What Are Moving Averages?
In technical analysis, one of the commonly and widely used tools to analyse the price action is a Moving Average. Whether you are watching stocks, futures, FX pairs or cryptocurrencies, Moving Average helps to visualize the average price on the chart.
What is a Moving Average (MA)?
Moving average is an indicator of price action based on the historical data. The indicator calculates the average price of an asset in a set timeframe on the chart. For the reason of strictly relying on the historical data, the Moving Average is classified as a lagging indicator. The calculation of a moving average is simple, yet someone might think that the moving average simply adds a set of data and divides it by it’s quantity, however it’s not entirely like that.
How is MA calculated?
Moving averages take a subset of data and divide that by the number of sets. For example, to calculate a 7-day moving average on Bitcoin’s daily chart, the calculation is done as follows:
Average prices of Day 1 + Day 2…. + Day 7 / 7 = 38 195.24
Average price of Day 1 is the calculation of 7 subsets, i.e. Day 1 has the Moving Average calculation as described above and so on.
And as the day ends and the average price is set, the calculation begins from the daily average of the price 6 days before the current day, the last bar is summed.
Same calculation method is applied to other time-frames, monthly, weekly, hourly and minute. It is worth mentioning that the length of the MA is strictly based on the average price of an asset within the set time-frame. See example of a MA on an hourly chart below.
Going 7 candles back, we start calculating the MA, the same way as above.
Hour 1 + Hour 2 +...+ Hour 7 / 7 = 38.632,31
When the last bar closes, and the new one opens for the next hour, the MA recalculates 6 previous bars and the new bar.
In other words, in the example with the set length at 7, the MA doesn’t calculate the whole set of historical data and divides it by 7, but uses 7 last subsets.
Why are Moving Averages important?
In accounting and finance, moving average helps to identify the average price of the money flow to have a clearer balance sheet and to predict the future average flow. For instance, a company may see based on the historical data the average weekly money flow based on a quarterly, annual historical data and set a goal and predict the future average flow over the next fiscal period.
In financial markets, MA are used to identify support and resistance levels of an asset. MA when used in a combination of RSI and Volume indicators may provide a clearer picture of the next price action. Whereas, MA can show the average price over the period of time, RSI can show the asset’s power and Volume can indicate the strength of the market participants and their willingness to support the either direction of an asset.
Types of Moving Averages.
There are several types of MA, but the most commonly used ones are SMA and EMA.
SMA - Simple Moving Average (SMA), the simplest calculation of data is used to identify the average price of an asset. The calculation is the same as described above and to ease your understanding we will show a mathematical formula of the SMA calculation.
SMA = AP1 + AP2 + AP3 +...+APn / n
AP = Average price
n = the defined time period / length
EMA - Exponential Moving Average (EMA) adds weight to the calculation in order to better predict the future price movements. To calculate the EMA, first SMA for the designated time period has to be completed, then a smoothing factor/multiplier is applied. The multiplier is found by this formula - [2 / (time-frame) +1]. So for the 7-day EMA the multiplier would be [2 / (7 +1)] = 0,25.
Mathematical formula for EMA calculation is as follows:
EMA = [AP - EMA (yesterday)) x multiplier + EMA (yesterday)]
AP = average price
Multiplier = [2 / (time-frame) +1]
Moving Averages still remain an essential part of the technical analysis, and used to generate various indicators such as John Bollinger’s - Bollinger Bands. MA’s identify support and resistance zones of an asset and are best when applied with other oscillators and momentum indicators.


My name is Shelby Goulart and I am your child's 6th grade math teacher! I am very excited to start the third quarter and look forward to meeting you and your child. I was born in Antioch, California, and attended the University of Nevada Reno to get my degree in mathematics and secondary education. This is my first year teaching and I am so excited to get this journey started at Mendive MS. I was also a tutor for the program Upward Bound through UNR. We served low income first generation High School students, and our main focus was STEM education, but also helped in History, English, and some language classes.
I have a dog named Cali, and my family all live in California where I was born and grew up for a majority of my life. I have two sisters, Morgan and Jaelyn, and I am smack in the middle of them!
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3 edition of Proceedings of the Joint Bulgarian-Hungarian Workshop on Mathematical Cybernetics and Data Processing found in the catalog.
Proceedings of the Joint Bulgarian-Hungarian Workshop on Mathematical Cybernetics and Data Processing
by Computer and Automation Institute, Hungarian Academy of Sciences
Written in English
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In homogeneous media the one-way extrapolation operator in the kx-w (wavenumber-frequency) domain is a simple analytical function. The advantage of computation in the kx-w domain is that the desired result is obtained by multiplication of the data with the operator. But simple multiplication in the kx-w domain rules out the possibility of applying a laterally varying operator. Another disadvantage is the numerical artefact in x due to undersampling in kx. To allow laterally varying medium functions and less numerical artefacts a convolutional operator in the x-w (space-frequency) domain should be used. When the spatial extrapolation operator is used in an explicit recursive depth migration algorithm it must be calculated in an optimum way to obtain reliable and stable results. There are several ways to obtain a spatial convolution operator. For homogeneous media one usually starts with the exact analytical expression in the kx-w domain and transforms this operator back to the spatial domain. In recent years many methods have been developed to do this transformation in an efficient and optimum way. For the one-way extrapolation operator Holberg (1988), Blacquiere (1989), Hale (1990) and Nautiyal et al. (1993) have proposed methods to arrive at spatial operators which are unconditionally stable in a recursive extrapolation scheme. In DELPHI Volume IV, Appendix D (1993) an alternative method is presented for an efficient and controlled transformation back to the spatial domain. This method can be used to calculate extrapolation operators which should be stable and accurate in a recursive depth migration algorithm. First some examples of extrapolation operators for homogeneous media are given. The theoretical derivation for the proposed numerical optimization scheme was already given in Appendix D of the DELPHI Volume IV (1993). The proposed method is compared with other numerical optimization methods and finally some results of recursive depth migration, in acoustic media with the optimized extrapolation operators, are given in DELPHI Volume V, Appendix A.
The operators obtained with the weighted least square optimization procedure are economic, stable and accurate. Reducing the operator length will decrease the computation time, but for very short operators the steep dip will become inaccurate and unstable. Comparing the weighted least square operators with the computationally intensive non-linear optimized operators, it may be concluded that only a small difference occurs at the high angles: the weighted least squares operator decays a little in amplitude while the non-linear operators keep the amplitude correct (although they give rise to small artefacts at the high angles). In the DELPHI project we have chosen for the weighted least squares method to compute the operator table, because of its stable and accurate behaviour for a broad range of operators and the relatively small computation time. The weight function used in the optimization procedure can also be optimized in order to give the spatial operator an even more controlled behavior. This optimization of the weight function is a topic for future research. The length of the optimized operator is for a certain error a function of the wavenumber. In calculating the table of operators this length dependency could be taken into account to arrive at an even more efficient extrapolation. At the moment we are also investigating a similar optimization process for 3D operators.


CARROLLTON, GA Carrollton High School senior Audrey Bests academic success led CHS Principal David Brooks to name her the schools 2020 STAR Student, and what has become a recent tradition at the high school, surprised her STAR Teacher selection with a quick visit to her classroom Wednesday to make the announcement. Audrey chose CHS math teacher Kim Eason.
Eason taught Audrey as a sixth grader in an accelerated math class and later at the high school where she teaches advanced algebra and analytic geometry. Why did Audrey pick Eason?
She taught me everything I needed to know for the math portion of the SAT, she said.
Audrey Best presents a framed certificate to CHS math teacher Kim Eason honoring as her STAR teacher.
This is the third time in five years Eason has been chosen as STAR Teacher, first by William Curvino in 2016 and Katie Rubino in 2018. All three cited Easons influence on them as middle school accelerated math students in addition to the high-level coursework they were exposed to at CHS under her charge.
It is such an honor, said Eason. I feel like lightning struck three times and the fact that the STAR Student makes the decision is extra special. I couldnt be more humbled.
The STAR student award is presented to the graduating senior who posts the highest SAT score of his or her cohort and is in the top 10 percent of the class. Audrey is in the process of choosing between the University of Georgia or University of Alabama to study engineering. In September, Audrey was named a National Merit Scholarship Program Semifinalist, joining an elite group of less than 1 percent of high school seniors nationwide.
In addition to her strong academic performance, Audrey is also an athlete who competes in tennis and cross country. She is the daughter of Ronald and Mary Jo Best of Carrollton.
The pair now will compete at the region level with hopes of advancing to the state competition this spring. The STAR Student/Teacher program is sponsored locally by the Carroll County Chamber of Commerce and by the Professional Association of Georgia Educators thereafter.


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In Killygarry National School we teach all the subjects in line with the Irish Primary School Curriculum. We teach English, Gaeilge, Maths, History, Geography, Science, Music, Drama, Visual Arts, Physical Education, Social, Personal and Health Education, Religious Education and Information and Communication Technology. These are taught in a dynamic and modern way using new programmes and state-of-the-art technology such as iPads, Chromebooks, Interactive Whiteboards and Soundfield Systems.
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A Comprehensive Approach Toward Dyscalculia
Sitting at the table with your child teaching the same basic math skills over and over can be exasperating for even the most patient of parents. Your child can finally learn how to solve a type of math problem but then can’t remember how to do it the very next day. Panic sets in and anxiety about your child’s future plays out several different scenarios of your child not being able to go to college, get a job, or move out of the house.
Dyscalculia doesn’t just affect your ability to do math, but it also interferes with other basic abilities as well. Managing time is a common issue that causes tardiness, grossly underestimating the amount of time it can take to complete a task, and the ability to recall or understand a sequence of steps or instructions to complete a task. Poor navigational results in getting lost easily and becoming disoriented.
How We HelpBuilding a larger working memory is just one of the ways we help these students. One of the ways we achieve this is by putting away calculators. It sounds dreadful and it is – in the beginning, but over time, the brain keeps basic math skills accessible and encourages neuronal connections to form pathways for mathematical thinking.
Algebra is going to be tough, but it doesn’t have to be a nightmare. They won’t count on their fingers forever!Get in Touch
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Updating the singular value decomposition
If we compare the users based on individual movies, however, only those movies that both users have rated will affect their similarity.This is an extreme example, but one can certainly imagine that there are various classes of movies that should be compared. examined the dimensionality reduction problem in the context of information retrieval .There are several reasons we might want to do this. If we have a dataset with 17,000 movies, than each user is a vector of 17,000 coordinates, and this makes storing and comparing users relatively slow and memory-intensive.It turns out, however, that using a smaller number of dimensions can actually improve prediction accuracy.Calculating the PSVD of large term-document matrices is computationally expensive; hence in the case where terms or documents are merely added to an existing data set, it is extremely beneficial to the previously calculated PSVD to reflect the changes.It is shown how updating can be used in LSI to significantly reduce the computational cost of finding the PSVD without significantly impacting performance.Some numerical examples are given to confirm the performance of the algorithms.
wherein the step of determining updated estimates of the singular values and singular vectors includes weighting of a contribution of the orthogonal projections of the input and output vectors into the updated estimates of the singular values and singular vectors with a weighting factor of less than 1.For example, suppose we have two users who both like science fiction movies.If one user has rated highly, then it makes sense to say the users are similar.comprising a step of estimating a rank of the matrix transfer function from one of the orthogonal projections of the output vector onto the left singular vectors and the orthogonal projections of the input vector onto the right singular vectors for detecting a change of said rank.wherein the step of computing an orthogonal correction vector for each singular vector further comprises the step of computing (p−1) orthogonal expansion coefficients for each singular vector from the orthogonal projections of the output and input vectors onto initial estimates of the right and left singular vectors using the initial estimates of the singular values.


Scientific notation is typically used to display large or very small numbers that are not easy to read in standard form. These numbers are also called scientific, exponential and/or binary notation. This answer will introduce you to the concept of scientific notation, how it compares with other forms of representation and its importance in everyday life.,
Scientific notation is a way of expressing numbers in the form “x.y” where x and y are integers or real numbers, respectively. It is used in scientific fields to simplify large numbers and can be found in everyday life as well. Here are some examples of how it is used.
When writing extremely big or very tiny numbers with fewer digits, Notation in Science is employed. Learn how scientists use this notation to express cosmic distances like the distance between planets, as well as tiny distances like the length of a blood cell.
What are some instances of Notation in Science, for example?
Notation in Science
- Example: 700. Why is 700 written as 7 × 102 in Notation in Science ?
- For instance, 0.0055 is expressed as 5.5 10-3. Because 0.0055 = 5.5 0.001 = 5.5 10-3, 0.0055 = 5.5 0.001 = 5.5 10-3
- For instance, 3.2 is expressed as 3.2 100.
- Suns, Moons, and Planets, for example.
- 0.00012 is expressed as 120 10 in this example.
what is Notation in Science and why is it used? Notation in Science is used to write numbers that are too big or too small to be conveniently written in decimal form.
Also question is, which is the best example of a number written in Notation in Science?
A number is written in Notation in Science when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in Notation in Science as 6.5 ✕ 10^8.
How does Notation in Science help us?
Notation in Science is a system for writing and working with numbers that makes it much easier to deal with numbers that are very small or very large. This makes it convenient to represent very large or very small numbers using exponential notation. A number written correctly in Notation in Science has two parts.
Answers to Related Questions
Which is a correct representation of .000025 in Notation in Science?
are written in the Notation in Science. If the decimal is shifting to right side, the power of 10 is negative and if the decimal is shifting to left side, the power of 10 is positive. As we are given the 0.000025 in standard notation. As, the decimal point is shifting to right side, thus the power of 10 is negative.
Where is Notation in Science used?
Description: Notation in Science is used to write very large or very small numbers using less digits. Discover examples of Notation in Science used in real life and acquire the comprehension of complex concepts such as polynomials and exponents.
How do you write 0.00001 in Notation in Science?
To write 0.0001 in Notation in Science, we will have to move the decimal point four points to right, which literally means multiplying by 104 . Hence in Notation in Science 0.0001=1.0×10−4 (note that as we have moved decimal one point to right we are multiplying by 10−4 .
What is the meaning of Notation in Science?
Notation in Science is a mathematical expression used to represent a decimal number between 1 and 10 multiplied by ten, so you can write large numbers using less digits. An example of Notation in Science is when you write 4 x 10³ for 4,000. YourDictionary definition and usage example.
Why is Notation in Science important?
Notation in Science is useful because it allows us to easily write and make calculations with extremely small and extremely large numbers.
In what situations does standard form come into play?
When dealing with the speed of light and the vast distances between galaxies, scientists employ standard form. Because bacteria and atoms are so little, they may also be referred to in standard form.
What does standard notation look like in practice?
Standard notation is the normal way of writing numbers. Key Vocabulary. mantissa = this is the integer or first digit in any Notation in Science. For example in 1.3 ×106, the mantissa is the “1”
What is Notation in Science and give examples?
Notation in Science is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing 0.0000000056, we write 5.6 x 10-9.
How do you write 100 in Notation in Science?
The Notation in Science for 100 is 1×102 This comes from the fact that in the number 100, the decimal point is after the second zero, and to put this number into standard form, you must move the decimal point backwards two places, giving you 1.00 , which, if you then move the decimal point forwards two places, gives
How do you write 60 in Notation in Science?
Why is 60 written as 6 x 101 in Notation in Science?
- To find a, multiply the integer by one and move one decimal point to the right.
- Count how many positions to the right of the decimal to get b.
- Building upon what we know above, we can now reconstruct the number into Notation in Science.
- Examine your work:
Who created Notation in Science?
What does the number 10e6 mean?
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 1,000,000 ohms or 1 Megohm Resistor
In arithmetic, what is standard form?
Standard form is a convenient method to write either big or tiny numbers. Since 103 equals 1000, 4 103 equals 4000. As a result, 4000 may be written as 4 103. This concept may be used to quickly write down much greater numbers in standard form. Standard form may also be used to write small numbers.
Scientific notation is a way of expressing very large or very small numbers in terms of the number of significant figures. It is mainly used in scientific fields, but can be applied to other areas as well. This article will examine how scientific notation is used in everyday life. Reference: scientific notation examples.
Frequently Asked Questions
How is scientific notation used in real life?
A: Scientific notation is the use of powers of 10, in which numbers are multiplied or divided by a power. For example, 12345 would be written as 1.23 x 104, and 3.456 would be written as 0.0003 x 10-4
Why is scientific notation important in modern day society?
A: Scientific notation is important for processing large numbers of data.
What is scientific notation used for?
A: Scientific notation is a system for writing and doing arithmetic with numbers that are too big or too small to be written out in decimal form. Also, some scientific fields use it as the standard way of representing very large or very small numbers respectively.
- scientific notation in the medical field
- real life examples of very small numbers in scientific notation
- scientific notation in the real world activity sheet answers
- why is it important to use scientific notation in chemistry?
- how is scientific notation used in nursing


If you’ve completed secondary (high school) school, the chances are you have a vague understanding that the Earth and Planets orbit the Sun in a series of concentric rings. You may also know of solstices (winter/summer) and equinoxes (spring/autumn), which are markers for Earth’s seasons. What you may not know is “precession”, which is described […]Read More The World is Falling!
As with all gematria there are many levels of interpretation and understanding in numbers. Each level is unique and cannot be conflated with another level. Hopefully you will soon understand what this means… The number 666 is infamously called the number of Evil. Not because there is any evidence of this attribute, but the conflation […]Read More 666 Decoded
The Radius of an Orbit found from the Radius of the Orbiter. This only applies to orbiters having axial rotation. An experiment: A bicycle with wheels of 10″ radius cycles round a velodrome and completes the course in 740 turns. This makes the radius of the velodrome track 10″ x 740 = 7400″ (or 616.6 […]Read More Is this magic?
The length of a degree is in a ratio to the radius of a circle. (The centre of the circle is the eye! The viewing device). Whatever length of unit is used to define one, equally dictates the other. Earths radius of 3963 miles produces a degree length of 24887.64 ÷ 360 = 69.13 miles. […]Read More A formula for finding the length of a degree.
Axial rotation describes a point on the edge of a plane that moves at right angles to its centre in a way that will cause it to first approach, then recede from any given direction. In other words, if you place a marker on a wheel standing on the ground, that marker will first travel […]Read More “The moon rotates on its axis” Oh, no it doesn’t!
Data used for calculating moons distance from earth: Earths dimensions: Wikipedia Moons rise/set times – Time and Date Moons location above earth: Sub Solar/Lunar Point The diagram above shows the minimum distance for an object to be seen by half the planet simultaneously. Any farther, then like the sun, half the planet […]Read More The moons distance revisited
The second diagram below shows the minimum distance for an object to be seen by half the planet simultaneously. Any farther, then, like the sun, half the planet would see the object and its distance could not be calculated using rise/set observations. But the moon cannot be observed simultaneously over 180˚. For example, when it […]Read More The moon’s distance – calculations explained
DATA: Earth’s circumference is 24887.64 miles( 40044.2 km) 24887.64 x 365.25 cycles= 90900210 miles The radius of this circle is 1447485.7miles, the distance to the sun The sun appears to be 0.5degrees The length of the circle divided by 720(360×2) will give the real diameter of the sun 90900210/ 720 =12625miles( 20313.6 km) You may […]Read More Distance to the Sun
It is described as a process whereby the earth wobbles on its axis in such a way that every 2160 years, on the Spring equinox (March 21/22) a new zodiac sign will rise just as the sun gives a new dawn. On the Spring equinox, half an hour after the sun had risen, Aquarius followed Pisces. […]Read More THE PRECESSION AND RETURN OF THE HEAVENLY KING
It was not until man began to explore the universe with telescopes that he began to consider the question of the speed of light. In the early seventeenth century, the famous Italian scientist, Galileo, first attempted to measure the speed of light, unsuccessfully. But, about fifty years later, the Danish astronomer, Ole Römer, in 1676, measured the speed of light by […]Read More The Speed of Light


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12-Year-Old Genius Expands Einstein's Theory of Relativity, Thinks He Can Prove It WrongCan't wait to see if the kid can do it! Take that Sheldon Cooper!!!
Could Einstein's Theory of Relativity be a few mathematical equations away from being disproved? Jacob Barnett of Hamilton County, Ind., who is just weeks shy of his 13th birthday, thinks so. And, he's got the solutions to prove it.
Barnett, who has an IQ of 170, explained his expanded theory of relativity — in a YouTube video. His mother Kristine Barnett, who admittedly flunked math, did what every other mother would do if her genius son started talking mathematical gibberish. She told him to explain the whole thing slowly while she taped her son explaining his take on the theory.


A 45-year former teacher and supervisor at Bridgewater-Raritan High School died Tuesday at Bridgeway Care Center in Bridgewater.
Frank Chiaravalli, 70, was a math teacher and supervisor at the school for years, and also served as supervisor of the math department.
"He was incredibly dedicated to the kids in Bridgewater, his staff and the community," said Steve Kane, high school math teacher.
According to an obituary in the Asbury Park Press, Chiaravalli was born April 24, 1942 in Somerville, and was a lifelong Bound Brook resident and graduate of Bound Brook High School.
After earning his bachelor's degree from Montclair State College and a master's degree in education from the University of California, he worked at BRHS, the obituary said.
Chiaravalli was also a member of the National Council of Teachers of Mathematics, the National Council of Supervisors of Mathematics and the Association of Mathematics Teachers of New Jersey.
Funeral services for Chiaravalli will be held at 8:45 a.m. Saturday at Hagen-Chamberlain Funeral Home in Bound Brook, followed by a 9:30 a.m. funeral mass at St. Mary's Church.
Interment will be at St. Joseph's Cemetery in Bridgewater.
There will also be a viewing at the funeral home from 4 p.m. to 8 p.m. Friday.


Logarithmic scales are groovy.
The opinions expressed are mine only. These opinions do not necessarily reflect anybody else’s opinions. I do not own, operate, manage, or represent any band, venue, or company that I talk about, unless explicitly noted.
About the music playing underneath the narration:
Frost Waltz by Kevin MacLeod is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/)
Here’s the narration script, if you like:
The decibel – what is it?
The decibel is a nonlinear unit of measure created by Bell Telephone Laboratories. In telecommunications systems and professional audio applications, it is often necessary to compare large differences in measured power. This can be inconvenient with linear units.
The decibel solves this problem using a logarithmic scale. No, no, not phat beats being produced by striking a piece of wood at regular intervals. The logarithm: The inverse of an exponent. Logarithmic scales compact large, linear ranges of values into a much more manageable form. The logarithm used by the decibel is concerned with powers of 10, hence it is a base-10 logarithm. Be sure that any decibel calculations you perform use a base-10 logarithm; Some mathematics systems default to the natural logarithm instead.
The decibel is a unit that describes a power ratio. As such, you should be aware of three main rules for the use of this unit: First, that the decibel has no meaning unless a reference point is designated. Second, this reference point is the denominator for the ratio, and thus, must not be zero. Third, logarithms are only valid for ratios with a positive value. A decibel value can be negative, but the input ratio must not be.
All sorts of reference points for decibels exist. There is dBW, which references one watt of power. There is dBu, which references 0.775 volts RMS, un-terminated. There is dBSPL, which references 20 micro Pascals, the threshold of human hearing at 1 Khz.
For a power ratio, the decibel value is the 10 times the base-10 logarithm of the ratio. A ratio of one – that is, the reference point itself, is always zero decibels. Ratios greater than one give positive decibel values, whereas ratios less than one give negative results.
But wait, you say! Professional audio is often concerned with voltage, yet the decibel is concerned with power. How can we square that circle?
Remember that voltage can be related to power in various ways. One such form is this: Power equals voltage squared over resistance. Because we are concerned with the ratio of voltages, and not the actual power value, we can set the resistances as being equal to one. This leaves us with voltage squared over voltage squared. This may seem clumsy to calculate, but never fear! The same result may be obtained by multiplying the base-10 logarithm of the simple voltage ratio by 20 instead of 10. Isn’t that swell?
The decibel is a versatile unit of measure that can be adapted to many needs in the professional audio world. Know it, and use it well.


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The individual score of Statistics & Probability Class was reported as below
72 73 78 78 72 75 70 78 92 82
87 93 88 55 77 90 78 63 73 73
85 65 92 80 62 77 73 73 49 80
a) Organize the data using stem-leaf display (4 points)
b) Calculate the mean and standard deviation (4 points)
c) Create the box plot of the data (show the formula and how the quartiles are calculated ! not only the answers). (4 points)
d) Calculate the skewness of the data using Pearson’s method, and name the shape of the frequency polygons based on the skewness. (4 points)
e) Define the range of values which is categorized into outliers. (4 points)
b) Mean: 76.1 Standard Deviation: 10.32
c) Min: 49 Max:93 Q1:72 Q2:77 Q3:82.75 then draw the box plot using these values
d) skewness= 3(mean-median)/standarddeviation = 3(76.1-77)/10.33 = -0.26 (moderately negative skewed)
e) Outliers > Q3+1.5(Q3-Q1) or < Q1-1.5(Q3-Q1)
Q3+1.5(Q3-Q1) = 98.75 Q1-1.5(Q3-Q1)=55.875
Hence, outliers are defined for values > 98.875 or < 55.875
PROBLEM 2 (Chapter 5, Bayes Theorem)
A cell phone salesperson has kept records on the customers who visited the store. 40% of the customers who visited the store were female. Furthermore, the data show that 35% of the females who visited his store purchased a cell phone, while 20% of the males who visited his store purchased a cell phone. Let A1 represent the event that a customer is a female, A2 represent the event that a customer is a male, and B represent the event that a customer will purchase a phone.
a) What is the probability that a male customer will purchase a cell phone?
Based on above description, since 20% of males who visited the store purchased a phone, the probability that a male customer will purchase a cell phone is P(B|A2)=20% (0.2)
b) What is the probability that a female customer will purchase a cell phone?
Based on above description, since 35% of the females who visited the store purchased a phone, the probability that a female customer will purchase a cell phone is P(B|A1)=35% (0.35)
c) The salesperson has just informed us that a cell phone was purchased. What is the probability that customer was female?
Based on Bayes Theorem,
P(A1|B)= ( P(B|A1)xP(A1) ) / ( P(B|A1)xP(A1) + P(B|A2)xP(A2) ) = (0.35×0.4) / (0.35×0.4 + 0.2×0.6) = 0.14/(0.14+0.12) = 0.14/0.26 = 0.538
Just to remind you:
P(A1|B) is the posterior probability
P(B|A1) is the likelihood, P(1) is the prior probability
The denominator P(B|A1)xP(A1) + P(B|A2)xP(A2) is evidence.
Bayes Theorem defined posterior probability as likelihood x prior probability / evidence
PROBLEM 3 (Chapter 6, Discrete Probability Distributions)
Sponsors of a local charity decided to attract wealthy patrons to its $500-a-plate dinner by allowing each patron to buy a set of 5 tickets for the gaming tables. The chance of winning a prize for each of the 5 plays is 50-50. If you bought 5 tickets, what is the chance of winning 4 or more prizes?
This problem can be solved by using Binomial Distribution formula,
P(x) = C(x,n) x p^x x (1-p)^(n-x)
p=0.5, n=5, x=more than 4 = 4 and 5
P(x=4)=C(4,5) x 0.5^4 x 0.5^1 = 0.15625
P(x=5)=C(5,5) x 0.5^5 x 0.5^0 = 0.03125
P(x more than 4) = 0.15625 + 0.03125 = 0.1875
PROBLEM 4 (Chapter 7, Continuous Probability Distribution)
A large manufacturing firm tests job applicants who recently graduated from college. The test scores are normally distributed with a mean of 500 and a standard deviation of 50. Management is considering placing a new hire in an upper level management position if the person scores in the upper 6 percent of the distribution. What is the lowest score a college graduate must earn to qualify for a responsible position? (20 points)
Upper 6% of the distribution, means that the area between the mean (500) and x is 0.5-0.06 = 0.44. Refer to the Table /1 (Areas under normal curve), the area is 0.44 when z=1.56.
1.56 = (x-500)/50
x=(1.56×50) + 500 = 578
The lowest score is 578.
PROBLEM 5 (Chapter 8, Sampling Limit & Central Limit Theorem)
Human Resource Consulting (HRC) is surveying a sample of 60 firms in order to study health care costs for a client. One of the items being tracked is the annual deductible that employees must pay. The state Bureau of Labor reports the mean of this distribution is $502 with a standard deviation of $100.
Compute the standard error of the sample mean for HRC
What is the chance HRC finds a sample mean between $477 and $527 ?
standard error of the sample mean is obtained by 100/root(60) = 100/7.746=12.91
z1=(477-502)/12.91 = -1.94 (area=0.4738) z2=(527-502)/12.91 = 1.94 (area=0.4738)
The probability is found by 0.4738+0.4738 = 0.9476


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Why is math important? By now, it is obvious to see that computers are taking our jobs. In a few years, robots will take more than 15% of our current jobs. It teaches us about the importance of math. So why is math important? It’s not too complicated. We use math everyday. For example, we use math when crossing the road, cooking, telling the time, and many more.
It’s possible to live our lives with basic addition, subtraction, and multiplication. Moreover, computers can do more than simple arithmetic. Engineers created the technologies that are taking our jobs. Math is important because if we can’t do what computers can’t do, then we can kiss our jobs goodbye. We can fix it by learning higher math. Students must come together, and we must decide why math is important for our lives.
As college students, we’re expected to have mastered high school math standards. Moreover, some of us had mathematical difficulties in high school.
That’s not a problem because we’re teachable. Brain scan has shown us that the brain can be regrown. It can be regrown through games, food, reading etc. Some of us enrolled in degrees such as nursing, art, math, etc.
All of us in this degree are expected to take math. We all have different reasons for enrolling in math requirement courses, so there’s no need to drop our degrees. It is necessary to understand that everyone has trouble in math, and our teachers had problems in math.
Therefore, we can improve our weaknesses in math by knowing our technological aid, our educational background, and our classroom environments.
Firstly, technological aid are technologies that assist students to learn and help teachers to teach easier. This includes calculators, math multimedia programs, and electronic boards, etc. Mymathlab is a popular technological aid at our school. It’s excellent because it educates students both in class and at home.
It is a sufficient condition because it takes us through the hard problems and provides answers with suitable explanations. According to Abbas Johari, “inductive multimedia programs help students understand math better”. Mr. Johari expanded on a study of multimedia programs using graph and word problems to educate 98 undergraduate students of a large southwest college who were enrolled in a computer literacy course. The research was successful. Because by the end of the research, students showed high improvement in their grades.
The problem is that MyMathLab prevails in spatial learning than in kinesthetic (hands-on learning), auditory (Listening learning), and linguistic(language learning). However, some of us learn differently, and some of us abuse the program because we copy and paste answers. Some researchers believe that students’ performance in math depends on the mathematics curriculum.
According to John K Alsup and Mark J. Sprigler, the ” traditional method(Houghton-Mifflin) showed positive results than the reform method (Cord Applied). The traditional method is based on non-reality problems, but the reform method is based on real problems. It depends on the teachers who teach it. There were about 335 eighth-graders in western United State from different areas that participated in this research. They did it by comparing SAT results of students from both curriculums.
It makes sense because schools such as Harvard University, M.I.T, and UMUC use different math curriculums. Because if schools used the same math curriculum, it wouldn’t make sense to pay high tuition for Harvard. Instead, we can pay less for UMUC and achieve equivalent knowledge.
Mymathlab is part of our curriculum that is given to us by our schools. If we know the program isn’t sufficient, then we should tell the school board. We need to take responsibility for our failures and do better.
Secondly, Educational background refers to our family’s educational values, our learning styles, and our understanding of math. If we know our educational background, then it prepares us for our careers. It is not late to prepare our mindset. Because it reveals our strengths and our weaknesses in math, it gives us the opportunity to grow our weaknesses.
It is a necessary condition that helps us keep track of the lesson. If our parents have a high educational value, then they can help us in math. It helps us know our learning styles. It facilitates learning to the best of our understanding, and it will lead us to do better in math. Knowing all of this can exponentially increase our understanding and performance in mathematics.
Moreover, some of us are doing well without the knowledge of our educational background. So why does it matter? Some of us have tried it so many times and gave up on it. It is not surprising, math is hard. Some of us have math learning disabilities. The ability of low understanding in math. According to Emmanuel Manalo, Julie K. Bunnell, and Jennifer A. Stillman, “Students with math learning disabilities can improve highly through process mnemonics”.
They conducted a study with 13-14-year old’s, and they were distributed to various groups. Two Experiments were conducted to test Process mnemonics, no instruction, and demonstration imitation. They used different variables. Process mnemonics are using techniques such as rhymes to remember things. Demonstration imitation is the modeling of what you see.
We all know it’s a challenging subject. Some of us have come far without any knowledge of our educational background; If we attain it, then we’re guaranteed to improve our current educational values in math by 5%. Some of us with learning disabilities can improve. According to John Woodward, ” Strategies of teaching facts and extensive practice drills can help develop automaticity in math”.
This study was conducted on 58 fourth graders. Some with learning disabilities, and some with no disabilities. It proves that practice drills and strategies that teachers use to teach us can improve our math understanding.
For example, the speech teacher asked Brandon and his classmates if they knew their learning styles. Since Brandon knew his learning style because his DVR-0061 teacher taught him. He was among the students who knew what she was talking about. It shows how important learning styles are.
Thirdly, the classroom environment is an important aspect of the understanding. The classroom environment includes climate, teachers, and classmates. Climate is an important fact in understanding math. Because if students are not comfortable in their environment, then they will have a hard time perceiving and processing mathematical information.
For instance, if it is hot outside and a student goes to class. He/she will expect the classroom to be cold. If the temperature in the classroom is the same as the temperature outside, then the student will have a hard time learning. Sometimes, we fail to ask our teachers questions when we don’t understand. It’s important to have a teacher that cares about math.
If teachers don’t care, then students won’t care. We don’t take into consideration that our classmates can tutor us. At times, we understand better from classmates than from our teachers.
According to Karen J. Graham and Francis Fennell, ” Successful teaching depends on teachers’ ability to make decisions based on their knowledge of mathematics, the curriculum expectations, the classroom/ school environment, and the needs of the students”. Our teachers are part of our misunderstanding. If so, why are our teachers allowed to teach us?
Because teachers are meant to teach us depending on our understanding, they are supposed to boost our self-esteem and self-concept in math. Furthermore, teachers are also responsible for everything in the classroom. It implies that teachers need to fix the temperature if it doesn’t correlate with the students in the class.
Is it right to blame our teachers for our failures and misunderstanding? If we think about it as college students, it’s our responsibility to fix our classroom environmental issues. First, we must suggest our opinions with our teachers on class environmental changes. If our teachers can’t help, then we can dress depending on the classroom temperature.
If we don’t understand, then it’s our responsibility to go and find a tutor. For instance, our schools provide us with free tutoring for every subject available. It s up to us to carry ourselves there to learn.
Improvement in mathematical skills is possible through our technological aid, educational background, and classroom environments. Mathematics is important in many ways. First, it is the foundation of the world. Because currently, robots are already taking our jobs, no one will want to employ a person if a computer is faster and better than them. Plus, they don’t need to pay for a computer. Many majors we take today require math, and we need math in our daily lives.
Computers are structured using math, but their math skills are limited. Math is a hard subject, but we can understand it by managing our tech-aides, learning background, and environments. We need to take advantage of the resources around us. Especially us in community colleges because the world does not care about who does the job.
They only want people who can get the job done and fast. We must keep practicing until we understand. Therefore, we must not give up on math under any circumstances because we have dreams to conquer.


EDX Education – Missing Number Slider
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This set is an excellent tool for children to learn number sequences, addition, subtraction, multiplication and pattern recognition. 4 Colour sliders, start from easy to advanced number arrangements, clear windowns divided into two different levels.
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Modes of calculation
The XiP application provides a few modes of calculation, the section describes the modes.
The standard Run mode perform calculations of flow/flows existing in an active canvas. Below there are simple rules of calculations in 'standard' mode.
- components are calculated step-by-step
- if there is branch-out then branch starting from edge having higher start priority is calculated first.
- if there is more than one flow (not connected with the use of flow control edge) all flows are calculated in parallel.
The Partial Run enables for the user to perform calculations of flow which starts from selected by user component. Lets consider model below:
Whether calculations are started using standard Run both flows are calculating in parallel. Suppose that the user wants to perform calculations of only one flow (e.g. one showing the ARF_stabilization_30.csml model), to do this the Partial Run can be used.
The Partial Run causes that only flow which starts from the selected component will be calculated.
The Step Run mode performs operations in the same order as standard run. The difference is that calculations of model are divided into steps. Belows there is list of rules of Step Run mode:
- one click on the Step Run button causes that one step of calculations is performed.
- whether more that one flow exist one step means calculations of one level of each flow.
- calculations can be performed in the standard mode when the user uses Resume button.


Main / Comics / Linear Representations of Finite Groups
Linear Representations of Finite Groups
It describes the correspondence, due to Frobenius, between linear representations and charac ters. This is a fundamental result, of constant use in mathematics. Buy Linear Representations of Finite Groups (Graduate Texts in Mathematics) (v. 42) on andianna.com ✓ FREE SHIPPING on qualified orders. Mathematics Subject Classification: 20Cxx. Library of Congress Cataloging in Publication Data. Serre, Jean.. Pierre. Linear representations of finite groups.
Let G be a finite group, let K be a field, and let V be a finite-dimensional vector space over K. Denote by GL(V) the group of invertible linear transformations from V to itself. A group homomorphism ρ: G → GL(V) is called a linear K-representation of G in V (or just a representation of G for short). Linear representations. Let be a –vector space and a finite group. A linear representation of a finite group is a group homomorphism. The vector space is called representation space of Often the term representation of is also used for the representation space. 14 Sep Basic notions of multilinear algebra. Exercises on Chapter 1. Chapter 2. Representations of finite groups. Linear representations.
Jean-Pierre Serre, Linear representations of finite groups. Bull. Amer. Math. Soc. 84 (), no. 5, andianna.com In general, if G is a finite group, the number h of irreducible characters of G is equal to the number of conjugacy classes of G. This essentially. 14 Dec 2 Linear group representations. Example; Irreducible representations. 1 Example. Matrix representations. 3 Schur's lemma. Linear Representations of Finite Groups has 22 ratings and 2 reviews. Pietro said : Extremely elegant proofs and logical structure. Lacks intuition a bit. Buy a cheap copy of Linear Representations of Finite Groups book by Jean- Pierre Serre. This book consists of three parts, rather different in level and purpose.
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Area students compete in Math Masters challenge
MARSHALL — It’s all a matter of numbers. Representing 15 schools from around the area, 40 teams, comprised of 20 fifth-graders and 21 sixth-graders, competed individually and as teams on eight sets of mathematical problems in the competition.
Two hundred and five students from southwest Minnesota competed Thursday afternoon in the annual Math Masters competition at Southwest Minnesota State University.
“Math Masters was a challenge, but I got through it and it was fun,” said Katelynn Jensen, a sixth-grader at Tracy Area Public School.
Dr. Heather Moreland, an SMSU mathematics professor who was the site coordinator for the event, said the students were excited for the day.
“They’re really gung ho,” she said. “It’s fun for them to come to a college. It’s cool to see them cheer for each other.”
Moreland said the event was a day to promote math.
“It’s to get students excited about math, not be phobic,” she said.
It doesn’t hurt that a possible side effect would be to promote SMSU.
“They can see SMSU as part of their future,” she said. “They can remember this great thing.”
The conference center at SMSU is a great location, Moreland said, large enough so the fifth and sixth grade can be combined.
“It’s nice for teachers not to have to go to different sites,” she said.
Amanda Zeug, the Tracy fifth- and sixth-grade math teacher, said students have been practicing for the competition since January.
“Math Masters is a good opportunity for students to practice their problem solving skills and work as team,” she said.
SMSU math professor Dr. Wije Wijesiri, was the master of ceremonies for the event. The students started out with a fact drill, then individual rounds, then team rounds.
Tracy sixth-grader Alex Munson said an example of one of the easier individual problems is “what is the sum of prime numbers up to 30?”
Moreland said the college’s food service provider, Chartwells, had healthful snacks on hand for the breaks between tests — water, bananas and pretzels.
Statewide sponsors include The Hormel Foundation and IBM.


JULIE LANE PHOTO Todd Gulluscio was granted tenure by the Board of Education Monday night.
There will be changes to Shelter Island’s summer school program that previously offered separate sessions for literacy and math.
Academic Administrator Jennifer Rylott told members of the Board of Education Monday night that the combined sessions would add hours of instruction to the program that runs from July 5 to July 28.
Classes are scheduled from 8 to 10 a.m. weekdays, except Friday. An hour and 10 minutes will be devoted to English language arts and 45 minutes to math. (more…)
JULIE LANE PHOTO
Young ‘architects’ in Michael Cox’s fifth grade class show off their projects that demonstrated not only creativity, but mathematics. They are (from left) Jerry Card, Riley Renault, Emmett Cummings and Olivia Overstreet. Parents view the projects and hear from the today between 1:15 and 2:30.
You can memorize times tables and various mathematical formulas, but fourth and fifth grade math and science teacher Michael Cox thought there must be a better way. (more…)


Overview of Mathematics in Witton-le-Wear Primary School
The teaching of Mathematics in Witton-le-Wear Primary School is a clear, whole-school vision of teaching, learning and assessment that promotes high expectations and consistency from EYFS to KS2 and beyond. We believe that everyone can do maths, through taking small steps in our mathematical journey and working hard – every child can succeed at maths.
In Early Years, children start to develop their understanding of number while utilising their everyday surroundings and its mathematical meaning. Carefully designed activities are provided through continuous play to enhance the children’s classroom-based learning. Number Blocks, White Rose resources and concrete manipulatives are all used to enhance maths in EYFS.
From Year 1 onwards, mathematics is taught daily. This incorporates a discrete arithmetic session as well as a mathematics lesson. Arithmetic sessions allow children to practise recently learned number skills as well as to revisit previous objectives. Time is given to allow for mathematical discussion and links are made clear.
Mathematics is taught in progressive short blocks which are pedagogically sound sequences of lessons to ensure consistent mastery progression for each mixed-age class.
Short teaching blocks provide a loose spiral curriculum, allowing children to revisit each topic within a fairly short time span. This ensures that children’s confidence is boosted by regular encounters with a specific skill or concept and, in turn, aiming to reduce the need for re-teaching.
Each short block states the main daily focus of teaching as well as the outcomes for each day. Medium term plans include links to suitable weekly mathematical investigations.
Daily lessons consist of whole-class teaching where children are taught and brought along together in short, sharp bursts (ping-pong style). They are given opportunities for mathematical talk where they are encouraged to use correct mathematical terms in their discussion and reasoning. Concrete, pictorial and abstract representations are used to support main teaching as well as independent work. Children work independently, in pairs, groups or in teacher-led groups, on mathematical activities to develop their skills, knowledge of concepts and their reasoning abilities.
Daily lessons underpin children’s conceptual understanding through the development of a consistent set of images and models; they engender procedural fluency, and provide frequent opportunities for reasoning and problem-solving. Extra support and interventions are given the same-day/next-day to pupils individually as well as in groups, to address misconceptions and to strengthen conceptual knowledge. Problem solving and reasoning questions allow the assessment of children’s understanding of the unit’s objectives and whether they have fully integrated the skill or concept into their understanding.
Our curriculum is complemented by White Rose through the use of Concrete to Pictorial to Abstract, which underpins our approach to calculation, as well as that of the Maths Hubs and White Rose. A developmental approach to models and images, provides consistency and enables children to progress from concrete experiences through to visual and finally abstract understanding.
Promoting consistency in mathematical models and images within the framework of our whole-school calculation strategy, strengthens pupil’s own learning and assessment practice in maths.
By having a clear and consistent curriculum strategy throughout the school, our teachers can ensure that children are hearing consistent language and using progressive methods that build from one year to the next, without requiring them to confront new pedagogy at every year or key stage transition. All teachers aim to work progressively using complementary and pedagogically sequential language, models and images.
The Calculation Methods document sets out methods of mental and written methods for addition, subtraction, multiplication and division from Year 1 through to Year 6. Articulated for each year group, these methods ensure consistency of teacher input and progression in pupil learning as well as a framework to help parents and carers, when supporting their child/children, in maths. They include the steps that children need to take to master these four operations. The Calculation Methods document shows progression in calculation methods from Year 1 to Year 6. By ensuring that the language is pedagogically correct, the strategy helps teachers promote understanding in Key Stage 1, while laying the correct building blocks for understanding with greater sophistication in Key Stage 2.
The addition and subtraction methods cover place value and models mental and written addition and subtraction methods from Year 1 through to Year 6. Counting on, counting up, number facts and compact and expanded column addition are progressively described and illustrated.
The multiplication and division methods cover mental and written multiplication and division methods from Year 1 through to Year 6. Clever counting, grouping, doubling and halving, grid multiplication and short and long written division are progressively described and illustrated.
Pairs of operations are presented as complementary functions that facilitate explanation and comprehension.
Visual representations, produced through White Rose, also complement daily teaching and learning.


Positively impacting the future, one day at a time...
Whew what a busy week! This week we have studied Herpetology, World War II and reviewed sentence parts. In Math, Group B has worked with fractions and common denominators and Group A learned to solve equations with variables of all types. In addition, we wrote in our journals three times based on different prompts, including one about Martin Luther King Jr.
Math games with Group B!
Future Problem-Solving Skit!
Thanks for taking time to read the latest entry in the Bluejays' Journal!
As always, feel free to email us with any questions, concerns, or even requests for this newsletter!
If you haven’t already… click the link below and join the Classroom’s Facebook Group to get updates even quicker!


This plugin performs simple operations such as add, subtract, divide, and multiply. Arguments of those operations may be values from payload, profile, etc. The result is returned as an object of new values.
Each operation must be in separate row. Operations may share variables.
This calculation will divide the value from profile that is located in traits.private.interests.sports by the number provided in payload (time_passed). Value of time_passed can be a time that passed from the last visit. The above equation will return the following result.
Example 2 - variables
This simple calculation assigns value to variable decay_rate. Then uses this value to compute result.value. This equation will return the following result.
This way you can construct object that have different values that are calculated and assigned to variables. Of course the variable ca be assigned to profile, session, etc. This is the last example with variable result.value assigned to email@example.com
Calculations may have several operations.
The result of this calculation is:
Each number can be replaced by variable or a field from profile, event, etc.
The result of this operation is:
And the event@counter equals 1.


Can the performance of a message-oriented system be improved by adding periods of idle execution?
A period of time required for the scheduler to switch the CPU from one actor to another.
Spinning before a context switch potentially improves performance.
But not always.
An actor should delay the context switch only if it is likely that a message will arrive.
1. When should an actor spin?
2. How long should an actor spin?
There exists a simple upper bound.
d (delay) < c (context switch)
How to pick a delay in [0, c>?
Assume that P is the probability that a message arrives after some time d.
The actor also needs to occasionally sample P, i.e. spin several times to determine P.
We will assume that the actor samples with some probability φ.
Conclusion: given a probability p that a message arrives after δ, an actor should delay the context switch if:
δ < p
Before the context switch:
1. With probability φ << 1, spin c time.
2. Record the message arrival times ti.
3. After collecting N samples, group the delay times into M buckets, and report the pairs δi, pi.
Before a context switch:
1. Take the last reported M pairs δi, pi.
2. Pick the pair with minimal δi - pi.
3. If the difference is positive, wait δi time before context switching.
For 95% confidence that the sampled probability P lies within 15% of its true value, we need n = 43.
For a sampling probability φ = 0.01, the expected number of activations per actor is ~4300.
But, actors are short-lived.
In many applications, most actors are not activated 4300 times.
How to obtain a sample more quickly?
Always set the sampling frequency φ to a value proportionate to the running best probability pi.
Intuition: If the message arrival probability P is high, then more frequent sampling is not detrimental.
I.e. an actor spends more time sampling, but it is likely that messages will arrive during sampling, saving a context switch.
If the message arrival probability P is low, then less frequent sampling is not detrimental.
I.e. it might take a long time to collect the sample, but it's unlikely that it will help anyway.
Initially, set the sampling frequency to some small value φ0. After each sampling, set the frequency to:
Expected number of messages before obtaining a sample:
Lower bound on speedup:
Shams and Sarkar, AGERE 2014
Fork Join Throughput
Use a spacebar or arrow keys to navigate


Sudoku 9x9 1.05
Game with 9x9 grid and goal of filling empty cells with numbers between 1 and 9
|Minimum OS:||macOS 10.9.0|
|Vendor Name:||Sylvain Becker|
Version History 1.05
- Fix TouchPad issue
Sudoku is played with 9x9 grid, divided into 3x3 subgrids called 'regions'.
The object is to fill empty cells with numbers between 1 and 9, so that number should appear only once on each row, column and region.
- unlimited Undos
- mode Easy, Normal, Difficult, Nightmare


Kellstadt Graduate School of Business
Students should have sufficient knowledge in calculus, statistics, and mathematical sciences to enter the program. If students need to acquire these skills one or more of the following courses will be required: GSB 420; MAT 135; MAT 137.
Students complete the MS in Marketing Analysis by taking seven required courses and five elective courses for a total of 12 courses.
Students are to select two additional courses from marketing electives and three courses from the Analytical Group for a total of five courses from the following list of approved electives. Please note that approved electives may have prerequisites that are not part of the MSMA curriculum and will not be waived.
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As a parent or caregiver, you want to provide the best possible start for your child’s development. Two key areas that are essential for young children to develop are number sense and spatial thinking. These are the building blocks for future success in math and science, and can help children with a range of cognitive tasks. Here are some strategies that you can use to help your child develop their number sense and spatial thinking.
Number sense is the ability to understand and work with numbers. It involves concepts such as counting, comparing, and recognizing patterns. Developing number sense is important for children as it provides a foundation for future math skills. Here are some ways that you can help your child develop their number sense:
Counting is one of the most basic math skills and is an essential component of number sense. To help your child develop their counting skills, start with counting games and songs. You can count objects around the house or in nature, and encourage your child to count with you. You can also play counting games like “I Spy” or “Counting in the car”. These simple activities can help children become comfortable with counting and develop their number sense.
2. Number Recognition
Number recognition is the ability to identify numbers and understand their value. You can help your child develop this skill by pointing out numbers in everyday life, such as on signs, clocks, and calendars. You can also use number flashcards to help your child recognize numbers and their values.
3. Comparing Numbers
Comparing numbers is an important part of number sense, and involves understanding concepts like “more than” and “less than”. You can help your child develop this skill by using everyday objects to demonstrate the concept. For example, you could give your child two snacks and ask them which one has more. You could also use number cards to help your child compare numbers.
Recognizing patterns is an important part of number sense and is useful for predicting future numbers. You can help your child develop this skill by pointing out patterns in everyday life, such as the pattern on a shirt or the sequence of numbers on a calendar. You can also use pattern blocks or tiles to help your child create and recognize patterns.
Spatial thinking is the ability to understand and work with spatial relationships. It involves concepts such as shapes, directions, and spatial reasoning. Developing spatial thinking is important for children as it provides a foundation for future success in math, science, and engineering. Here are some ways that you can help your child develop their spatial thinking skills:
Shapes are a fundamental part of spatial thinking and can help children understand spatial relationships. You can help your child develop their shape recognition skills by using shape toys, such as blocks or puzzles. You can also point out shapes in everyday life, such as the shape of a stop sign or the shape of a plate.
Understanding directions is an important part of spatial thinking, and involves concepts like up/down, left/right, and forward/backward. You can help your child develop this skill by playing direction games, such as “Simon Says” or “Follow the Leader”. You can also use a compass or map to help your child understand directional concepts.
3. Spatial Reasoning
Spatial reasoning is the ability to understand and manipulate objects in space. It involves concepts like rotation, reflection, and symmetry. You can help your child develop their spatial reasoning skills by using shape toys, such as tangrams or pattern blocks. You can also encourage your child to build structures with blocks or Legos, which can help them develop their spatial reasoning skills.
Visualization is an important part of spatial thinking and involves the ability to imagine objects and spatial relationships in your mind. You
can help your child develop their visualization skills by encouraging them to draw pictures and create their own designs. You can also play games that involve visualizing objects in your mind, such as “I Spy” or “Memory”.
5. Spatial Language
Using spatial language is an important part of developing spatial thinking. This involves using words like “above”, “below”, “next to”, and “inside” to describe spatial relationships. You can help your child develop their spatial language skills by using these words in everyday conversation and asking them to describe the spatial relationships between objects.
Tips for Helping Your Child
Here are some tips for helping your child develop their number sense and spatial thinking skills:
- Keep it fun and engaging: Children learn best when they are having fun. Use games, songs, and toys to make learning these skills enjoyable.
- Be patient: Learning these skills takes time and practice. Be patient and encourage your child to keep trying.
- Use everyday objects: Use objects from around the house or in nature to help your child develop their skills. For example, use leaves to help your child count or sticks to help them create patterns.
- Use technology: There are many apps and websites that can help children develop their number sense and spatial thinking skills. Use these resources to supplement your child’s learning.
- Encourage exploration: Encourage your child to explore their environment and ask questions. This can help them develop their curiosity and critical thinking skills.
- Model problem-solving: Model problem-solving skills for your child by talking through problems and coming up with solutions together.
Developing number sense and spatial thinking skills are important for children as they provide a foundation for future success in math, science, and engineering. As a parent or caregiver, you can help your child develop these skills by using games, toys, and everyday objects to make learning fun and engaging. With patience, practice, and exploration, your child can develop these essential skills and become a confident learner.
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Chaotic Fishponds And Mirror Universes
Earn 8 loyalty points, worth £0.16, with this purchase.
If you thought mathematics was scary in school, this book is for you.
From the mathematical model for making a fortune to how Einstein helps you find your way around, this book explains the weird world of mathematics is far more familiar than you thought
Format Paperback | 368 pages
Dimensions 128 x 196 x 28mm | 339.99g
Publication date 26 Jul 2016
Publisher Quercus Publishing
Publication City/Country London, United Kingdom


Maths and physics isn't everything in life, autistics often understand maths and physics perfectly but they are still retarded losers.In my experience even the lower socioeconomic scale East Asian children (like middle to high school age) have an extraordinarily consistent and firm grasp of the in-depth mechanics of university-level physics and math that far exceeds many American college and graduate students who aren't in a hard-science field or engineering. And the East Asian peasants didn't have fancy graphing calculators or Wolfram Alpha with which to check their work until the last few years.
Even more remarkably is that they retain that proficiency through much of their life, unlike Americans. I know in the American academic culture, once final exams are over, you kind of chuck it out of your mind unless there's a recurring career-type need for you to use it.
But I will be regularly bumping into some elderly East Asian people who last sat in a math or physics class more than 50 years ago and learned by chalkboard and slide rule and had no major career-pressure to keep up with it, yet they have a better working knowledge of theory and practice of just about every mathematical or physics topic than I, who am only a few years removed from the last math or physics course!
For me, math and physics is just the most readily available example on account of how poorly I retain it and how often am forced to relearn it, but it holds true for many other disciplines and subjects, I'm sure


by student writer Chloe Puryear
Assistant principal Mrs. Joye Phipps wanted to bring more color to Dogwood, so she wrote a grant with teachers. That grant resulted in four different murals that now decorate the walls of the school. With the murals in the halls, the one by Mrs. Phipp’s room intrigued math teacher Mr. Lewie Carmichael the most.Then the idea to use the wall as a learning experience came to his mind.
In 4th grade, Mr.Carmichael’s class used the mural beside Mrs.Phipps' room to see what angles they could find. Mr. Carmichael’s students had a lot of fun, “even if it was just a short trip down the hall,” Carmichael said. “I loved getting out of the room and having a walk around the school.”
The unit in math that they had been working on was angles. The class brought the protractors with them and started finding the angles, using creativity in math. “I enjoyed making my own angles and measuring them,” said fourth grader Hadley Lawrence. “Sometimes we would work in groups and other times we would compare answers.”
“I liked being able to measure them (angles) on the lockers, so I could measure them on paper,” said fourth grader Ben Pressler. “It helped us practice. I think it was fun because we could look at it with our own eyes instead of just with a protractor.”
The angle project would not have been possible without the grant. “I think my favorite part of this project was working with a small group of teachers to decide on the different designs for the walls,” Mrs. Phipps said. “I think the most valuable thing I learned from this whole thing is that there are many creative ways to add to and brighten up an old building.”
Those brighter walls helped the students practice necessary skills.


** Warning! Bit of an ultra-long-brain-required-halfway-through post. **
‘Crazy girl!’ I hear you exclaim. I concur.
If you’ve checked out my Ravelry profile, you’ll see I’m a bit more mad than that with six blanket projects in my works at the moment. But I made a hard decision to focus on only three. They are:
- The Star Anise Blanket
- Blanket Polka
- Blanket Scrabble
I’ve made a move on Blanket Scrabble. After working out what the plan was going to be two weeks ago, it was time to get started on the math. Here’s how I’ve worked it:
First we (me, myself and I) need to understand what the finished blanket is going to be. Cue graphic:
I’ve decided on the parameters for the yarn: It needs to be 8 ply, DK weight. It needs to be soft on the skin and last a lifetime, so no pure wools or acrylics. It needs to come in a range of colours so I’m able to buy the right ones! It also needs to be cost effective… If you’ve never made a blanket before (like me) you’ll know why soon!
I bought some great cashmere yarn from the craft department store, but it has a limited colour range and is being discontinued. However, it does meet all my requirements, so it will be a great sample yarn to work out the numbers. Speaking of which, we’ll need to know it was 100 meters in a 50 gram ball.
Count ’em in the plan, that’s 225 squares. It’s important that we choose the right kind of square. I want them to be the same all over the blanket so the centre of each square needs to be some kind of star, as an actual Scrabble board has a black star in the middle. I searched on Ravelry and the interwebs, through magazines to no avail. So I tried making a variation of the hexagon I’m using in the Star Anise Blanket and – success! I am happy.
I first tried with a 4mm hook, but since our squares need to be about 13cm x 13cm it was too small and a little tight. Upping the hook to 5mm made it the right size and floppiness!
Just a warning, if you’re not mathematically inclined and reading this with your morning coffee/after work/winding down for bed, this post ceases to be ‘easy-reading’ after this next heading…
Necessary evil in my view. So let’s get started.
We already know we need 225 squares, but how many of each colour? Count ’em:
- 8 Red
- 16 Pink
- 12 Dark blue
- 24 Light blue
- 164 Beige
- 1 Pink with black star
So! Back to the sample square, I unravel it 😦 ! and discover it takes 18.4m of yarn to make one.
And now for math…
With 100 meters in our sample ball, we can make about 5 and a bit squares with one ball (100m ÷ 18.4m = 5.4 squares). But we’ll get more accurate numbers with another calculation:
|No. of Balls
|No. of Balls
||8 × 18.4m =
||147.2m × 100m =
||2 + 1**
||17 × 18.4m =
||312.8m × 100m =
||4 + 1**
||12 × 18.4m =
||220.8m × 100m =
||3 + 1**
||24 × 18.4m =
||441.6m × 100m =
||5 + 1**
||164 × 18.4m =
||3017.6m × 100m =
||31 + 2**
* For making sure we have enough, we’ll include the pink and black star square in with the pinks!
** Just to be sure, add an extra ball or two! It would be awful to run out so close to the end, and the Stash needs to be cared for! 😀
Awesome! Now we have the first part of our shopping list, but there’s still the white yarn to work out, the yarn to join of the squares and add the border…
This one is different, we don’t have a square to unravel. But we do know that all the squares are going to be joined by a tr crochet. So how much thread do we use for one tr? Let’s make a stitch, mark the end with a pen. Unravel one stitch, mark the start with a pen. Measure between the two dots and… My tr stitch is 12cm!
Next question, how many stitches join one side of a square? We can count them with the picture, and I see 20 stitches. Right-o, how many stitches can we get out of a ball? A rude estimation of 830 stitches! (100m ÷ 0.12m = 833.3333333 stitches).
Now this is where my mind really started to wander, but stick with me…
We need 225 squares and each square has 4 sides; That’s 900 sides of squares (225 squares × 4 sides = 900 sides). But as we’ll be joining 2 sides of two squares, we’ll only stitch half that: 450 sides (900 sides ÷ 2 = 450 sides). Now, if 1 side takes 20 stitches, we’ll make 9000 stitches to join 225 squares (450 sides × 20 stitches = 9000 stitches). Excitement! So with a rude 830 stitches to a ball, we can say that we’ll need 11 balls! (9000 stitches ÷ 833.3333333 stitches = 10.8 balls, round it up to the nearest whole number!).
Finally, we work out the border. There are 15 squares along each side of the blanket. Each of those squares will be edged with 20 stitches, so along one side of the blanket there will be 300 stitches. (15 squares × 20 stitches = 300 stitches). 4 sides to the blanket; 1200 stitches (300 stitches × 4 sides of blanket = 1200 stitches). I want two rounds of tr on the border, so we’ll times this by two to get 2400 stitches (1200 stitches × 2 rounds = 2400 stitches). Again with the rude estimate of stitches to a ball, we can say 3 balls to do the border! (2400 stitches ÷ 833.3333333 stitches = 2.88 balls, round it up to the nearest whole number!).
This is where the brain protests and says ‘STOP! NO MORE MATH!’ So let’s say we want to add a final round of single crochet egding with picots or something, and chuck in another 2 balls and say that will be heaps.
Argh! So finally we can write the shopping list!
Climatic music with drum roll please…
- 3 Red 50g DK weight balls
- 5 Pink 50g DK weight balls
- 4 Dark Blue 50g DK weight balls
- 6 Light Blue 50g DK weight balls
- 33 Beige 50g DK weight balls
- 18 White 50g DK weight balls***
- 1 Black 50g DK weight ball
*** Yep. Throwin’ in two more for that Safe/Stash position!
Total 70 balls of yarn!! Dude this blanket better be loved. Now you see why it must be cost effective! I would not attempt this at $12.99 a ball on my current budget, if ever!!
After all this numberin’, A quick phone call to a known knitter made the helpful suggestion of working out how much it will weigh. In her experience, she said, it’s no good making up a jumper if no-one can lift their arms in it. So one last easy-peasy calculation: The finished blanket would weigh about 3.5 kg! ((50g × 70 balls) × 1000g = 3.5kg). An acceptable weight for a blanket methinks.
Armed with a shopping list, it’s now time to seriously consider what yarns to buy. I know the Internet is full of beautiful yarns, but I’m a beginner and new to this wonderful world of yarn so I need my purchase to be made in person. I need to know the yarn feels right before I fork out for 70 balls of it! This is going to be some hunt! More Country Drives!!
I really do feel like I’m getting somewhere with this blanket – And I hope my math and blanket calculations assist with that old
‘How long is a piece of string’ ‘How much yarn do I need for a blanket’ question. That said, if you’re better at math than me and notice something awry with my calulations above, please let me know! 😀
Oh my goodness! Now with all that math done, I’m going back to a freeform project for a while!
Stay creative 😀


Geogebra software download for windows 10
Click here to Download
However, if you already are experienced and usually deal with arithmetic, geometry, algebra, and calculus on a regular basis, it is very flexible to utilize.
- Download GeoGebra for Windows |
Free digital tools for class activities, graphing, geometry, collaborative whiteboard and more. GeoGebra, free and safe download. GeoGebra latest version: Flexible and free mathematical software. GeoGebra is a complex but all-in-one application p.


Maths is easy. Sounds like an oxymoron, right? Well it is not. Maths is indeed easy!
Think about those three words for a minute…Maths is easy.
The Bible says as a man thinks, so is he.
You see, when I was but a little girl, probably 6 or thereabouts, I remember my dad telling my brother and I those 3 words. Before fear of Maths could set in, or I could be influenced by the ‘masses’ who believed the opposite, it had been drummed into me.
And because I developed that mindset from the cradle (more or less), Maths became my favourite subject, (and my brother’s too!). I had a good attitude towards Maths, enjoyed Maths and therefore found it easy.
I was A* all the way in my education where Maths was concerned, expected to win and did win a prize every blessed year in Maths from primary to secondary school. However, perhaps over confidence earned me a B in Maths A’ levels 😦
(Long story…but I cried, wept, howled and wailed when I got those results…especially being that I had coached all my friends…who ALL ended up with an A!!).
Anyway, lets not go further on that painful reminder :-), but you need to let your children learn to LOVE Maths. I never took any extra tuition for Maths till my second year of A’ Levels (although before that time, my dad would coach me at home when I got stuck).
I am a firm believer that imbibing in your children a positive mindset about their approach to Maths is half the battle won. So get telling your children that Maths is easy! After all, they have a sound mind.
I love Maths so much; so much that I momentarily considered doing a degree in it. But I thought if I did my option would be to end up as a teacher if I did…!
But then life can throw you a few curved balls, huh? Hmm…nuff said!!!


Image sampling described in (6.86) refers to the acquisition of samples at a point (also known as impulse sampling). Consider a finite-aperture image sampling in which
(a) Express sfa[m, n] in terms of s[m, n] and sc(x, y).
(b) Determine the 2D Fourier transform of sfa[m, n] in terms of 2D continuous Fourier transform of sc(x, y). Compare it with that of s[m, n].
(c) Based on your results in part (b) above, comment on the visual quality of finiteaperture sampling in terms of resolution-loss versus aliasing trade-off.