MathEdge is an educational program focusing on the problem-solving skills that lead
students to success in both academics and the real world. It taps into intellectual
curiosity and helps foster the mathematic potential of your child.
More importantly, though, MathEdge gives students confidence and the skills to tackle
any type of problem, academic or otherwise. Problem solving is what math is all about.
As one discovers how to solve problems one previously thought were impossible, he/she
would apply the same calm thought process to all of life's problems!
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Huang,, Grace Huang, Kevin Chen, Andrew Xu, Yick Cheung(Coach)


Lloyd Shapley (2 June 1923 – 12 March 2016) was an American mathematician and economist. In 2012, he was jointly awarded the Nobel Prize in Economic Sciences.
Life and Career
He was born on 2 June 1923, in Cambridge, Massachusetts. He completed his undergraduate studies at Harvard University, where he developed a strong interest in mathematics. He then pursued his graduate studies at Princeton University, earning his Ph.D. in mathematics in 1953. During his time at Princeton, Shapley worked under the supervision of Albert W. Tucker, a prominent mathematician who introduced him to the field of game theory.
His work primarily focused on game theory and cooperative game theory. He made significant contributions to these fields, developing innovative concepts and models that have had a profound impact on various disciplines, including economics, mathematics, and computer science.
One of Shapley’s most notable contributions is the development of the Shapley value. This concept provides a method for fairly distributing the payoff or rewards of a cooperative game among its players. The Shapley value takes into account the contribution of each player and the different possible ways in which coalitions can be formed within the game. It has proven to be a fundamental tool in analyzing and understanding cooperative behavior.
Shapley also worked on the study of matching markets, particularly the stable matching problem. He collaborated with David Gale to propose the Gale-Shapley algorithm, also known as the deferred acceptance algorithm. This algorithm provides an efficient way to solve the stable matching problem, where agents with preferences need to be optimally paired with each other based on their preferences.
In addition to his theoretical contributions, Shapley also applied his research to real-world applications. He worked at the RAND Corporation, where he applied game theory to analyze strategic decision-making and cooperative behavior in various contexts, including military and economic settings.
He died on 12 March 2016, in Tucson, Arizona.
Award and Legacy
In 2012, he was jointly awarded the Nobel Prize in Economic Sciences, along with Alvin E. Roth, for their contributions to the theory of stable allocations and the practice of market design.
His contributions continue to influence the fields of mathematics, economics, and game theory. His work has provided fundamental insights into the analysis of strategic decision-making, cooperative behavior, and fair distribution mechanisms. Shapley’s legacy remains an inspiration for current and future generations of researchers in these areas.


Literacy, numeracy and digital competence are skills that should be found across the curriculum and in all areas of learning. These are a range of skills that are essential for learning and for pupils to be able to participate successfully in every day life.
Priority has already been given to literacy and numeracy within the Welsh curriculum through the LNF. Digital competence is increasingly fundamental to learning and life and now shares similar status within the curriculum to that of literacy and numeracy. Pupils should have frequent opportunities to develop, extend and apply these skills across the curriculum.
The literacy part of the LNF is organised into:
The Maths part of the LNF is organised into:
- Developing mathematical proficiency
- Understanding the number system
- Learning about geometry
- Learning that statistics represent data and probability models chance
The DCF is organised into:
- Interacting and collaborating
- Data and computational thinking


SUDOKU BOARD: This wooden Sudoku board is 11.11 x 11.11 x 1.77 inches with two sliding drawers for storage of pieces. Our classic wooden set is versatile because any Sudoku puzzle can be played on it.
PLAYING PIECES: Includes 90 large number pieces and 90 thinking pieces. Each is crafted from natural wood and made to withstand years of play. Includes starter puzzles, history of sudoku and game directions.
GREAT GIFT: Looking to give a unique and thoughtful gift this holiday season? Sudoku helps reinforce basic math skills for people of all ages.
GOOD FOR YOU: Did you know that playing board games can teach important social skills like verbal communication, being patient, sharing, taking turns and enjoying interactions with others? Games like Sudoku foster the ability to focus and lengthens the players attention span. Playing games is an easy and excellent way to spend unhurried, enjoyable time together.


Title: The Elusive Royal Flush: Unraveling the Odds in a 9-Handed Game of Hold'em Poker Meta Description: Discover the expert analysis of the odds surrounding the mythical royal flush in a 9-handed Texas Hold'em poker game in the US. Delve into the probabilities, strategies, and the thrill of pursuing this coveted hand. Introduction: In the vast and exciting world of poker, few hands are as coveted as the royal flush. Representing the pinnacle of success, a royal flush consists of the Ace, King, Queen, Jack, and Ten of the same suit. While the prospect of being dealt such a hand may seem like a distant dream, understanding the odds can provide insight into the rarity and thrill of this remarkable occurrence. In this expert review, we will explore the odds of receiving a royal flush in a 9-handed game of Hold'em poker in the United States. Calculating the Odds: To determine the probability of being dealt a royal flush, we must first understand the number of possible combinations in a standard 52-card deck. With four suits and thirteen ranks, the deck contains a total of 2,598,960 different five-card combinations. The odds of obtaining a royal flush are determined by relating the specific combination we
What are the odds of getting royal flush
Title: The Royal Flush: What Are the Odds of Hitting the Jackpot? Hey there, card game enthusiasts and fellow risk-takers! Today, we're diving into the thrilling world of poker to explore the ever-elusive Royal Flush. So, grab your favorite deck of cards and let's shuffle our way through the mesmerizing mathematics behind this rare and exhilarating hand. What are the odds of getting a Royal Flush? Buckle up, and let's find out! For those not yet acquainted with this illustrious combo, a Royal Flush is the crème de la crème of poker hands. It consists of the ten, jack, queen, king, and ace of the same suit. Picture yourself holding that magical hand, and imagine the excitement of revealing it to your opponents. Are you ready for the adrenaline rush? In the vast universe of poker possibilities, the odds of getting a Royal Flush are quite slim. But don't let that discourage you; remember, fortune favors the bold! Statistically speaking, the chances of achieving this holy grail of hands are roughly 1 in 649,740. Yep, you read that right. It's as rare as finding a four-leaf clover in a field of daisies! To put those odds
How often do you flop a royal flush?
Originally Answered: In poker, what are the odds of making a royal flush after the flop in Texas Hold 'Em? With five cards, there are 52C5 = 2,598,960 possible hands. Four of those are royal flushes. So the probability is 4 / 2,598,960 or 1 in 649,740.
What are the odds of hitting a royal flush?
As above. The royal flush is a case of the straight flush. It can be formed 4 ways (one for each suit), giving it a probability of 0.000154% and odds of 649,739 : 1.
What are the odds of flopping a straight flush?
Odds of Making a Straight Flush on the Flop We specifically need to start out with two suited connected cards for this to be possible. The odds of flopping a Straight Flush are so unlikely (0.02% or less) that the majority of poker equity calculators don't even show the precise odds.
How often does AK hit the flop?
Of course, AK won't hit the flop every time…in fact it misses the flop on average 2/3 of the time. This is very standard for hands with unpaired broadway cards, so knowing how to play when the hand misses the flop is crucial. But even when AK misses the flop it still usually has some equity.


Whenever you take out a home, car or personal loan; your repayments are separately servicing interest and principal repayment. The CUMIPMT and CUMPRINC functions enable you to calculate the proportion of each mortgage payment attributable to repaying the mortgage and the proportion attributable to interest servicing.
The arguments required for both functions are identical. Thus it makes sense to learn the two formulas side by side. The worked Excel example attached calculates the principal/interest repayments attributable to the first mortgage payment made on a loan, alongside the total principal/interest repayments due to be made over the entire term of the loan.
- rate – The interest rate applicable. Note that most stated interest rates are annual rates of interest with payments made monthly. The rate should therefore be entered as, for example, 2%/12. If payments were made annually, you would just utilise 2% as the interest rate.
- nper – Represents the total number of payments for the loan. For a 25 year loan with monthly repayments, you would enter 300 (i.e. 25 years * 12 months). If payments were made annually, you would enter 25.
- pv – The present value of the loan balance today (i.e. the total balance of the loan). Whilst perhaps unintuitive, this must be entered as a positive value.
- start_period – The start period for the calculation. Use 1 if you wish to start from the first period.
- end_period – The end period for the calculation. This will depend upon the ‘nper’ value you selected. In this instance, the total number of payments is 300. Therefore, to calculate total principal or interest repaid over the duration of the loan, the figure used should be 300. Alternatively, if you wish to calculate the proportions attributable to your first payment only, you can enter 1.
- type – If payments are made at the end of the period (i.e. in arrears), use type 0. If payments are made at the beginning of the period (i.e. in advance), use type 1.
Interest is higher in earlier periods
Bear in mind that due the decreasing total loan balance over time, payments made towards the start of a loan term will include a higher interest repayment than in later years. Within the example file provided, this is illustrated in the tabs ‘Payment over 25 years – annual’ and ‘Payment over 25 years – monthly’. In year 1, principal payments total £8128 and interest payments £5145. By year 10, the prinicipal repayment increases to £9729 whilst interest repayments fall to £3543.
The CUMPRINC function will return the cumulative principal paid on a loan between two periods, whilst the CUMIPMT function will return the cumulative interest.


In this module, students are introduced to spreadsheet software. They learn to enter data, text and formulas into cells. They can copy data, replicate formulas and understand that spreadsheets carry out calculations automatically. They can use spreadsheet software to create graphs or charts. They begin to understand the power of spreadsheets for modelling situations, and how data and formulas can be modified to test predictions, or to work out what happens when something is changed.
Students should be able to enter text and data into spreadsheet software to create a working spreadsheet.
Students should be able to enter simple formulas like =A1+A2. They should be able to use the SUM function to total a range of cells. (Note: This should involve creating the SUM function and not just using AutoSum from the toolbar.) They should be able to copy a formula to another location. The assessment may prescribe which formulas to put where.
Students can select a given range of data and use it to create an appropriate graph. Students give the graph a meaningful title.
In addition to the pass criteria, students can manage to change the data as instructed and make appropriate checks to make sure that their spreadsheet still works.
Students need to demonstrate an understanding of the effect of changing data and should be able to answer questions to modelled scenarios, such as: ‘If the cost goes up by … would there still be a profit?’.
At the end of this course, student will take the ICT Starters Assessment of Next Steps Stage 1 Module 3 : Exploring Spreadsheets.
Cambridge Certification is available at TWO stages.
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When a force is applied to an object connected to a pivot, it can cause the object to turn about that pivot. This process is referred to as the turning effect or moment of a force. From doors to steering wheels, the turning effect of forces helps to drive all sorts of simple and sophisticated technology that we take for granted today.
To fully comprehend the intricacies of this turning effect of forces, we have to explore the underlying concepts and calculations involved. Let’s start with the most fundamental definitions of moments themselves.
The moment of a force is a vector quantity that measures the tendency of a body to rotate about a pivot or axis. Moments can act in a clockwise or anti-clockwise direction and can cause the object to spin in the corresponding direction.
Consider the see-saw above. There are four forces acting on it, each with a different moment and direction. How then can we determine the overall turning effect? Here’s when the mathematical definition of moments comes in:
- Formula: Moment of a force = Force (N) x Perpendicular distance between the pivot and the line of action of the force (m)
- Simplified formula: Moment = F x d
- SI Unit: Newton metre (Nm)
Using this formula, we can easily deduce the magnitude and direction of each moment. From left to right, they are:
1. 7N x (2+4)m = 42Nm, Clockwise
2. 8N x 4m = 32Nm, Anti-clockwise
3. 9N x 5m = 45Nm, Clockwise
4. 10N x (3+5)m = 80Nm, Anti-clockwise
The overall turning effect can be deduced by adding up all the moments acting on the see-saw. Taking the anti-clockwise direction to be the ‘positive’ direction, the overall turning effect is 80+32-45-42 = 25Nm, Anti-clockwise.
Do note that the direction in which a force is applied can change the moment significantly, even if there is no change in the force’s magnitude.
The moment of the force in the left figure is 4N x 8m = 32Nm, Clockwise. However, the moment of the force in the right figure is reduced, at 4N x 5m = 20Nm, Clockwise. This is because the line of action is now directed at an angle towards the pivot. This, in turn, lowers the perpendicular distance between the pivot and line of action.
Equilibrium & Stability
Stability refers to how well an object or system can return to its original state after being displaced. The concept of stability can be explained in terms of equilibria. An object is said to be in equilibrium when two conditions have been fulfilled.
1. The resultant external forces acting on the object adds up to zero.
2. The resultant moment around the pivot is zero.
The second criterion is in line with the Principle of Moments, which states that an object is in equilibrium when the sum of clockwise moments is equal to that of the anti-clockwise moments about the same pivot.
There are three main types of equilibria in physics:
1. Stable: As the name suggests, this ranks the highest in stability. When displaced, the system experiences a net force in the opposite direction of the displacement. (e.g. a ping-pong ball at the bottom of a cup)
2. Unstable: When displaced even slightly, the system moves even further away from its equilibrium position. (e.g. a ball balanced on the tip of your finger)
3. Neutral: When displaced, the system remains in its new state. (e.g. a pencil placed lengthwise on a table)
Centre of gravity
The centre of gravity of an object is an imaginary point on an object, from which the full weight of the object is considered to act. One can also think of it as the point in an object which mass or weight is evenly distributed around.
The concept of the centre of gravity comes in handy when designing infrastructure and equipment. There are two simple ways to increase the stability of an object:
1. Lowering the object’s centre of gravity.
2. Increasing the object’s base area.
The turning effect of forces can be a tricky topic to grasp at first, especially given the diverse and numerous concepts that surround it. However, with a strong foundational understanding and enough practice, you will be a master in moments.
To help you along, there are several excellent physics tuition centres that can teach you the concepts in a concise yet in-depth manner. Join us for an engaging and effective physics curriculum that is bound to give you the boost you need to ace your exams.


Before you learn how to figure interest on a car loan, it is a good idea to have a basic knowledge of what interest actually is. If you secure credit to purchase your vehicle, it means that the lender is the one who actually owns the car until you have paid it in full. The interest rate you pay is essentially a fee you pay the lender for using their money to purchase your vehicle. There are a few factors that can affect the amount you pay in interest for the vehicle of your choice.
Principal Amount: The principal amount is the actual amount you are looking to borrow from the lender.
Loan Term: This term means the length of time you will be repaying the loan. If you have a shorter loan term, you usually can expect higher monthly payments, but the benefit is that you will end up paying less in interest. If you opt for a loan with longer terms, you can expect to pay less per month, but you’ll end up paying more in interest.
Repayment Schedule: Usually, you will end up only making one car payment per month, but you have the option of making your payments more often. Thanks to compounding, when you make more payments you end up paying less in interest.
Repayment Amount: With every car loan payment you make, a portion goes to interest and a portion goes to repay your principal.
How to Calculate Auto Loan Interest for First Payment
There is a quick and easy way to figure out how to calculate auto loan interest for the initial payment.
Divide your interest rate by the number of monthly payments you will be making this year.
Multiply it by the balance of your loan, which for the first payment, will be your whole principal amount.
This will let you know how much interest you will be charged for the first month of repaying your loan.
How to Figure Interest on a Car Loan For Future Months
Once you have started to pay down your initial principal, it is necessary to calculate your new balance so you know how much interest you will be paying going forward.
Subtract the interest you just calculated from the payment you just made and this will leave you with the amount that you have paid off the loan principal.
Deduct this total from your original principal to get your new loan balance.
Because these numbers are rounded, your calculations won’t always be exact, but they provide a good estimate for how to calculate the interest rate on a car loan.
Turn to Stohlman Volkswagen for Financial Information


Height difference between two points in relation to their horizontal distance in percent. The angle is calculated with: arcus tangens x (height difference broken by distance). An upward slope is called slope, a downward slope (the two terms are only linguistically different, mathematically there is no difference). At 30% slope, the other 100 meters (horizontally) distant point is 30 meters higher, giving an angle of 16.69 °. An inclination of 75% gives 36.87 °. A slope at 100% corresponds to an angle of 45 °, ie 100 meters horizontally and 100 meters vertically. Up to this tendency is in viticulture the employment of Monorackbahnen A monorail of 200% corresponds to an angle of ~ 64 °. For inclination angles just below 90 °, the slope grows to infinity. A slope of 90 ° corresponds to a vertical wall. More than 90 ° correspond to overhanging walls.


Now, imagine we have some purely imaginary growth rate Ri that rotates us until we reach i, or 90 degrees upward. How about the exponent. In the same spirit of assuming -1.
We should expect a complex number on the unit circle -- there's nothing in the growth rate to increase our size. But what about. Locate this point on the y axis. A complex number is the fancy name for numbers with both real and imaginary parts.
Point-Slope form of a line: Connect these three points and label to graph it correctly. Why Is This Useful. Again, it's two ways to describe motion: And our secret weapon: But for complex numbers, how do we measure two components at 90 degree angles.
Regular growth is simple: Good luck figuring that out on your own. And, just for kicks, if we squared that crazy result: Something to keep in mind while drawing your graph is that the larger the bottom, or run, is in relationship to the rise the closer the slope will be to the x-axis.
It follows the post; watch together, or at your leisure. Math discussionor another argument on why imaginary numbers exist. A review of the main results concerning lines and slopes and then examples with detailed solutions are presented. What is the implicit growth rate.
Now let's figure out how the e side of the equation accomplishes it.
Remember to put your calculator in radian mode when punching this in. Now put in the x,y point and solve for b. This stunning equation is about spinning around. We can convert our growth into "e" format: Algebra First the slope. But remember, We want an initial growth of 3x at the end of the period, or an instantaneous rate of ln 3.
Write the equation of a line that passes through 9, 3 and Algebra 1 Write an equation in slope-intercept form for a line that passes through the given point and is perpendicular to the given line. But with our analogies we can take them in stride.
It seems crazy, just like negatives, zero, and irrationals non-repeating numbers must have seemed crazy at first. But better to light a candle than curse the darkness: What, exactly, does that mean. Just wait until college. And now we modify that rate again by i:.
Calculus BC Multiple Choice Practice A calculator may not be used for questions Question 1: 1 0 1 ∞ Question 2: If f is a continuous function for all real x, then is equal to: 0 f(0) a f(a) f'(a) Question 3: A curve is described by the parametric equations x = t 3 + 2t and y = t 2 + t + degisiktatlar.com equation of the line tangent to the curve at the point determined by t=-1 is: 2x + 3y = 5 2x.
Dec 21, · Define the slope-intercept formula of a line.
The formula of a line in slope-intercept form is y = mx + b, where m is the slope, b is the y-intercept, and x and y are variables that represent coordinates on the line; generally, you will see them remain as x and y in the equation.
Perpendicular lines have negative inverse slopes. y = 4x + 6 has a slope of 4, so a line perpendicular to it must have a slope of -1/4. So we have y = -1/4 x + c where c is some constant (the y-intercept in this case) we know x = 2, y = 7 satis.
Find the slope of the line perpendicular to the line y = (1/3)x - 7 Solution Two lines are perpendicular if the product of their slopes is equal to The slope of the given line is equal to 1 / 3.
Jul 01, · Write the equation of a line that is perpendicular to the line y = 1/4x + 2 and contains the point (11,4).?Status: Resolved. Graphs of Functions. Identify equations of lines parallel and perpendicular to a given line; Recognise, draw and interpret straight line, quadratic, reciprocal and cubic graphs eg.
x=a, y=b, y = ax2+bx+c, y=a/x, y=ax3, y=ax+b+a/x, y=ax3+bx2+cx+d, y=kx for integer values of x and simple positive values of k.Write an equation that is perpendicular to y 4x 2


Different problem formats
Traditional and more advanced formats.
- The basic format is the traditional format for flashcards.
- The advanced format of guess the number, or missing addend equations, helps encourage critical thinking.
- No timer so learners can practice at their own pace without feeling rushed.
Parents can view trends to see where focus might be needed.
- Helps identify where additional additional practice is needed.
- Are they having issues with addition with 3's?
- Are they having issues with multiplication with 7's?
Rapid feedback & Repetition
Practice and repetition are critical for building fluency with math operations.
- Problems missed 3 or more times are remembered and become part of the next problem set to ensure repetition.
- When a problem set is completed, there is feedback that shows how many attempts were needed to solve each problem.
Easy to setup
Simple to set up for all operations.
- Flash cards can be configured for all operations, individually or combined.
- Choose a constant number and that number will be in every problem.
Widgets allow a quick view of the last set of problems.
- The small widget provides a view of the last set of problems and how much time has passed since last practiced.
- The medium widget provides a view of individual problem proficiency.


Miss Faber's Fourth Grade
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This Week in 4th Grade
Fourth Grade Happenings
5th Grade ELA
We work with our second grade poetry partners each Friday. Below are some pictures of the fourth graders playing a game to help their partners practice math facts. What wonderful 4th grade leaders!
The fourth graders learned about how to work as a team and problem solve to save Fred, the gummy worm!
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Function Interpolation with known
Function interpolation with known piecewise averages
In a typical interpolation problem, values are estimated within a discrete set of known data points. Recently, we had to “interpolate” a function from which we only knew the averages at certain time intervals. A set of known data points was not available and regular interpolation techniques could not be applied. This post explains the solution that we implemented by way of an example.
Solution outline for function interpolation with known piecewise averages
The example used to illustrate the interpolation methodology is based on a small photovoltaic power plant. The hourly average generation for a given day is shown in Table 1.
|Hour of the day||Average generation (kW)|
The target function is the power plant’s production curve on a minute-by-minute resolution. Note that the measured power curve is only available on an hourly basis.
The subsequent steps are followed to interpolate the power generation data:
- Calculate the cumulative function. This is equivalent to cumulative generation in our example (see Table 2). Note that 1 kWh is the energy generated by a power plant producing 1 kW during 1 hour. For example, the total generation until 10am was 2.5kWh (0.5kWh generated between 8:00 and 9:00 and 2.0kWh generated between 9:00 and 10:00am).
- Interpolate the cumulative function. Standard interpolation techniques can be applied to the cumulative function as a set of data points are known. For example, we know that the cumulative generation equals 0.5kWh at 9:00.
- Differentiate the interpolated cumulative function to obtain the target function. As the cumulative function is the integral (or sum) of the target function, the target function is the derivative of the cumulative function.
|Time of the day||Cumulative generation (kWh)|
A third-order spline interpolation was applied to the solar PV cumulative values in Table 2. Given that a third order Spline interpolation is twice differentiable, its derivative, the target function of our example, is continuous and differentiable. The result for the target function compared to the original hour-by-hour data can be seen in the figure below.
Example code implementation in Python
An example code implementation in Python is as follows.
# 0. Start by importing Numpy and interpolate from Scipy import numpy as np from scipy import interpolate # 1. Get cumulative function cumulative_generation = np.array([0, 0.5, 2.5, 7.5, 15.5, 25.5, 35.5, 45, 53.5, 60.5, 65.5, 67.5]) hours = np.arange(8, 20) # 2. Interpolate the cumulative function (Spline interpolation) interpolator = interpolate.CubicSpline(hours, cumulative_generation) # 3. Differentiate and substitute. # For example, differentiate and interpolate the power at 10am: print(interpolator(10, 1)) # 3.37 is the output of the interpolation at 10am.


Mathematica Link for Microsoft Excel
There are dozens of useful features in the completely reworked Mathematica Link for
Microsoft Excel. Most of the limitations of the earlier version have been effaced, and
the user interface is much more developed. Among the items at the top of user's
wish list, Mathematica graphics can now be generated inside Excel. Arrays of any
type can be sent and received. Calculations can be interrupted, messages can be received,
and a terminal window for quick communication with the kernel is provided. An easy-to-use Mathematica
Wizard guides users through the process of entering Mathematica functions into a
spreadsheet. For Mathematica programmers, this simply means that their code has the
potential of being used by more than just the Mathematica literate. This session
will provide a brief tour of the new product and illustrate examples of functions written
in Mathematica that are conveniently used inside Excel.
More information on Mathematica Link for
Microsoft Excel is available in the Wolfram Research Store.


Dating math secretary problem
Does the secretary problem apply to dating the secretary problem has many suitable approach to dating but a warning: if you try to use math to reason. Preparing for pre-employment math testing objectives 1 students will become familiar with different types of math problems 2 students will demonstrate knowledge of math word. Mathhelpcom is the smart way to conquer math we provide the exact math help you need with online test prep courses for over 100 standardized tests tutoring and homework help for. Sample problems are under the links in the sample problems column and the corresponding review material is under the concepts column new problems are given each time the problem links. Tough math problem 4 real life dating application hi, i have a variation on this problem: 12-07.
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I recently attended an excellent conference at the British Academy on Quantitative Skills, with a focus on international comparisons. The main question posed by the conference was, ‘How well trained are UK social science students in quantitative skills?’ The resounding answer was ‘Not very well’!
The conference examined some of the reasons for this, starting with secondary education. In a survey of 24 countries, England, Wales and Northern Ireland were the only countries in which fewer than 20% of upper secondary students study maths. Of these 20% who study maths at A-level, a large proportion go on to study STEM subjects at university. A much smaller proportion choose social science degrees and herein lies the first challenge to improving quantitative skills at undergraduate level – students come to university having done little or no maths since GCSE. The Nuffield Report ‘Is the UK an outlier? An international comparison of secondary mathematics education’ is certainly worth a read, and it clearly shows that the way to raise the percentage of students who study maths post-16 is to make it compulsory, as it is in the Czech Republic, Estonia, Finland, Japan, Korea , Russia, Sweden and Taiwan. http://www.nuffieldfoundation.org/uk-outlier-upper-secondary-maths-education
In his fascinating report on undergraduate quantitative methods training in the social sciences (excluding psychology and economics which historically have a much greater focus on statistics), Professor John MacInnes highlights some of the other challenges the UK faces.
- Cost pressures and lack of skilled staff lead to inadequate teaching (MacInnes’s research found that only 10-15% of staff at UK institutions have the skills needed to teach an introductory statistics course!)
- Teachers face hostility to numbers from students who had a negative experience of maths at school or haven’t studied any maths since GCSE and have never before encountered maths in an applied setting
- Methodology and quantitative skills are divorced from the rest of the substantive curriculum and therefore seen as an optional extra
- Students aren’t aware of the career advantage of having good quantitative skills
Though not a new problem, MacInnes is optimistic that change is possible now and through his role as the ESRC Strategic Advisor on Quantitative Methods Training is involved in numerous initiatives to improve quantitative skills teaching at UK universities, including the launch of a network of 20 universities selected by the ESRC, Hefce and the British Academy to run innovative projects aiming to develop skills using quantitative methods. Read the press release here!
David Willetts, Minister for Universities and Science, gave the keynote address and agreed that raising quantitative skills was a battle worth fighting, not just for the sake of social science research, but for a more statistically literate society. In a breakout session led by David Walker of the Guardian, who is the figurehead for the RSS initiative Getstats (http://www.getstats.org.uk/) which is campaigning to make Britain better with numbers , we brainstormed ideas for improving journalists’ statistical literacy. Newspapers regularly misreport research mistaking correlation for causation, comparing incomparable numbers and completely misunderstanding probability and risk, and this results in a misinformed public. However, the problem of statistically illiterate journalists is not easily solved. Journalists and bloggers come from a wide variety of educational backgrounds and many will not have had any formal statistics training. Is the answer more short courses like the BBC and RSS’s science training for journalists programme? Does statistics need an engaging popular media spokesperson à la Brian Cox to educate the general public about why stats matter and train them to spot gross errors in what they read? Does the academic statistics community need to do much more to shame newspapers when they misreport their research? If PR offices at universities are responsible for pushing out press releases, what can be done to ensure this isn’t where errors are cropping up? A combination of all of the above (and much more) need addressing if we’re to make headway, and the challenge is knowing where to start when there is limited time and money to throw at the problem.


You need to center a data series before further analysis.
Centering in this context refers to the process of removing a bias or offset in a series of data so that the resulting series values fluctuate approximately about 0. Centering is often required before processing data using forecasting techniques, and can be accomplished quite easily in Excel.
There are a number of ways to center a data series, and here we’ll use the standard approach of subtracting the average of the data in the series from each data item in the series.
The first column contains the month label, while the second column contains the original data series before centering. This series represents average monthly temperatures.
To center the data, I first computed the average of all the temperature values in the original data series. Cell D27 contains the formula =AVERAGE(D3:D26) that computes the average of all temperatures.
The column adjacent to the original data series contains the centered data (column E). The formulas in this column are of the form =D3-$D$27. All this does is subtract the average temperature contained in cell D27 from every temperature value in the original series. The result is a centered data series with the offset removed.
Fig. 6-18 shows the original data series and Fig. 6- 19 shows the centered data series.
The original data series oscillates about the average temperature up in the 60s, while the centered data series oscillates about the 0 axis.
This isn’t the only way to center data. Some techniques involve computing a weighted average of the data and using the result to center the series.
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On February 18, the State School Superintendent, Richard Woods, named North Forsyth High School one of 609 Advanced Placement Honor Schools. The Georgia Department of Education presented the award in six categories: AP Challenge Schools, AP Access and Support Schools, AP Merit Schools, AP Stem Schools, AP STEM Achievement Schools, and AP Humanities Schools. Superintendent Woods awarded NFHS in the latter four categories.
According to the GADOE:
AP Merit Schoolsare schools with at least 20 percent of the student population taking AP exams and at least 50 percent of all AP exams earning scores of 3 or higher.
AP STEM Schoolsare schools with students testing in at least two AP math courses and two AP science courses.
AP STEM Achievement Schoolsare schools with students testing in at least two AP math courses and two AP science courses and at least 40 percent of the exam scores on AP math and AP science exams earning scores of 3 or higher.
AP Humanities Schoolsare schools with students testing in all of the following AP courses: at least one ELA course, two social science courses, one fine arts course and one world language course.


Welcome to The Decimal Review with Mr. J! Need help with how to add, subtract, multiply, and divide decimals? You’re in the right place!
If you’re looking for a quick refresher on decimal operations, this is the video for you. Mr. J will go through adding, subtracting, multiplying, and dividing decimals examples and explain how to solve each problem.
Looking for a more in depth explanation?
Adding and Subtracting Decimals: https://youtu.be/PnwLv6khwk8
Multiplying Decimals Instructional Video: https://youtu.be/ha8udGpjkMI
Dividing Decimals Instructional Video (whole divisors): https://youtu.be/Sah_q6YkF5o
Dividing Decimals Instructional Video (decimal divisors): https://youtu.be/6SCROCbSGts
About Math with Mr. J: This channel offers instructional videos and mastery checks (practice videos to gauge understanding) that are directly aligned with math standards (5th grade, 6th grade, 7th grade, etc.). Videos can be used to introduce content, reteach content, or as a study tool. Teachers, parents/guardians, and students from around the world have used this channel to help with math content in many different ways. All material is absolutely free.
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Hopefully this video is what you’re looking for when it comes to decimal operations and this helps you with how to add, subtract, multiply, and divide decimals.
Have a great rest of your day and thanks again for watching!


The 'Rule of 72' is a simplified way to determine how long an investment will take to double, given a fixed annual rate of interest. By dividing 72 by the annual rate of return, investors can get a rough estimate of how many years it will take for the initial investment to duplicate itself.http://live-forex-signals.com/ref/308133
For example, the rule of 72 states that $1 invested at 10% would take 7.2 years ((72/10) = 7.2) to turn into $2. In reality, a 10% investment will take 7.3 years to double ((1.10^7.3 = 2).
When dealing with low rates of return, the Rule of 72 is fairly accurate. This chart compares the numbers given by the rule of 72 and the actual number of years it takes an investment to double
|Rate of Return||Rule of 72||Actual # of Years||Difference (#) of Years|
Notice that, although it gives a quick rough estimate, the rule of 72 gets less precise as rates of return become higher. Therefore, when dealing with higher rates, it's best to calculate the precise number of years algebraically by means of the future value formula.
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A couple of days without math and I am feeling itchy and unfulfilled. I am working through the last half of Saxon’s Algebra II in order to start Advanced Math after Thanksgiving. The boys and I work silently at the table on our 30 problems for about an hour and a half. It feels exactly like the clean burn after a sweaty exercise, without the need for a shower. It makes me feel stronger all day, and this week after missing a three days I feel the restlessness to get back in the zone.
I find this a bit of a surprise.
I’m the same way with math. I love it!


Our workshops are held in the following cities. Please click on the city name to view facility information.
Our program consists of a three day preparatory session in the classroom where, using our self-study workbook as a guide, we define the scope of the exam, illustrate the complexity of problems to be encountered, review all required basic math skills (not a separate class), discuss test strategy, examine reference materials and present a model home study program. In our workshops, you are provided with a 500 page professionally published workbook, BCSP approved scientific calculator, pencils, notepad, highlighter, and Las Vegas Safety Workshops exclusive EXAM PREP Software CD. The Las Vegas Safety Workshops, LLC Exam Prep Software which includes over 800 questions with expanded answers and practice test simulations is available as part of the workshop ($275 value!).
During the workshop, we discuss how to develop a follow on study program and provide the workbook specifically designed to enhance the candidate’s ability to solve the problems on the Exam. The launches the Las Vegas Safety Workshops, LLC Exam Prep software, the most powerful OHST/CHST/ASP/CSP/CHMM/CHMP exam simulation software in the world. The CDs prepare the candidate for the actual Computer Based Testing environment utilizing precise learning and exam taking techniques developed by Las Vegas Safety Workshops, LLC CSPs who are certified in curriculum design for professional exam preparation. Each contains over 800 targeted questions with multiple enhanced learning, exam simulation, and performance tracking capabilities. The workbook and are updated annually.
During each workshop, we work and discuss approximately 400 questions typical of those encountered on the examination. Our questions are complete with explanations, not just answers, and all the explanations are keyed to the same reference material suggested by the BCSP. This allows our students to gain understanding of the subject matter rather than attempting to memorize an impossible number of questions and answers.
Integrated Math for Certification Exams
Unlike other workshops, Las Vegas Safety Workshops include essential math skills throughout each 3 day professional workshop (ASP, CSP, CHST, OHST) instead of a separate one day math review. This provides a more applied approach to the prerequisite exam mathematics during the focused 3 day preparatory workshop. Our certified Instructional Technologist and degreed adult education curriculum designers have developed strategies to integrate applied exam mathematics including simple strategies that will optimize your math skills without the need to learn or re-learn complicated mathematical theory. During each 3 day safety workshop participants will learn all domains identified on the BCSP Exam Blueprint and the following integrated Math:
- Conversions – SI and English conversions of mass, length and time
- Dimensional analysis – multi-step conversions (e.g., converting miles per hour to feet per second, pounds to micrograms)
- Number manipulation – exponents, scientific notation, significant digits, answer accuracy and rounding and logarithms
- Shapes and formulae – area, circumference and volume of rectangles, triangles, circles, trapezoids, cubes and cylinders
- Graphing – two dimensional graphing of linear, exponential, trigonometric and logarithmic functions
- Algebra – laws and concepts, word problems
- Trigonometry – right angles, trigonometry functions and word problems
- Operation of a scientific calculator
Workshops are held 8:00am until 5:00pm daily and are Guaranteed!! If you fail the exam within 12 months of attending a workshop, you can retake the workshop free of charge.


Casino Game Expertise
You can find currently three main types of casino games available: card games, video poker games, and electronic casino games. Video poker video games are played by one individual at a time and don’t require the participation of modern casino staff to play. These game titles are ever more popular among non-gamers because they’re relatively easy to learn and play. They also have a tendency to provide a more competitive playing experience than almost every other games are.
Blackjack is just about the best-known card game on the globe, and for good reason. Blackjack is often the initial casino game individuals are introduced to and is a good introduction to the more difficult games that the casino gives. If you are playing blackjack at an on the web casino, you will find that you have the best odds of winning once you come to bet. That’s because the house usually has blackjack cards, and the cheapest possible house edge (or benefit) is two per card. The lower your chances of getting an edge increase, the better off you are. The minimum bet amount is definitely lower than the utmost bet amount, so the lower you are ready to go with an individual card, the better off you’re.
Another simple blackjack strategy is by using basic statistics to analyze what sort of blackjack player may be behaving. One such statistic is called the binomial distribution also it compares the winning possibility of blackjack with the probability of picking any number in the set, up to specified control. The binomial distribution plots the probability as a work of the number of successes and failures. For instance, the standard deviation can be used to plot the data points for each and every 100 hands played. The typical deviation uses a normal curve to plot the info points so as to see the range of behavior and how it differs with the number of successful plays and the period of each successful have fun.
Blackjack players can make use of the standard deviation to compute the casino’s odds of winning more money in the popular games. Standard deviation is most readily useful in researching the random distribution of the results of gaming functions, like spins on roulette wheels or spins on slots. It is also used to review the behavior of the odds in non-stop jackpots on slots and video poker machines. One casino refers to these as “montee game titles,” because players can win a number of prizes simultaneously over many palms.
The random distribution of the results of casino slot machines is comparable to the odds of striking the jackpot in slot machine games. When players place wagers, they take the chance that the modern casino will hit a jackpot. If you are gambling with a 10-item slot machine game, then the best odds that may be given to you’d be if you get yourself a hit every time with among your bets. But, since you don’t know what’s the best payout will be, you will not know whether you’re getting the very best odds on slots or not necessarily.
To study the real odds at playing slot game titles, a player should multiply the amount wagered plus the casino’s expected payout for each spin. For instance, in case a player is betting ten cents about the same spin, the casino’s anticipated payout per spin is $.10. With this particular number, the player can perform a quick computation to determine the volume wagered, multiplied by the expected payout to find the casino’s true odds of winning. Then, he is able to multiply that number by the number of times he really wants to bet and see if he gets a winning bet every time. This way, the player can calculate his likelihood of winning without having to depend on the numbers generated by the device.
In roulette and blackjack, players need to follow a strategy of matching the quantity of opponents that come up with a particular number. A good player must do this consistently to increase his chances of winning. This can be the same in playing other internet casino 메리트 카지노 조작 games such as for example craps and baccarat. It requires strategic thinking, which is part of the real skill factor.
Overall, playing casino games online is better because it includes a lower house edge than slots games. Even so, both roulette and slots video games have the tendency to create larger jackpots. There are also casino games online that employ random range generators for drawing numbers. Compared to these, the home edge is smaller in gambling house games online.


The mission of the ChiArts mathematics department is to provide all students with a complete understanding of the logical structure of mathematics and how it prepares adolescents to become successful citizens in an ever-changing society. Through the study of mathematics, students will conceptualize math as a unique language in order to be effective problem solvers and critical thinkers. Students will further develop their abstract and quantitative reasoning skills to creatively solve mathematically modeled situations.
Understand that mathematics is a language the can be used to interpret and conceptualize the world we live in; Construct and communicate viable mathematical arguments; Determine the meaning of a problem and persevere in solving it through various avenues; Reason abstractly and quantitatively by making sense of different relationships in problem situations; Model real life situations as mathematical problems and apply learned knowledge to creatively solve them; And analyze problems closely to discern a pattern or structure and then generalize that discovered pattern.
The goal of this course is to reinforce fundamental algebra concepts by developing quantitative thinking necessary in a college preparatory class. The teacher will foster a classroom environment so students can develop mathematical confidence by honing their problem solving skills. The students will learn about concepts including but not limited to: order of operations, numerical fractions, decimals & percents, Cartesian plane, ratios, rates, & proportions.
Integrated Math I
The goal of this course is to expose students to abstract thinking through algebraic structures and challenge students to solve problems logically. This course is designed to help students conceptualize math as a language. Students will apply learned skills through modeling real-world situations. Topics investigated are expressions, exponents, functions, solving equations/inequalities, linear functions, linear systems, patterns/sequences, comparing linear and exponential functions, properties of angle pairs, properties of triangles and quadrilaterals, parallel lines, perpendicular lines, scatterplots, correlation, and box plots.
Integrated Math II
This course is an extension of the Math I course. Students expand on their prior knowledge of Algebra with further investigation of functions such as quadratic functions. Students will analyze, interpret, build, transform, and model quadratics. In addition, students explore concepts of geometric similarity, right triangle trigonometry, and geometric proofs. An emphasis on integrating geometric concepts with algebraic skills is reinforced throughout the year. Lastly, students will extend the number system beyond their prior knowledge of non-real solutions and students will analyze applications of probability. Students apply learned skills via real-world applications and approach problem solving both logically and creatively. Overall, we want our students to leave our course with a strong sense of problem solving while understanding that mistakes are part of the problem solving process.
Integrated Math III
This course is designed to help students conceptualize math as a language, expose students to abstract thinking through algebraic structures, and challenge students to solve problems both logically and creatively. Students will master mathematical concepts and skills such as data analysis; fitting data to equations; linear, quadratic, exponential, rational, radical, logarithmic, and trigonometric models; and formulas.
In order to prepare students for calculus and other higher-level math, this course is designed to have students develop a deeper understanding of such topics as exponential, logarithmic, and trigonometric functions. We will focus on these functions’ properties and graphs and apply them to real-world situations. Students will apply many of the learned skills from previous courses and will find their algebra and graphing skills very useful. To do well, problems in this course must be approached both logically and creatively. At the completion of this course, students with interest should have the necessary skill set to pursue a specific branch of mathematics, whether Calculus, Statistics, Theory, Physics, Engineering, and even the biological and medical sciences.
Financial Statistics takes the math skills that students have acquired since freshmen year and reveals their value and purpose in the real world of finance. Students will explore how math is used and applied in the stock market, modeling of businesses, marketing and advertising, credit, loans, taxes, income, budgeting, and more. This course is designed to reinforce previously taught concepts from a different, more relatable perspective while preparing students for life after high school.
AP Calculus is a challenging, college-level course applying previously learned concepts in math (ie. slope, rates of change, functions) along with many new concepts such as limits, derivatives, and integrals. The course provides students with the opportunity to work with functions represented in a variety of ways — graphically, numerically, analytically, and verbally — and emphasizes the connections among these representations. Students are expected to learn and apply multiple definitions and proofs of theorems that will help in completing problems and exploring the general properties of mathematics. AP Calculus explores math on infinitesimally large and small scales, so students should have open, creative minds and be willing to think outside the box. AP Calculus is challenging and fast-paced as well as extremely interesting and rewarding. Those who work hard will find the beauty of mathematics while uncovering many applications for the sciences.
AP Statistics is the high school equivalent of a one semester, introductory college statistics course. In this course, students develop strategies for collecting, organizing, analyzing, and drawing conclusions from data. Students design, administer, and tabulate results from surveys and experiments. Probability and simulations aid students in constructing models for chance behavior. Sampling distributions provide the logical structure for confidence intervals and hypothesis tests. Students use a TI-83/84 graphing calculator, Fathom and Minitab statistical software, and Web-based java applets to investigate statistical concepts. To develop effective statistical communication skills, students are required to prepare frequent written and oral analyses of real data.


Univariate Analysis: basic theory and example
Univariate analysis: this article explains univariate analysis in a practical way. The article begins with a general explanation and an explanation of the reasons for applying this method in research, followed by the definition of the term and a graphical representation of the different ways of representing univariate statistics. Enjoy the read!
Research is a dynamic process that carefully uses different techniques and methods to gain insights, validate hypotheses and make informed decisions.
Using a variety of analytical methods, researchers can gain a thorough understanding of their data, revealing patterns, trends, and relationships.
One of the main approaches or methods for research is the univariate analysis, which provides valuable insights into individual variables and their characteristics.
In this article, we dive into the world of univariate analysis, its definition, importance and applications in research.
Techniques and methods in research
Research methodologies encompass a wide variety of techniques and methods that help researchers extract meaningful information from their data. Some common approaches are:
Summarizing data using measures such as mean, median, mode, variance, and standard deviation.
Drawing conclusions about a broader population based on a sample. Methods such as hypothesis testing and confidence intervals are used for this.
Exploring relationships between multiple variables simultaneously, allowing researchers to explore complex interactions and dependencies. A bivariate analysis is when the relationship between two variables is explored.
Discovering insights and trying to understand subjective type of data, such as interviews, observations and case studies.
Analyzing numerical data using statistical methods to reveal patterns and trends.
What is univariate analysis?
Univariate analysis focuses on the study and interpretation of only one variable on its own, without considering possible relationships with other variables.
The method aims to understand the characteristics and behavior of that specific variable. Univariate analysis is the simplest form of analyzing data.
Definition of univariate
The term univariate consists of two elements: uni, which means one, and variate, which refers to a statistical variable. Therefore, univariate analysis focuses on exploring and summarizing the properties of one variable independently.
Importance of univariate analysis
Univariate analysis serves as an important first step in many research projects, as it provides essential insights and lays a foundation for further research. It offers researchers the following benefits:
Univariate analysis allows researchers to understand the distribution, central tendency, and variability of a variable.
Identification of outliers
By detecting anomalous values, univariate analysis helps identify outliers that require further investigation or treatment during the data analysis phase.
Univariate analysis helps identify missing data, inconsistencies or errors within a variable, allowing researchers to refine and optimize their data set before moving on to more complex analyses.
Researchers can use the univariate analysis to determine which variables are most promising for further research. This enables efficient allocation of resources and hypothesis testing.
Reporting and visualization
Summarizing and visualizing univariate statistics facilitates clear and concise reporting of research results. This makes complex data more accessible to a wider audience.
Applications of univariate analysis
Univariate analysis is used in various research areas and disciplines. It is often used in:
- Epidemiological studies to analyze risk factors
- Social science research to investigate attitudes, behaviors or socio-economic variables
- Market research to understand consumer preferences, buying patterns or market trends
- Environmental studies to investigate pollution, climate data or species distributions
By using univariate analysis, researchers can uncover valuable insights, detect trends, and lay the groundwork for more comprehensive statistical analysis.
Types of univariate analyses
The most common method of performing univariate analysis is summary statistics. The correct statistics are determined by the level of measurement or the nature of the information in the variabels. The following are the most common types of summary statistics:
- Measures of dispersion: these numbers describe how evenly the values are distributed in a dataset. The range, standard deviation, interquartile range, and variance are some examples.
- Range: the difference between the highest and lowest value in a data set.
- Standard deviation: an average measure of the spread.
- Interquartile range: the spread of the middle 50% of the values.
- Measures of central tendency: these numbers describe the location of the center point of a data set or the middle value of the data set. The mean, median and mode are the three main measures of central tendency.
There are several ways to describe patterns found in univariate data. The data can be displayed graphically as well. Some examples:
Frequency indicates how often something occurs. The frequency of observation thus indicates the number of times an event occurs.
The frequency distribution table can display qualitative and numerical or quantitative variables. The distribution provides an overview of the data and allows you to spot patterns.
The bar chart is displayed in the form of rectangular bars.
The chart compares different categories. The chart can be plotted vertically or horizontally.
In most cases, the bar is plotted vertically.
The horizontal or x-axis represents the category and the vertical y-axis represents the value of the category.
This diagram can be used, for example, to see which part of a budget is the largest.
A histogram is a graph that shows how often certain values occur in a data set. It consists of bars whose height indicates how often a certain value occurs.
The frequency polygon is very similar to the histogram. It is used to compare data sets or to display the cumulative frequency distribution.
The frequency polygon is displayed as a line graph.
The pie chart displays the data in a circular format. The diagram is divided into pieces where each piece is proportional to its part of the complete category. So each “pie slice” in the pie chart is a portion of the total. The total of the pieces should always be 100.
Example situation of an Univariate Analysis
An example of univariate analysis might be examining the age of employees in a company.
Data is collected on the age of all employees and then a univariate analysis is performed to understand the characteristics and distribution of this single variable.
We can calculate summary statistics, such as the mean, median, and standard deviation, to get an idea of the central tendency and range of ages.
Histograms can also be used to visualize the frequency of different age groups and to identify any patterns or outliers.
This univariate analysis helps organizations to better understand the age structure of the workforce in the company.
Now it’s your turn
What do you think? Do you recognize the explanation about the univariate analysis? Have you ever heard of univariate analysis? Have you applied it yourself during any of the studies you have conducted? Do you know of any other methods or techniques used in conjunction with univariate analysis? Are you familiar with the visual graphs used in univariate analysis?
Share your experience and knowledge in the comments box below.
More information about the Univariate Analysis
- Barick, R. (2021). Research Methods For Business Students. Retrieved 02/16/2024 from Udemy.
- Dowdy, S., Wearden, S., & Chilko, D. (2011). Statistics for research. John Wiley & Sons.
- Garfield, J., & Ben‐Zvi, D. (2007). How students learn statistics revisited: A current review of research on teaching and learning statistics. International statistical review, 75(3), 372-396.
- Ostle, B. (1963). Statistics in research. Statistics in research., (2nd Ed).
- Wagner III, W. E. (2019). Using IBM® SPSS® statistics for research methods and social science statistics. Sage Publications.
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At Oulton First School we believe that Maths should be fun, clear and challenging; we want every child to leave us with a love of Maths and a deep grounding in the basics needed to progress. We use the Maths No Problem scheme of work.
What is Singamore Maths?
In Singapore , children had some of the worst results across a range of countries. They realised they needed to change how they taught the subject so they focused their teaching on problem solving and making sure the underlying concepts were taught clearly using a CPA method.
So what is the CPA approach?
Children and adults can find maths difficult because it is abstract. The CPA approach helps children learn new ideas and build on their existing knowledge by introducing abstract concepts in a more familiar and tangible way. The approach is so established in Singapore maths teaching, that the Ministry of Education will not approve any teaching materials which do not use the CPA approach.
Concrete is the “doing” stage, using concrete objects to model problems. Instead of the traditional method of maths teaching, where a teacher demonstrates how to solve a problem, the CPA approach brings concepts to life by allowing children to experience and handle physical objects themselves. Every new abstract concept is learned first with a “concrete” or physical experience.
For example, if a problem is about adding up four baskets of fruit, the children might first handle actual fruit before progressing to handling counters or cubes which are used to represent the fruit.
Pictorial is the “seeing” stage, using representations of the objects to model problems. This stage encourages children to make a mental connection between the physical object and abstract levels of understanding by drawing or looking at pictures, circles, diagrams or models which represent the objects in the problem.
Building or drawing a model makes it easier for children to grasp concepts they traditionally find more difficult, such as fractions, as it helps them visualise the problem and make it more accessible.
Abstract is the “symbolic” stage, where children are able to use abstract symbols to model problems.
Only once a child has demonstrated that they have a solid understanding of the “concrete” and “pictorial” representations of the problem, can the teacher introduce the more “abstract” concept, such as mathematical symbols. Children are introduced to the concept at a symbolic level, using only numbers, notation, and mathematical symbols, for example +, –, x, / to indicate addition, multiplication, or division.
Although we’ve presented CPA as three distinct stages, a skilled teacher will go back and forth between each representation to reinforce concepts.
Our approach encourages teachers to vary the apparatus the children use in class, for example, one day they might use counters, another day they might use a ten frame. Likewise, children are encouraged to represent the day’s maths problem in a variety of ways, for example, drawing an array, a number bond diagram or a bar model. By systematically varying the apparatus and methods they use to solve a problem, we help children to make quicker mental connections between the concrete, pictorial and abstract phases.
When teaching young children, exposing to abstract concepts too early may mean that children are missing out on the opportunity to build the conceptual mathematical understanding which they need to take them through their education. However, it should never be a case of concrete ‘good’, abstract ‘bad’. It is important to recognise that the CPA model is a progression. By the end of KS1, children need to be able to go beyond the use of concrete equipment to access learning using either pictorial representations or abstract understanding. What is important, therefore, is that all learners, however young, can see the connections between each representation.
Impact Maths No Problem will have on our children
> Children will understand how to use resources to support their learning
> Provides consistent methods across the school for your child to access
> It will challenge them to grow as mathematicians
Please take a look at this in more depth here.
You can also look at some great Parent Videos if you would like any more information.
Oulton Promotional Video for Parents
This video illustrates the work we do as a school to ensure that all children in our care receive the best possible start to their educational journey. We have a responsibility to offer a broad, balanced, exciting and engaging curriculum that truly focuses on the whole child and gives them the oppor...


Table of Contents
The key to achieve the highest possible performance when working with splines is precalculation. In Curvy the following spline data is precomputed:
- Distances between positions
- Tangent (Direction) for each position
- Up Vector (Orientation) for each position
As you remember (perhaps read here again), a spline by nature has no resolution. You enter a F value and get a position in return. But of course the step width should be limited to reasonable values. At some point a lower stepsize makes no sense due float inaccuracy. We've seen spline solutions using doubles, but transforms and visual presentation in Unity are float based, so calculating doubles would produce a precision that can't be visualized.
To sum it up, calculating spline curves is about querying a formula continously with a given stepsize and retrieving approximated points. Those points connected form the spline you see on screen. The number of sample points a spline uses is calculated automatically based on it's length, but can be influenced by you. In general, sample points (we call them Approximation Points or cache points) are spread at equal distance over a spline segment (in fact the segment length is roughly guessed at calculation time by taking the distance between the two involved Control Points).
This spline parameter determines how many cache points you want to get calculated. Being a percentage the setting ranges from “None” to “Highest”. The default value of 50% is a good compromise between performance and precision most of the time. The real amount of cache points depends also on a global setting called
Max Cache PPU
This global setting (see Max Cache PPU) determines the maximum possible number of cache points per world unit. For example, if you set it to 10 and set the spline's Cache Density to maximum, a spline segment with a length of 20 units will calculate 200 cache points.
Memory vs. Accuracy
In general, having more sample points will result in a higher degree of accuracy. As a downside, precomputing takes longer and more memory is used. You can (but don't neccessarily need to) tweak the above two settings if you need more accurate values or a faster calculation. Which values work best for you depends on your setup.
Curvy uses a sophisticated caching system. If you alter a spline, only the neccessary values are being recalculated (usually on the next call to Update). On top of that you can enable threading to speed up calculation. Threading comes with a management overhead, so it's most useful for very large splines that are continuously changed.


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Calculus&Mathematicaintegrals : measuring accumulated growth
- 342 Pages
- 4.25 MB
- 1178 Downloads
Addison-Wesley , Reading, Mass
Mathematica (Computer file), Calculus, Integral -- Data processing., Growth -- Data proces
|Other titles||Calculus & Mathematica., Calculus and Mathematica., Integrals.|
|Statement||Bill Davis, Horacio Porta, Jerry Uhl.|
|Contributions||Porta, Horacio., Uhl, J. J.|
|LC Classifications||QA311 .D38 1994|
|The Physical Object|
|Pagination||ix, 342 p. :|
|LC Control Number||94138866|
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Apr 10, · I was one of Bill Davis' undergrad Calc students during the development of the course material and the writing of "Calculus and Mathematica". There were a number of times when the course material was merely days old when Dr.
Davis was presenting it to us.5/5(1). Mar 12, · I Calculus&Mathematica book very happy to encounter "Mathematica for Calculus Based Physics" which provided me with a number of insights into to the calc based sequence itself and how I can use this to enhance my students educational experiences.
If you are considering using Mathematica for either calc or calc based physics I strongly recommend that you obtain this Cited by: 2. In calculus even more than other areas, the Wolfram Language packs centuries of mathematical development into a small number of exceptionally powerful functions.
Continually enhanced by new methods being discovered at Wolfram Research, the algorithms in the Wolfram Language probably now reach almost every integral and differential equation for which a closed form can be found.
This unique book is a collection of Mathematica notebooks, designed to be used through the Help Browser. It is mathematically complete enough to be used as a text for a highly Mathematica-focused, three-semester calculus sequence.
It can also be used as a supplement to a more traditional text in courses that have a Mathematica lab component. Advanced Calculus Using Mathematica: NoteBook Edition is a complete text on calculus of several variables written in Mathematica NoteBooks.
The eText has large movable figures and interactive programs to illustrate things like "zooming in" to see "local linearity.". Publisher Summary. This chapter discusses the study of model epidemics using calculus.
Calculus is the language of Calculus&Mathematica book and that language allows studying change in. Large collection of Mathematica and Wolfram Language-based books and references written by leading experts.
Search by topic or language. Jun 17, · From 31 MarchYouTube services in the UK will be provided by Google LLC. Advanced Calculus with Mathematica Version is a complete electronic text in multivariable calculus in Wolfram Notebook format. The eText includes many interactive programs that illustrate fundamental concepts such as a movable plane tangent to a surface, a moving osculating circle, or the flux of.
Advanced Calculus Using Mathematica: NoteBook Edition is a complete text on calculus of several Calculus&Mathematica book written in Mathematica NoteBooks. The eText has large movable figures and interactive programs to illustrate things like 'zooming in' to see 'local linearity.' In addition to lots of traditional style exercises, the eText also has sections on computing with Mathematica.
These "How tos" give step-by-step instructions for common tasks related to calculus in the Wolfram Language. Get this from a library. Calculus & mathematica. Part 1, Give it a try.
[Donald P Brown; Horacio Porta; J J Uhl] -- Calculus & Mathematica, Part 1, contains 30 lesson units covering the first two terms of calculus, both on disk and in printed form. Each disk-based unit is organized with three components: "Basics". Jan 01, · Buy a cheap copy of Vector Calculus & Mathematica book by Bill Davis.
A computer-based calculus course consisting of a complete interactive electronic text combined with a rich set of well chosen real life problems. The easy access to Free shipping over $Pages: 1.
Abstract The Calculus with Mathematica project is devoted to improving conceptual understanding of the calculus by making use of the Mathematica technical computing software to solve more challenging kinds of applications than are traditionally examined in undergraduate calculus.
This MUSPIN-funded pilot project has been implemented at South Carolina State University for two. Calculus: Mathematica / Edition 1.
by Roland E. Larson | Read Reviews. Multimedia Set. Current price is, Original price is $ You. Buy New $ Buy Used $ $ $ Save 13% Current price is $, Original price is $ You Save 13%.
Publish your book with B&dsc-sports.com: $ Dec 21, · For the latest information, please visit: dsc-sports.com Speaker: Keith Stroyan Wolfram developers and colleagues discussed the latest in innovative.
Vector Calculus book. Read reviews from world’s largest community for readers. A computer-based calculus course consisting of a complete interactive elec 4/5(1). Note: Citations are based on reference standards.
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However, formatting rules can vary widely between applications and fields of interest or study. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.
Aiming to "modernise" the course through the integration of Mathematica, this publication introduces students to its multivariable uses, instructs them on its use as a tool in simplifying calculations, and presents introductions to geometry, mathematical physics, and kinematics.
One of the authors' stated goals for this publication is to "modernize" the course through the integration of Mathematica.
Besides introducing students to the multivariable uses of Mathematica, and instructing them on how to use it as a tool in simplifying calculations, they also present. Calculus & Mathematica: Vector Calculus: Measuring in Two and Three Dimensions, Volume 4. Bill Davis, Horacio Porta, J. Jerry Uhl.
Addison-Wesley, - Mathematics - pages. 0 Reviews. From inside the book. What people are saying - Write a review. We haven't found any reviews in the usual places.
Contents. Measuring in Two.
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4: Advanced Mathematics for Applications Mathematica Notebooks These Mathematica notebooks are all used for teaching and illustrating concepts. Most have some "discovery learning" built in. These notebooks are used in the course Advanced Mathematics for Applications at. Using the medium of the Mathematica notebooks, helps students explore and discover calculus concepts by exposing them to real data and real problems.
Contains thirty lesson units covering the first two terms of calculus. The manuals support the courseware by allowing students to review the printed problems when they are not working on the computer. Mathematica® for Rogawski's Calculus 2nd Edition Based on Mathematica Version 7 Abdul Hassen, Gary Itzkowitz, Hieu D.
Nguyen, Jay Schiffman W. Freeman and Company New York. Can you find your fundamental truth using Slader as a completely free Stewart Calculus solutions manual. YES. Now is the time to redefine your true self using Slader’s free Stewart Calculus answers.
E-Book Review and Description: Visualizing Differential Equations with Mathematica, and Animating Calculus: Mathematica Notebooks for the Laboratory. From Evaluations of the Second Version: 'The underside line is that’s an impressive book containing many examples of actual makes use of of Mathematica for the novice, intermediate, and.
For questions on the book or the algebra Please let us know if you have any questions relating to the book or algebra, particularly errors or omissions. How to do matrix calculus in Mathematica. Ask Question Asked 4 years, 3 months ago.
Active 4 years, 3 months ago. Viewed 1k times 7. 2 $\begingroup$ I would like to differentiate Ax with respect to A where A is a matrix. Now, obviously, I know the derivative is x but for more nasty expressions, is there a way to differentiate expressions with.
Calculus has occupied a central position in scientific thought ever since its discovery by Newton and Leibniz more than years ago. The combination of elegance, utility, and rigor that characterize this subject have led to its extensive use in theoretical approaches to diverse fields such as economics, finance, and biology.
Oct 08, · An introduction to vector calculus with the aid of Mathematica® computer algebra system to represent them and to calculate with them. The unique features of the book, which set it apart from the existing textbooks, are the large number of illustrative examples.
Level curves and surfaces can be plotted in Mathematica.
Description Calculus&Mathematica PDF
These are the constant-value regions of a particular function. The command behaves very much like the Plot and VectorPlot command.It introduces these teachers to the content and pedagogy of the Calculus&Mathematica course. This module is suitable for any mathematics teacher interested in learning more about the Calculus&Mathematica course or, more generally, in interactive mathematics texts.
Sponsored by the University of Illinois at Urbana-Champaign Center.Jul 28, · An introduction to vector calculus with the aid of Mathematica® computer algebra system to represent them and to calculate with them.
The unique features of the book, which set it apart from the existing textbooks, are the large number of illustrative examples.
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Frequency, how often something happens, the frequencies most often coming to mind are the 20 to 20,000 cycles per second (abbreviated as Hertz) of good human hearing (not mine, for sure!) or the radio frequencies of 550 kiloHertz to 1800 kHZ of the AM band, or the GigaHertz processing speed of computer chips.
Related to this equation is finding the distance between fringes; instead of fringes per mm, how big is a fringe cycle? (= the distance from the center of one bright fringe to the next.) It is simply the inverse of the spatial frequency equation:
(And don’t forget theta 2 is a negative angle, otherwise you will have an error!) (Or to make life easier, forget about the sign convention, and just add the sines of the two angles as positives together! But watch your step when getting too far off the track!)
Alternatively, to find the fringe spacing distance, you could simply use the 1/x button on the calculator once you have your spatial frequency. In either case the distance will be in millimeters, and the digits will usually all pop up behind the decimal point, so if you want to convert to microns, move the decimal point over three places to the right.
Onward and upward, as my Abstract Algebra teacher used to say
. (while I nodded off!)