So this new video of an apparent teacher training session on Common Core math — in which the trainer explains how getting the wrong answer is right — will come as no surprise (via Stanley Kurtz):
The twisted pedagogy is the same in all of these curricular fads: Encourage “critical thinking” and “explaining” of “how and why” over time-tested, efficient methods of “drill and kill” first. Abandon memorization and computation for social justice, multiculturalism , and self-esteem.
This cartoon I posted back in 2007 still says it all about constructivist, “strategy”-obsessed, non-math math:
January 28, 2015 08:03 AM by Michelle Malkin
January 10, 2015 05:51 AM by Doug Powers
January 5, 2015 02:29 PM by Doug Powers
December 10, 2014 10:11 AM by Doug Powers
December 9, 2014 09:51 PM by Michelle Malkin


There are three sections of the SAT with math questions. One of the sections is 20-minutes long and the other two are 25-minutes long. There are a total of 44 multiple choice problems and 10 student-produced response problems in which you must “grid in” your answer. Try out our free online tests to help with your SAT math practice. These multiple choice SAT math problems are similar to the questions found on the actual test.
SAT Math Practice Tests
- SAT Math Practice Test 1 (Easy)
- SAT Math Practice Test 2 (Medium)
- SAT Math Practice Test 3 (Medium)
- SAT Math Practice Test 4 (Difficult)


How to generate a list of random Numbers (random integers, floating point, unique numbers, etc!) "Click here http://www.hothotsoftware.com/videoImage.php?mainname=10 for more details on Random Number Generator to create random number sequences software, random integers and random floating point numbers Create a list of random numbers using this great random number generator! Some of the main features include: You can specify minimum and maximum ranges of numbers that you would like to generate. Choose the number of random numbers you would like to generate (100,000) Choose whether or not to include only unique random numbers Random Integer Number Generation: Choose what digits to include in random number generation of integer numbers Specify whether you only want odd or even integer sequences of random numbers to be created Floating Point Random Number Generation: Specify the floating point precision Other Features: You can use these sequences of numbers for anything, including programming projects, game development, and more in c++, java, python, asp pages, php, vbscript and so forth. Excellent source of random numbers for seeding data Choose your own delimiter between the random numbers, and then save the resulting output Get it now, or try it for free!"
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It All Adds Up
9/11/2013Central Catholic Teacher Awarded Raytheon Grant
Raytheon Corporation has awarded a Math Hero Award and grant of $2,500 to Central Catholic math teacher, Jarrod Brown, through Raytheon’s “Math Moves U” program. The “Math Moves U” awards program recognizes 35 full-time mathematics teachers from across the USA who have made great strides in instilling a love of math in students and for their dedication to enriching math instruction in high schools across the US.
Brown was nominated for the Raytheon award by current and former students, Mary ‘15 and William Rayno ‘13, for his instructional creativity and patience, varied use of technology resources, and his ability to share his enthusiasm for mathematics with his students. Brown will use the Raytheon grant to complete his Master’s Degree in Mathematics Education.
Raytheon’s “Math Moves U’ program has also awarded a matching $2,500 grant to Central Catholic in Brown’s name. The matching grant will be utilized to fund “math apps” on students’ iPads and expand technology-based mathematics resources for students.
Brown, a 1998 Central Catholic graduate, earned a B.S. in Mathematics from the University of Massachusetts at Lowell. In his 10th year as a math instructor, Brown’s teaching experience includes leading classes in Algebra 1, Geometry, Algebra 2 & Trigonometry, Pre-Calculus, and Calculus. Brown also serves as an assistant coach in football and track in addition to being the instructor for the Karate and Martial Arts Club at Central Catholic.
Brown and his wife, Ashleigh Ward Brown, a 2000 CCHS alumna, have two children, Adalayde and Allyson. They make their home in Dracut.About Central Catholic
Founded by the Marist Brothers in the heart of Lawrence, Massachusetts in 1935, Central Catholic High School enrolls approximately 1,350 students from over 40 cities and towns and four countries. Students come from diverse backgrounds to form a caring community of faith, learning, and service. They advance to college in overwhelming numbers (nearly 100%) and move on to successful careers and positions of leadership in government, business, industry, academia, and professions. For more information, please visit our website www.CentralCatholic.net
or call 978-682-0260.


First you need to know about the Mandelbrot set... a simple mathematical formula (That's right I'm talking maths). The Mandelbrot set was created / discovered over 35 years ago. We know it to be a "fractal" a type of shape that often shows complex detail that replicates itself forever. No matter how far you zoom into the formula new replicated detail is seen.
The Mandelbrot fractal however is 2D and flat. The 3D Mandelbulb story starts with a guy named Rudy Rucker, an American mathematician, computer scientist and science fiction author (and in fact one of the founders of the cyberpunk science-fiction movement). Around 20 years ago, along with other approaches, he first imagined the concept behind the potential 3D Mandelbulb, and also wrote a short story about the 3D Mandelbrot in 1987 entitled "As Above, So Below". Back then of course, the hardware was barely up to the task of rendering the 2D Mandelbrot, let alone a 3D version - which would require billions of calculations to see the results, making research in the area a painstaking process to say the least.
When computers did catch up the first 3D fractals created lacked the finite detail that 2D fractals showed. Simply replicating the standard 2D fractal formula, spinning it 360 degrees in the Z direction yeilded un-exciting results.
Another fractal explorer, computer programmer David Makin was the first to render a 3D Mandelbulb that showed the results everyone was searching for. These first images reminded me of a newborn plant, with leaves and roots shooting off in all directions.
With each new completed render the true organic natural beauty of these 3D fractals became apparent and just how much they looked like naturally occuring life-forms. These organic mathematical shapes can be seen all around us, from the tinyist seashell in a rock pool to the coastlines and beyond.
I feel special but at the same time humbled, like a creative kid in a psychedelic fantasy microcosm, viewing rare visuals that I can control. I can't help but think that these formulas could be what we need to create true A.I. in the not to distant future.
By now you're thinking I'd like to try this for myself. The good news is there is free software for you to download. While the learning curve differs in each package there is a huge community online that can provide help.
Static images of 3D Fractals are great but the animation videos below will simply amaze. These videos especially the HD versions can take days even weeks to produce due to the processing power needed to produce each frame.
A variety of fractal related links. Various sites that contain more technical related information, galleries, papers and resources.


Inspired by a recent query at one of the Excel forums I occasionally visit, I would like to share a formula-based solution for the task of generating an nxn grid of random integers, where each of those integers is unique within that range.
For example, for the case of n=10, we might have, in A1:J10:
where I have formatted the cells in this range as custom type: 00 (applying a TEXT function to the formula would complicate matters, in the sense that this would interfere with the functioning of our FREQUENCY construction).
Last week I set readers the challenge which can be found here.
This one was perhaps a little less complex than ones I’d set in previous weeks, though of course it would still, in my opinion, fall within the boundaries of what I would deem “advanced Excel”.
It also demonstrates some techniques which we can apply to solving problems involving non-contiguous ranges, and in particular tell us which functions may be applicable to such set-ups.
Two good solutions received from John Jairo V and cyrilbrd (and Bill‘s was practically there as well, but for a small amendment – and the fact that I didn’t structure the question in full to begin with – sorry!).


What's company mathematics? Well, it's the discipline of employing mathematical theories to create business plans and enhance budget and management management. Indeed, the company world is frequently described with entrepreneurs and businesses relying upon business math to address all kinds of problems, as the area in the world. Let's take a good look at this discipline to understand the way it can contribute to your company and what it is.
Business math is made up of several different mathematical essay helper online concepts which may be applied to business situations. banane licorne Below are a few of the concepts employed by business math experts. They are the growth of new strategies, division of work, effective utilization of limited resources, and also the ideas of strategy.
Plan involves the idea of determining how a task can be effectively performed by a company. For instance, many business math experts talk about the idea of a plan matrix, a matrix used to assess the progress of an organization or business. peluche pokemon The matrix, the whole organization set on precisely the side of the matrix and also on each of the individuals .
The people on the very first line of this matrix could be considered while the folks on the lines would masterpapers be regarded as the faces of each individual, to be the face of the business. cover iphone x xs Thus, where the individuals were positioned in the matrix could determines the direction the company is headed.
The business matrix can be used to determine the number of areas to be covered, the benefits to be realized, the time needed for a certain task, the amount of money to be invested in acquiring these benefits, and the amount of money needed to acquire each benefit. This process can also be applied to new development in business.
Cost is another concept associated with business math. Cost could be the amount of money that has to be invested in acquiring the required resources to perform a certain task or it could also refer to the amount of money that will be required in the future to perform that task.
A concept is the idea of division of work. Employing the idea of division of labor, a specific task's necessities can split .
It's important to understand that the division of labor is defined differently by different business managers. Some people will agree to do certain tasks, but they will also insist on one person doing https://www.linfield.edu/assets/files/chem/Courses/CHEM%20321/2015_FigureandTableGuidelines.pdf the same task. Others may prefer a more individual approach.
As we discussed earlier, a very strong purpose to divide labor is to maintain the unity of the whole. serviette licorne When you have a team of people, each person contributes in a particular role, and when there is one person who has a strong motive to work on a certain area, other people are less likely to let that person take over for another person.
Efficient management's principles may be based on the usage of division of work. goed iphone hoesje Whether it's the notion of creating particular problems by having one person handle one issue or problems or earning decisions labor can save valuable time.
Business math is not about the use of mathematical concepts, but it's also about making informed decisions.


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Definition: A customized momentum indicator that measures the convergence/divergence of a short length trend line and long length trend line.
shortLength: The number of previous values in calculating for short trend.
longLength: The number of previous values in calculating the long trend.
Return: Time series measuring convergence/divergence
Description: The Moving Average Convergence Divergence (MACD) is a popular technical indicator that measures the relationship between two moving averages of an asset's price. It is calculated by subtracting the 26-period exponential moving average (EMA) from the 12-period EMA. The MACD line can be used to identify trend changes, momentum, and potential buy and sell signals.
macdValue = SPY.close -> macd(15, 30)
length= the number of previous values used in the calculation
Return: A time series of smoothed values
Description: Simple moving average (SMA) is a widely used technical indicator that calculates the average price of an asset over a specific time period. It is a lagging indicator, meaning it responds slowly to changes in price. Traders use SMAs to identify trends and potential buy and sell signals, with longer periods (e.g., 50-day SMA) used for long-term trends and shorter periods (e.g., 10-day SMA) used for short-term trends.
avgSimpleValue = SPY.close -> sma(30)
Definition: Combines values from a list of input time series. The values from all inputs at each point in time are combined using a specified calculation.
combine- what calculation to use when combining values
weights- optional, is used to adjust the weighed average.
Return: Single time series of combined values from each point in time
Description: Supported combination methods are:
mean- value is the average of values from inputs
max- value is the maximum of values from inputs
min- value is the minimum of values from inputs
sum- value is the sum of values from inputs
The default value is
How does Weight get calculated:
We multiply each number by its corresponding weight, sum up the weighted values, and then divide them by total weight.
Weighted Average = (Number1 * Weight1 + Number2 * Weight2) / (Weight1 + Weight2)
combined_values = [SPY, ORCL].close -> combine_lists(combine=”max”, weights="7,9")


- How much are bricks per 1000?
- How do you calculate construction cost?
- How do I calculate how many bricks I need for a patio?
- How many bricks do I need for a 10×10 patio?
- How many square feet does 1000 bricks cover?
- How many bricks do I need for 300 square feet?
- How many bricks do I need for 200 square feet?
- How many bricks do I need for a 100 square foot patio?
- How many bricks do I need for a patio per square foot?
- How many sq ft is 20×20?
- How many bricks are in a square foot?
- How many bags of cement do I need for 1000 bricks?
- How do I calculate how many bricks for a 4 inch wall?
- How many bricks do I need for a 1200 sq ft house?
- How much does it cost to brick a 2500 square foot house?
- How do I calculate how many bricks I need?
How much are bricks per 1000?
Bricks are $1.32 each and delivery is $154 per thousand in Sydney metro..
How do you calculate construction cost?
Approximate cost on various work of material to complete the construction for 1000 ft 2Total Cost. =Builtup area×Approx cost per sq. ft. = Builtup area × Approx cost per sq. ft. … Amount of Aggregate Required. =Builtup area×0.608. =1000×0.608. =608.00 Ton. Aggregate Amount. … Flooring. =Builtup area×1.3. =1000×1.3. =1300.00 Sq. ft.
How do I calculate how many bricks I need for a patio?
How to Calculate Brick Pavers for a PatioMeasure the size of the top of the chosen style of paver. … Divide a square foot, or 144 inches, by the area the paver will cover. … Measure the area planned for the patio. … Multiply the number of pavers needed to cover one square foot of patio by the number of square feet of the patio.More items…
How many bricks do I need for a 10×10 patio?
450 bricksFor our example, this means you’ll need 450 bricks to cover your 10’x10′ patio space.
How many square feet does 1000 bricks cover?
For example, if you are using King Size brick on 1000 square feet, your calculation would be 1000 * 4.7 = 4700 bricks for the job. The number of masonry cement bags will then be 470/1000*6 = 2.82 bags. Bricks/sq. ft.
How many bricks do I need for 300 square feet?
Determine the amount of bricks needed for the job by multiplying the square footage — 120 square feet — by the number of bricks in a square foot — 4.5. For this instance, 540 bricks are needed.
How many bricks do I need for 200 square feet?
For example: If the height of the wall is 10 feet and its length is 20 feet, the area of the wall is 200 square feet. About seven modular thin brick are needed to cover a square foot, so 200 square feet X 7 thin brick per square foot = 1,400 thin brick to cover the wall.
How many bricks do I need for a 100 square foot patio?
In this case, 144 divided by 32 is 4 1/2 pavers per square foot. Multiply that number by the area square footage; if you have 100 square feet to fill, you need at least 450 pavers.
How many bricks do I need for a patio per square foot?
4.5 bricksDivide 144, the number of square inches in one square foot, by the square inches of the brick to determine the number of bricks needed to cover 1 square foot of patio surface. For the standard brick size of 32 square inches, 4.5 bricks are needed to cover 1 square foot of patio.
How many sq ft is 20×20?
400 square feetSo if a area is 20 foot wide by 20 foot long, 20 x 20 = 400 square feet.
How many bricks are in a square foot?
7 bricksCalculating the Number of Bricks Needed. A wall built with a standard modular brick will require 7 bricks per square foot to complete the project. Projects using different brick sizes will require a different amount.
How many bags of cement do I need for 1000 bricks?
3 bags cementTo lay 1000 bricks = 3 bags cement + 0.6 cu. m. sand.
How do I calculate how many bricks for a 4 inch wall?
first stage is just to measure the height and length of the wall in metres, multiply them together to give the area in square metres, and then multiply this by 55. Hence for brick wall calculation, 55 number of brick is required in 4 inch wall of 1 square metre brick wall.
How many bricks do I need for a 1200 sq ft house?
Site Size: 30×40 site house construction cost (Ground + 1, 3 BHK) upto 1875 Sq. ft built up area.Materials RequiredQTYUnitConcrete M Sand52Tonnes40mm Jelly410Cft20mm Jelly2305Cft4″ Clay Bricks16200Nos.4 more rows•Jan 21, 2019
How much does it cost to brick a 2500 square foot house?
The average cost to add bricks to a 2,500-square-foot home is $12,000 to $25000, including the materials needed and the labor involved.
How do I calculate how many bricks I need?
For a singular layer brick wall, multiply the length of the wall by the height to get the area. Multiply that area by 60 to get the number of bricks you should need, then add 10% for wastage. That’s the short answer and assumes ‘standard’ brick and mortar sizes. It can also vary based on the type of structure.


I am a postdoctoral researcher at Oxford in the Centre for Topological Data Analysis. My research concerns applied algebraic topological approaches to dynamical systems. I completed my PhD at Rutgers University under Konstantin Mischaikow, with the support of a NSF Graduate Fellowship. I spent half of 2018 as an NSF GROW Fellow at VU Amsterdam working with Rob Vandervorst. I was a long term visitor at the Mathematical Biosciences Institute over the fall of 2016 and an NSF EAPSI Fellow at Kyoto University with Hiroshi Kokubu over the summer of 2013. Here is a brief CV.
Broadly speaking, I am interested in the development of mathematical theory and computational tools for the analysis of nonlinear or high-dimensional data generated by dynamical systems. I typically work within the realms of applied topology or computational dynamics, in particular on computational Conley theory, connection and transition matrix theory, and topological data analysis. I'm also interested in the applications of these tools to sytems biology and general data analysis. For more details, see my research statement or google scholar page.
With Stefanos Leonardos and Georgios Piliouras.
Abstract: The interplay between exploration and exploitation in competitive multi-agent learning is still far from being well understood. Motivated by this, we study smooth Q-learning, a prototypical learning model that explicitly captures the balance between game rewards and exploration costs. We show that Q-learning always converges to the unique quantal-response equilibrium (QRE), the standard solution concept for games under bounded rationality, in weighted zero-sum polymatrix games with heterogeneous learning agents using positive exploration rates. Complementing recent results about convergence in weighted potential games, we show that fast convergence of Q-learning in competitive settings is obtained regardless of the number of agents and without any need for parameter fine-tuning. As showcased by our experiments in network zero-sum games, these theoretical results provide the necessary guarantees for an algorithmic approach to the currently open problem of equilibrium selection in competitive multi-agent settings.
Submitted. Here is the arxiv preprint (2021).
With Shaun Harker and Konstantin Mischaikow.
Abstract: We introduce the notion of a template for discrete Morse theory. Templates provide a memory efficient approach to the computation of homological invariants (e.g., homology, persistent homology, Conley complexes) of cell complexes. We demonstrate the effectiveness of templates in two settings: first, by computing the homology of certain cubical complexes which are homotopy equivalent to Sd for 1 ≤ d ≤ 20, and second, by computing Conley complexes and connection matrices for a collection of examples arising from a Conley-Morse theory on spaces of braids diagrams.
Submitted. Here is the arxiv preprint (2021).
With Hannah Alpert, Uli Bauer, Matt Kahle, and Bob MacPherson.
Abstract: We study the configuration spaces C(n;p,q) of n labeled hard squares in a p by q rectangle, a generalization of the well-known "15 Puzzle". Our main interest is in the topology of these spaces. Our first result is to describe a cubical cell complex and prove that is homotopy equivalent to the configuration space. We then focus on determining for which n, j, p, and q the homology group Hj[C(n;p,q)] is nontrivial. We prove three homology-vanishing theorems, based on discrete Morse theory on the cell complex. Then we describe several explicit families of nontrivial cycles, and a method for interpolating between parameters to fill in most of the picture for "large-scale" nontrivial homology.
Submitted. Here is the arxiv preprint (2020).
With Shaun Harker and Konstantin Mischaikow.
Abstract: The connection matrix is a powerful algebraic topological tool from Conley index theory, a subfield of topological dynamics. Conley index theory is a purely topological generalization of Morse theory in which the connection matrix subsumes the role of the Morse boundary operator. Over the last few decades, Conley’s approach to dynamics has been cast into a purely computational form. In this paper we introduce a computational and categorical framework for connection matrix theory. Broadly speaking, this contribution promotes the computational Conley theory to a computational, homological theory for dynamical systems. More specifically, within this paper we have three specific aims:
1. We cast connection matrix theory in an appropriate categorical, homotopy-theoretic language. We demonstrate the relationship to the previous definitions of connection matrix. Lastly, the homotopy-theoretic language allows us to formulate connection matrix theory categorically.
2. We describe an algorithm for the computation of connection matrices based on algebraic-discrete Morse theory and formalized with the notion of reductions. We advertise an open-source implementation of our algorithm.
3. We show that the connection matrix can be used to compute persistent homology. Ultimately, we believe that connection matrix theory has the potential to be an important tool within topological data analysis.
Here is an official version in Journal of Applied and Computational Topology and the arxiv.
With Bree Cummins and Tomas Gedeon.
Abstract: We present a theoretical framework for inferring dynamical interactions between weakly or moderately coupled variables in systems where deterministic dynamics plays a dominating role. The variables in such a system can be arranged into an interaction graph, which is a set of nodes connected by directed edges wherever one variable directly drives another. In a system of ordinary differential equations, a variable x directly drives y if it appears nontrivially on the right-hand side of the equation for the derivative of y. Ideally, given time series measurements of the variables in a system, we would like to recover the interaction graph. We introduce a comprehensive theory showing that the transitive closure of the interaction graph is the best outcome that can be obtained from state space reconstructions in a purely deterministic system. Our work depends on extensions of Takens' theorem and the results of Sauer et al. [J. Stat. Phys., 65 (1991), pp. 579--616] that characterize the properties of time-delay reconstructions of invariant manifolds and attractors. Along with the theory, we discuss practical implementations of our results. One method for empirical recovery of the interaction graph is presented by Sugihara et al. [Science, 338 (2012), pp. 496--500], called convergent cross-mapping. We show that the continuity detection algorithm of Pecora et al. [Phys. Rev. E, 52 (1995), pp. 3420--3439] is a viable alternative to convergent cross-mapping that is more consistent with the underlying theory. We examine two examples of dynamical systems for which we can recover the transitive closure of the interaction graph using the continuity detection technique. The strongly connected components of the recovered graph represent distinct dynamical subsystems coupled through one-way driving relationships that may correspond to causal relationships in the underlying physical scenario.
Here is an official version in SIAM Journal on Applied Dynamical Systems.
With Jesse Berwald and Tomas Gedeon.
Abstract: Complex dynamical systems, from those appearing in physiology and ecology to Earth system modelling, often experience critical transitions in their behaviour due to potentially minute changes in their parameters. While the focus of much recent work, predicting such bifurcations is still notoriously difficult. We propose an active learning approach to the classification of parameter space of dynamical systems for which the codimension of bifurcations is high. Using elementary notions regarding the dynamics, in combination with the nearest-neighbour algorithm and Conley index theory to classify the dynamics at a predefined scale, we are able to predict with high accuracy the boundaries between regions in parameter space that produce critical transitions.
Here is an official version in Mathematical and Computer Modelling of Dynamical Systems.
slides | video for an introductory talk on Conley-Morse theory for maps, with an application to game theory given at the Fields Institute Symposium on Machine Learning and Dynamical Systems and the Oxford Applied Topology Seminar.
slides for a talk given at the CRM 2019 Workshop on Data Driven Dynamics, the SUNY Albany Algebra/Topology Seminar, the Fall 2018 IAS-Penn-Rutgers joint workshop Identifying Order in Complex Systems, and the UPenn Applied Topology seminar.
slides for a talk at the MBI Visitor Seminar in December 2016.
My Ph.D. dissertation is available here. Roughly one third of the thesis is the material contained in A Computational Framework for Connection Matrix Theory.
I wrote a User's Guide for the Conley-Morse database during my time as an NSF EAPSI Fellow at Kyoto University. It is available here. The intended audience is potential users of the Conley-Morse database who have had little exposure to dynamics or even mathematics.
In Fall 2019 I was a TA at Large for Math 252: Elementary Differential Equations.
In Fall 2018 I was a TA for Math 151: Calculus I for the Mathematical and Physical Sciences Sections 25-27.
In Fall 2017 I was a TA for Math 244: Differential Equations for Engineering and Physics at Rutgers.
Over summer 2017 I was the instructor for the introductory algebra course (Math 351) at Rutgers University. The textbook we used was baby Hungerford. Here are some lecture notes I wrote for the course, which were popular among the students.
In Spring 2018 I was TA for both Calculus II and Linear Algebra for Business Analytics at VU University in Amsterdam.
spendlove at maths.ox.ac.uk
University of Oxford
Radcliffe Observatory Quarter
Oxford, OX2 6GG, UK
S3.08, Andrew Wiles Building


I'm sure many have started the calculations. :)
LHDN has came up with their new BE2010 format, therefore i have also updated mine to incorporate the minor changes. Nothing much, hope you find this useful.
You can download the latest Borang BE2010 calculator HERE
Let me know if you find any errors as well as if you find it useful! Thanks guys.
P/S: If you need additional info on the new BE2010, head on to LHDN website or you can download the sample form and its explanations HERE


DDr. Philipp Hungerländer
The two main fields of my research are semidefinite, conic and polynomial optimization and quadratic programming. In the first field the objective of my research is to provide guaranteed optimal or near-optimal solutions for important classes of large-scale discrete nonlinear optimization problems arising in engineering and economic applications. My current interests are in developing new models and algorithms for solving problems in the areas of graph drawing and layout. In the second field I work on developing new active-set algorithms with fair convergence properties and a strong practical performance that can be applied to convex/nonconvex, bound-constrained/equality constrained, continous quadratic problems. Additionally I am fascinated by game theory and do some research on different aspects of dynamic games.
I recently finished my PhD in Economics and Business Administration and I am currently working on my "habilitation" in Operations Research and Applied Mathematics.


Objective In order to address the nagging issue of laboratory errors, we develop and assess a strategy to detect mismatched specimens from nationally collected blood laboratory data in two tests. curves (AUCs) and with contract statistics. LEADS TO Test 1 the network was most predictive of mismatches that created medically significant discrepancies between accurate and mismatched ratings ((AUC of 0.87 (0.04) for HbA1c and 0.83 (0.02) for blood sugar), performed well in buy 211254-73-8 identifying mistakes among those self-reporting diabetes (N = 329) (AUC = 0.79 ( 0.02)) and performed significantly much better than the established treat it was tested against (in Rabbit polyclonal to AKAP5 every situations p < .0.05). In Test 2 it performed better (and in no case worse) buy 211254-73-8 than 7 from the 11 individual experts. Typical percent contract was 0.79. and Kappa () was 0.59, between experts as well as the Bayesian network. Conclusions Bayesian network may identify mismatched buy 211254-73-8 specimens. The algorithm is most beneficial at determining mismatches that create a medically significant magnitude of mistake. = ?G, P? includes a representing graph, G, and an linked joint possibility distribution, P. The graph, G, in the network is certainly described with a finite group of nodes V and a binary relationship, R on V. A binary relationship on a couple of nodes V is certainly a subset of purchased pairs (vi, vj) in V V. The relationship R characterizes sides in the graph, where R = (vi, vj) V V: vi is a vj. Allow viRvj denote vi is certainly a vj. The relation R is usually (for every vi V, not viRvi) and (for any finite sequence of distinct elements v1,v2,,vk V such that k > 1 and vjRvj+1 for all those j 1, 2, , k-1 , not vkRv1). An irreflexive graph is called a (DAGs). The DAG, G, in the Bayesian network, = ?G, P?, represents the probability distribution, P, where nodes in V characterize random variables and directed edges describe stochastic dependence. If vi is buy 211254-73-8 usually a variable in the graph then the graph specifies conditional probability distributions P(vi|(vi)), where (vi) are parents of vi. While each variable vi is dependent on its parents, it is also conditionally impartial of any of its non-descendants given its parents. Hence, given a directed acyclic graph G with a set of nodes V = v1, , vn the buy 211254-73-8 joint probability distribution of the network may be factored as follows: or gives the probability of a mismatch between glucose and HbA1c for any switching pair. We implemented this switching process to produce three mismatch scenarios: 1) 50% of specimens mismatched (i.e., = ?), 2) 10% of specimens mismatched (i.e., = 1/10), and 3) 3% of specimens mismatched (i.e., = 3/100). Note that by the aforementioned process there is an equal probability of an analytic value being switched with any other. In a sub-analysis, we made a switch contingent on the size of the error it would produce (small, medium or large). The classifier results presented here may be vunerable to bias if the opportunity of mismatch in observational research is certainly linked highly with analyte rating. Such a romantic relationship would attenuate classification functionality, because switches would occur even more among like outcomes frequently. This effect will be mediated through another variable that affects both possibility of analyte and switch score. There are in least two potential mechanisms where test switching may occur. Right here we talk about how these systems might or may not have an effect on mismatch possibility being a function of analyte rating. The first is through after samples reach the laboratory. Because laboratories label a large number of samples arriving from different locations, collected at different times and the introduction and labeling happen in a nonsystematic manner (i.e., medical sites and laboratories do not coordinate when blood is definitely sent or labeled), there is no discernible pathway by which analyte score may be associated with increased probability of a switch. A second mechanism for switching is at collection and processing from the phlebotomist. With this system a romantic relationship between analyte switch and score could possibly be mediated through time-of-draw. It really is plausible that, because of fatigue from the phlebotomist, pulls might event more turning mistakes later. Further, other factors that have an effect on analyte rating, like health-status of the individual, might relate with time-of-draw also. Because this stands like a potential danger to the present analysis, we measure the aftereffect of time-of-draw in detailing analyte rating variance. If time-of-draw is an unhealthy predictor of analyte rating we are less concerned that time-of-draw after that.


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We work directly where elementary kids learn, live, and play because it’s here that our attitudes about math and ourselves are formed. By starting at the source, we’re creating a positive math culture by starting from the ground up. Your engagement as a volunteer can help reframe math as fun and relevant so that all kids, teachers, and families can build math confidence and lifetime skills.
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Mumbai: The Central Board of Secondary Education (CBSE) has remodelled its assessment scheme and makes six subjects as compulsory subject for the class 10th board exams. The students appearing for Class 10th board exams from next years will ahve six subjects instead of five.
The CBSC board has offered a vocational subject as an “additional subject” as compulsory subject. Presently class 10th students have five subjects which includes two languages, social science, mathematics and science. However, from the 2017-18 academic year, it will be compulsory to study a vocational subject.
The CBSE has remodelled its assessment scheme, vocational subject as compulsory subject under the National Skills Qualifications Framework (NSQF).
“If a candidate fails to pass in any one of the three elective subjects — science, social science, mathematics, then it will be replaced by the vocational subject (offered as sixth additional subject),” a CBSE circular said.
The circular also mentioned that if any students failed in a subject and desire to reappear can appear in the compartmentexamination. For the sixth subject which is made compulsory, the students have 13 options in which they have to choose one as their sixth subject. The thirteen options of subjects are Dynamics of Retailing, Information Technology, Security, Automobile Technology, Introduction to Financial Market, Introduction to Tourism, Beauty and Wellness, Basic Agriculture, Food Production, Front Office Operations, Banking and Insurance, Marketing and Sales, and Health Care Services.
According to the circular, the maximum marks will be 100.
Out of the total 100 marks, the board exam will be of 50 marks, and 50 marks are allocated to internal assessment/practical examination.
A candidate will have to score 33 per cent marks in both board exam and practical exam to pass the subject.
(With inputs from PTI)


by J. S. Marron
This page is intended as a "table of contents".
Each analysis has a teaser image to motivate the viewer to look at the
more detailed pages available on the links.
1. A SiZer
by P. Chaudhuri, J. S. Marron, J. C. Jiang, C. S. Kim, R. Z. Li, V. Rondonotti, J. de Uña Alvarez
SiZer was developed by Chaudhuri and Marron (1999, JASA, 94, 807-823), to address the problem of "which features in a smooth are important underlying structure, and which are unimportant sampling artifacts?"
Here is one screen shot, using the famous "incomes
data", that establishes the statistical significance of the "two modes".
For a web based introduction to SiZer, more examples showing the practical
efficacy of SiZer, and discussion of other aspects, go here
2. CHETA (Curve Height at Event Time Analysis)
by T. Graves, J. S. Marron, A. Mockus and A. Glazner
This is a method for assessing statistical significance of connections between a curve and a point process. In particular, do the events of the point process occur more or less often depending on the height of the curve?
Our approach to this is based on evaluating the curve at the event times, and then comparing the resulting population with an appropriate "background" population.
Here is an interesting example from software engineering.
This provides strong evidence (p-value ~ 0.000001) that there is a connection
between rate of faults and perfective maintenance, in a large software
Here is another example from geology. This shows a statistically
significant (p-value ~ 0.002) connection between glaciation and volcanism.
To learn more about this example, and the CHETA method,
(linked page still under construction)
by J. S. Marron, R. Z. Li and C. A. Giuliani
Here is one trace of a repetitive human movement. Changes in amplitude
are clearly visible. Are there changes in frequency? Which
frequency changes are statistically significant? The first question
is answered using Fourier analysis. The second question appears to
need non-Fourier methods. An approach based on "movies" is investigated.
For the full story, go here.
Functional Data Analysis of Corneal Images
by N. Locantore, J. S. Marron, D. G. Simpson, N. Tripoli, J. T. Zhang and K. Cohen
The raw data are a set of corneal curvature images, as shown here. What is the underlying population structure of this set of data?
for an answer to this question (using movies in the data analysis), for
a new type of robust PCA, for the related paper to appear with discussion
in Test, etc.
Significance in Scale Space
by F. Godtliebsen, J. S. Marron and P. Chaudhuri.
This addresses the same question as SiZer, see 1 above, but in the 2 dimensional case. Current versions work for 2d density estimation, and images (i.e. equally spaced regression). One problem in 2 dimensions is how to visualize the result. This is solved by using movies, where time represents the amount of smoothing (i.e. bandwidth). Another problem is that "derivative" becomes more complicated in 2d. This has motivated the development of some new visual paradigms.
Here is one frame of one of these movies
(but don't stop here!):
(Caution: this is only a "screen shot", so the buttons don't work. Click here to see this movie, but better is...)
for much more about this approach to finding structure in 2-d smoothing
contexts, including movies, papers, and downloadable software.
Go to Marron's movie page
Back to Marron's


While point spread wagers are the most popular option among NFL bettors, over/under numbers are also widely played every Sunday and Monday during the season on betting companies like Bet Olimp. There are many factors to be aware of when handicapping an NFL total.
On average, a typical NFL game will have a total score of about 40 points. When a bettor analyzes the weekly NFL slate, most over/unders will be right around the number of 40. If a couple of dynamic offenses are matching up, the total can get up anywhere from the high 40′s to the low 50′s. In turn, a defensive battle could lead to over/unders in the low 30′s.
Average Total Score
An oddsmaker will look at a couple of basic concepts to determine what a total should be. The main factor involves the average total score for each team. As an example, team A scores 23 points per game while giving up 20 points per outing. This gives team A an average total score of 43. With this information, the bookmaker will go through the same numbers for team B. For this example, team B averages 24 points on offense while giving up 21 on defense for a total of 45. The two averages combined would yield a number of 44. From here, the oddsmaker can fine tune the number by looking at additional variables outline below.Continue Reading


Today, I had the horror of reading the speech made by Elizabeth Truss to the North England Education Conference on Thursday. This speech advocates, amongst other things, the almost forced return to the teaching of algorithm calculation methods.
I initially felt very worried after reading this, and this afternoon decided to pen some form of response to Elizabeth Truss, which you can find below I’ve decided to blog this, an ‘open letter’ if you like, as I would be very interested in what you think 🙂
A bit of background here- my Mathematics Specialist Teacher second year project is on developing a conceptual understanding of calculations with a focus on division, and I have been meaning to (and still will) blog more about this. I also feel I need to put a reminder that these views are my own and not necessarily those of my employer etc etc…
Anyway, my thoughts are below…
I read with quite considerable alarm the speech you made to the North England Education Conference on the 17th January 2013. As a committed teacher, who wants their children to not just learn facts but develop understanding, this speech made me feel very un-easy.
In your speech you state that children must learn to speak the ‘language of maths’- something which I fully agree with- we need to develop a conceptual understanding of maths within our children, so that they are able to effectively use and apply their mathematics skills, and are able to problem solve beyond the dreaded and much over taught ‘word problems’. I would like to address just some of these issues from your speech.
Let’s first tackle your accretion that those ‘new’ methods which are based on conceptual understanding do not allow for progression- are you able to provide evidence of this? By their very nature the methods taught in many schools now are rooted in the structure of our number system– and therefore can easily be extended to any number. Children frequently do this themselves- for example, when taught how to subtract by finding the difference on the number line for 2 digit positive numbers, they are easily able to extend this, often independently, to subtracting larger numbers, decimal numbers, negative numbers and indeed time intervals. The same applies for division by grouping/chunking, and multiplication using the grid method (which, in reality takes multiplication back to what it is- an array)
The ‘algorithm’ methods bode little resemblance to what is actually happening with the numbers. Can you explain why long division works? There is no logic to these methods- they work by simply following n a set of instructions, which, to many children at least, ‘magically’ end up with the correct answer- and I believe this means children will struggle to extend these methods. After all, maths is not ‘magic’.
You correctly state that no-one can predict when a child will experience the ‘light bulb’ moment- but by removing the conceptual understanding behind calculation, you will be virtually eliminating the chance of this happening- as a child will not truly be able to say ‘ahh…I understand’- all they will be able to say is ‘I can follow the method…’
There is a considerable bank of research evidence showing that the ‘new’ methods which foster a conceptual and relational understanding of number and calculations lead to far greater accuracy and confidence than the ‘traditional’ algorithm based methods.
In fact, you don’t have to go far to find evidence of this- for 3 pieces of leading research in your very own county of Norfolk[i] have consistently shown that methods which foster conceptual understanding ‘win’ when it comes to children being able to calculate accurately. Surely it is by using methods based on a conceptual understanding that children are more likely to spot their errors- for they actually ‘see’ what they are doing to a number, rather than just robotically following a set of instructions ‘just because it works’. And further research clearly states the importance of developing conceptual understanding.[ii] Can you provide research to prove that these methods lead to greater errors as implied in your speech?
Of course, this is not the first time you have heard this. Many groups and organisations have tried to explain this before, and many of us responded in a similar vein to the (absolutely appalling in parts) draft curriculum published in March 2012. Indeed, the joint response[iii] to the proposed curriculum by the Association of Teachers of Mathematics (ATM) and the Mathematical Association (MA), which together represent some of the leading thinkers when it comes to mathematics education, clearly states and provides evidence for the need to develop a conceptual understanding and not rush to formal algorithms too quickly. Could I suggest that you re-read this response and ask if the new version of your curriculum addresses the many issues raised within it before it is released in a few weeks time?
The government has spent money on, and now continues to support the Mathematics Specialist Teacher Program, of which I am now in the second year, and this very program, designed to ensure that each primary school has a mathematics specialist and therefore raise the standard of mathematics teaching, advocates conceptual and relational understanding and the calculation methods which are based on these.
Indeed, these ‘new’ methods are, in fact, nothing ‘new’- leading academics, backed up by research, have consistently proven the case for relational understanding (Skemp, 1976[iv]). Without methods based on this understanding you constantly find in classrooms that children who struggle with maths find the algorithm methods incredibly confusing and are unable to use them.
I also take great issue with your statement that these methods are not efficient. These methods may not be efficient for you- I’m guessing because you are not comfortable with the method, nor do you probably have the conceptual understanding of number which underpins these methods- this is demonstrated by your rather lax explanation of these methods in your speech. This is of course, not surprising as they are different to the way you were taught.
But for the children who are taught these methods they are efficient. They, used alongside robust teaching of mental strategies, which themselves are rooted in a conceptual understanding of our number system allow for efficient and accurate calculations in all four operations (yes, whilst they would work for any calculation, even the most simplest, it’s never been advocated to conceptual based written methods ‘blindly’ used for any calculation), . Surely a method is only efficient if it means the child is actually able to get the correct answer?
East Asia, and specifically Singapore, is, yet again, used as an example by you as a country where things are done ‘right’. So are you proposing we import all of this teaching, if so, let’s first look at Singapore’s mathematics teaching, which includes a very refreshing approach to the purpose of mathematics teaching (for the solving of problems) , which encourages mathematical thinking and includes the Singapore bar methods for calculation and solving problems- based on a conceptual understanding of number and can be which can be seen to be similar in its thinking to the conceptual methods taught by teachers in the UK.
You state that parents are not able to understand these methods. Yes- these methods are different to the way in which most parents were taught themselves at school, and it is the job of the school to ensure that parents are aware of the different methods taught in school- something that many schools do through successful calculation events, in which many parents realise for the first time themselves what division, subtraction, multiplication or addition actually means. Once aware of the new methods and the reason behind them, parents are normally, in my experience anyway, very supportive. But despite this, are you therefore creating a maths curriculum for parents? I would assume that a curriculum is meant to be written for the benefit of the pupils not their parents? Children understand and are able to easily explain the conceptual methods they are taught, they are accurate when using them and can use them ‘quickly’- this is what matters to me as a teacher. (It is also worthwhile pointing out that in only a few years time our new parents will, themselves, have been taught the conceptual based methods- so we could end up with the same problem in reverse!)
I am also not advocating the complete abolishment of the use of algorithm methods, however ideal that would be, as I appreciate this would never happen- but do believe it is about using the right methods, backed by conceptual understanding, at the right stage for the child. For many children, the forced introduction of algorithm based methods in primary school when they do not have this conceptual understanding is too early, and will ruin their chances of actually understanding maths and increase their chances of becoming one more of adults who say ‘I can’t do maths’ (when they are normally really saying ‘I don’t get maths’) that you refer to in your speech (I agree by the way, that is an awful attitude to have!). [Of course, the converse is true, for a few children, they will be ‘ready’ and be able to extend their conceptual understanding for the traditional algorithms by the time they leave primary school- surely we should be reactive to the child?]
There is one glimmer of hope in your speech- that the new curriculum will state that children must be taught efficient methods- and I could argue that by teaching the methods based on conceptual understanding, that these methods are the most efficient for the children I teach.
But, then you state that, from 2016 children will achieve a ‘method’ mark only if they have used the ‘prescribed’ algorithm methods. [By the way, what will this mark be awarded for? as by the very nature of algorithm methods there is little margin of error.]
This means you are effectively forcing schools to take a calculated ‘gamble’- do they solely teach the algorithm methods, which they know (as backed up by research as stated earlier) will lead to a far greater error rate but which will pick up a ‘method’ mark, or do they stick to the research proven methods, which they know children will generally stand a higher chance of getting the correct answer, and therefore two marks, but with the risk that if they do not arrive at the correct answer they will be penalised for using a method which they do not understand?
All this strikes me as change for changes sake- a dangerous change which stands a good chance of reducing our children’s ability to calculate and solve problems, but which will please many traditional conservatives and elements of the press who do not understand the real issues in mathematics education, and a change which, yet again, erodes the professional judgement and expertise of teachers. Please do not think, as I am sure someone will be quick to suggest, that teachers are simply resisting change. I am not teacher who resists change and am more than happy for change, and embrace it, after all teaching has to be a profession where we are constantly moving forward. But change has to be positive change that will have a positive impact on the education and lives of the children which I teach- and I, as many teachers do, believe this change certainly will not.
Of course, there are many more things in your speech which were incredibly worrying, but I do not have the time to get started on, for example, why rote learning times tables up to 12 times is unnecessary (the structure of our number system means that tables up to 9x would be sufficient) or why children’s ability to think mathematically can be increased by calculator use (but not by dependence on calculators . What your speech simply proves, is yet again, this government is not listening to what teachers and leading academics are saying- but why am I surprised?
[iv] R Skemp: ‘Relational understanding and instrumental understanding’, Mathematics Teaching, 81.


Choosing the appropriate strategy and recording in mathematics are important tools for furthering the understanding of ideas and for communicating those ideas to others. A useful written method is one that helps children carry out a calculation and can be understood by others. At our school, written methods are taught and used alongside mental methods and should not be seen as separate from them. We encourage children to use mental methods when appropriate, but for calculations that they cannot do in their heads they should be able to use an efficient written method accurately and with confidence. This document identifies progression in calculation strategies at our school.


A slot machine is a gambling machine that features three or more spinning reels. After you place a bet and spin the reels, symbols emerge randomly on the reels. If these symbols appear in a row, you award prizes dependent on whatever symbols appear on that “payline.”These games have been around since the late 1800s, and their popularity has only increased since then สล็อต were mechanical machines that spun the reels using springs and gears.A computer program known as a random number generator utilizes to determine which symbols land were in modern slot machines.
A random number generator is computer software that generates hundreds of different numbers every second.The application comes to a standstill, where it is when you touch the spin button.These numbers correspond to the reels’ stops and symbols.
Slot Machines from the Beginning
Early สล็อต machines had easy-to-understand math. You might have three reels, each containing ten symbols. The chances of getting any given sign were the same—1/10. You multiplied 1/10 X 1/10 X 1/10 to achieve a value of 1/1000 if you wanted to calculate the probabilities of getting a specific combination of symbols on a line.
The machine’s payback percentage can compute by comparing the prize for lining up those symbols with the likelihood of hitting the combination. A casino would have a slight edge if it provided a 998 to 1 payoff on a bet with a 1/1000 chance of winning. They’d make money over time.
Slot machines in the modern era
The symbols and reels programmed into the computer make modern slots tough to calculate. In many ways, this makes the games more adaptable. They aren’t constrained by reel size, for example.There was a limit to how many symbols could be on a reel in old mechanical slot machines before the game got too big to play.
On the other hand, a computer-driven game might have 20 symbols per reel. Another advantage for producers they can change the likelihood of a particular symbol appearing. Some symbols appear once every ten spins, while others appear only once every 20 or 30 tries. It allows manufacturers and casinos to offer bigger payouts while remaining profitable.
The Ultimate Guide to Slot Machines
We want to provide a complete resource for slot machine experts on the Internet with this slot machine guide.This article covers the major topics in broad strokes. The majority of the sections on this page offer links to subsections that go into greater depth on specific topics.Although this may not be the case in some European countries, it is the case in Australia, where the games are known as “poker machines” or “pokies.”However, if you study all of the pages in this portion of our website, you’ll be sufficiently knowledgeable about these games to call yourself a slot machine expert.


OK, let's start the discussion with variable costs. Assume that we are going to be manufacturing tables.
Let's assume that we are going to use wood to manufacture our tables. So wood would be a raw material that's used in the manufacture of our tables.
Let's assume that each table requires five dollars of wood. So based on this information, let's go to the table that I have prepared for you here.
If we manufacture one table, the unit variable cost that is the amount of wood per unit table would be five dollars, and the total wood cost for one table will also be five dollars. But look what happens when we go and manufacture two tables.
When we manufacture two tables, the amount of wood used per table is still five, so our unit variable cost stays constant, does not change at five dollars a table.
But look at what happens to the total wood cost, the total variable cost when we manufactured two tables. The total wood cost now has changed to ten dollars from the earlier five.
Let's go down with three tables. When we manufacture three tables. Again the amount of wood per table does not change that stays the same at five dollars per table, so your unit variable cost stays constant at five dollars.
But look at the total wood cost. The total wood cost now has gone up to fifteen dollars.
So what conclusions can we draw from this table. The conclusions are that your unit variable cost stays constant with changes in volume. But your total variable cost changes with changes in volume.
If your volume goes up, your total variable cost goes up. If your volume drops, then your total variable cost comes down.
So wood is an example of a variable cost, and I have just illustrated that behavior pattern of both unit variable costs as well as total variable costs.
Now one of the assumptions we make here is that there are no volume discounts granted for large volume purchases, so that's the assumption we make. So whether we buy, you know, small amount of wood or whether we buy a large amount of wood, we are going to continue paying the same amount for each square foot of wood. So that's the assumption here no discounts given for volume purchases.
OK, let's pay attention now to fixed cost. So if we assume that the fixed cost we have is rent, rent of $1,000 a month. Again let's assume we will be paying a rent of $1,000 a month. So if we have to pay rent at $1,000 a month, let's see what would be the behavior pattern of unit fixed costs and total fixed costs as we change the volume of tables manufactured.
So when we manufacture one table, the total rent I pay my landlord is $1,000, because my landlord does not care whether I make one tables or 10 tables. He still wants his $1,000. But If I want to take that total $1,000, and allocated among the tables manufactured which in this case is only one table then one single table gets allocated the entire $1,000 of rent. So my unit fixed cost also in this case is $1,000.
But look what happens when we go to two tables. When I manufacture two tables, my landlord still wants his $1,000 of rent, doesn't he? So my total rent fixed costs still stays the same at 1,000. But when I go to allocate the $1,000 among the two tables I have manufactured, then this time each table picks up only $500 as $1,000 over two picks up only $500 of rent.
So when unit fixed cost is dropped from $1,000 per table to $500 per table. But my total rent cost has stayed constant at $1,000 regardless of where they manufactured one table, two table or three tables. So when I manufacture three tables again, my landlord still wants the same $1,000 of rent. So my total fixed cost at three tables still remains constant at $1,000
But look what happens to my unit fixed cost, that is when I take the $1,000 of rent and I allocated over the three tables that I manufactured, each table now picks up only $333 of rent as opposed to the $500 earlier and the $1,000 before that.
So what conclusions can we draw about the behavior patterns of fixed costs from this example. Your unit fixed cost changes inversely with changes in volume. It was a $1,000 first, then 500 then 333. But look at your total fixed cost as I said before and I repeat your total fixed cost does not change with changes in volume stays the same as well within a relevant range.
Total cost and Unit cost
Now I introduce a new concept, your new term, relevant range. What do I mean by the term relevant range? In this case let's assume for instance that if I were to operate my factory 24/7 three shifts a day, let's assume I could manufacture a maximum of 10,000 units. So in this case we would say in this example the relevant range is between one unit and 10,000 units.
What does that mean? That means what we are saying is that my total fixed cost of $1,000 will stay at 1,000 regardless of whether I manufacture one table over there manufacture 10,000 tables. So as long as I stay within the relevant range, my total fixed cost of $1,000 stays at 1,000.
But If I want to manufacture more than 10,000 tables, I would have to probably rent another building and pay another $1,000. In that case if I went over 10,000 units of manufacture, then my fixed cost would increase, would go pass the 1,000, because I'm going outside of my relevant range. So that's a little bit about the concept of relevant range.
Now let's take these two items that we have talked about, and look at the effect on your total cost. So if you look up here on this part of the whiteboard, your total cost is equal to your total fixed cost plus your total variable cost.
We can express the same equation on a unit cost basis, so my unit total cost will be equal to my unit fixed cost plus my unit variable cost.
So let's look at this table to understand the effect of fixed costs and variable cost on my total unit cost. So if I were to manufacture one table, from our previous tables my unit fixed cost is $1,000, my unit variable cost is $5, so my total unit cost is $1,005. It's combining the two.
But look what happens to my total unit cost when I manufactured two tables. Now my unit fixed cost again from the previous tables is 500, my unit variable cost stays the same at $5. So this time my total unit cost has dropped from 1,005 to 505, lot cheaper to make two tables than to make one table.
And see how that unit cost drops when we make three tables, going to make three tables. What happens to my unit fixed cost we get from the previous tables is down to 333. My unit variable cost does not change, it stays the same at $5, so now total unit cost is only $338.


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Order Of Operations The order of mathematical operations, with computations inside parentheses to be done first, and addition and subtraction from left to right done last. Terms in this set (52) acute angle. Math vocabulary Worksheets – PDF printable math vocabulary math worksheets for children in: Pre-K, Kindergarten, 1 st grade, 2 nd grade, 3 rd grade, 4 th grade, 5 th grade, 6 th grade and 7 th grade. Write. Match. Perfect Square An integer n that can be written in the form n= k², where k is an integer. Learn seventh grade math for free—proportions, algebra basics, arithmetic with negative numbers, probability, circles, and more. Sequence A list of terms ordered by the natural numbers. Slant Height An altitude of a face of a pyramid or a cone. supplementary angles. Created by. Match. a number by which another number is to be divided. Dividend. Interest can be calculated using I = Prt, in which P is the principal amount of money, r is the rate of annual interest and t is the time. Math 4th grade word list - area, ATTRIBUTES, average, diagram, expression, mathematics, mean, pattern, PROPERTIES, quotient, symbol Obtuse Angle An angle whose measure is greater than 90 degrees and less than 180 degrees. Kids actually look forward to studying more complicated math! Texas State College of Science and Engineering Mathworks Math Explorations Middle School Curriculum Additional resources for teachers Online Math Learning Tools Illustrated Glossary Of Important Math Terms 6th Grade Mathematics - Important Vocabulary Words This seventh grade vocabulary list was built from an analysis of difficult words that appear in basal readers and other books commonly taught in the 7th grade. Read MoreRead Less. Some of the worksheets for this concept are Vocabulary power workbook, Seventh grade vocabulary student workbook, 300 seventh grade spelling words, Grade 4 national vocabulary list, Grammar practice workbook, Grade 7 english language arts practice test, Social studies vocabulary 7th grade, … Negative Integers Integers less than zero. At the 7th grade level, learning the meaning of middle school math vocabulary is vital to succeeding in middle school. Represent and analyze quantitative relationships between dependent and independent variables. This set of 7th grade math vocabulary cards, with neon giraffe background, is perfect to display in your classroom. Full curriculum of exercises and videos. Students in 7th grade should know a lot of important math vocabulary words. Notation A technical system of symbols used to convey mathematical information. the answer to a subtraction problem. Match. Parallel Lines Two lines in a plane that never intersect. Simplifying The process of finding equivalent fractions to obtain the simplest form. Numerator The expression written above the fraction bar in a common fraction to indicate the number of parts counted. 7th Grade Vocabulary Power Answers - Displaying top 8 worksheets found for this concept.. Key Concepts: Terms in this set (36) sum. the answer to a multiplication problem. Prime Factorization The process of finding the prime factors of an integer. Keep reading to find out how you can help at home. Spell. The purpose of this resource is to help students with increasing their mathematics vocabulary. Number Line Model A pictorial representation of numbers on a straight line. 7th Grade Common Core Math Vocabulary Crossword Puzzle 1. The total of the lateral area and the two bases of a cylinder. Check yourself on the meaning of these words. Learn. the top number in a fraction. Each card contains the ac For any numbers x, y , and z: (x + y) + z= x + (y + z). Your 7th grader is likely learning a lot of new vocabulary at school not only in English, but in all subjects. 7th Grade Math Lesson Plans. STUDY. Venn Diagram A diagram involving two or more overlapping circles that aids in organizing data. When completed, there will be a whole years worth of … For any x, |x| is defined as follows: | x |= x, if x > 0, and | x |= −x, if x < 0. Volume A measure of space; the number of unit cubes needed to fill a three-dimensional shape. Develop understanding of statistical variability. Polygon A polygon is a simple, closed, plane figure formed by three or more line segments. Play Vocabulary TestMe with a 7th grade Math list. … Whether in algebra, geometry or statistics, 7th grade math definitions are presented in an accessible and engaging manner that 7th graders enjoy. Rebate Money that the customer receives, typically from the manufacturer, after making a purchase. Straight Angle An angle with a measure of 180 degrees formed by opposite rays. Learn. Test. Quotient The result obtained by doing division. Parallelogram A parallelogram is a four-sided figure with opposite sides parallel. The tests are aligned to CCSS and EDITABLE (Microsoft Word)!!! A mathematical model based on the area of a rectangle, used to represent multiplication or to represent fractional parts of a whole. If the lines are parallel the pairs of angles will have equal measure. If B is the reflection of A in line L, then L is the perpendicular bisector of segment AB. evaluate. 46 MATH WORD LIST at grade level: The words in CAPITAL letters (18) are used in six interactive vocabulary games at www.myvocabulary.com. Whether in algebra, geometry or statistics, 7th grade math … the answer to a division problem. 7th Grade Math Year in Review Part 1 - Duration: 17:48. y-axis The vertical axis of a coordinate plane. Percent A way of expressing a number as parts out of 100; the numerator of a ratio with a denominator of 100. 2:57. Also see Unit Rate. Spellers of the world, untie! a sentence that compares two different numbers. Virginia Department of Education 2018 Grade 7 Mathematics Vocabulary – Card 12 Proportional Reasoning About how many centimeters are in 2 feet if 1 inch is about 2.5 centimeters? Variable A letter or symbol that represents an unknown quantity. A term used to describe fractions, decimals, and percents that are equal. inequality. Stephanie_Steward. Included is a pre-test, post-test, and vocabulary quiz for every 7th grade math unit. Protractor An instrument used to measure angles in degrees. You can import the word lists into your account and use with any of our 35+ activities. Set 1 * 1, 5, 9, and 13 are different puzzles with the same words * 2, 6, 10 and 14, are different puzzles with the same words * 3, 7, 11, and 15 are different puzzles with the same words * 4, 8, 12, and 16 are different puzzles with the same words. for representing an interval as a pair of numbers. 1 24 2.5 x There are approximately 60 centimeters in 2 feet About how many liters are in 3 gallons if 1 quart is approximately 0.95 liters? Challenges for French/Haitian Creole-Speaking ELLs, Efficacy Study: Help Students Build Reading Comprehension, VocabularySpellingCity Acquires WriteSteps, White Paper on Effective Vocabulary Instruction. Complabteacher Recommended for you. 2020 7th grade math vocabulary. The math vocabulary lists are based on the Common Core Seventh Grade Math Standards. These worksheets cover most math vocabulary subtopics and are were also conceived in line with Common Core State Standards. Radical Notation A math symbol to denote the root of an expression, such as square roots. Whole Numbers The whole numbers are the numbers in the following never-ending sequence: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, .... x-axis The horizontal axis of a coordinate plane. An angle less than 90 degrees. Pi (3.14159…) is an irrational number because there is no repeating pattern. Math vocabulary Worksheets – Printable PDFs. the ratio between two related quantities. Vertical Angles If two straight lines intersect at a point, then each line is divided into two rays. 7th grade math vocabulary. 7th Grade Strengthen critical seventh grade reading skills and advanced math skills with lesson plans, 7th grade worksheets, and complex texts on a variety of topics. Standard Notation Mathematical notation that is commonly used. Relatively Prime Two integers m and n are relatively prime if the GCF of m and n is 1. Add to Cart This bundle is IN PROGRESS. Quantity. 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Nim - A Devilishly Difficult Game
Ages: 7 and up
Math Ideas: Subtraction, deductive reasoning, mathematical proof
Questions to Ask:
Want to figure out a strategy to always win?
Do you want to go first or second this time?
If you make that move, what do you think I will do?
Years ago, a teacher friend sent me an online version of the game Nim. "Try it out!" they said innocently enough, "See if you can figure out the strategy!"
The game seemed simple enough, basically just a set of three rows of objects. So I gave it a shot, and I lost. And then I lost again, and again. I finally walked away from my computer, a broken man.
In the years since then, I've moved cities and schools, had three kids, and STILL CANNOT BEAT THIS GAME.
In preparation for this newsletter, I finally gave in and looked up the solution. And having seen a lovely explanation from one of my favorite mathematicians, James Tanton, I think I can provide a way to turn this maddening little game into a meaningful mathematical exploration for you and your child.
How to Play
Nim is an ancient game with many variations, but each version is based on the same idea: rows of stones.
The original version I played had three rows of stones, as pictured. But you can have as many rows of stones as you want, and each row can contain as many stones as you like.
You and your opponent take turns choosing a single row of stones and then removing as many stones from that row as you want. You can remove a single stone, a few stones, or even the entire row. The person to take the last stone wins.
You can play an online version of the game with four rows here. The version I played has been lost to the sands of time (Good riddance).
Playing Nim with your Child
Have you played the version above a couple of times? Have you lost every time, just like me? Great, you're ready to explore this game with your child!
I don't usually get this prescriptive with my advice, but I think that Nim provides a great opportunity to show your child one of the greatest problem-solving skills of a mathematician: solving a simpler problem.
Introduce the game to your child, then play a couple of versions of Nim that start with two rows. Then ask them "Do you want to figure out a strategy to always win?" Kids love nothing so much as winning, so hopefully they'll be on board!
Start with a very simple version of Nim: a one-row version of the game. Lay out a row of stones and ask your child "Do you want to go first or second?" Hopefully, they choose to go first and snatch up all the stones! If not, snatch all the stones yourself on your turn, then set up the game again and ask if they want to go first or second.
This version of the game isn't very fun, but it does teach you and your child an important principle of the game: if there is only one row left on your turn, you win!
Now you're ready to play the two-row version of the game. Again, though, you want to start with a simplified version: one stone in each row. Again, ask your child "Do you want to go first or second?"
This time, going first is a guaranteed loser! No matter which stone you choose, your opponent can take the other stone to win. So now you and your child have another piece of strategy about the game: if you can get the stones down to a single stone in each row on your opponent's turn, you win!
One last mini-game before the final reveal: set up a game with two stones in each row and ask your child "Do you want to go first or second?"
Now you can start to discuss all the possible ways the game can go: If you choose to go first, you can either take a single stone from one row, or you can take both stones from one row. But taking both stones is a bad move, since your opponent will just snatch up both stones from the other row and win!
So you have to take a single stone from one row. But wait! Your opponent can take a single stone from the other row, leaving you with one stone in each row, a situation we know is hopeless! So two rows of two stones are equally as hopeless as two rows of one stone. In fact, two equal rows of stones are a guaranteed loser, no matter how many stones are in each row.
And now the strategy becomes clear: On your turn, take stones from the bigger row until both rows are equal. That way, you force your opponent to make the rows unequal on their next turn, and you can make the rows evenly matched again on your turn. Eventually you will winnow down the rows until each row has exactly one stone, and your opponent is doomed!
The beauty of this game is that this strategy works no matter how many stones are in each row. Once you know the goal of making the two rows equal, you can play any variation on the two-row version of Nim. And what if the two rows start out equal? Simple, just ask your opponent to go first! She'll break up the evenness of the rows, and you are back on track to victory.
I think for most kids in elementary school, the two-row version of Nim is perfect. They get the feeling of accomplishment that they know how to beat the game, and they're sure to teach their friends how to play, simply to show off their prowess.
More importantly, though, they have gone through the experience of solving a game by solving simpler versions of a complicated problem. This is a tool that I teach my students to use in middle school, and it's a tool I use as an adult to solve mathematical problems that I've never encountered before. By modeling this process, you are giving your child an opportunity to experience the joy of mathematical discovery.
But wait - we haven't solved the three- and four-row versions of Nim, the ones that drove me crazy for years! That's true. But we have learned something valuable about the structure of Nim, which is that keeping the rows even somehow is a good strategy. In order to see how you can keep three or four rows even, you'll have to watch that lovely video from James Tanton that I mentioned earlier.


Video: Watch this demo – Wood
Description: A demonstration to show the angle of repose: the angle at which gravity overcomes the force of static friction and the block starts to slide.
- Angle of repose apparatus (see photo)
- Blocks of various masses and material
- Wooden block
- Block with sandpaper
- Block with leather
- Plastic block
- Gather together all the materials; make sure everything is in working order.
- Place block at the top of the ramp.
- To adjust the angle, loosen the wing nut on the apparatus.
- Find the angle of repose.
Concepts: Shows the concept of angle of repose. Can be used to show the approximation that:
where, μs is the coefficient of static friction, and θ is the angle of repose.


This paper analyzes, from theoretical and algorithmic perspectives, a class of problems recently introduced in the literature of Markov decision processes—configurable Markov decision processes. In this new class of problems we jointly optimize the probability transition function and associated optimal policy, in order to improve the performance of a decision-making agent. We contribute a complexity analysis on the problem from a computational perspective, where we show that, in general, solving a configurable MDP is NP-Hard. We also discuss practical challenges often faced in solving this class of problems. Additionally, we formally derive a gradient-based approach that sheds some light on the correctness and limitations of existing methods. We conclude by demonstrating the application of different parameterizations of configurable MDPs in two scenarios, offering a discussion on advantages and drawbacks from modeling and algorithmic perspectives. Our contributions set the foundation for a better understanding of this recent problem, and the wider applicability of the underlying ideas to different planning problems.


I've been such a neglectful blogger. Shame on me. I've been caught up raising my Baby Boy and keeping up with 25 5th graders :)
I'm off for the week and to get ready for the holidays in school, I made my own version of the 12 Days of Christmas: "12 Days of School-mas" a math version. I hope I can upload the science one soon. I so look forward to doing this with my students.
Also, when we go back next week, we'll be diving right into non-fiction and FRACTIONS!!! Wish me luck!!!


Tech Savvy 2016
Saturday, May 14, 8:30 a.m. – 3:30 p.m.
A hands-on day of fun with Science, Technology, Engineering and Mathematics (STEM) for girls in Grades 6 through 9. Parents are invited to attend and participate in special parent activities.
On the campus of Stark State College, 6200 Frank Ave. NW, North Canton, OH
Cost: $5 per student; $5 per parent/guardian. Breakfast and lunch are included with registration, also T-shirts/ Freebies/ Handout materials.
Questions? E-mail us at: email@example.com
Breakout sessions/ classes include: “It’s a Rocky World Out There,” “Lava, Lava, Lava Lamps,”
“Microscopic Investigation: Who Stole the Coin at the Museum?” “AutoCAD: I Design A Bicycle Like a Girl,” Allometry: Not ‘a Llama Tree,'” “Diggin’ for DNA,” “Creating the Ultimate S’More,” “NASA Design: Science That Is Out of This World,” “Code Girl,” and others. Girls will select three to attend. Instructors include teachers, members of NASA, agents from the FBI, manufacturing engineers and others. Parents’ programming includes sessions on STEM career planning, cybersafety, financing and affordability of education.
Tech Savvy is a daylong science, technology, engineering and math career conference designed to attract girls in sixth through ninth grade to these fields and to inform families about STEM education and careers. A grant from ALCOA Foundation has helped to provide funding for this program.
This conference is sponsored by ALCOA, AAUW and AAUW Medina County Branch, and Stark State College.