sounds and thesis help can also be determined by sight or symbols.
Our brains function within a blend of people. As an example, we at times believe we are considering of ourselves, but in reality, we could possibly be thinking of a person else. It is only when we genuinely believe about it that we comprehend this can be the case.
A number is just a mixture of letters and sounds. The letters will be the basic constructing blocks on the quantity. A set of numbers are numbers which have 1 or more of your letters “A”, “B”, “C”D”. Additionally, the set is composed of 5 or additional of these letters. We then have a set which has at least one of these letters and a minimum of 5 of those letters.
We may well wonder how a set of numbers is often referred to as a quantity. This can be due to the fact delta mathematics https://www.iup.edu/counseling/ does not permit us to work with algebra. And if we did, we would only have the ability to define the set. When we speak of a set of numbers, this can be utilized inside a different way.
In delta mathematics, we’ve to start using the value ofa quantity. From there, we are going to look at sets and how they relate to this worth. If we don’t come across a connection in between a set and a quantity, we can not have a set.
A quantity is usually good or negative. A constructive quantity is really part of the number if it is inside the set. Nevertheless, if we uncover a quantity that is certainly negative, then we can not contact that quantity a quantity.
If we contemplate what would happen if we did not understand anything about calculus and we had to operate with a set in math, we would possess a large amount of difficulty. It will be just about not possible to calculate issues properly. And we would not have a approach to figure out how substantial a set is.
You need to be capable of calculate complicated numbers, which are another kind of math that appears like sets. This sort of math is utilized to calculate items like angles, lines, numbers, and points. This math works greatest for undertaking calculations where we ought to know what the angles are, what the line is, and what the number is.
Delta Mathematics basically requires into account that we’re always changing our thoughts. This implies that it is vital to constantly assume in regards to the same set of factors. The problem with delta mathematics is the fact that for those who come up with a set of objects, it might not necessarily apply to the next time you need to apply https://www.ewriters.pro it.
The numbers are different in the way we assume about numbers in genuine life. Numerous students believe that they’ve to be particular in regards to the way numbers appear to be able to be very good at mathematics. The delta way of understanding numbers might help individuals be superior at math, nevertheless it is just not set in stone.
These are some interesting information about mathematics. Ifyou assume you’ve a knack for it, then you can take the delta mathematics that you understand and make it your personal.


Given vectors that represent words, how do we construct sentences? Do we add the vectors? Do we find centroids? Do we normalize before, after or not at all?
In fact, can we even say we are dealing with a vector space?
Remember, a vector space has the following 8 properties:
- Identity (of addition and multiplication)
- Distributivity (of scalars and vectors)
- Addition also has commutivity and associativity plus an inverse.
- Compatibilty: (ab)v = a(bv)
"The commutativity property of vector addition does not always hold in semantics. Therefore, this property shouldn't (always) hold in the embedding space either. Thus, the embedding space should not be called a vector space.
E.g. attempt to treat semantic composition as vector addition in the vector space:
vrescue dog = v rescue+ vdog (a dog which is trained to rescue people)
vdog rescue = vdog+ vrescue (the operation of saving a dog)
The phrases "rescue dog" and "dog rescue" mean different things, but in our hypothetical vector space, they would (incorrectly) have the same vector representation (due to commutativity).
Similarly for the associativity property."
At the same time, erroneous assumptions are not necessarily unacceptable (as the post points out). It's just a high-bias model.
For fun, I tried the vectors that Word2Vec gave me. Now, there is no reason I could think of why the vectors this algorithm gives me for words should be used to form a sentence. But the results were surprising.
|Raw vector addition||81.0|
|Normalized vector addition||27.9|
|Raw vector centroids||7|
|Raw vector addition then normalizing||7|
That is, adding together Word2Vec generated word vectors to make a sentence meant my neural net produced decent (but not stellar) results.
More promising was combining vectors from category space. The results looked like this:
|Normalized vector addition||94.0|
|Normalized vector centroids||92.1|
|Adding unnormalized vectors||6.2|
|Normalized vector addition then normalizing||5.3|
Finally, concatenating (and truncating if there were more than 10 words per text and padding if there were fewer) the word vectors for a sentenceand feeding it into an ANN produced an accuracy of 94.2%. Naive Bayes and Random Forest gave a similar results (92.3% and 93.3% respectively)
Note: multiplying each vector by a factor that was between 0.5 and 1.5 made no difference to the accuracy of an ANN. Weights will simply change accordingly.
It seems like an ANN can take data in pretty much any format (although it's better when we're using variations on the category space rather than TF-IDF).
When I asked a Data Science PhD I work with which technique I should use (adding vectors; finding centroids, concatenating vectors etc) his answer was: "Yes".


2 edition of representation of statistics by mathematical formulae. found in the catalog.
representation of statistics by mathematical formulae.
Francis Ysidro Edgeworth
Written in English
|The Physical Object|
|Number of Pages||82|
Statistics & Mathematics Find free statistics and mathematics books in this category. Are you looking for a specific subject? Try one of the mathematics or statistics books which will . COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.
( views) A First Course In Mathematical Statistics by C.E. Weatherburn - Cambridge University Press, This book provides the mathematical foundations of statistics. It explains the principles, and proves the formulae to give validity to the methods of the interpretation of statistical data. This course provides an elementary introduction to probability and statistics with applications. Topics include: basic combinatorics, random variables, probability distributions, Bayesian inference, hypothesis testing, confidence intervals, and linear regression. The Spring version of this subject employed the residential MITx system, which enables on-campus subjects to provide MIT.
These are the formulae you may be expected to know for the appropriate exams (please check with your teacher) as they are not listed in the AQA formulae booklet. Use the links below to view lists of additional formulae with which you will need to be familiar, under each of the specific areas of mathematics. (data) Return the sample arithmetic mean of data which can be a sequence or iterable. The arithmetic mean is the sum of the data divided by the number of data points. It is commonly called “the average”, although it is only one of many different mathematical averages. It is a measure of the central location of the data.
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Statistics is a branch of mathematics which deals with numbers and data tics is the study of the collection, analysis, interpretation, presentation, and organization of data.
Statistical theory defines a statistic as a function of a sample where the function. The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mathematical formalism uses mainly a part of functional analysis, especially Hilbert space which is a kind of linear are distinguished from mathematical formalisms for physics theories developed prior to the early s by the use of.
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Mathematical Tables and Formulae, the content of such a book was reconsidered. The previous edition was carefully analyzed, and input was obtained from practi-tioners in the many branches of mathematics, engineering, and the physical sciences. The consensus was that numerous small additions were required in several sections.
The definition of what is meant by statistics and statistical analysis has changed considerably over the last few decades. Here are two contrasting definitions of what statistics is, from eminent professors in the field, some 60+ years apart: "Statistics is the branch of scientific method which deals with the data obtained by counting or.
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in convention, these applied methods are beyond simple geometry, such as differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, and other computational methods.
A Level Further Mathematics papers may be required to use the formulae that were introduced in AS or A Level Mathematics papers. It may also be the case that students sitting Mechanics and Statistics papers will need to use formulae introduced in the appropriate Pure Mathematics papers for the qualification they are sitting.
Besides, the book contains six historical interludes written by Dr. Slava Gerovitch.1 These interludes, written in an accessible and ab-sorbing style, tell about the life and mathematical work of some of the mathematicians who played a major role in the development of modern algebra and representation theory: F.
Frobenius, S. Lie. 76 The Quadratic Formula 77 Quadratic Inequalities in One Variable 79 Fitting a Quadratic through Three Points Chapter Complex Numbers 80 Complex Numbers ‐ Introduction 81 Operations with Complex Numbers 82 The Square Root of i 83 Complex Numbers – Graphical Representation.
This book Formulae of Mathematics is being specially brought out of all hardworking sincere students aspiring for IIT-JEE, MCA, and other engineering avenues. It is aimed to provide apt unfailing support to the anxious confused students whose performance decides his and his guardian’s dream career.
Formulas — you just can’t get away from them when you’re studying statistics. Here are ten statistical formulas you’ll use frequently and the steps for calculating them. Proportion Some variables are categorical and identify which category or group an individual belongs to.
For example, “relationship status” is a categorical variable, and an individual could be [ ]. The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot.
We also acknowledge previous National Science Foundation support under grant numbers, and 1. Mathematical statistics. Mathematical statistics—Data processing. Tsokos, Chris P. Title. QAR –dc22 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library.
ISBN For all information on all Elsevier Academic Press. Many students are using our Free Statistics Lab Manual\rwhich loads into most spreadsheets.\rIt is really a Quick way to learn.\rIt is a stand alone but was designed to use with our free\rQuick Notes Statistics textbooks.\rThis textbook free pd\.
] Representation of Statistics by Mathematical Formulae. The process of different values of P2 is abridged by several limitatioins. First, positive values of P2 may be excluded, for they correspond to " suibtractive " solutions, according to which one comronent frequency is not superadded to, but deducted from.
Given that this is an introductory statistics textbook, many of the theoretical topics such as formulas, definitions, concepts, etc. covered will not change over time and as a result this text book will not need to be altered within a short period of time.
Project Euclid - mathematics and statistics online. Featured partner The Tbilisi Centre for Mathematical Sciences. The Tbilisi Centre for Mathematical Sciences is a non-governmental and nonprofit independent academic institution founded in November in Tbilisi, general aim of the TCMS is to facilitate new impetus for development in various areas of mathematical sciences.
] Representation of Statistics by Mathematical Formulce. A somewhat similar feeling seems proper with respect to certain received formule whiclh present, in a less extreme degree, the characteristic of our third division. I venture to place in this category two of.
Statistics is about the mathematical modeling of observable phenomena, using stochastic models, and about analyzing data: estimating parameters of the model and testing hypotheses.
In these notes, we study various estimation and testing procedures. We consider their theoretical properties and we investigate various notions of optimality.
Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians.
excellent guide into the often-challenging ﬁ elds of mathematics and statistics. I hope and wish that the knowledge gained via this book would help them succeed in their business endeavors.
As is often the case with equations and numbers, I am sure this book still has some errors. If you ﬁ nd some, please let me know at [email protected] GCE in Mathematics Mathematical Formulae and Statistical Tables For use in Edexcel Advanced Subsidiary GCE and Advanced GCE examinations Core Mathematics C1 - C4 Further Pure Mathematics FP1 - FP3 Mechanics M1 - M5 Statistics S1 - S4 Modified large print version produced by.
The book will serve as a text in courses aimed at advanced undergraduates and masters students in statistics, engineering, and applied mathematics as well as quantitatively oriented MBA students.
Those in the finance industry wishing to know more statistics could also use it for self-study."Reviews:


Ajmone Marsan, Marco and Goyal, Suresh and Xu, Shugong and Fernández Anta, Antonio and Prodanovic, Milan and Christensen, Ken (2012) Proceedings of the 3rd International Conference on Energy-Efficient Computing and Networking, e-Energy'12, Madrid, Spain, May 9-11, 2012. ACM.Full text not available from this repository.
|Subjects:||T Technology > T Technology (General)|
|Divisions:||Faculty of Engineering, Science and Mathematics > School of Electronics and Computer Science
Faculty of Engineering, Science and Mathematics > School of Engineering Sciences
|Depositing User:||Antonio Fernandez|
|Date Deposited:||07 Nov 2012 09:21|
|Last Modified:||05 Dec 2016 10:13|
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There are four related functions for mixed effects analyses:
mixed_anova( data, Y_value, Fixed_Factor, Random_Factor, Df_method = "Kenward-Roger", SS_method = "II", ... )
a data table object, e.g. data.frame or tibble.
name of column containing quantitative (dependent) variable, provided within "quotes".
name(s) of categorical fixed factors (independent variables) provided as a vector if more than one or within "quotes".
name(s) of random factors to allow random intercepts; to be provided as a vector when more than one or within "quotes".
method for calculating degrees of freedom. Default is Kenward-Roger, can be changed to "Satterthwaite".
type of sum of square, default is type II, can be changed to "I", "III", "1" or "2", or others.
any additional arguments to pass on to
lmer if required.
ANOVA table of class "anova" and "data.frame".
This function uses
lmer to fit a linear mixed effect model and provides the model object, which could be used for post-hoc comparisons. The model object is converted to class
lmerModLmerTest object by
as_lmerModLmerTest. This is then passes on the model to
anova and provides the ANOVA table with F and P values.
It produces a type II sum of squares ANOVA table with Kenward-Roger approximation for degrees of freedom (as implemented in
It requires a data table, one dependent variable (Y_value), one or more independent variables (Fixed_Factor), and at least one random factor (Random_Factor). These should match names of variables in the long-format data table exactly.
This function is related to
More than one fixed factors can be provided as a vector (e.g. c("A", "B")). A full model with interaction term is fitted.
This means when
Y_value = Y, Fixed_factor = c("A", "B"), Random_factor = "R" are entered as arguments, these are passed on as
Y ~ A*B + (1|R) (which is equivalent to
Y ~ A + B + A:B + (1|R)).
For simplicity, only random intercepts are fitted (
#Usage with one fixed (Student) and random factor (Experiment) mixed_anova(data = data_doubling_time, Y_value = "Doubling_time", Fixed_Factor = "Student", Random_Factor = "Experiment") #> boundary (singular) fit: see help('isSingular') #> Type II Analysis of Variance Table with Kenward-Roger's method #> Sum Sq Mean Sq NumDF DenDF F value Pr(>F) #> Student 16.824 1.8694 9 18 0.4725 0.8744 #two fixed factors provided as a vector mixed_anova(data = data_cholesterol, Y_value = "Cholesterol", Fixed_Factor = c("Treatment", "Hospital"), Random_Factor = "Subject") #> Type II Analysis of Variance Table with Kenward-Roger's method #> Sum Sq Mean Sq NumDF DenDF F value Pr(>F) #> Treatment 1968.38 1968.38 1 20 46.2485 1.301e-06 *** #> Hospital 131.43 32.86 4 20 0.7720 0.5561366 #> Treatment:Hospital 1482.35 370.59 4 20 8.7072 0.0003066 *** #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Reading through the student worksheet will give you an idea of how this lesson works as I have not typed up a lesson plan for this activity yet.
This lesson can be a lot of fun during the Halloween season and it is also a great way to hit several Math and Science standards at one time. Incorporate writing standards into this lesson by having students write a descriptive paper about their finished shrunken head. Then read the papers out loud to the class. See if the students can pick out which shrunken head belongs with each paper.


Finance Quick Answers
This article is part of the Missouri Saves Program
What is compound interest?
Compound interest occurs when interest is earned on a principal sum along with any accumulated interest on that sum. In other words, you're earning interest on interest. This principal helps your money grow. For example, if you deposit $100 and the interest rate is 5% each year. At the end of year one, you will have $105. At the end of year two, the compound interest is calculated by multiplying 5% by $105. At the end of year two, you would have $110.25. At the end of each year, interest is calculated on the amount in the account.
Check out "The
Miracle of Compound Interest" to see the difference
compound interest makes.
Dr. Joyce Cavanagh, Former Assistant Professor and State Specialist, Consumer and Family Economics
Last update: Friday, July 25, 2008


How do you use a compass ruler?
What is a compass in math?
A compass is used in mathematics, drawing and drafting to create arcs, circles or other geometric figures that can be determined by measuring intersecting line segments. A compass can be used to bisect lines, find midpoints and help solve problems in geometry.
What is a compass in drawing?
A compass, more accurately known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, it can also be used as a tool to step out distances, in particular, on maps. Compasses can be used for mathematics, drafting, navigation and other purposes.
How do you measure with a compass?
What is the difference between ruler and compass?
A ruler is for measuring segments and drawing segments of a specific length. A protractor can be used to measure angles as well as draw angles of a specific measure. A compass constructs circles and copies segments without measuring.
Why is it called a compass?
The mathematical instrument for describing circles was so called in English from mid-14c. The mariners’ directional tool (so called since early 15c.) took the name, perhaps, because it’s round and has a point like the mathematical instrument.
Is compass a measuring tool?
A compass (or pair of compasses) is a drawing tool that can be used to draw circles or arcs, parts of circles. They can also be used to measure distances, in particular on maps. Compasses can be used for mathematics, drafting, navigation, and more.
What is a compass and a protractor?
The compass is used to draw circles and arcs, while the protractor helps you measure and make plane angles. Signing up for a geometry class means you’ll likely need two essential supplies: a compass and a protractor.
What is a compass simple definition?
1 : a device having a magnetic needle that indicates direction on the earth’s surface by pointing toward the north. 2 : an instrument for drawing circles or marking measurements consisting of two pointed legs joined at the top by a pivot —usually used in pl.
How do you use a compass tool?
Can I use a protractor as a ruler?
What does protractor look like?
A protractor is either a circle or a semicircle. Protractors have been around since antiquity, but currently are made of plastic or can be printed out on paper. Compasses, which have also been around for centuries, consist of two legs on a hinge.
What are the two uses of a protractor?
A protractor is a device used in drafting and drawing: it’s mainly used for drawing and measuring angles. Don’t show up to geometry without your protractor! In math class, you use many tools, such as a calculator. Another is the protractor, which is handy when you’re studying geometry.
What can you use if you don’t have a protractor?
Is there an online protractor?
The online protractor tool can be used to practice measuring angles. It can be used at a variety of different grade levels. At its most basic for teaching about types of angles, acute, obtuse or reflex.
How do you use a protractor for beginners?
Can angle measure without protractor?
The easiest way to measure an angle is to use a protractor. However, if you don’t have a protractor handy, you can determine the size of an angle using the basic geometric principles of triangles. You’ll need a scientific calculator to solve the equations.


High school students who are currently in Year 10 and 11 as well as advanced Year 9 students are invited to participant in the UWA Academy for Young Mathematicians in 2015.
The program for the Academy is suitable for a broad range of mathematically able students. The aim is to broaden and deepen their mathematical knowledge, to involve them in problem solving and to extend the range of their mathematical skills.
All sessions of the Academy will be held on Saturdays from 10am to 11.45am on the following dates:
14, 21 and 28 March
9 and 23 May
1, 15 and 29 August
17 and 24 October
The sessions will be held in the Mathematics Lecture Room 1 of the School of Mathematics and Statistics, UWA. Parking should be available in Fairway.
During the sessions, in addition to problem-solving, students will receive printed handouts and problem sets, and will be expected to solve some problems for homework. Certificates will be awarded for excellent performance. The lectures at the Academy will be presented mainly by staff members of the Schools of Mathematics and Statistics of UWA. The preliminary program for 2015 (different from that in 2014) includes sessions on:
combinatorics and probability
coordinate and circle geometry
game theory and
problems from mathematics competitions.
Students can enrol online at the UWA Academy website. Early applications will be favoured.
The fee for the whole year, including printed material, is $50. Students are to supply their own stationery. Please do not included payment with your initial application.
The University of Western Australia
School of Mathematics and Statistics
UWA Academy for Young Mathematicians
35 Stirling Hwy, Crawley WA 6009
Phone: 08 6488 3393


Maths Programs at Educate Tutoring
Maths is like building a house. If the foundation isn’t solid, then the rest of the house won’t stand. If students have gaps in their foundational understanding of numeracy, they will struggle to advance to more complicated mathematical concepts. In order for students to be able to build on their existing knowledge, concepts need to be mastered before moving on to other, more challenging aspects.
To further understand this idea of mastery learning, see this TED talk by Khan Academy founder Sal Khan:
At Educate Tutoring, the first step we take is to identify the gaps in a student’s knowledge, using a variety of assessments.
After assessments have highlighted areas requiring further instruction, a personalised Mathematics program is developed for each student.
At Educate Tutoring, we use a Singapore Maths based approach in the development of our programs. Resources that utilise concrete models and encourage different reasoning and problem-solving methods assist us in teaching deeper understandings of concepts and skills.
Singapore Maths trains students in using a mathematical vocabulary, and understands that learning is a two-way dialogue requiring students to think critically and explore methods of solving problems.


Mrs. Powell's Class
8th Grade Math
Math Tools & Games!
Geometry Assignment Calendar
GEOMETRY UNIT 5:
5A- Arc length, are, radians, and degrees
practice changing from degrees to radians
practice changing from radians to degrees
how to change degrees to radians and radians to degrees
video: Developing Area of a circle - using a rectangle...
finding the area of sectors and the length of arcs
this is section 11-3 (pg. 764) in our Geometry book.
how to construct tangent lines to a circle from a point outside the circle
hOW TO CONSTRUCT A CIRCLE THAT PASSES THROUGH THE 3 VERTICES OF A TRIANGLE.-CIRCUMscribing A TRIANGLE
How to inscribe a circle in a triangle
Using TRIG ratios to find missing angles
Midpoint Formula Video and Practice - Khan Academy
Using Proportions to solve problems - holt Geometry Book
Using Similarity to solve problems - Holt Geometry book
determining similarity - HOlt Geometry book
Geometry Unit 3
Need some help with Proofs?
In our Geometry book: Section 2-6 pg. 110 is a good place to start!
Online practice with proofs from our book
PROOF PRACTICE part 2
TAco cart video
Geometry Unit 2
Practice finding distance and perimeter
practice finding equations of parallel and perpendicular lines
GEOMETRY UNIT 1B
Constructions videos - Math Open Reference
TRIANGLE CONGRUENCE POSTULATES VIDEOS: SSS, SAS, ASA, AAS
Create your own unique website with customizable templates.


Grade: 2nd grade, high school
Level of implementation complexity: medium
Correlations and interdisciplinarity:
- Personal and social development
- Civil education
Find tips and instructions for using digital teaching tools at e-Laboratory. (in Croatian language)
Key Words: exponential function, loan, logarithmic function, compound interest calculation, savings
- determine the final and initial value of a deposit with compound interest (A, B)
- explain the relationship between the initial and the final savings amount depending on the term of savings and the interest rate (A, C)
- apply an exponential and logarithmic function on a complex interest calculation (A, B, C, D)
- associate the understanding of interest calculation with real life situations (C, D)
*In parentheses, there are letters indicating the teaching scenario activities, and their implementation contributes to achieving the respective outcomes.
A Linked cards
In this activity, students practice compound interest calculation – the calculation of one of the four variables. Before doing exercises, have the students remember what compound interest calculation is, what is its basic principle and how it is calculated. Talk about the variables which appear in the formula, and what values these variables usually take in reality. Talk to students about the use of compound interest calculation in everyday life situations and about the importance of knowing how to calculate it. After the discussion, encourage the students to practice by doing exercises in pairs.
Give each pair eight cards (in Croatian) with exercises. You can create the exercise cards yourself by using a word processor, for example Word. The pairs should complete all the exercises given in the cards. The cards are linked – the result of one card is the default data in another exercise. Students will notice that they cannot complete the exercises in a random order and that they are expected to combine the exercises in order to complete them in the fastest and most productive way possible. Hand out cards with the QR code revealing the answers (in Croatian) to each student pair after completing all the given exercises. You can create a QR code by using the QR Stuff generator.
Follow the students’ work and offer them help. At the end of the activity, discuss the exercises, their answers, the most common mistakes and the best solving strategies, in the online tool Tricider.
Given the complexity of the problem solved in this activity, it is very important to provide students with disabilities with simple, brief and clear instructions related to the exercises, and to check their understanding. If necessary, split the exercises into smaller stages, and give the students instructions in each stage. For students with specific learning disabilities (dyscalculia, dyslexia, dyspraxia), it is necessary to adjust the number and the difficulty of the exercises and give them enough time to complete them. Students with attention-deficit/hyperactivity disorder need to be introduced to the planned exercises in advance, and the exercises must be structured so that students can successfully complete them. Generally, it is useful to provide most students with disabilities with a completed exercise to serve as an example when doing similar exercises.
B Which interest rate is the right one?
By doing this activity, have students establish what interest rate and how long of an interest period is more favorable for a saver, and how can the exponential function be associated with everyday life.
Apply the exponential function to compound interest calculation, and find out how much do students know about calculating interest by using the Desmos activity entitled Interest Rate (example of activity in the Desmos tool in Croatian). Have students access activities by entering the class code which you can generate by logging into Desmos, where you can monitor the activity of each student. By filling in the table, the student will find that it is more favourable for the saver to have as short of an interest period as possible (including the same interest rate). They are introduced to the concepts of a nominal, relative and conforming interest rate. After the activity, discuss their use together so that students can think critically about the conditions provided by banks.
To a large extent, this activity is related to the everyday, and especially to the future life of students, and it develops the foundations of financial literacy. Therefore, it is important for students with specific learning disabilities and attention-deficit/hyperactivity disorder to be provided support in various ways to gain the knowledge which will be of utmost importance for them. The terminology should be further explained (nominal, relative and conforming interest rate) so students can understand them well. It is advisable to explain them firstly by using small numbers to allow the students to learn the stages of the procedure. Students can have a glossary in their notebook so that they can always recall what each term means. Instructions for tool use, support and step-by-step explanation of exercises and additional clarifications are only some of the possible support procedures, which are described in more detail in the Didactic-Methodical Guidelines for Natural Sciences and Mathematics for Students with Disabilities. (in Croatian language)
C I choose to save
Ask students whether they save money and what do they know about savings. What conditions are offered by banks? Is it worth to save at a bank?
Divide students into groups and assign a bank to each group. Give them an assignment:
Find the annual interest rate on fixed-term savings in Croatian kuna for the selected bank. Determine the amount you want to place on time deposit (joint savings) until the 21st birthday of the youngest member of the group. How much interest would you receive if the interest is imputed a) annually, b) quarterly, c) monthly?
Choose the most favourable option from the available imputing interest options offered by the selected bank, and answer the questions: a) How much would you have to wait for the fixed-term deposit amount to double? b) How much would you have to wait to be able to withdraw HRK 20,000?
Have groups find the required information on the web pages of the selected bank. Help them choose interest that matches the assignment requirements.
Have them make an infographic using the results of their research in Piktochart, and have them present the infographics to the rest of the class.
After the presentations, discuss the conditions offered by different banks and ask again if it is worth to save money at a bank.
Are the results what the students expected? Comment on why the period required for the fixed-term deposit amount to double does not depend on the deposit amount.
In this activity, most of the support to students with disabilities can be provided by students within the group, e.g. in reading data from the bank’s web pages to students with visual impairment and dyslexic students. If necessary, the text can be read several times, and students may write down important data in an appropriate way to create a personal problem-solving chart. It is also important to provide step-by-step guidance, more specifically clear instructions before each new stage in completing the exercises. Assess whether the student with disabilities is to complete all the proposed exercises or just those related to basic knowledge (e.g. calculating the annual interest and attributing it to the principal) according to the prior knowledge and abilities of the students with disabilities.
Talk to students about loans. What loan terms do students know? Does anyone close to them pay a loan? Why do people take out loans? Is it better to plan a loan or savings in the long run?
Explain to the students that annuity (periodic payment amount) consists of a repayment quota (the loan payment part) and an interest (the part paying the fee for using the funds transferred). The interest is calculated on the remainder of the debt. After each payment, the debt is reduced in the amount of the repayment quota.
The most common ways of repaying loans relate to equal annuities or equal payment quotas. An overview of loan repayment is given in the repayment table (in Croatian).
Have some students find someone in their surroundings who pays a loan. Have them collect information about the loan amount, interest rate and repayment time. Have them work in pairs and use Excel Online, a table calculation programme, to develop repayment tables for the two repayment methods – in equal annuities and in equal repayment quotas. To calculate an annuity in case of a loan repayment in equal annuities, use the Excel function called PMT (you can show advanced students how the amount is determined mathematically; knowledge involving the sum of a geometric series required). Other data in the tables is calculated simply from the default data. After developing the repayment table, have the students determine the total amount of interest to be paid in both cases.
Looking at the tables, have them consider which method is better and why. Have them share their thoughts via Edmodo. Have the students comment on their findings with the person who gave them the information about their loan.
By encouraging their participation in the introductory discussion, students with disabilities will be motivated for further work. After explaining the concepts of annuity, repayment quota and interest, it is necessary to check whether the students understand them, and if they do not, the concepts should be explained again by using simple language and small numbers. If the tables or their content are too challenging for some students with disadvantages (students with specific learning disabilities), they can be summarized and given to the students as a template and a reminder. Only after you are sure the students understand the basic concepts, you can involve them in further independent activities and activities in pairs. To use digital tools, you need to give them detailed instructions and check whether the students understand them. Adjust the method of loan repayment calculation to the students’ prior knowledge. Have visually impaired students who are not able to use digital tools, work calculations with a calculator and a custom result record.
For students who want to know more
Encourage students to find the following by browsing web pages: (in Croatian)
- what is the difference between the decursive and the anticipatory interest calculation
- what are prenumerando and postnumerando periodic payments (payoffs).
Then have them visit several banks and ask which method is used more often, in which cases and why. Have them shape their knowledge into a web page by using Tackk, where they can easily add different content (text, images, videos, links, location on the map etc.). Have them share their work with the rest of the class and then comment on it.
Additional literature, content and links
You can find additional clarification of terms on relevant web pages
- Google Scholar
- Struna (Croatian vocational terminology)
- Croatian Encyclopedia etc
Note: All network links were last validated on 10th March 2017
Did you apply this scenario in teaching? Tell us your opinion by filling out the questionnaire on this link. (in Croatian)
This text is licensed under Creative Commons Attribution 4.0 International. When using this text, you need to designate the authorship of the work in the following manner: CARNet (2017) e-Schools Teaching Scenario ˝ (enter the title of the teaching scenario) ˝, https://scenariji-poucavanja.e-skole.hr/.


[Photo: Maths racers Aadil Waghat and Zainul Adam prepare for the National Finals of the Jaguar Maths Challenge with their Maths teacher Patel looking on]
By Elham Asaad Buaras
A team from Blackburn’s Tauheedul Islam Boys’ High School (TIBHS) has secured a place in the Jaguar Maths in Motion Challenge national final, beating off stiff competition from thousands of schools across the country.
The annual competition involves teams competing against each other in an effort to win a Grand Prix type race and become UK Champions. This activity involves a wide range of basic mathematical skills, some practical, being used and applied.
The Challenge attracted entries from more than 100,000 pupils, making it the largest maths challenge of its kind in the UK. School children aged 8 to 16 are tasked with setting up a virtual racing car to compete on a circuit against other schools. The teams have to use all their mathematical expertise to accurately measure the length of the track, the angles of the bends and consider other factors such as fuel load, tyres and speeds. This data is then entered into a computer-based simulation and all the challengers eventually race against each other.
Team TIBHS Racers won a series of internal school races and regional heats within the north-west region before triumphing in the semi-final knock-out round. They will now compete in the national final at the British Heritage Motor Centre in Gaydon on June 26.
For the final the teams will have an hour and a half to prepare their cars, with competing teams categorised into three age ranges: Primary and Secondary aged 11 to 13 and 14 to 16.
The winners from each age group will fight it out for title of overall national champions.
In a statement to The Muslim News Mo Matadar, Assistant Head Teacher for Specialisms at TIBHS, said: “All credit to our pupils for the hard work and dedication they’ve shown to get this far. This Maths Challenge fits nicely with our school’s promotion of sport and academic study, and has also given our boys a new dimension with how they view maths as an academic subject. We wish Team TIBHS the best of luck and hopefully look forward to them bringing the title back to Blackburn.”


A killer sudoku is a type of Sudoku puzzle with an extra constraint. In addition to the usual Sudoku rule that each row, column and box must contain a set of the numbers 1 through 9, it adds a constraint that the sums of the numbers in some additional regions (shown as dashed boxes to the right) must match some given numbers. Solving a tough killer Sudoku typically requires knowing the combinations that sum to various targets. I built this calculator as an assistant to have to hand while I'm solving some of these problems having not yet memorized many of the common combinations.
Select your target number, and the number of constituent numbers that must sum to that. Optionally, select any numbers that should be excluded from the available combinations. Additionally, click any combination to strike it out. Clicked combinations will be marked with an asterisk to denote that they were manually deselected.


Definition of the Distributive Property
The distributive property is a fundamental concept in mathematics that is used to simplify expressions by breaking them down into smaller, more manageable parts. Specifically, the distributive property allows you to distribute a factor outside of a set of parentheses to each term inside the parentheses.
In algebraic terms, the distributive property can be represented as a(b+c) = ab + ac. This means that if you have a factor (a) outside of a set of parentheses containing a sum (b+c), you can distribute the factor to both terms inside the parentheses to simplify the expression.
For example, if you have the expression 2(3+4), you can use the distributive property to simplify it as follows:
2(3+4) = 2(3) + 2(4) = 6 + 8 = 14
Without the distributive property, you would have to perform the addition inside the parentheses first and then multiply by the factor outside, which can be more time-consuming and cumbersome for larger expressions.
Overall, the distributive property is a powerful tool in mathematics that allows you to simplify expressions and solve equations more efficiently.
How the Distributive Property Works
The distributive property is based on the idea that multiplying a sum by a factor is equivalent to multiplying each term in the sum by the factor and then adding the results.
For example, consider the expression 2(3 + 4). By applying the distributive property, we can rewrite it as 2(3) + 2(4), which simplifies to 6 + 8 = 14.
This works because when we multiply 2 by the sum of 3 and 4, we can break it down into two separate products: 2 times 3 and 2 times 4. Then, we can add the results to get the final answer.
The distributive property can also be applied in reverse to factor out a common term from an expression. For example, consider the expression 4x + 8y. We can factor out a 4 to get 4(x + 2y), which shows that 4 is a common factor of both terms in the expression.
Overall, the distributive property is a powerful tool in algebra that allows us to simplify expressions and equations by breaking them down into smaller, more manageable parts. By understanding how it works, we can become more proficient in solving problems and manipulating algebraic expressions.
Real-Life Applications of the Distributive Property
The distributive property has a wide range of real-life applications, particularly in areas that involve calculations and computations. Some examples include:
Calculating sales tax: When you purchase an item that is subject to sales tax, the total cost of the item can be calculated using the distributive property. For example, if the sales tax rate is 8% and the cost of the item is $20, you can use the distributive property to calculate the total cost as follows: $20 + 0.08($20) = $20 + $1.60 = $21.60.
Distributing resources: In business and economics, the distributive property can be used to allocate resources among different groups or individuals. For example, if a company has a budget of $100,000 to distribute among its employees, it can use the distributive property to calculate the share of each employee based on their performance or other criteria.
Factoring polynomials: The distributive property is a key concept in factoring polynomials, which is an important skill in mathematics and engineering. By factoring a polynomial into its individual terms, we can simplify expressions and solve equations more easily.
Overall, the distributive property has many practical applications in everyday life, from calculating taxes to distributing resources and solving complex problems in mathematics and engineering. By understanding how it works, we can apply it to a wide range of situations and improve our problem-solving skills.
Common Mistakes to Avoid When Using the Distributive Property
While the distributive property is a powerful tool in algebra, it is also easy to make mistakes when applying it. Some common mistakes to avoid include:
Forgetting to distribute the factor to each term inside the parentheses: When applying the distributive property, it is important to distribute the factor to every term inside the parentheses, not just the first one. For example, 2(3+4) should be written as 2(3) + 2(4), not as 2(7) or 6+8.
Misapplying the signs of the terms inside the parentheses: When distributing a negative sign outside of parentheses, it is important to change the signs of each term inside the parentheses. For example, -2(3-4) should be written as -2(3) + 2(4), not as -2(-3) or -6+8.
Confusing addition and multiplication: The distributive property involves multiplication, not addition. It is important to remember that you are multiplying the factor by each term inside the parentheses, not adding them together.
Forgetting to factor out a common term: When factoring out a common term from an expression, it is important to divide each term by the common factor, not just some of them. For example, 3x + 6y should be factored as 3(x+2y), not as x+2y or 6(x+y).
By being aware of these common mistakes, you can avoid errors and improve your proficiency in using the distributive property in algebraic expressions and equations.
Practice Problems to Enhance Your Understanding of the Distributive Property
Practice problems are a great way to improve your understanding of the distributive property and build your proficiency in using it. Here are some examples of practice problems:
Simplify the expression 5(2x + 3y) using the distributive property.
Solution: 5(2x + 3y) = 10x + 15y.
Factor out the common factor from the expression 4a + 8b.
Solution: 4a + 8b = 4(a + 2b).
Simplify the expression 3(4x – 5y) – 2(2x + y) using the distributive property.
Solution: 3(4x – 5y) – 2(2x + y) = 12x – 15y – 4x – 2y = 8x – 17y.
Factor the expression 6x^2 – 12xy.
Solution: 6x^2 – 12xy = 6x(x – 2y).
Simplify the expression 2(3x – 4y) + 5x – 2(2y + x) using the distributive property.
Solution: 2(3x – 4y) + 5x – 2(2y + x) = 6x – 8y + 5x – 4y – 2x = 9x – 12y.
By practicing these types of problems, you can build your skills and confidence in using the distributive property in algebraic expressions and equations.


Y11 students 2018/2019 make outstanding progress at Castleford Academy!
We are delighted to report that yet again Castleford Academy Y11 students 2018/2019 achieved fantastic results this year. This is the second year that the new GCSE exam system has been in place for all subjects where students are graded 1-9 and are assessed by a terminal exam with no coursework element. On average pupils at Castleford Academy achieved over a third of a grade higher than expected across all of their subjects. In English, 79% of students achieved grade 4 (equivalent to a GCSE grade C), 63% grade 5 (the new strong pass standard) and 15% grade 7 (equivalent to a GCSE grade A). In Maths, 76% of students achieved grade 4, 64% grade 5 and 25% grade 7. An amazing 72% achieved a grade 4 in both English and Maths with 54% achieving a grade 5 in both respectively showing a significant rise in both these measures on last year's incredible results. Over 66% of students achieved a grade 4 in the new Science trilogy qualification worth 2 GCSE's. Attainment grades achieved by Yr 11 in all other subjects were well beyond early national averages. A record breaking, 20% of pupils at the academy achieved the EBACC qualification.
However, these headline figures do not highlight the most important aspect of the results; the progress students make from their starting points. Based on this measure, the Academy is on track to be amongst the highest performing schools in Wakefield. The Headteacher George Panayiotou beamed, "We are very proud of their achievements. Every year the students' work ethic and determination to succeed increases which has led to such outstanding results. The progress this year made by the students is exceptional. The achievement is even more special as nationally assessment becomes more challenging. I must also take this opportunity to thank staff for their continued hard work.
The Chair of Governors John McNichol added "We wish all year 11 students every success in the future and thank parents for their support over what has been a very successful year."
Other highlights for Year 11 2018/2019
Provisional Progress 8 score + 0.40 (Significantly above national average)
Attainment 8 score 48.31 (Significantly above national average)
3 grades 9-7's (24%)
5 grades 9-7's (13%)
Over 70% GCSE Subjects (4-9) – Biology, Chemistry, Computer Science, English, English Literature, Food, Italian, Maths, Media, Music, PE, Physics, Product Design, Religious Studies and Russian.
Over 85% A* - C equiv. Non GCSE subjects – BTEC Art, BTEC Construction, BTEC Drama, BTEC Engineering, BTEC Health and Social Care, BTEC Media, BTEC Music and CiDA.


Papers on cross-over trials that have appeared in the first 25 years of Statistics in Medicine are reviewed. Papers on bioequivalence are also considered. After a brief statistical summary, individual papers are discussed under seven headings: 1. The two-stage analysis of AB/BA trials, 2. Baselines, 3. Binary and categorical data, 4. Survival data, 5. Modelling carry-over, 6. Bioequivalence and 7. Components of variation. Finally, a brief assessment of the importance in this field of Statistics in Medicine is given.
- Binary data
- Survival analysis


Enrichment at STEM includes after-school care, clubs and activities.
Jessica Bates joined the STEM Secondary Math Team in August of 2021. Before joining STEM, she taught for 13 years in Colorado and Oklahoma, teaching math courses from 6th grade to college. She graduated from the University of Central Oklahoma with both a bachelor’s degree in Mathematics Education and a Master’s of Science degree in Applied Mathematics.
Jessica is originally from Colorado, although she has lived in four different states and is happy to be back in her home state. She loves the mountains and spends as much time there as she can. Jessica also enjoys crocheting, reading and spending time with her family.
Favorite Starbucks Drink or Snack: Blonde Vanilla Latte
Favorite Snacks: Chocolate, Almonds, Chips
Favorite Places to Eat: Texas Roadhouse, Hacienda, Raising Cane’s
Favorite Drinks: Dr. Pepper, Tea
Favorite Place to Shop: JoAnn, Hobby Lobby, Amazon
Hobbies: Crochet, Photography, Reading
Favorite Colors: Blue


We provide Mathematics and Numeracy Powerpoint Mental Starters, and Math Topics Powerpoints for Teaching Mathematics, for use in Primary and Secondary Schools at Key Stages 1, 2, 3 and 4.
Our products are highly visual and ideal for starting off mathematics and numeracy lessons, and also for the teaching of topics themselves. We also produce powerpoints which are not maths related, such as our popular Weekly General Knowledge Quiz CDs (which are timeless and can be used again and again with different year groups). We can also write bespoke powerpoints if you ask us.
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Luminaires are joined together to become pairs.
Four points become a square.
An example: The arrangement of two square shapes into four round shapes is reorganised into two groups of five according to the law of shape for symmetry.
This principle of sameness also applies when the shapes of a group are not identical but only similar. For example, circles of different sizes are perceived together. Rectangles and squares also sometimes belong to a group due to their similar shapes.
Within an outline, complete enclosure is not necessary to group the objects within it. The suggestion of a closed shape is sufficient to feign a closed whole.
The arrangement of the points in the ceiling can be joined into two lines according to the law of good shape.
This arrangement is interpreted as two superimposed rectangles.


2019 / 9 / 29
Mathematization of philosophy consists of presenting philosophical theories through the usage of mathematical equations. According to this philosophical paradigm, it is possible to accurately mathematize any philosophical theory. This is because any theory (possessing genuine content´-or-possibly true content) is a de-script-ion and/or an analysis of reality´-or-possible realities, while any actual´-or-possible reality is mathematical in nature, given that mathematical equations are the foundations of any possible reality.
For example, we could successfully mathematize Plato’s theory of knowledge. Plato says that knowledge is justified true belief. This means that there are three conditions which should be satisfied in order for us to have knowledge. These conditions are: believing, being justified in what we believe in, and the truthfulness of what we believe in. For instance, we know that people are good if and only if we believe that people are good, we are justified in believing that people are good, and our belief that people are good is true.
Plato’s theory of knowledge could be accurately presented in a mathematical equation, according to which, knowledge = believing x being justified in our belief x our belief is true (i.e. knowledge is equal to believing multiplied by justification which is in turn multiplied by true belief). This mathematical equation represents Plato’s theory of knowledge because given that knowledge = believing x being justified in our belief x our belief is true, it follows that knowledge is obtained if and only if one believes, is justified in believing, and one’s belief is true, exactly as Plato defines knowledge. This shows that we can successfully mathematize Plato’s theory of knowledge.
Moreover, the mathematical equation of Plato’s theory of knowledge entails philosophically interesting conclusions. For instance, since knowledge = believing x being justified x true belief, it follows that knowledge is a matter of degree, such that we could know more´-or-less. If knowledge = believing x being justified x true belief, then when believing, being justified, and the probability of having a true belief are maximized, knowledge is maximized, otherwise it is minimized. This implies that knowledge is a matter of degree.
Plato’s theory of Forms could also be presented in a mathematical equation. According to Plato, the Forms exist in a realm´-or-universe separate from and independent of our material universe, such that the material objects are as they are in virtue of participating in the Forms, given that the Forms are the real existents. For example, all of us are good because we participate in the Form of goodness. Plato’s theory could be mathematized in the following way: our universe = matter + participation in the Forms. It follows from this mathematical equation that participation in the Forms = our universe – matter (i.e. participation in the Forms is equal to our universe minus matter). Hence, participation in the Forms and thus the Forms themselves are separate from and independent of matter, leading to Plato’s account that the Forms exist in a realm independent of and separate from our material universe. The success of this mathematical equation in expressing Plato’s theory of Forms shows that it is an accurate representation of Plato’s account, and hence we can successfully mathematize his theory.
Yet Aristotle rejects Plato’s theory that the Forms exist independently of and separate from our material universe. Instead, for Aristotle, the forms exist in our material universe. Aristotle’s theory could also be mathematized through presenting it in the following mathematical equation: our universe = matter x forms (i.e. our universe is equal matter multiplied by forms). It mathematically follows from this equation that our universe divided by matter is equal to the forms, and our universe divided by the forms is equal to matter. Therefore, forms could not exist independently of and separate from matter, exactly as matter could not exist without forms, otherwise our universe becomes indefinite (given that whatever is divided by zero, such as zero matter´-or-zero forms, is indefinite). This shows that this mathematical equation (i.e. our universe = matter x forms) is successful in presenting Aristotle’s theory. And all of these examples of the mathematization of the previous philosophical theories prove that we could successfully mathematize any philosophical theory, leading to the conclusion that mathematization of philosophy is possible.


Reckon you're good with numbers? Dots Connect Number is sure to prove you wrong - and will frustrate the heck out of you in the process.
The idea is to look at the image of numbers made from dots and guess what the number is, within the allotted time. You can take a hint which reveals one of the digits in the number, but it's still much, much harder than you'd think.
Dots Connect Number is very basic and the nag screens get annoying. But if you like a challenge you'll certainly find one here.


This sophisticated piece of software turns your computer into a modern, State-of-The-Art spectrum analyzer giving you features that go far beyond the possibilities of any stand-alone hardware unit.VST Plugin support
Basic statistical analysis software. Frequency histogram; Empirical function; Reconstructed distribution parameters (LSE); Normal, Exponential, Weibull and Uniform laws check; Kolmogorov's and Pearson's tests etc.
EqPlot plots 2D graphs from complex equations. The application comprises algebraic, trigonometric, hyperbolic and transcendental functions. EqPlot can be used to verify the results of nonlinear regression analysis program.


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It was introduced in and is the first calculator that is capable of symbolic computation.
HP series – Wikipedia
For example, you can use it to solve quadratic equation symbolically. And, it is also one of the first graphing calculator.
This is a RPN calculator, and manaul also a programable calculator. The first graphing calculator is Casio fxG It is actually the HPs that i did my first programing. I never took any programing course, but am a avid learner of math and computer stuff. I read the manuals from cover to cover.
My first program is a program to solve the Eight queens puzzle. It was a puzzle posted to CompuServe ‘s math forum. At the time, i’m also a crazy fan of recreational math.
I took it upon myself to solve this by programing my super calculator to automatically generate the solution. The 8-queens puzzle is typically solved by a backtracking algorithm.
HP S QUICK REFERENCE Pdf Download.
This is what i did, even though at the time i know nothing about computer science or programing. That is, my program misses 8 solutions or was it 4? Aroundi’m taking music classes. One mahual the things in music theory and training, is to understand the various chords, and being able to identify by ear. The HPs is capable of playing simple beeps of various frequencies.
Thus, i actually wrote jp28s relatively large program that plays musical chords and scales. These programs can spell and play any triad or seventh chords. Enharmonic chords using double sharp or double flat as roots are not generated nor recognized.
Chords starting with other keys are similarly entered. You can also change the ratio between adjacent notes to get 24 note per octave micro turning or other strange h28s.
To do so, simply change the value stored in DUR or R. For more information, see the variable diagrams in Section 3 of this book. This system will be expanded in later version.
HP-28S Advanced Scientific Calculator
The following functions are good candidates for expansion: Readers are welcome to send in their. You can download the full documentation and program here: The file in Microsoft Word format. I’ve written a bunch of other simple programs that help me study math in college.
Here they are, in image format from screenshot of Microsoft Word doc. What’s the Latest and Greatest in Calculators?


Kahlil Reynolds is among six students nationwide to receive a scholarship of up to $10,000 and an internship from the National Naval Officers Association (NNOA).
Reynolds received the Spring 2014 National Black Data Processing Associates (BDPA) Student Member NNOA Science, Technology, Engineering and Mathematics Scholarship with the Naval Research Enterprise Internship Program.
Reynolds, a member of BDPA Baton Rouge chapter, is one of three BDPA student members nationally selected as NNOA Scholars. Each student receives up to $10,000, including paid internships with the Department of the Navy this summer.
Read the rest of the SU article.


Field calculations can be performed in a database by adding a formula field. Field calculations allow you to perform addition, subtraction, multiplication, and division operations on any numeric fields in your database. Operations can also be grouped using parentheses (ie. (Field A + Field B) * Field C) The calculated value is then stored and displayed in the formula field.
To add a formula field to a database:
1. In your iMeet® Central database click on Options > Edit > Create New Field
2. Complete the details for the new field and select Formula, Numeric (With Decimals) as the Field Type. An optional Unit of Measure can be entered which will be added to the value within the formula field.
3. Click Create New Field
4. You will be redirected to the Edit Existing fields page. Now, you can create the formula for the new field. Choose from the available numeric database fields and click the Insert button to add the field variable to the formula. Available operators are: + - / * ()


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Or putting myself in WRIP, quite yet. Although I probably should.
I started taking online courses in my spare time, instead of writing, and working from home has been a drag. I have been hot and cold with gaming but work has extra responsibilities with this Pandemic, and when I get a spare hour I have been doing Python programming and/or some Linear algebra.
My company has all this data sitting around, so I started taking courses on Machine Learning, Data Science, and the like to see if I can put any of that data to good use.
It’s been fun to program and do math again (I like math. I am a weirdo). So that has been taking up what little spare time I have. I do my hour of exercise every day, and then move to work, and then move to hobbies/fun, which happens to not be gaming right now.
I haven’t kept up with what is going on in the gaming world, but HAVE snuck onto your blogs to read now and again. I’ve always loved the blogging community but my interest and lack of spare time now has me doing other things. For now.
Hope everyone is staying safe and healthy!
-Isey / Chris


- June 13, 2020
- Posted by: Pankaj Agrawal
- Category: Uncategorized
Why Q Is Fun?
Is amongst the absolute most asked questions from small kids why mathematics is fun. It’s their wish to know mathematics is interesting because it isn’t understood by them, they wish todo it. It’s led to a few parents telling them to sit and do it right because you’ll never know mathematics by hanging around doing it and crying in their kids.
Does mean you shouldn’t ever https://srilankaholidaytours.com/mathematics-varieties/ talk to your child about mathematics? No! There are nonetheless a few things that are possible to train your kid, like you did when you were a youngster even though you might not find everything out.
Explain the logic behind what mathematics is. Can they understand very well what there is a few? Can they understand very well what there is a few until they add it? Do they understand just how you can multiply numbers? Explain to them that math is all about adding and adding things so they are able to determine what this you’re discussing.
Don’t explain mathematics only when this is asked to by them. In that way if they don’t understand math, you can supply them an illustration or guide along them.
Let them play with it and also let them allow it to be more fun. No one wishes to complete the mathematics and also be defeated. If you are sitting there and staring at the plank, they are not planning to need to work with it .
Explain t using art, which means pictures, visuals, and sounds. Put in a circumstance at the place where they may view and discover exactly what it really is you are trying to teach them.
A film could be better because then your little one can learn it and have pleasure. This will not mean that you can’t let them form but make certain to don’t utilize vocabulary they don’t understand.
Do https://paramountessays.com not be mad if your child doesn’t do well in mathematics. There’s nothing wrong with this. If they really do a issue you think is wrong and also you yell at them, you’re damaging their self esteem and so they are going to not ever find math.


direct from . . .
Top Ten Obscure Math Theorems
The mass of a chocolate brownie increases infinitely until it reaches your thighs.
The Axiom of Choices: In a test situation, given a choice between two possible answers, you will randomly select the wrong one more than half the time.
Golf scores are proportional to the amount of people present.
The sum of the police officer's dimensions (height, width, and breadth) in inches is equal to the number of donuts he can eat in a period of 30 minutes.
The Mathematic Law of Choosing the Sesame Street Number of the Day
Given any theorem of mathematics, there exists a theorem more obscure than that theorem.
The Al Gore Algorithm - The act of performing a mathematical calculation over and over again until you get the results you want
It is impossible to divide a Chocolate-cookie-shaped object into two equally sized parts, if you have two children.
The pick-up-line theorum: The amount of pick-up lines said is always equal to the number of black-eyes recieved.
McPi are Squared: The equation used by Mcdonalds to assure that cherry pies fit into the box
(The Lizard Queen)
Copyright © 1995-2015, Scott Atwood and Christian Shelton
Scott Atwood and Christian Shelton (hereafter the authors) retain full
copyright of all material on this and all other pages of "Christian's &
Scott's Interactive Top Ten List." The authors grant to all other parties
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Last modified: Oct 15, 2001


Algorithms with numbers In binary, for instance, the maximum possible sum of three single-bit numbers is 3, which is a 2-bit number. 21.
What is the largest binary number that can be held in: 8
255 (number) This article This is the maximum value representable by an eight-digit binary number, that can be assigned to elements in the 24-bit RGB
Most negative number (in octal and hex) of a 16-bit one's
What is the largest binary number that can be generated in eight binary bits from ECT 109 at DeVry Chicago
What Is The Largest And Smallest 16-bit Binary Num
We can represent floating -point numbers with three binary largest. smallest. largest (24-bit) binary representation of 0.10 actually
What is the largest binary number that can be generated in
So i try to find the largest number in my binary tree so i can delete it, you're making it a bit too complicated. rev 2017.11.24.27843
BIN2DEC conversion for large binary numbers - Google Groups
Solution for Homework 2 What is the largest positive number one can represent in n-bit 2 The following binary numbers are 4-bit 2's complement binary numbers.
Maximum decimal and binary values - MATLAB Answers
01.10.2001 · Binary and Decimal Numbers different binary numbers with one bit: value for a binary The largest value for a binary number with a specific
binary - What is the "biggest" negative number on a 4-bit
02.11.2004 · 8 bits of a 32-bit address. The largest number that 8 8-bit binary number, the interface addressing. The company ID is still 24
What is the Largest 16 bit number - Answers.com
30.11.2010 · What is the largest binary number that can be held in: Largest Binary Number. Maximum decimal number in an 8,16,32,64,and 128-bit binary system?
Representation of Numbers - Swarthmore Home
07.09.2014 · This video demonstrates the math required to convert a decimal (base 10) number to an unsigned 8-bit binary number.
Вернем деньги из 24-Binary! - Бесплатная консультация!
What Is The Largest Unsigned Integer Number That Can Be you add the value 1 to a 3 bit binary number: largest unsigned eight bit number we can store
What is the largest number in the binary number system?
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1: Algorithms with numbers - EECS at UC Berkeley
Answer to What is the largest and smallest 16-bit binary number that can be represented with: a) Unsigned numbers? b) Two's comple
32-bit - Wikipedia
Largest Positive Integer in N Bits. The representation scheme we are looking at is called unsigned binary because no negative numbers are and think a bit.
Chapter 2. Binary and Number Representation
28.08.2010 · how to represent a very large range of numbers in binary. 24 . danscourses Carl Herold 153,509 views. 21:58. Converting Decimal Numbers to 8-bit
Binary, Hexadecimal, Octal, and BCD Numbers
04.12.2017 · Magic Numbers: Integers. Blue in a 24 bit RGB format. Green in a 24 bit RGB format. 65521. 0xFFE1. Largest 16 bit prime. 65535.


Content is focused on research and curriculum development for mathematics teaching and learning. There are over 80 different topics and over unique worksheets. Mathematics resources are available at the pre-school, primary and secondary levels. Sign up is free.
When a question is answered correctly, the player can move his or her piece across the board. The combination is designed for the most part as reinforcement and practice at the end of a unit.
He wanted to help his kids learn about math using all the worksheets he created by himself. Though this skill will not work as she is introduced to increasingly complex problems, it is a great start for her at the level she is working at.
Group Score Sheet located on your student website. SuperKids Math Worksheets --a free site to generate drill and practice worksheets with customization options provided e.
You will find it includes "internal links" by using "anchors". You might consider using EQuIP rubrics. Keep track of your progress. Exercise 8 from Ch. They try to use clear definitions in discussion with others and in their own reasoning.
They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. These opportunities should start in kindergarten and continue through high school. Edit this template and save it as your reflection. Include the following in your paper: Several modules are narrated in English, Spanish and Navajo.
Process Standards Rubric by the NCTM’s Principles & Standards for School Mathematics. The drill sheets contain 11 Timed Drill Sheets and 6 Warm-Up Drill Sheets, featuring real-life problem-solving opportunities. exercises written to the NCTM Process and Content Standards and is inspired by the Principles outlined below.
Bridges in Mathematics is a standards-based K–5 curriculum that provides a unique blend of concept development and skills practice in the context of problem solving.
It incorporates the Number Corner, a collection of daily skill-building activities for students. Jan 11, · Inthe National Council of Teachers of Mathematics published their process standards for mathematics in Principles and Standards for School holidaysanantonio.com Process Standards.
According to the NCTM, their process standards ”highlight the mathematical processes that students draw on to acquire and use their [mathematical] content knowledge.”.
Register now for the NCTM Annual Meeting & Exposition in Washington, D.C., April The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in.
NCTM Process Standards (Need description and a real world example of each of the following standards) Standard 1 Problem solving 2 Communication 3 Representation 4 Reasoning and proof 5 Connections Submitted: 7 years ago.Nctm principles and process standards worksheet