By Matthew Piechalak | email@example.com
Two Parker Upper School students earned the highest possible score on their ACT test.
Alexandra Coyle McDonald and Alec Sheres, both Class of 2022, each earned a composite score of 36 on the standardized test, which is used for college admissions in the United States. Fewer than one percent of all test takers earn the top score, according to ACT. Roughly 1.67 million students nationwide took the test this year.
The ACT consists of tests in English, Mathematics, Reading, and Science, each scored on a scale of 1-36. A tester’s composite score is the average of the four test scores. According to ACT, a student who earns a composite score of 36 has likely mastered all of the skills and knowledge they will need to succeed in first-year college courses in the core subject areas.
“Earning a top score on the ACT is a remarkable achievement,” says ACT CEO Janet Godwin. “A student’s exceptional score of 36 will provide any college or university with ample evidence of their readiness for the academic rigors that lie ahead.”


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Trapdoor functions or one-way functions are essential for the working of public key cryptography or asymmetric cryptography where computing the reverse of the function is not feasible by modern day computers. Multiplication of two primes is easy but factoring a product of two primes is difficult, and this forms the basis of RSA cryptography, the widely used public key cryptography system. If you do not know what RSA is, I suggest reading this. In this post, I talk about another asymmetric cryptography system known as Elliptic Curve Cryptography.
Elliptic Curve Cryptography
Elliptic curves are planar curves defined by the following equation.
where and are constant and to avoid singular points.
The elliptic curves are symmetric about the x-axis.
To use elliptic curves for cryptography, a random large prime, (or a perfect power of ) is chosen, and all the points on the curve are the points satisfying equation where each operation is under modulo . The elliptic curve over the finite field of integers modulo would look like this:
Now we define addition and scalar multiplication among the points on the plane.
Consider two points, and on the curve, now draw a line joining and . This line intersects the curve at another point . Let the reflection of the point about x-axis be . Since elliptic curves are symmetric about the x-axis, is also on the curve and is denoted .
Under modulo arithmetic, the XY plane is bounded. The line joining and once when crosses the bounded plane on one side wraps around and comes out from the other side of the plane at the opposite point with slope same as the original slope and continue further until it intersects at some point on the curve.
Now, consider and its reflection of about the x-axis as . The line joining and never intersect the curve. We can think of it as the line meeting the curve at infinity(), i.e. .
We call as the inverse of and as the identity under this specially defined addition operation. is also written as .
Lets first define . For this, we consider the tangent at and find the reflection about the x-axis of the point at which the tangent intersects the curve. This point is defined as . Inductively, we can define (scalar multiplication).
Let . Since all these points are over the finite field of integers modulo , it turns out that computing from and is easy, but it is not feasible to compute from and . The reason for infeasibility is the difficulty of computing discrete logarithm in this finite field. This scalar multiplication is the one-way function that forms the basis of the elliptic curve cryptography.
Encryption and Decryption
There are many proposed algorithms for encryption/decryption using elliptic curves. The one I describe here is analogous to ElGamal public key encryption algorithm.
Consider that Alice wants to send a message to Bob. Both Alice and Bob decide on the elliptic curve equation, and a point on the curve called as the generator. The recommended equation and generator pair is given by Standards of Efficient Cryptography. Bob chooses a random number and calculates . The integer forms the private key and forms the public key.
Alice chooses a random integer (each time Alica has to choose different ) and calculates the cypher text as follows:
Here is the public key of Bob.
Bob receives the cypher text and decrypts the message as follows:
ECC with a private key of size 256 bits offers the same security as RSA used with 3072 bits size key1. Hence ECC is more used when compared to RSA for mobile devices where the size of the key matters. The operation of encryption and decryption is symmetric in case of RSA hence the same can be used for Digital Signatures, but it is not the same in ECC, and hence a different algorithm is used for signing2.


Norman Paris: Exploring Math in the Real World
Norman Paris is a lecturer of physics and mathematics at Santa Clara. He has a Ph.D. in Physics from UC Davis. In this conversation, we cover why someone should study advanced math, why he loves teaching, and his career journey.
“Question what is given or shoved down your throat. There are so many outlets to gain information—we should pause and ask ourselves if something seems right. Is it a feeling or bias that I have? Or is this what the numbers state?”
1:30 – Why study Calculus?
2:35 – Norman’s favorite part of teaching
3:30 – How math connects to all disciplines
6:00 – The importance of statistics
9:15 – How Norman decided to study math and teach
11:45 – Memorable moments from graduate school
15:05 – My final 4 questions


Predict the next powerball winning numbers using the three awesome tools provided by How to Win Powerball. Although, all lotteries are a game of random chance, an informed player can gain the odds. There are nine ways to win Powerball! One, match the Powerball number and two, match 3 out of 5 numbers drawn from a pool of 69 numbers. Those are the minimum requirements to win a prize. The odds of matching the Powerball number is 1 in 26 and the odds of matching 3 out of 5 white numbers are 1 in 580. When considering the odds, matching the Powerball number is your best bet.
How to Win Powerball, provides you with three tools that will assists you in predicting the next powerball wininng numbers. One tool for picking the white numbers (1-69) and two tools for picking the powerball number/s (1-26). First, the white numbers. Above, the table shows the last eleven drawings. Choose 3 odd numbers and two even from the table. Since the group of numbers containing 3 odd numbers and 2 even numbers has more combinations then any other group, it just makes sense to use this to your advantage. The group containing the second most combinations is 3 even and 2 odd numbers.
Next, the powerball number. The powerball number, just to be clear, is the red number. To help make it easier to pick a powerball number and spot a trend, divide the numbers into 3 groups. Low, Mid Range, and High. Low numbers are 1-12, mid-range is the number 13, and high numbers are 14-26. Now you only have to choose your numbers out of the three groups. To do this, use the frequency, last drawn and previous drawn tools to determine how the powerball numbers are trending. Don't forget to use your intuition, your gut feeling.
The last word about lottery numbers: mathematically each and every number has the same exact chance of being drawn. Regardless when or how often or not they appear in the list. However, by using your intuition, your gut feeling, and carefully picking your numbers, you may be surprised with your increased winnings. Pay special attention to the powerball number. Matching the powerball number makes you an instant winner. Finally, as one of my good friends once said: "You're just a buck away". Good Luck!


We use the Primary Advantage Maths Programme at St. Dominic’s.
PRIMARY ADVANTAGE MATHS PROGRAMME AT ST. DOMINIC’S
The National Curriculum for England and Wales has at its heart the underpinning of problem solving, reasoning and fluency (DfE, 2014). By highlighting them in this way the DfE have indicated that these aims should underpin the maths curriculum by threading through all mathematical teaching and learning.
The PA Maths programme supports this approach and believes that through developing children’s problem solving, reasoning and fluency skills, there will be a range of positive outcomes, including the development of children’s conceptual understanding, their ability to use maths in meaningful ways and positive attitudes from the EYFS to year 6.
The PA Maths programme aims to empower young people to achieve their potential, to use their knowledge of mathematical language to talk about their work and explain their findings, and ultimately use their skills to make informed and responsible choices throughout their lives.


How to Play
Super 5 is a game of chance in which five numbers are randomly drawn from a field of numbers from 1 to 45. To win just match at least three of your selected numbers on one ticket to the numbers drawn. You can play Super 5 by filling in a coupon or verbally at any MALTCO LOTTERIES point of sale. The different playing methods are listed below:
When playing Super 5 using the simple method only 5 numbers should be chosen.
In this example;
Numbers selected: 1, 8, 11, 15, 41
Columns created: 1 column
Cost of ticket: 1 column x €2.00 = €2.00
A Fully Expanded System, also known as a Combination Coupon, is an alternative way to play Super 5 and increase your chances of winning. Just select more than 5 numbers in any Game Area so that more columns can be created with your numbers.
In this example a Fully Expanded System with seven numbers is created.
These seven numbers are then combined to create 21 columns of 5 numbers each.
The cost of the ticket would be €2.00 x 21 = €42.00.
By marking the Quick Pick option the terminal randomly picks your numbers.
To use this option just mark the Quick Pick box in the Game Area of your choice and choose and mark a number (up to 20) from the Game Area to indicate how many numbers you would like the terminal to choose.
In this example the Quick Pick option was marked together with the number 6, meaning that six
numbers will be randomly picked by the terminal.
This will create 6 combinations (or columns) of 5 numbers, and will therefore cost €12.00 (6x €2.00).
You may choose different playing methods on one coupon. For example on one coupon you can play:
Game area A:
A Simple Coloumn
Game area B:
A fully Expanded system
Game area C:
A quick pick section
The cost of the ticket would be €46.00:
Game area A : 1 Coloumn - €2.00 x 1 = €2.00
Game area B : 21 Columns - €2.00 x 21 = €42.00
Game area C : 1 Coloumn - €2.00 x 1 = €2.00
With the same coupon you may participate in more than one draw with the same numbers.
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This example shows that by selecting the boxes  and [x2], your coupon will
participate in twenty consecutive draws.
Ambo on Super 5 is a Super 5 game type with fixed winnings whereby you select two (2) numbers from a field of numbers from one (1) to forty-five (45). If your two (2) selected numbers match any two (2) of the five (5) randomly drawn numbers during the Super 5 draw, you win with Ambo on Super 5.
This game type is played verbally. Once you communicate the numbers you want to play to the Agent, the Agent will execute your play and generate the ticket via the on-line terminal with your selected numbers. Always check your ticket after each play to ensure that the selections printed on the ticket are the ones you chose.
If you would like to participate in more than one (1) draw, you must verbally inform your agent before issuing the ticket, the amount of draws you would like to participate in up to a maximum of 30 consecutive draws.
Ambo on Super 5 can be played as follows;
When playing Ambo on Super 5, using the simple method you are to select any two (2) numbers from the field of 45 numbers. The cost of a simple column is €1.
Fully Expanded System
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For Ambo on Super 5 game type, you shall verbally inform the agent for the online terminal to randomly select two or more numbers.
Through the Multiplier, you will have the option to multiply your minimum stake by verbally communicating your choice to the agent. By verbally communicating the Multiplier option to the agent, you have the possibility to multiply your stake by two (2) up to five hundred (500) times. For example, if you communicate the multiplier five (5) to the agent, your stake will be multiplied by five (5) times. Alternatively, you can just tell the agent the amount you would like to play and the agent will take care of applying the multiplier as needed. Always check your ticket after each play to ensure that the selections printed on the ticket are the ones you chose.
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A) If (a, b) is a critical point and det(HJ(a,b») > 0 then, at (a, b), f has a local maximum if ~:; (a, b) < 0 and a local minimum if ~:; (a, b) > O. (b) If (a, b) is a critical point and det(H/(a,b») < 0 then (a, b) is a saddle point. (c) If (a, b) is a critical point and det(H/(a,b») = 0 then (a, b) is a degenerate critical point and other methods are required in order to determine whether it is a local maximum, a local minimum or a saddle point. FUnctions of two variables 32 Example 27. Let f(x,y) = x 2 - 3xy - y2 - 2y - 6x.
OfR and 8x 2 ' 8y2' 8x8y and 8y8x all eXlst and are all contmuous then 82 1 82 1 8x8y = 8y8x' We will define continuous functions soon but will not prove this proposition. However, we will provide a method for recognizing many functions which satisfy the hypothesis of this proposition. This will not involve working out all the derivatives and so will be quite practical. 'IT . h functlOns . £,or wh'ICh 8x8y 8 21 = 8y8x' 8 21 ne now assume we are d eal'mg WIt These derivatives are called-for obvious reasons-the mixed second order partial derivatives.
Since e Y =/: 0, no matter what the value of y, we have arrived at something which is impossible and so we cannot have a solution in this case. 4). 4 Now 82 f 8 8x 2 = 8x (e zY (1 = 82 f and 8x 2 (0, 1) = 1eo(1 + + xy - y)) ye zY (1 + xy - y) + ye zy °- 1) + -88y2f = -8y8 ((x 2 82 f and 8y2 (0, 1) 82 f 82 f = (0 - 1) . eO. 1)xe zy ) °. °= eO . 1 = 1. Also = (x - 1)xe zy ; x 0 8 8x8y = 8y8x = 8y (e ZY (1 + xy - y)) = xe zY (1 + xy - y) + eZY(x - 1). 82 f 80 88- (O,1)=O·eO(1+0·1-1)+eO(O-1)=-1. x y Functions of two variables 34 We have Hf(O,l) = (_~ -~) and det (Hf(O,l») and (0,1) is a saddle point of the function = -1 < 0 f.
Introduction to fourier series and integrals by Seeley


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With public opinion polls showing a tight race again in this year's Presidential election, it might be useful to take a look at how polls are conducted.
A poll conducted by Newsweek from September 2-3 shows 52% for Bush and 42% for Kerry among "likely voters." This poll has a "margin of error" 0f +/- 3%. It might be noted that this is actually one of the larger differences we have seen for a while. Had we been closer to a 50-50 split, it would have been more difficult to determine who was ahead. Even at 52% vs. 48%, we could not say with much certainty who was actually ahead.
Why such a large margin? The above survey was based on a survey of 1,008 respondents. With so many people, why can't we make more precise determinations?
Computing the margin of error is based on the idea of a "confidence interval" within statistics. If we tossed a coin ten times and got six heads, we would not have much reason to doubt that the coin was unbiased. On the other hand, if we threw 10,000 and got 60% heads, we would worry more.
To determine a confidence interval, we start by determining the "standard deviation" of the percentages for a given sample size. First, we need to make a slight modification since 52% and 42% figures do not add up t0 100%--people could vote for a third candidate or still be undecided. Therefore, we will base our calculations on those who are--and those who are not--supporting one of the candidates. For Bush, we have 52% for (p) and 48% "not for" (1-p).
The formula for the standard deviation of a "proportion"--or percentage--is
That is, the square root of the quantity p times 1-p over n.
To put in actual numbers:
(0.52(0.48)/1,008)^0.5 = 0.0157
To be 95% certain—an arbitrarily selected standard favored by many statisticians in the U.S.--that our confidence interval will cover the true proportion, we must go 1.96 standard deviations on either side of the sample proportion. (You would have to look up this number in a table). We thus have
1.96(0.0157) = 0.0308.
The 95% confidence interval for those supporting Bush is therefore 0.52 +/- 0.0308 or from 48.92% to 55.08%. Repeating the calculations for Kerry, his confidence interval turns out to be 38.95% to 45.05%.
It is interesting to observe that the margin of error is so large precisely because the two candidates are so close to each other. Note that, in the numerator of the formula for the standard deviation, the figures p and (1-p) figure prominently. 0.5(0.5) = 0.25, which is much larger than the (0.99) (0.01) = 0.0099 figures we would have if we were determining the margin of error for a 99% to 1% race. From an intuitive point of view, looking at any one voter, it is difficult to tell how he or she will vote in a 50-50 race. In a 99-1 race, not only is the sample outcome overwhelming, but on top of this, the margin of error will be much less because there is little doubt how each individual voter will behave.
In principle, we could reduce the margin of error proportionately by increasing the sample size. If we had 3,000 respondents instead of 1,008, the margin of error would be only about 1%. Sampling such larger groups would be more expensive, and because of the time sensitive nature of polling data, this increase could also result in delays in finishing the poll.
An important issue is conducting opinion polls is the question of who should be surveyed. The above survey is based on "likely voters." If the sampling base is all eligible--or at least all registered--voters, Kerry's figures appear to be higher. From the point of view of the representation of people in a democracy, that may be a more appropriate figure. However, it is a reality that only those voters who actually turn out will decide the election outcome. Thus, the estimate based on "likely voters" is likely to represent a more accurate prediction of actual election results if the election were held at the time of the election. It should also be noted that despite the best efforts, it is not possible in practice to identify a perfect sampling base of either all eligible voters or those most likely. Some individuals that should have been included will be omitted from any practical survey, and some that are not eligible will be included by mistake. Professional pollsters, however, do the best they can do minimize such biases.


LiNA -- A graphical MATLAB tool for analyzing intrinsic noise in biochemical reaction networks
LiNA provides a simple, but easy-to-use, GUI from within MATLAB running under R2010b or higher. In its current form it comprises the following features:
- calculates the variance-covariance matrix for mass-action networks under steady state conditions based on the linear noise approximation of the chemical master equation
- automatically detects and takes care of conservation relations in the network
- parameter scans for the mean values and stochastic quantities such as the Fano factor, the coefficient of variation and correlation coefficients
- allows to define parameter combinations as new parameters (e.g. to analyze the Fano factor as a function of a dissociation constant rather than separately for forward and backward rates)
- allows to calculate stochastic quantities along different stable branches in bistable systems
- easy export of plots as MATLAB figure for further processing
- 12/2014: New version of LiNA (v1.1) has been released which contains minor bug fixes.
(Thanks to Qurat-Ul-Ain Azim for his bug report.)
LiNA has been developed by Bastian Hagel, Axel von Kamp and Ronny Straube.
Unzip the Lina_v1.1.zip archive to your HOME directory which will create the directory LiNA_v1.1
Startup MATLAB and change to the LiNA directory. Type 'startlina' at the console.
Note that LiNA requires the 'Symbolic Toolbox' of MATLAB.
LiNA is free software, i.e. it can be redistributed and/or modified under the terms
of the GNU General Public License as published by
the Free Software Foundation.
For a detailed version of the License conditions, please see http://www.gnu.org/licenses/.
Comments, suggestions and bug reports can be sent to firstname.lastname@example.org.


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Objective 1: Adding, subtracting, multiplying and dividing fractions Objective 2: Operations involving fractions and integers Part 1: () Part 2: BIDMAS and fractions [Brackets, Indices, Division, Multiplication, Addition, Subtraction] () () Extension: Mixed questions () What is the reciprocal of the following: Write these times as decimals Dividing Fractions T1S1 . Title: Microsoft Word - divide Author: educurve 13 Created Date: 4/4/2017 12:00:36 PM ... Multiplying and dividing fractions; ... To multiply fractions simplify multiply the numerators and multiply the denominators. Question 2: 1 pts . To divide one ... DIVIDING DECIMALS To divide decimals: 1) set up like a regular long division problem 2) if the divisor (# on the outside) is a decimal, move the decimal point to the right until it is a whole number (if the divisor is a whole number, just divide as usual) Multiplying and Dividing Mixed Fractions (A) Answers Find the value of each expression in lowest terms. 1. 32 7 1 1 4 = 92 35 =2 22 35 2. 12 3 3 1 3 = 1 2 3. 21 4 1 1 ... Use the buttons below to print, open, or download the PDF version of the Multiplying and Dividing Fractions with Three Terms (A) math worksheet. The size of the PDF file is 43867 bytes. Preview images of the first and second (if there is one) pages are shown. Activity 6: Dividing a Fraction by a Whole Number; Activity 7: The Division Poster Project; Activity 8: Dividing Fractions & Whole Numbers Post-Assessment; Independent Worksheet 1: Sharing & Grouping: Multiplying & Dividing; Independent Worksheet 2: Operating with Fractions & Whole Numbers; Independent Worksheet 3: More Fractions & Whole Numbers Fractions: multiplying and dividing mc-TY-fracmult-2009-1 In this unit we shall see how to multiply fractions. We shall also see how to divide fractions by turning the second fraction upside down. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. LESSON 6: Fractions—Multiplication and Division Lesson Summary: First, students will solve a word problem involving fractions. In Activity 1, they will practice multiplying fractions. In Activity 2, they do a real-life application problem. In Activity 3, they will practice dividing fractions and mixed numbers. In Activity 4, they will Multiplying and dividing fractions; ... To multiply fractions simplify multiply the numerators and multiply the denominators. Question 2: 1 pts . To divide one ... Dividing Fractions . Dividing fractions is very similar to multiplying fractions but with one extra step. Extra step: First, take the second fraction and flip it so that the top number becomes the bottom number, and the bottom number becomes the top number. Now multiply the two fractions together just like before . Reduce the answer if possible. Multiplying Fractions 1. Convert mixed numbers to improper fractions 2. Multiply across the top and bottom 3. Simplify Dividing Fractions 1. Convert mixed numbers to improper fractions 2. Keep the first fraction the same, switch the sign from division to multiplication, flip the second fraction 3. Multiply across the top and bottom 4. Simplify Students can use math worksheets to master a math skill through practice, in a study group or for peer tutoring. Use the buttons below to print, open, or download the PDF version of the Multiplying and Dividing Fractions (A) math worksheet. The size of the PDF file is 35486 bytes. Whether you're adding, subtracting, multiplying or dividing fractions, you should always aim for the "tidiest" answer possible. Tell your fraction if "its bum looks big in this" and simplify it down to the smallest option (e.g. 3/6 becomes 1/2, which retains the same proportions but is less clumsy). MULTIPLYING AND DIVIDING ALGEBRAIC FRACTIONS. The rule. Reducing. Section 2. Complex fractions -- Division. T O MULTIPLY FRACTIONS, multiply the numerators and multiply the denominators, as in arithmetic. To divide a number by a fraction, multiply the number by the reciprocal of the fraction. Example 3 Find 3 — 7 ÷ 5 —. 6 Example 4 Find 8 ÷ 2 1 —. 3 3 — 7 ÷ 5 — . 6 = 3 — 7 ⋅ 6 — 5 Multiply by the reciprocal of 5 — , which is 6 6 —. 5 8 ÷ 2 1 — 3 = 8 ÷ 7 — Rewrite 2 3 1 — 3 as 7 — 3 = Multiply. 3 ⋅ 6 — 7 ⋅ 5 ... Math Problems For Class 3 - Simple Addition Worksheets For Kindergarten. Alphabet Mirror Image Worksheets. Halloween Multiplication Coloring Worksheets. Adding Subtracting Multiplying And Dividing Fractions Worksheet PDF. Mental Math Worksheets For Class 2 PDF. Free Fun Activity Sheets For Kids. May 02, 2018 · Multiplying and dividing algebraic fractions – PowerPoint; multiplying and dividing algebraic fractions – worksheet . 5. Alternative versions. feel free to create and share an alternate version that worked well for your class following the guidance here Jan 08, 2015 · This mini-assessment is designed to illustrate cluster 5.NF.B, which sets an expectation for students to apply and extend previous understandings of multiplication and division to multiply and divide fractions. This mini-assessment is designed for teachers to use either in the classroom, for self-learning, or in professional development ... Dividing Fractions T1S1 . Title: Microsoft Word - divide Author: educurve 13 Created Date: 4/4/2017 12:00:36 PM ... Simply Simplifying Fractions Martin says he has a short cut for simplifying final answer fractions when he is multiplying fractions. He says, "If you can spot a common factor between a diagonal nurrerator and denominator pair, you can simplify before you complete the fraction multiplication." For example: 9 82 18 Oct 09, 2014 · Infinite Pre-Algebra - Multiplying and Dividing Fractions Created Date: 10/9/2014 3:35:30 PM ... Basic Arithmetic Skill Dividing Mixed Numbers Find each quotient. 1) 3 7 8 ÷5. Answers to Dividing Mixed Numbers 1) 31 45 2) 4 5 81 3) 1 19 33 4) 5 32 5) 3 Effective teaching includes multiple and carefully selected representations for multiplying and dividing fractions 43 Specific suggestions for understanding multiplication with fractions 51 Specific suggestions for understanding division with fractions 54 7. RECOMMENDATIONS 55 Supporting High Quality Teaching of Fractions Operations 56 To divide two fractions, flip the second fraction over and multiply the two fractions using canceling and reducing when possible. This also works when dividing a whole number by a fraction (create a fraction wholenumber 1, flip the second fraction and multiply). • When dividing a fraction by a whole number, create a fraction with the Cypress College Math Department – CCMR Notes Multiplying and Dividing Fractions - Intermediate, Page 1 of 8 Multiplying and Dividing Fractions - Intermediate Objective 1: Find the Factors of a Number The factors of a number are numbers that we can multiply together to get that number. They are numbers that divide evenly into the number. Math Problems For Class 3 - Simple Addition Worksheets For Kindergarten. Alphabet Mirror Image Worksheets. Halloween Multiplication Coloring Worksheets. Adding Subtracting Multiplying And Dividing Fractions Worksheet PDF. Mental Math Worksheets For Class 2 PDF. Free Fun Activity Sheets For Kids. Multiplying and Dividing Fractions Word Problems Task CardsCCS: 4.NF.B4, 5.NF.B4 Included in this product:*20 unique task cards dealing with multiplying and dividing fractions word problems*5 different recording sheets*Answer KeyThese cards are great for math centers, independent practice, "SCOOT" a View Homework Help - Unit 17 Worksheet 1 Key.pdf from MATH 101 at Kimberly High School. Multiplying and Dividing Fractions and Mixed Numbers Worksheet 1 Key Solve the problems below using your Alternate Algorithms for Dividing Fractions Now that we know inverting and multiplying is simply a shortcut when dividing fractions, we can explore further and discover some interesting and useful information. For example, some problems (such as 5/12 ‚ 1/3) can be solved more quickly and easily by simply dividing, as you can see below: Multiplying and Dividing Fractions 2.1 Fractions and Estimation 2.2 Multiplying Fractions and Whole Numbers 2.3 Multiplying Fractions 2.4 Multiplying Mixed Numbers 2.5 Dividing Fractions2.5 Dividing Fractions 2.6 Dividing Mixed Numbers 2.7 Writing Decimals as Fractions 2.8 Writing Fractions as Decimals ou say that MOST humans ” does that mean To Multiply Two Fractions Example 1 Multiply: Solution: First divide out any common factors to both a numerator and a denominator; then multiply. The same principles apply when multiplying rational expressions containing variables. Before multiplying, you should first divide out any common factors to both a numerator and a denominator.


Math isn’t always the fun subject, but have Oksana Neveselaya as your teacher you will love to study. Oksana is a math teacher from Minsk, Belarus. A video taken by a student was uploaded to YouTube and it quickly grabbed the attention of the internet. She is now being dubbed ‘the world’s hottest math teacher’.
Oksana is a “da bomb” maths teacher from Minsk, Belarus. Someday, while she was teaching in the class a student of her taken her video and uploaded that to Youtube. And the noticeable thing is that within a heartbeat the video grabbed the attention of the internet. Pretty Oksana has now almost 17500 followers following her video at Instagram. Apart from video, her beautiful selfies are also there on her Instagram account. They have just added more sensation to the video.


This unit contains vector and matrix procedures and functions for TURBO-PASCAL, partly written as inline assembler code for a 387 coprocessor. They are about two to three times faster than the equivalent "pure PASCAL" code
KSIM is a collection of units that provide combined descrete event & continuous simulation. The descrete event simulation is handled via a descrete event calendar. The continuous portion of the simulation is handled via Runge-Kutta-Fehlberg 4-5 integrator which has been modified to handle threshold crossing. KSIM generates both a report & a data file, both which can be taylored to fit the needs of the simulation. KSIM is follows SLAM (Simulation Language for Alternative Modeling) conventions & terminology. Reference to the book, "Introduction to Simulation and SLAM", by A.Alan B. Pritsker & Claude Dennis Pegden is encouraged.
Пакет базовых математических программ для BP. Содержит 4 модуля: работа с целыми и вещественными числами; модуль базовых математических функций; модуль расширенной тригонометрии; а также модуль для графического отображения
Very Large Numbers - allows the Pascal programmer to work with numbers up to 1000 decimal digits or more. VLN can also handle numbers to 1* 10 ^ -1000 or smaller as well as add, subtract, multiply, divide, and perform with roots and powers.
The following programs were written by Allen Miller and appear in the book entitled "Pascal Programs For Scientists And Engineers" which is published by Sybex, 1981. They were originally typed and submitted to MTPUG in Oct. 1982 Juergen Loewner. They have had minor corrections and adaptations for Turbo Pascal by Jeff Weiss.


IIT ( Indian Institute of Technology) Patna launches three new UG programmes. They are – BTech in AI( Artificial Intelligence) and Data Science, BTech in Engineering Physics, BS in Mathematics and Computing. Admission to these courses will be based on JEE Advanced score. The new courses have been launched to cater to the technological advancements and also to help students to have a deeper understanding in these fields. Rajendra Paramanik, Assistant Professor Economics as well as Professor in-charge of Public Relations said, ” The institution has alloted 36 seats for admission in AI and Data Science, 36 for Engineering Physics, and 48 for BS in Mathematics and Computing”. According to the official statement, AI and Data Science program will help students in handling large data volumes . It also mentioned that Engineering Physics course is a mixture of Engineering, Physics and Mathematics and on the other hand, Mathematics and Computing is a blend of mathematical as well as analytical components. The seat capacity has been raised from 427 to 547 .


1. Introduction to the theory of complex optimization: computational complexity, combinatorial problems, NP-hard problems (K1-K4).
2. Evolutionary algorithms I (K1-K4).
3. Evolutionary algorithms II (K1-K4).
4. Simulated annealing (K1-K4).
5. Ant colony and bee colony algorithms (K1-K4).
6. Particle swarm optimization (K1-K4).
7. Hybrid optimization methods (K1-K4).
8. Test (1 hour).
1. Introduction to the workshops: organization, set up of work teams, assignment of topics. Introduction to available software tools to be used for solving optimization tasks (S6).
2. Presentation of literature review on selected optimization methods and their real-world applications (S9).
3. Problem definition, presentation of projects concepts proposed by every work team (S1, S2, S3, S5, S7).
4. Mastering software used for solving the selected optimization task (S6).
5. Practical realization of the projects, discussion (S2, S5, S6, S8, S9, S10).
6. Presentation of the project reports and obtained results by every work team
(S8, S9, S10).
Individual activity: 70 hours.


Immanuel Kant said, ‘All our knowledge begins with our senses’. How true this statement is.
As toddlers, our parents taught us concepts like colours, numbers and name of things by either seeing, hearing, touching, tasting or smelling tangible objects.
As we get older, concepts get more difficult to understand and comprehend; yet a touch of multisensory techniques can ease the conceptual grasp for a student.
Some multisensory techniques are:-
1) Beads and cereals – this is a great technique for kids as the mathematical operations are represented by beads utilized by abacus math for kindergarten , cereals or even dried beans.
Concepts like addition and subtraction can be easily understood using this multisensory techniques. More challenging concepts like multiplication and division can be done in groups or pairs.
‘Tapping out numbers’ is a higher level teaching technique which helps the student connect the objects to the actual number and ‘feel’ the number or value.
This makes multiplication and division possible on an individual level.
2) Tiles or cubes – concepts like skip counting and identifying the missing numbers can be taught with ease using tiles or cubes. These can also be in different colors to represent different objects.
Then a connection between the objects and the numbers they are to represent are established.
Other multisensory techniques that are used for high level concepts are building with base 10 blocks- where the different sizes of blocks represent different base values.
This helps in identifying place values. Create a hundreds chart- helps in the concepts of number relationships. This is very effective for topics like fractions and percentages.
3) Music – learning maths rules, memorizing formula, dealing with fractions and grouping are easy with music. Dancing to music and snapping fingers help in concepts like grouping and fractions.
4) Drawing problems – the teacher draws on the board to show the children how concepts like addition, subtraction, multiplication, division, skip counting, fractions and other such topics are derived.
This is an old and effective inductive method of teaching. No matter how technology and techniques have progressed, certain old fashioned techniques of teaching can never go out of style.
Pictorial representation makes these concepts more concrete than abstract. http://www.cma.edu.sg has a well defined curriculum which caters to the child-s needs as per the child-s abilities.
These techniques are fun and useful for both the students and the teacher as the teacher can easily assess a student’s capabilities and potential. This helps the teacher segregate between effective and non-effective techniques that work for his class in general and also on an individual level.
http://www.cma.edu.sg helps in catering to the needs of each and every student.


In preparation for a geometry test, John Lewis Childs fourth graders in Mrs. Tyrrell’s class put their skills to the test with a “marshmallow math” review. Using marshmallows as points and toothpicks as lines, students were challenged to create geometrical designs. They modeled points, line segments, parallel and perpendicular lines, angles, triangles, quadrilaterals, and patterns. As a bonus, the students were given a sweet opportunity to use their creativity to design a figure with line symmetry!
Date Added: 3/2/2023


Websites to help you:
2 months ago
Math XL for School
(online resource from the CMP3 math textbook)
This website gives students opportunities to practice various skills at their own pace. If your child needs help, go to the assigned lesson and you will find more help and practice.
Homework assignments will be given on this website periodically.
In Order To Log-in:
- Log into your Google Account
- Click on the 9 boxes at the top right hand corner
- Scroll to Pearson Easybridge


Algebra is among the many most important elements of Mathematics by means of which widespread symbols and letters are used to characterize parts and numbers in equations and formulae. The further main elements of algebra are known as elementary algebra and further abstract elements are known as fashionable algebra or abstract algebra. Algebra is important as a result of it consists of all of the items from elementary equation fixing to the analysis of abstractions resembling rings, groups and fields.
Algebra is a division of Mathematics that substitutes letters for numbers. An algebraic equation depicts a scale, what is accomplished on one aspect of the scale with a amount could be carried out to each aspect of the scale. The numbers are constants. Algebra moreover consists of precise numbers, superior numbers, matrices, vectors and much more. X, Y, A, B are basically essentially the most usually used letters that characterize the algebraic points and equation 1b.
Algebra helps in fixing the mathematical equations and to derive the unknown portions, just like the financial institution curiosity, proportions, percentages. The letter variables within the algebra can be utilized to symbolize the unknown portions that are coupled with the flexibility to rewrite the equations making it simpler to find the info for a given set of equations.
The algebraic formulation are utilized in our every day life to seek out the gap, the amount of containers, and to determine the gross sales costs as and when wanted. Algebra may be very useful in stating a mathematical equation and relationship by making use of letters or different symbols representing as entities. The values of the equations of unknown portions could be solved by means of algebra.
Important Formulas in Algebra
- a2 – b2 = (a – b)(a + b)
- (a+b)2 = a2 + 2ab + b2
- a2 + b2 = (a + b)2 – 2ab
- (a – b)2 = a2 – 2ab + b2
- (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
- (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
- (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
- (a – b)3 = a3 – 3a2b + 3ab2 – b3
- a3 – b3 = (a – b)(a2 + ab + b2)
- a3 + b3 = (a + b)(a2 – ab + b2)
- (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
- (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
- a4 – b4 = (a – b)(a + b)(a2 + b2)
- a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
- If n is a natural number an – bn = (a – b)(an-1 + an-2b+…+ bn-2a + bn-1)
- If n is even (n = 2k), an + bn = (a – b)(an-1 + an-2b +…+ bn-2a + bn-1)
- If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +an-3b2…- bn-2a + bn-1)
- (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….)
- Laws of Exponents (am)(an) = am+n ; (ab)m = ambm ; (am)n = amn
- Fractional Exponents a0 = 1 ; aman=am−n ; am = 1a−m ; a−m = 1am
- Roots of Quadratic Equation
- For a quadratic equation ax2 + bx + c where a ≠ 0, the roots will be given by the equation as (b±√b2−4ac) /2a
- Δ = b2 − 4ac is called the discriminant
- For real and distinct roots, Δ > 0
- For real and coincident roots, Δ = 0
- For non-real roots, Δ < 0
- If α and β are the two roots of the equation ax2 + bx + c then, α + β = (-b / a) and α × β = (c / a).
- If the roots of a quadratic equation are α and β, the equation will be (x − α)(x − β) = 0
- n! = (1).(2).(3)…..(n − 1).n
- n! = n(n − 1)! = n(n − 1)(n − 2)! = ….
- 0! = 1


Now, let’s say by chance you discover a lottery number pattern. How can this improve your chances of winning the lottery?
Intuitively, you already know the answer. If something has a pattern to it, if there is a trend, you have a better chance of predicting what will happen next. If there is no discernible pattern then the only option left is to guess, which is exactly what most lottery players do every drawing. It’s either that or buy some Quick Picks and let the state guess for you.
So, for all serious lottery players, our path is clear. To improve our chances, we must find those lottery patterns. And, that my friend is no easy task. If slaving over stacks of paper you’ve generated trying to find a lottery number pattern by hand, is not your thing then listen up. The easiest way to do this is to let a good lottery software program do it for us. This type of problem is what computers were made for. This is where they shine. But, how do we tell the difference between a pattern or trend that will improve our play and one to avoid? It is quite easy, actually. In a nut shell, here is how it’s done.
For example, let’s say we start out by guessing. By doing so over many drawings, we average 1 correct winning lottery number per drawing. Matka This becomes our baseline. From this point forward, we are looking for any pattern or trend that does better than this and all others we avoid.
Now, if we followed this procedure over a period of time, we would see an improvement in our play. But, we would still be missing the big picture.
Do you want to know what the real secret is? Here it is.
You can’t win a battle with one soldier. You need an army. You need to take advantage of many lottery patterns and trends to build a respectable play list. Then, over time, you make changes and adjustments to push the average number of correct numbers higher and higher; increasing your chances of winning in the process.
Some Words of Advice: Without the aid of a decent lottery software program to do all of the heavy lifting, this method would be a nearly impossible task. But, with the right tools, playing the lottery will become much more fun.
Playing the lottery with a strategy gives you a competitive edge over the average player because you are using mathematical calculations to ascertain your selected numbers based off of the preferred strategy you wish to utilize. How is this any different than picking numbers at random or using my birthday and anniversary? I’ll tell you.
Using a strategy such as a lottery wheeling system can dramatically increase your chances of winning the lottery by using math, the universal language, to your advantage. Wheeling systems arrange a group of numbers into multiple combos (games) that will provide you with either full or partial cover of all the combos within a section of numbers. By using a wheeling system, you are almost guarantying yourself a win each time.
Typically most people generate their wheels by hand but many lottery strategy experts, including myself, recommend using software to assist you with generating your wheels to eliminate any chance of human error.


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Consider how you wish to compose your private faith statement. Sometimes letters have to be adjusted to fit in a particular space. When a letter does not have any verticals like a capital A or V, the very first diagonal stroke is regarded as the stem. The connected and slanted letters will be quite simple to form once the many shapes re learnt well. Even something as easy as guessing the beginning letter of long words can assist your child improve his phonics abilities. Worksheet Writing Number 4.
There isn't anything like a superb story, and nothing like being the person who started a renowned urban legend. Deciding upon the ideal approach route Cursive writing is basically joined-up handwriting. Practice reading by yourself as often as possible.
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I was grabbing lunch over at the student center before a big meeting today and saw a colleague from the math department carrying a sack that had e to the i pi, except using math symbols that I don't know how to reproduce in blogger or wordprocessors. (So, that's e, the symbol of the base of the natural logarithm thingy; i, the symbol of the imaginary square root of negative one; and pi, the ratio of any circle's circumference to its diameter--which has to be one of the coolest things to learn is a constant, no?)
Now, I pretty much understand the concept of i and pi, but e I just didn't get at all. I remembered from sixth grade math or something that it's the natural log, but what the heck does that mean?
So I asked! And it's SO COOL! My colleague started drawing stuff on the campus newspaper lying nearby, and it made sense! (My colleague's stuff looks much like these Wikipedia illustrations.)
What a very, very cool number! Why didn't they teach us that part in sixth grade?
I love that I can learn things in casual conversation that answer questions I never quite knew I had until the conversation starts.
Now I want to track down a chemistry colleague and ask why there are 6.02 x 10 to the 23 (10 superscript 23, however one does that on blogger) particles per mole. Why did ol' Avogadro choose that number? Because it always seemed to me so arbitrary, like a dozen, just an arbitrary extra name for a weird number that we had to learn. But, knowing chemists, there's some really great reason for that particular number.
There are lots of things in life that I semi-remember from grade or high school, and love to get a good explanation from my colleagues about. And the delightful thing is, my colleagues here are usually incredibly good at explaining things and helping me understand them, and willing to do so with a generous spirit and great kindness.
What questions would you line up?


Relationship : the way in which two or more concepts, objects, or people are connected, or the state of being connected.
Complicated : consisting of many interconnecting parts or elements; intricate
When I heard word “complicated”, I was reminded in “simple” as opposed word. I remembered with one of the topic in math when I was sitting in elementary school. The curve.The curve is a straight line or curved line that it’s edges meet at a single point or not met at all. If the edges are met then it is called a closed curve. If the edges are not met then it is called a closed curve.
Both types of curves can still be grouped into two groups. If the open curve does not have a point of intersection, it is called a simple open curve. Conversely, if it has a point of intersection, it is called a nonsimple open curve.
Meanwhile, if the closed curve does not have a point of intersection, it is called a simple closed curve. Conversely, if it has a point of intersection, it is called a nonsimple closed curve.
In my opinion, a complicated relationship look like a nonsimple closed curve or nonsimple open curve. Complicated relationship is a relationship in which there are many ideas and interests clash.
When establishing a relationship, there must be a goal to be achieved. If the people who are in a relationship have similar thoughts, interests, vision, and mission, then the relationship will go smoothly like to draw a line down the image of a simple open curve or simple closed curve.
However, when the people who are in a relationship have different ideas, interests, vision and mission, then the relationship will be complicated like to draw a line down the image of a nonsimple closed curve or nonsimple open curve. It would appear many clashes and intersections.
Humans are complicated creatures. Therefore, the relationship between them is certainly complicated.
[EF#18] What Is Complicated Relationship For You
Read Another English Friday Series :
- [EF#25 Weekly Challenge] Iftar Together
- [EF#24 Weekly Challenge] Dates and Juice
- [EF#23 Weekly Challenge] If I Mudik
- [EF#22 Weekly Challenge] Failed Holiday You Wish To Do It
- [EF#21 Weekly Challenge] Ragunan Zoo
- [BEC-GIVEAWAY] What Will You Do If You Were An Administrator Of BEC?
- [EF#20 Weekly Challenge] Sadness and Books
- [EF#19 Weekly Challenge] Traces in the Heart
- [EF#18 Weekly Challenge] The Curve
- [EF#17 Weekly Challenge] From Accounting to Programming
I agree with the last sentence. Human being is a very complex and complicated creature who, sometimes, also acts irrationally, making them even more complex and complicated 🙂 .
While I agree with this sentence: “Complicated relationship is a relationship in which there are many ideas and interests clash.”
🙂 *pembaca setia BEC*
thank you for that and for visitting this blog 😀
thank you… so it is “emang udah dari sananya” 😀
Kalau gak complicated ya resto padang ya mas *komen balasan*
So true. Human is one complex being. And when they build a relationship, it become more complex. More complicated.
but everyone like to make a relationship like that 😀
Yes. It is the best relationship. Like Inul said, it will be like sayur asam tanpa garam
as a social creature we need to be connected with others
Now I wonder, could we make a relationship less complicated?
maybe, it could be.


A Guaranteed Win for the Casinos
If you enter the casino to make a lot of money, you will go out very disappointed … most of the time. In each match at the casino, the house always has the advantage. Your best chances to win in these games are trying to increase your probability as much as possible of the best game at the casino to play where you can increase your chances of the most blackjack. There are many different สล็อต 888 strategies to increase your chances of winning blackjack. The most successful strategy is known as card counting.
Fun With Daily Casino Trips
Counting the card works by assigning numeric values to each card in the bridge, then keeping a count on the “account” in your head. “The count” is the sum of the numerical values attributed to the cards that have already been treated. The number is an indicator of the temperature of the bridge (whether hot or cold). If the bridge is burning, it means that there are higher cards, usually cards more significant than 10, including Aces who are still in the bridge, which means they are about to be distributed. If the bridge is cold, it means that there are more small cards left in the bridge. A standard card counting technique assigns +1 to 2-6 cards, a zero value to 7-9 cards, and a value of -1 to 10-A cards. As the cards are processed, each value of the cards has passed. This gives you your count in progress. Your “real account” is the current number divided by the number of bridges left to be treated. The actual account counts that you base how much money you will bet on your next hand.
A second blackjack strategy is a second reflection at all and is fun to try. This is called negative regression, and it works by doubling your bet every time you lose a hand. This ensures you that you are going out at the top next time you earn a hand. The only low side of this สล็อต 888 strategy is that the casino tables put a maximum bet limit on the tables to not continue to double it bet until they win because the casino always loses someone who can afford it.


Women can now get a head start on their career with the Housatonic Community College (HCC) Advanced Manufacturing Boot Camp. This free, three-week training program begins January 13, 2020, and gives women who are interested in pursuing a career in the manufacturing industry a starting foundation in these technical skills.
Any and all learning institutions and individual educators interested in adopting best practices in STEM education are invited to attend a Carnegie STEM Excellence Pathway workshop at Housatonic Community College (HCC) on Saturday, January 11.
On Wednesday, November 20, Housatonic Community College (HCC) celebrated student entrepreneurs as they displayed their business concepts at the 3rd Annual VentureLab Showcase.
Housatonic Community College (HCC) invites the community to STEAMFest 2019 – a celebration of Science, Technology, Engineering, Art and Mathematics on Wednesday, November 6th and Thursday, November 7th on the HCC campus.


عنوان مقاله [English]
نویسندگان [English]چکیده [English]
One of the most important exploration problems in geophysics is to estimate the geophysical parameters from the observed or residual gravity anomaly related to a buried structure, such as depth, amplitude coefficient and geometrical shape factor. The gravity anomaly expression produced by a simple geometrically shaped model (sphere orcylinder) can be represented by an appropriate analytical formula. Several interpretative methods have been developed to interpret gravity field data assuming a fixed simple geometrical model such as a sphere, a horizontal cylinder or a vertical cylinder. In most cases, these methods consider the geometrical shape factor of the buried body to be apriori assumed, and the depth variable may thereafter be obtained by graphical methods applied to the residual anomaly. However, only a few methods have been developed to determine the shape of the buried structure from the residual gravity anomaly. Consequently, the accuracy of the results obtained by these methods depends on the accuracy within which the residual anomaly can be separated from the observed gravity anomaly. In this study, a new and simple method has been developed to estimate the depth, amplitude coefficient and geometrical shape factor of a buried structure from the observed (composite) or residual gravity anomaly related to a cylinder or sphere-like structure. The method is based on nonlinearly constrained mathematical modeling and also stochastic optimization approaches. This method consists of three main steps: The first step is oriented to formulate a nonlinearly constrained optimization model (NCOM) which mathematically describes the geophysical gravity problem related to the studied structure. The (NCOM) model is to optimize a mathematical objective function on an unbounded subset (defined by mathematical inequalities constrains in which the geophysical parameters are generally surmised to satisfy) contained in the free geophysical parameters. Ignoring these mathematical constrains probably leads to general error estimations of the parameters. In this research, the objective function was taken as the statistical likelihood function which depends on the deviations between the observed and synthetic points and also on the number of observations. The second step is directed to suggest an interior penalty function to transform the (NCOM) model into a nonlinearly unconstrained optimization one (NUOM). The goal of using the penalty function is to eliminate the constraints of the (NCOM) model and make them reactive in a new target function of the (NUOM) model[E1]Â . The target function of the (NUOM) model considers both the objective function of the (NCOM) model and the suggested interior penalty function. The third step is to solve the (NUOM) model by the adaptive simulated annealing algorithm, a stochastic approach, well-known for optimizing numerical functions of several real decision variables. The obtained solution of the (NUOM) model includes the geophysical gravity parameters of the studied structure such as: depth, amplitude coefficient and shape factor. A statistical analysis has been carried out to demonstrate the accuracy and the precision of the suggested interpretative method. We applied this method to some theoretical synthetic examples in order to evaluate the precision of the suggested method. We also used the method to estimate the mentioned parameters for the gravity anomaly of the Abadeh site. The obtained results had an appropriate agreement with other methods.
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Correlation must not be confused with causality. TradingView. A value of zero indicates no relationship between the two variables being compared. will test their theories by creating isolated environments where only one factor is changed (where this is possible). Consider the following two variables x andy, you are required to calculate the correlation coefficient. Correlation coefficients range from -1 to 1. You’re are done! Values over zero indicate a positive correlation, while values under zero indicate a negative correlation. The value of Person r can only take values ranging from +1 to -1 (both values inclusive). We can see the correlation coefficient (bottom of the chart) is currently at 0.97, which is signaling a strong positive correlation. Spearman correlation coefficient: Definition. As variable x increases, variable z decreases. In fact, it is very possible that there is a third factor involved. If two factors have a coefficient of 0, that means they are in no way related whatsoever. When two variables are correlated, it simply means that as one variable changes, so does the other. Dictionary entry overview: What does correlation coefficient mean? By Deborah J. Rumsey In statistics, the correlation coefficient r measures the strength and direction of a linear relationship between two variables on a scatterplot. If the value of r is greater than zero, there is a positive or direct correlation betwe… The amount of weight I gain is positively correlated to the amount of food I eat. Multiple linear regression (MLR) is a statistical technique that uses several explanatory variables to predict the outcome of a response variable. An example of positive correlation would be height and weight. If there is weak correlation, then the points are all spread apart. (2003). TradingView. 1. How Do You Find the Linear Correlation Coefficient on a Calculator? When ρ is -1, the relationship is said to be perfectly negatively correlated. ρ For example. As you eat more food, you will probably end up feeling more full. However, the two methods do differ. In statistics and probability theory, correlation is a way to indicate how closely related two sets of data are. Press enter until the calculator screen says “Done”. There are several methods to calculate correlation in Excel. A correlation is a statistical measure of the relationship between two variables. Values can range from … a sample; strength. Measures of Correlation 2. The correlation coefficient is a statistical measure that calculates the strength of the relationship between the relative movements of two variables. The computing is too long to do manually, and sofware, such as Excel, or a statistics program, are tools used to calculate the coefficient. In the financial markets, the correlation coefficient is used to measure the correlation between two securities. B. There is a correlation between ice cream sales and shark attacks (they both go up as the temperature goes up in this case). There are basically three possible results from a correlation study: a positive correlation, a negative correlation or no correlation. operational definition. If the correlation coefficient is greater than zero, it is a positive relationship. When interpreting correlation, it's important to remember that just because two variables are correlated, it does not mean that one causes the other. These include white papers, government data, original reporting, and interviews with industry experts. relationship between oil prices and airfares, How to Calculate a Correlation Coefficient on a TI-84 Calculator. the strength; direction of the relationship. 3.If there is a ^, or hat, above a variable, what does that mean? Negative coefficients represent inverse correlation and produce a downward slope on a graph - as one variable increases, the other variable tends to decrease. Strong and weak are words used to describe the strength of correlation. The correlation coefficient represents two things the _____ of the relationship and its _____. The closer the value of ρ is to +1, the stronger the linear relationship. For example, it can be helpful in determining how well a mutual fund is behaving compared to its benchmark index, or it can be used to determine how a mutual fund behaves in relation to another fund or asset class. The fit of the data can be visually represented in a scatterplot. However, the degree to which two securities are negatively correlated might vary over time (and they are almost never exactly correlated all the time). These figures are clearly more volatile than the balanced portfolio's returns of 6.4% and 0.2%. This correlation coefficient is a single number that measures both the strength and direction of the linear relationship between two continuous variables. how they got this information." This is important to repeat: You never have to do this again unless you reset your calculator. What does it mean when the coefficient of determination is 100%? R code What if, instead of a balanced portfolio, your portfolio was 100% equities? correlation, increase, same. This is a positive correlation. The correlation coefficient, typically denoted r, is a real number between -1 and 1. A reading above 0.50 typically signals a positive correlation. "JPM Stock Chart." Both the Pearson coefficient calculation and basic linear regression are ways to determine how statistical variables are linearly related. In short, any reading between 0 and -1 means that the two securities move in opposite directions. The value of r is always between +1 and –1.  You put in data into a formula, and it gives you a number between -1 and 1. The correlation coefficient is calculated to be -0.96. When working with continuous variables, the correlation coefficient to use is Pearson’s r.The correlation coefficient (r) indicates the extent to which the pairs of numbers for these two variables lie on a straight line. However, politicians, salesmen, news outlets and others often suggest that a particular correlation implies causation. Simplify linear regression by calculating correlation with software such as Excel. The value of +1 for the correlation coefficient denotes that the two variables are have a very strong negative correlation. These are positive or negative. When the value of ρ is close to zero, generally between -0.1 and +0.1, the variables are said to have no linear relationship (or a very weak linear relationship). A correlation coefficient of +1 indicates a perfect positive correlation. the direction; a cause. 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If you don’t already know the struggles my Littlest has had with math through the years, let me tell you, it’s been rough. It’s not that he doesn’t get it. He can math life like nobody’s business. As long as he can relate it to reality, he’s good. In fact, he can do math in his head quicker than I can.
He had gads of trouble getting his multiplication down and skads of woes when it came to fractions. Over the years, I’ve tried everything: Making up games, buying books, hiding in the bathroom with a bag of M&Ms and a novel.
The problem wasn’t that he couldn’t learn. It was that once we moved on to something new he forgot what he had already learned. Every. single. time. We’re doing multiplication? He forgets how to subtract. We’re doing fractions? He forgets how to multiply. Not a little bit, either. He forgets Everything.
If you think I sound frustrated, you should see my poor baby when it happens. And the more frustrated he gets, the more he struggles. Since I’m not the best in the world at math anyway, I pretty much just end up staring at him in complete discombobulation. I literally have no idea how to help him in those moments.
But for the past month he’s been doing something new, something so awesome he’s actually starting to retain. And my friend, I am not even involved.
When Smartick offered to let Littlest try their program in exchange for a review, I thought, “Meh, why not try it?” Not that I wasn’t super-interested, just… Was it going to be one more thing that didn’t work?
Yeah, no it wasn’t. This. Worked.
Smartick claims to be able to teach your child math online in about 15 minutes a day. Littlest has been doing the program for about a month now, and I don’t think it’s ever taken him more than that to complete his day’s work.
Smartick started with an easy tutorial that showed Littlest what to do, then tested him to see what types of problems he should be working on. He was up and running in a few short minutes. I was pleasantly surprised to receive an email that afternoon giving me a progress report. It was nice to give him the independence of working on his own while still being able to check up on him.
Even better? One day our geography class ran a bit long–rabbit trails– and I offered to end school and let the boys pick up their other subjects the next day. You can imagine my delight when Littlest said (with no hesitation whatsoever), “I want to do my math first.”
The boy who has dreaded math pretty much since birth is excited about it now. He doesn’t want to skip it.
The Proof is in the… Consumer Math
We decided to continue doing consumer math as a family class and make Smartick his independent learning while Middle does algebra. I know, it sounds a bit outrageous that they both have 2 math classes this year, but Middle loves algebra and didn’t want to skip it for consumer math and Littlest..?
Littlest loves Smartick.
Mama loves Smartick, too. Because we’re doing all kinds of multiplication, percentages, decimal problems, and division, and his speed at these on-paper problems has quadrupled. In a month of doing Smartick online, his overall math performance has surpassed anything I have tried, anything I could have done as a mama, and anything he expected of himself.
Am I recommending this program for your homeschool? Heck yes. A thousand times yes. And you know how I feel about using technology, but this…
Smartick is a minor miracle
All this yummy goodness has relieved a tension in my homeschool I hadn’t even realized was there. I think getting to do his math independently (without me hanging, cringing, over his shoulder) has upped his confidence. Smartick even gives him the opportunity to go back to questions he missed and correct them. Listen, it doesn’t just give him the answers, it tells him what he got wrong and asks if he wants to make corrections. And he never misses the second time around. But what has surprised me even more is that he has never gotten more than 3 problems wrong in a day.
It’s like he’s finally got this math thing. He doesn’t even grumble about consumer math anymore, he just gets the work done.
Which is great, because it helps me step back a little as my boys traverse middle and high school, and I am well aware I need to start letting go. I can even leave the room.
You know. So I can enjoy my M&Ms.
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The last term made me feel like I have learned so much and I have to review many things that I have learned this year such as fraction, prealgebra, Triangle and more. This term is a bit more confusing to me, not that I didn’t get it, but because we got to learn a lot different than the last terms. There are many news lessons I just got to learn, and of course I am not that confident and comfortable about it yet,but hopefully I will after the small test we take because all of us are going to try and take what we understand all in this test so that the teacher know what level we are and what to improve too. This is the last term of the year I just want to take a moment to look at myself of how I am doing this year compared to last year. It was a huge different for me ,last years I just like I was just born so everything was just like confusing and news,but started this year I feel like I have gotten into more of math and started to understand it more and more and how helpful it is to our everyday life and also our brain system. It is not just something you can learn and forget because you will use it a lot in life and it is one of the most important lessons in school. Math is hard for me and I think it is for most of us too. It is not just learning,but it is about practicing and there are some math things that we won’t even use in real life, but we learn it because it is important for us to learn most of it even we rarely used it in real life, but if someday we need to it is easy for us.
One of my tough lesson in math class that I feel like I haven’t comfortable with is Fraction. It is one of my least favorite things because I am not comfortable with it, but I believe that when I understand and comfortable with it I will definitely like it. I don’t know if there anyone feels or happen the same as me because whenever I learned fraction I got it, but after a while when we have a new lesson I would forget it easily and I think I have to work on review the lesson a lot. I always wonder why I used to not like math and now I know one main is that because I didn’t get the concept of it I didn;t understand it and I am being quite in class I rarely ask questions and I would always just listening to the teacher, but the way it is was not what I wanted myself to me . Now I am a whole new different person. I can feel started to like math and also asking questions when I don’t get it and also not only asking, but also helping my friends out too. This year is one of my year that I can call as “success” and I hope I can keep up the good work and also improve what I need to next year.