Ordering positive and negative decimals worksheet tes
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- Order of operations – non positive integers: 725.4 kB: 5588: September 3, 2019: Order of operations – non positive decimals: 602.6 kB: 2153: September 3, 2019
- The game is based on the following Common Core Math Standards:. CCSS 6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world ...
- Practice putting positive and negative numbers in order. For example, -28, 12, -51, and 43.
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- whether an integer is positive or negative; whether the operation is add or subtract; When we do operations (like adding and subtracting) with integers we often end up with two signs next to each other. This can be confusing but the rules below can help: +3 means positive three. 3 is the same as +3
- Decimals Worksheets Addition and Subtraction Worksheets with Decimals Vertical Format. This Decimals Worksheet will produce addition and subtraction problems. It may be configured for 1, 2, and 3 digits on the right, and up to 4 digits on the left of the decimal. You may select up to 25 problems per worksheet.
- 7th grade math worksheets on math topics covered in grade 7. Get seventh graders to have more math practice by downloading all worksheets under this category. Each 7th grade math topic links to a page with PDF printable math worksheets covering subtopics under the main category.
- From Spain. NEGATIVE Form. Subject. Verb(positive).
- This year they'll be working towards consolidating the Lower Key Stage 2 (years 3 and 4) math topics, which you can do with our year 4 counting and year 4 decimals worksheets amongst many others, helping to prepare for year 4 maths tests and assessments.
- IXL brings learning to life with over 200 different decimal skills. Engaging questions and fun visuals motivate students to master new concepts.
- Write each as a decimal. Use repeating decimals when necessary. Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com. ©7 M210n1B25 aKmuEt1aH pSHolfEtFwxagrweM SLOLuCm.w c hAllHly sreiFgQhqtRsM 7rvefspe2rjvyeXdB.D c...
- Analyses revealed that the average of negative affect was significantly heritable (.53), but the average of positive affect was not; instead, the latter showed significant shared environmental influences (.42). Fluctuations across the month were significantly heritable for both negative affect (.54) and positive affect (.34).
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- In this number line, there are three negative and three positive integers. (i.e., -3, -2, -1, 1, 2, 3) Between each number there is an unlabeled tick. Since they are halfway between one number and the next, we can deduce that these unlabeled marks represent half values. (i.e., 1/2 or .5)
- Ordering Whole Numbers And Decimals. Ordering Whole Numbers And Decimals - Displaying top 8 worksheets found for this concept.. Some of the worksheets for this concept are Comparing and ordering fractions decimals and percents, Decimals work, Comparing and ordering decimals, Ordering fractions decimals and percents, Decimals practice booklet table of contents, Fractions and decimals, Comparing ...
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Batch file time 24 hour formatOur Adding and Subtracting Fractions and Mixed Numbers worksheets are designed to supplement our Adding and Subtracting Fractions and Mixed Numbers lessons. These ready-to-use printable worksheets help assess student learning! Be sure to check out the fun interactive fraction activities and additional worksheets below! Information. Du har inte tillåtelse att visa medlemslistan eller profiler. Forumindex; Alla tidsangivelser är UTC ; POWERED_BY Swedish translation by Peetra & phpBB ...
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- This worksheet helps your students practice place value for positive and negative numbers. Students write sets of positive and negative numbers in order from least to greatest. Other resources to use with this Ordering Positive and Negative Numbers Worksheet. If you are using this worksheet, your students are probably learning about ordering numbers.
- The worksheets below will help you supplement your lessons, and will also provide additional practice for your students. Our worksheets serve as great gap fillers during lessons, to help your students retain the grammar learned during the lesson.
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- Advertising can have both positive as well as negative effects on children based on the content, quality and the presentation of the advertisement. While there are a few positive influences of advertisements, they indeed fail to outweigh the negatives.Iron pony inventory
- Oct 20, 2020 · 21 Posts Related to Ordering Negative Decimal Numbers Worksheet. ... Ordering Negative Numbers Worksheet Tes. ... Ordering Positive And Negative Numbers Worksheet Ks2.Making lead molds from plaster
- The interactive quiz and worksheet will give you practice adding and subtracting decimals using word problems. These word problems help you understand how to treat numbers that have decimal points ...S85 standalone
- Objective: • Compare and order positive and negative numbers. • Math Link: You know how to compare and order whole numbers, decimals, and fractions.Outlook options
- Create numbers with two decimals Extra solution space ... No negative results for subtraction ... Apple: Cmd-D). Each day you want generate a unique daily worksheet ...Kimber stainless lw 1911 45acp 5 3700591


Based on the request from some users I have modified the result display of my AHP-OS online software. Beside the resulting priorities it is now possible to see the underlying consolidated decision matrix, which results from the aggregation of individual judgments (AIJ) using the geometric mean.
For decision hierarchies the result page shows the resulting local and global priorities (overall result) in hierarchical form, and the global priorities in descending order in a bar graph.
Then, in a breakdown by nodes, consolidated priorities, consolidated decision matrix and the priorities of individual participants are shown:
As in this example, the consolidated matrix for one participant is the same as the AHP decision matrix.
For alternative evaluation the breakdown is done by criteria. It shows the consolidated preferences for all alternatives with respect to each of the criteria:
In this example the House A from the alternative houses A, B, C has the best match with respect to the criterion “Size”.
I am now working on the extension to let you download the complete set of input values, i.e. all underlying decision matrices, to excel. In the current version only the resulting AHP priorities are available.


What is Milliradian (MIL)?
What is Milliradian (MIL)?
Milliradian (MIL) is a unit of angular measurement often used in the context of shooting and ballistics to describe the accuracy of firearms, scopes, and shot groupings. One MIL is equal to 1/1000th of a radian, and at a distance of 100 meters, it subtends approximately 10 centimeters (3.94 inches). MIL-based systems are commonly used in applications where metric measurements are preferred or more familiar.
The concept of MIL is used to quantify and communicate various aspects of shooting performance:
- Firearm Accuracy: The inherent accuracy of a firearm can be described in MIL, representing the expected shot dispersion at a specific distance. For example, a rifle with an accuracy of 0.5 MIL is expected to produce shot groupings within a 5-centimeter diameter circle at 100 meters, 10 centimeters at 200 meters, and so on.
- Scope Adjustments: Scope turrets have click adjustments measured in MIL or fractions of MIL (e.g., 0.1 MIL per click). These adjustments allow shooters to make precise changes to their point of aim using the metric system.
- Shot Groupings: MIL is used to describe the size of shot groupings, indicating how closely together shots land on a target at a given distance. Smaller MIL values represent tighter groupings and better shooting performance.
To calculate MIL, the following formula can be used:
MIL = (Group size in centimeters / Distance in meters) x 10
For example, if a 3-shot group measures 7.5 centimeters center-to-center at 100 meters:
MIL = (7.5 / 100) x 10 = 0.75 MIL
MIL vs. MOA
Another angular measurement used in shooting and ballistics is the Minute of Angle (MOA). MOA is equal to 1/60th of a degree and, at a distance of 100 yards, subtends approximately 1.047 inches. Both MOA and MIL are used in scopes, reticles, and ballistic calculations, and the choice between the two depends on personal preference, familiarity, and desired level of precision.
Key aspects of MOA in comparison to MIL include:
- Scope Adjustments: Similar to MIL, scope turrets can have click adjustments measured in MOA or fractions of MOA (e.g., 1/4 MOA per click). These adjustments allow shooters to make precise changes to their point of aim in a consistent, quantifiable manner.
- Reticles: MOA-based reticles are available for shooters who prefer working with the imperial system, offering a consistent method for measuring and adjusting for windage and elevation.
- Precision: While both MOA and MIL can provide precise measurements and adjustments, the choice between them depends on personal preference, familiarity, and the desired level of precision. Some shooters find it easier to work with MOA due to its direct relationship with the imperial system.
- Cleckner, R. (2016). Long Range Shooting Handbook: A Beginner's Guide to Precision Rifle Shooting. CreateSpace Independent Publishing Platform.
- Litz, B. (2011). Applied Ballistics for Long Range Shooting. Applied Ballistics LLC.
- Barsness, J. (2006). The Big Book of Ballistics. Skyhorse Publishing.


The Mathematics program at Branford High School is designed to blend the concrete with the abstract, application with theory, and skills with concepts. As students progress through this sequential program, they learn to display the mastery of mechanical skills through the development of higher-order thinking skills, such as analyzing, predicting, and drawing conclusions.
Our approach to the teaching of mathematics is predicated upon the conviction that instruction should strike a balance between formal presentation by the teacher and discovery by the student through such means as hands-on activities, classroom experiments, work with calculators/computers, and engagement in rich instructional tasks with peers. This varied instruction should accommodate the diversity of student learning styles and interests by providing each student the opportunity to find success through his/her/their own efforts and to gain the life skills necessary for success in a technological, information-based world.
Through varied instructional techniques, especially by engaging in rich instructional tasks with peers, students should become more motivated and persistent and should improve their sense of responsibility, self-reliance, and intellectual curiosity. Interpersonal relations and a sense of community as moral and ethical values should also be enhanced.
There are academic, school-wide Performance Graduation Requirements aligned with various courses offered in the mathematics section of the 2023-2024 Program of Studies. The following departmental performance expectations are the focus of the mathematics curriculum:
Analyze trends/patterns to create models and make predictions
Utilize tools and technology appropriately within a mathematical context
Apply mathematical concepts to multi-step, authentic problems


Published September 4, 2007
by Kaplan Publishing .
Written in English
|The Physical Object|
|Number of Pages||352|
Kaplan’s GRE Math Workbook includes more than 1, realistic practice questions to help you get comfortable and confident with the Quantitative section of the test. We’re so confident that GRE Math Workbook offers all the practice you need to excel on the GRE that we guarantee it: After studying with our book, you'll score higher on the GRE—or you'll get your money back/5(24). Kaplan’s GRE Exam Verbal Workbook, Third Edition comes complete with a targeted review of all the tested material on the Verbal section of the GRE, plus Kaplan’s renowned test-taking strategies. This powerful combination makes Kaplan’s GRE Exam Verbal Workbook the most effective way for you to score higher on what is often described as the most challenging section of the GRE. Always study with the most up-to-date prep! Look for GRE Math Workbook, 11th edition, ISBN , on sale November 6, Publisher's Note: Products purchased from third-party sellers are not guaranteed by the publisher for quality or authenticity. Kaplan’s Math Workbook for the GRE, 9th Edition, comprehensively addresses the math section of the GRE Revised General Test. This workbook is a highly effective way to prepare for the math section of the GRE Revised General Test. Kaplan’s Math Workbook for the GRE, 9th Edition includes: • 6 full-length Quantitative Reasoning practice setsReviews:
Gre Math Workbook Kaplan Test Prep. Welcome,you are looking at books for reading, the Gre Math Workbook Kaplan Test Prep, you will able to read or download in Pdf or ePub books and notice some of author may have lock the live reading for some of ore it need a FREE signup process to obtain the book. This workbook is a highly effective way to prepare for the math section of the GRE. Kaplan's GRE Math Workbook, 10th Edition, includes: 6 full-length Quantitative Reasoning practice sets Diagnostic tool for even more targeted Quantitative practice Review of crucial math skills and concepts (including arithmetic, algebra, data interpretation. Welcome to Kaplan Books Online. Use your online resources to get the best out of your prep. 1) To register your book, simply click on the register button next to the book you have purchased. GMAT Math Workbook. Buy on Amazon: Register: GMAT Verbal Workbook. Buy on Amazon: Register: Kaplan GMAT Buy on Amazon: Register: GRE. GRE Complete. GRE Math Workbook (Kaplan Test Prep) Paperback – 3 November by Kaplan Test Prep (Author) › Visit Amazon's Kaplan Test Prep Page. Find all the books, read about the author, and more. See search results for this author. Kaplan Test Prep (Author) out of 5 stars 82 s:
Score higher on the GRE with the GRE prep course that brings you the most realistic practice for test day and more live instruction than anyone else. Get GRE test prep from Kaplan in a classroom near you, live online, on-demand, or with a private tutor. Kaplan's GRE®& GMAT® Exams Math Workbook, Third Edition immerses you in all the math concepts you need to know. With comprehensive review and powerful strategies for every type of question, this intensive workbook provides you with the targeted math training you need to score well on the GRE® and GMAT® exams.4/5(13). Kaplan’s GRE Math Workbook includes more than 1, realistic practice questions to help you get comfortable and confident with the Quantitative section of the test. We’re so confident that GRE Math Workbook offers all the practice you need to excel on the GRE that we guarantee it: After studying with our book, you'll score higher on the GRE—or you'll get your money Edition: Proprietary, Third Edition. I got 99th percentile on my GMAT (49, 42) and i used 3 books: this one, Kaplan's book with CD and Verbal Workbook. I had access to PR book and GMAT Prep, but I did only tests from those. I found Kaplan's materials of quality and difficulty. Some whine that Kaplan is too hard, but that's good - if you can handle Kaplan, you can handle the GMAT/5(26).


Rachelle Walley(832) 726-1452
Rachelle graduated cum laude from East Texas Baptist University with a Bachelor of Science in Education. There she majored in Mathematics with a double-minor in Computer Information Systems and Music. After graduation she entered the teaching profession and for 13 years taught physics, calculus, algebra, geometry and consumer math to high school students.
Rachelle began working with Consider It Done and Jessica Riner in 2006 and her focus is client account servicing and leading special projects for clients. Her attention to detail, math and computer background make her a natural fit for our team.
She has an active family life with 4 young children: Connor, Cooper her biological children and Casey and Valerie were adopted from Ukraine.


Statistics with R – Beginner Level: Basic statistical analyses using the R program
- 4.4 (994 ratings)
- 59,961 students enrolled
- Created by Bogdan Anastasiei
- Last updated 3/2016
If you would like to find out the way to perform the essential statistical analyses within the R program, you’ve got come to the proper place.
Now you don’t need to scour the online endlessly so as to seek out the way to compute the statistical indicators in R, the way to build a cross-table, the way to build a scatterplot chart or the way to compute an easy statistical test just like the one-sample t test. Everything is here, during this course, explained visually, step by step.
So, what will you learn in this course?
First of all, you’ll find out how to control data in R, to organize it for the analysis: the way to filter your data frame, the way to recode variables and compute new variables.
Afterwards, we’ll lookout about computing the most statistical figures in R: mean, median, variance , skewness, kurtosis etc., both within the whole population and in subgroups of the population.
Then you will learn how to visualize data using tables and charts. So we’ll build tables and cross-tables, also as histograms, cumulative frequency charts, column and mean plot charts, scatterplot charts and boxplot charts.
Since assumption checking may be a vital a part of any statistical analysis, we couldn’t elude this subject . So we’ll learn how to check for normality and for the presence of outliers.
Finally, we’ll perform some basic, one-sample statistical tests and interpret the results. I’m talking about the one-sample t test, the binomial test and therefore the chi-square test for goodness-of-fit.
So after graduating this course, you’ll skill to perform the essential statistical procedures within the R program. So… enroll today!
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This sequence permits students to complete a primary major in one discipline and then to complete requirements for a second, “dual,” degree in mathematics. Students could graduate with both degrees simultaneously or, if necessary, graduate with the primary degree in one semester and complete the remaining dual degree requirements within one year. The requirements for the dual degree include 30 semester credit hours of mathematics as outlined below. Students must complete a minimum of 30 credit hours of courses above the total hours required for the primary degree. Thus, the minimum requirement for the two degrees is 150 credit hours.
Summary of Graduation Requirements
|General Education Core||40|
|Dual Mathematics Requirements||30|
|Total Credit Hours||150|
- Complete Primary Degree Requirements
(Minimum of 120 Semester Hours)
- Complete Dual Mathematics Requirements
(30 Semester Hours)
Course List Code Title Credits Requirements MTH 251 Calculus II 4 MTH 252 Calculus III 4 MTH 300 Linear Algebra 3 MTH 351 Probability & Statistics I 3 MTH 372 Differential Equations 3 MTH 373 Advanced Vector Calculus 3 Mathematics Electives Select one of the following: 3 Discrete Mathematics Algebraic Structures Probability & Statistics II Introduction to Applied Mathematics Select one of the following: 3 Numerical Analysis I Abstract Algebra Real Analysis Topics in Applied Mathematics Total Credits 26
- Complete 30-Hour Minimum Requirement
Take additional hours, if needed, to assure the completion of a minimum of 30 semester hours above the total hour requirement for the primary degree.


Here’s how the point distribution system is calculated.
Note: After GameWeek 5, We have decided to increase our point system.
HERE IS NEW SCORE POINT.
- 20 Points for correct score
For example, predict 3-0 and the result is 3-0 award 20 points.
- 10 Points for guessing a draw.
For example, predict 2-2 and the result is 1-1 award 10 points
- 5 Point for predicting a win even with a wrong score.
For example, predict 1-0 and the result is 2-0 award 5 points.
Points above are not cumulative, for example, predict 2-2 and the result is 2-2, you gain 10 points, NOT 30 points.


jwwelding.ca/wp-content/iphone-problemi/1626-programmi-per.html As a part of the TPCK initiative, participants were required to consider what algebraic reasoning means to them and the various forms that students concentrate on, think together about how students can develop their algebraic reasoning and transition from calculations to mathematical analysis, and assess the role of resources used in the teaching and learning of algebra. One of the many activities that teacher participants engaged in involved transfer problems. Differential equations, difference equations, integral equations I80 Functions of a complex variable, conformal mappings [complex numbers see F50 ] I90 Miscellaneous E. Basic geometrical shapes [prenumerical stage see F20 ] G30 Areas and volumes Lengths and areas, volumes and surface areas [quantities and units see also F70 ; word problems see F90 ] G40 Plane and solid geometry. Psychology of computer science education. By spectrum I mean 1 where a concept comes from 2 using it in the abstract and 3 using it in real life.
The understanding of slope as a ratio feeds into an even more fundamental emphasis in Common Core math: the analysis of functions. By thinking about the slope of a line as a ratio, students get in the habit of analyzing the parts of a linear function so they can see how changes in elements of the function affect the relationship between inputs and outputs.
Daro sees this shift from solving equations to analyzing functions as one of the biggest conceptual changes in the Common Core. The change from solving equations to analyzing functions seems benign, but that has not stopped the Common Core from becoming a charged political issue. As a result, even stalwart adopters are questioning whether the standards work.
The designers of NGSS, which came out three years after the Common Core without any kind of federal mandate, say they learned from the contentious rollout of the earlier standards. So far, 17 states plus the District of Columbia have adopted NGSS and 11 more states have implemented standards that are similar to varying degrees. Still, NGSS has had its controversies. The document includes standards related to climate change and evolution, which has motivated opposition in conservative states.
And, politics aside, the standards necessitate sweeping changes to the way science is taught. Like Common Core math with its long-running development of core concepts, NGSS reframes science in terms of a small number of basic ideas that inform the scientific perspective. This slow-building approach is at odds with some aspects of public education. Schweingruber agrees. The same mismatch between the standards and the way public education is set up occurs in another major area: assessments. There is progress in that direction.
Two recent initiatives, the Partnership for Assessment of Readiness for College and Careers and the Smarter Balanced Assessment Consortium , are developing standardized tests that incorporate a greater variety of question types, like constructed response questions in which students are asked to explain their reasoning, and technology-enhanced questions in which, for example, students manipulate a line on a graph to make it match a given algebraic function.
On the first and third Thursdays of every month, science teachers from around the country gather for NGSSchat , a Twitter conversation about how to implement the new science. Topics for discussion have included how to incorporate reading and writing into science instruction and how to use technological tools alongside the standards.
In a storyline, a teacher begins by introducing students to a phenomenon that prompts questions that students will investigate over the course of about two months. One storyline asks students to explain the biology behind the death of the Georgia high school football player Zyrees Oliver in after he drank too much fluid during practice. Another storyline asks simply: How does a seed grow into a tree? This is a significant change from the way teachers have traditionally understood their role in the classroom. During the July 7 chat, some participants doubted their ability to make the shift.
Shelton thinks the instructional changes entailed by NGSS are too big to internalize in isolated chunks of professional development. Along with professional networks, teachers also need curricular materials that fit the NGSS approach—textbooks, assessments and lab equipment that are well-suited to the basic method of gathering evidence and building arguments. One classroom technique that has gained currency is the building and analysis of models—functions that tune an input with some number of parameters and produce an output that describes phenomena in the world.
Programs like IMP confuse students and they end up not learning anything but instead they waste their time finding other ways to approach those problems that are useful. Before applying and understanding the concepts with real life problems the students need to know how to use the concepts and why it works. Once students learn to dominate the techniques they can apply them to real life. In my school, teachers are in a way doing what Gafunkel and Mumferd suggest by focusing on word problems.
The best solutions is for schools to go back to basics, teaching students the concepts and then making them practice them because once they gain the concept they can easily learn how to apply it. Not until this year have the school directives decided to start teaching us naked math. Juan, Joanna, Raymond, all of these made up people had problems.
By applying your knowledge to solve their problems, you learned. Honestly, I hated this system. What Mr. Mumford state in this article is acceptable. Why not make students learn the math they will need for what they will want to study. Also, the math you are taught will make you think faster in your life.
By being able to solve equations in a fast manner will help you remember things and answer standardized questions, like AP and SAT test questions, faster. In my opinion, schools should offer the traditional math curriculum as well as classes specialized in career math. If a student is positive he will study economics in college, then he could choose to study a course that will teach him the basic math for THAT career.
The dilemma exposed in this article happened at my school about five years ago, when the board of directors decided to change the Math program to one that developed upon real life situations. With it, students would see a variety of mathematic branches connected to different real life situations. How far from the Ferris Wheel should the Cart be located in order for the diver to land in the water? Therefore, mathematics teachers who were teaching prospect AP Calculus students started using IMP only as a complement of the math program and not as its core.
In my experience, being a passionate in Math, my reaction towards IMP was appalling. I felt my Mathematics skills were becoming dormant as I was no longer feeling challenged by difficult algebra or trigonometric drills. Thankfully, I had the opportunity to have a teacher who felt the same as me towards the IMP and she taught us old-school math instead of IMP. Also, I feel encouraged of pursuing an engineering career without the sensation of being beaten by other people in Mathematics.
Even though I plan on studying Mechanical Engineering, I feel completely identified with what the article proposes, a mathematical education in what people truly need, with real material they can use when CNG becomes a wonderful memory. As I compare both of my mathematics classes I arrive at the same conclusion as the article: some concepts are more valuable to an average college student than for the engineering major. The conceptualization of this question comes down to the true spirit of education: Should we learn the most valuable subjects, or those that have been taught for centuries and that have become part of what we call general knowledge?
Why should everyone learn the same things? This article took me back to my first statistics class a couple of weeks ago, when our teacher showed us a TED talk that addressed this same question. Math — what a broad word. As if anything could be changed nicely and efficiently without gaps, transition problems, and the students who basically just miss the old and traditional way. First of all, you would have to reteach and retrain math teachers, which would either put old teachers out of work, or cost millions of dollars simply putting teachers through certain classes and meetings.
Second of all, kids will be unfamiliar to this new style of teaching, why would children in elementary care about statistics? However, High school and middle school students should be exposed to real life problems. And finally, educators would have to a spend a lot of time adapting the curriculum and b focus on not allowing any gaps in the students learning and education. Why has it not occurred to anyone that the students need to be changed? Students in the USA, in my opinion, do not receive enough pressure, encouragement, or will to succeed beyond what is expected of them.
When I atttended a public school in the states, I only did what was expected, I did not try to learn more about the subject, or even feign interest. A think this relates to the unimportant way people discuss and deal with education.
Buy The Algebra Solution to Mathematics Reform: Completing the Equation on dynipalo.tk ✓ FREE SHIPPING on qualified orders. Editorial Reviews. Review. “For all those who care about the mathematical future of our nation's The Algebra Solution to Mathematics Reform: Completing the Equation - Kindle edition by Frances R. Spielhagen. Download it once and read it .
We carefully state the problem, plan out our solution, execute steps in the appropriate order, and evaluate the solution. I believe that the math program in the USA, which teaches students algebra, geometry, pre calculus, and calculus separately leaves in them a clear way and form to develop a problem and arise to its solution. This way of math creates in students the open-mind thinking strategies, to help them get through all the situations in their personal and professional lives.
On the other hand the math program at my school: IMP Interactive Mathematics Program is a book based on teaching through a set of world problems and hypothetical and non real situations. This type of teaching method could be considered close minded, since it creates self restrains and makes the student implement the idea in that specific situation. It can even, to a certain degree confuse and frustrate students. So I think that schools should go back to teaching the original methods, teaching the basic concepts and then when students have mastered these they can learn to apply them to real life situations.
Apparently, our friends Garfunel and Mumford see learning as an obligation and not as an opportunity. Finding a numerical value for a letter helps your brain organize information, assimilate it and use logic and previous knowledge to find an answer. What students learn in high school is not rocket science.
It should be made to help progress the mind while giving the student a litlle fun to learning math. I know that math is importan blah blah blah, BUT, math could be exciting and fun to learn!! If student were to see math as a fun and inviting subject, there would be less students failing math and more students acing math while having a good time!! Nobody can deny that a basic knowledge in mathematics is vital to interact with the wolrd we live in. Whether it be how far you need to place a ladder from a window, or how much cinnamon to put in your plastries.
In High School however, we learn about things that we will virtually never need, of course with the exception that you pursue a career in mathematics. We will find no need for quadratic fomula solving, or the understanding of complex numbers inour everyday lives. This too, can go wrong. For example, in my school the board of directors thought they would try out teaching mathematics through examples and they implemented the IMP Interactive Math Program.
How can we increase mathematics achievement among all students? This book provides a straightforward explanation of how changing mathematics tracking policies to provide algebra instruction to all students by at least eighth grade can bring about changes in both student achievement and teacher performance. Spielhagen chronicles the success of a large school district that changed the way mathematics was delivered and increased success rates across all populations. Featuring interviews with students and teachers, the author shows how all stakeholders were brought into the process of changing policy from the ground up.
Offering a model for success that can be replicated by other districts, this resource:. Frances R.


The "normal distribution" of data is important, which in simple words mean the bell curve of data spread. Half on one side of ‘mean’ and half on other side of ‘mean’. If the average weight of class of 50 students is 60 kgs. Then the range may be between 40 to 80 kg. Half may fall between 40 & 60 and other half between 60 & 80. This will provide us bell shaped graph of data which is called ‘normal distribution’.
The distribution of many test statistics is normal or follows some form that can be derived from the normal distribution. In this sense, philosophically speaking, the normal distribution represents one of the empirically verified elementary "truths about the general nature of reality," and its status can be compared to the one of fundamental laws of natural sciences. The exact shape of the normal distribution (the characteristic "bell curve") is defined by a function that has only two parameters: mean and standard deviation.
A characteristic property of the normal distribution is that 68% of all of its observations fall within a range of ±1 standard deviation from the mean, and a range of ±2 standard deviations includes 95% of the scores. In other words, in a normal distribution, observations that have a standardized value of less than -2 or more than +2 have a relative frequency of 5% or less. (Standardized value means that a value is expressed in terms of its difference from the mean, divided by the standard deviation.
Not all, but most of them are either based on the normal distribution directly or on distributions that are related to and can be derived from normal such as t, F, or Chi-square. Typically, these tests require that the variables analyzed are themselves normally distributed in the population, that is, they meet the so-called "normality assumption." Many observed variables actually are normally distributed, which is another reason why the normal distribution represents a "general feature" of empirical reality.
The problem may occur when we try to use a normal distribution based test to analyze data from variables that are themselves not normally distributed. In such cases, we have two general choices. First, we can use some alternative "nonparametric" test (or so-called "distribution-free test" , but this is often inconvenient because such tests are typically less powerful and less flexible in terms of types of conclusions that they can provide. Alternatively, in many cases we can still use the normal distribution based test if we only make sure that the size of our samples is large enough.
The latter option is based on an extremely important principle that is largely responsible for the popularity of tests that are based on the normal distribution function. Namely, as the sample size increases, the shape of the sampling distribution approaches normal shape, even if the distribution of the variable in question is not normal. However, as the sample size increases, the shape of the sampling distribution becomes normal.


Romania's national team puts maths equations on the back of training shirts
Footballers aren't always considered to be the most intelligent of people, but Romania's national team players have done something wonderful in a bid to promote maths to children in their country.
Ahead of their international friendly with Spain on Sunday, Romania put some maths problems on the back of their training shirts -- the answers to which reveal the players' real numbers.
Romania changed their training kit from numbers to maths calculations to help kids improve their maths. pic.twitter.com/bwbd3f2qZH- Coral (@Coral) March 27, 2016
Ok, it may not be quadratic equations or trigonometry, but what a brilliant initiative to bridge the gap between education and sport. Full marks!


A rigorous introduction to statistics for students intending to study economics and other quantitative fields. Examples are drawn from finance, decision analysis, and economic decision making. In addition to descriptive statistics, probability, inference, and regression modeling, this course also covers portfolio creation, decision analysis, and time series analysis. Students with prior exposure to introductory statistics will find some overlap of material but will be exposed to new applications and learn more advanced modeling techniques. The statistical software package Stata is used. Harvard has a site license for the software so it does not need to be purchased. The recorded lectures are from the Harvard Faculty of Arts and Sciences course Statistics 104. Students may count one of the following courses toward a degree, but not all four: STAT E-100, STAT E-101, STAT E-102, or STAT E-104.
Prerequisite(s): high school algebra.


When it comes to performance statistics in backtesting, every system builder has a favorite set for gauging the effectiveness of a strategy. One popular metric, the Sharpe ratio, was introduced in 1966 by Stanford professor Dr. William Forsyth Sharpe and measures return relative to volatility. Volatility is measured as the annualized standard deviation of returns. One drawback to the Sharpe ratio is that it penalizes both negative and positive return volatility, so a strategy such as trend following that cuts losses short and lets profits run could arguably be penalized unfairly. An alternative to the Sharpe ratio was developed by Dr. Frank A. Sortino in 1980. The Sortino ratio also measures return relative to volatility, but only considers negative return volatility.
In Trading Blox, the Summary Results are shown after a test is completed, and the Annual Sharpe ratio can be found among the statistics at the top of the report.


Rates of Change and Growth/Decay Characterization
This activity provides students with an opportunity to practice calculating rates of change and then to connect the patterns they see in these calculations to the growth/decay they see in the graph. This allows us to characterize linear functions as having a constant rate of change and to see that concave up functions have increasing rates of change and concave down functions have decreasing rates of change.
This is a slightly updated version of this activity https://sites.google.com/site/ruinstructorprecalcwiki/chapter-1-activities/course-activity-1-3-linear-functions and more implementation notes are provided there.
I have created the following Desmos activity to use in class after students have worked on this activity. The activity itself could definitely be assigned as out of class work and then you could follow up in class with the Desmos activity.


Step up to Learn for 11-14 year olds - £18 per class
Our 11-14 years old classes for secondary school students is known as - Step up to Learn. The classes are designed to support your child as they make the transition into secondary school and then through to the end of Key Stage 3. Each class will teach the maths and English skills that your child will need to know as they progress through Years 7-9 enabling them to become a proficient writer and confident mathematician.
Each lesson will have some or all of the following elements:
- Maths tuition in all of the key topics that your child will need to learn in Key Stage 3.
- English tuition in both language and literature enabling your child to become an excellent writer while developing the skills of analytical thinking necessary to fully understand and appreciate the texts that they will study.
- Exam paper practise in both maths and English.
- Exam techniques and revision support.
After each lesson, the parents are talked through a comprehensive summary of the lesson as well as guidance on additional activities that they could do with their child at home. Each 50 minute lesson includes a snack and drink. Classes are payable termly in advance, at a cost of £18 per session.


Credentialed Math Tutors
Experienced and Credentialed Math Tutors
Attempting to introduce supplemental curriculum to a struggling student causes confusion and further frustration. To help avoid these issues, we employ private math tutors that are experienced in teaching the current common core standards to ensure our instruction is aligned with your child’s school curriculum. Students in middle and high school will be partnered with specialized single subject math tutors, while elementary students will have tutors with multiple subject credentials.
Our credentialed math tutors teach math because they love it, and their skills and enthusiasm help students begin to enjoy math class again. We work to not only improve student’s grades, but also their self-esteem and general attitude towards school.


Learning to measure can be fun time
Young children are full of measurement questions. How long is it? How big is it? How far away is it? The answer is hard to explain without knowing measurement units. Understanding that measurement requires repeated use of a tool like a ruler is important for success in math and science.
Adults and children can measure distances between objects found at home using a non-standard measurement tool, your feet. This is called non-standard because everyone’s feet are different.
For more math ideas see grandparentsteachtoo.org or listen to wnmufm live 4:30 Tuesdays and 8:35 a.m. Saturdays. Educator Mary Davis contributed this column.
What to do
Trace an outline of an adult’s foot on paper and cut it out. Explain how to use this tool to measure distance in your home. Define distance as the amount of space between two objects. Have the children choose an object in the room. Show them how to use the foot cutout to measure the distance from where you stand (your home base) to the object’s location. Children can help by moving the cutout and keeping count. Record the results on a sheet of paper. Draw a picture of the destination piece and write the number of adult feet to get there.
Next, trace children’s feet, cut them out, and label them with their names. Compare the children’s little feet and adult’s big feet. Have children measure the distance to the same object using their little feet as the measurement tool. Record those numbers on the paper using a different color crayon. Repeat using three more objects.
Ask questions such as: What did you notice when you measured the distance between our home base and the objects? Which object needed the most feet or the least? The farther away the object is, the more feet are needed.
How did the total number of children’s feet compare with the adult’s feet as a measurement tool? The shorter the foot, the more feet are needed to measure the distance.
What else can we do?
Measure the distance using other objects such as crayons, hands, or blocks. Cut an oval shape from paper. Add eyes, whiskers, and a yarn tail to make a mouse. How many mouse lengths does it take to get from point A to B?
In Richard Fowler’s book, “Ladybug on the Move,” use the cardboard ladybug to measure distances it travels in the garden. In “Super Sandcastle Saturday” by Murphy, children learn about standard units of measurement as they measure sandcastles with shovels and spoons.
Find a foot-long standard ruler and explain standard measurement. This foot is always the same, therefore standard. Keep rulers handy for children to measure their own structures and their height as they grow.
Editor’s note: This column is penned by retired Marquette Area Public Schools teachers Iris Katers, Jean Hetrick, and Cheryl Anderegg. Esther Macalady is from Golden, Colorado. Tim Fox currently teaches at Superior Hills Elementary. It’s supported by Northern Michigan University Center for Economic Education and Entrepreneurship, the School of Education, U.P. Children’s Museum, U.P. Association for the Education of Young Children, and U.P. Parent Awareness of Michigan. Their book “Learning Through the Seasons” is available at area stores and www.grandparentsteachtoo.org. Their mission is to provide fun standards based activities that adults can do in the home to prepare children for school and a lifetime of learning and reduce the stress of child care.


Choose a NoteVestment Resource
The financial calculator is a very important tool to use as a real estate note investor. Note investors should become familiar with the financial calculator, to be able to accurately calculate note investment returns. Many investors are intimidated by financial calculators like the HP-12C or the Texas Instruments BA II Plus. Here we will help you start to conquer the calculator and boost your financial calculator game.
NASA's Human Calculators
Fun factoid in the 1940’s, before the dawn of computers, NASA had employees whose single job was to compute trajectories by hand. Pretty crazy to think about when we all have calculators on our smartphones now.
My Experience Using Financial Calculators
With a bachelor’s degree in finance, I have spent a fair amount of time plugging numbers into financial calculators to find returns, payment amounts and interest rates. I remember what it was like when I first started using my Texas Instruments BA II Plus in my finance classes. I eventually graduated to the HP-12C, which is slightly trickier because it uses Reverse Polish Notation (RPN) in its calculations. While I’ve used both of the financial calculators below, I prefer the HP-12C due to its design as well as finishes.
Recommended Financial Calculators
The BA II Plus was my first financial calculator and always performed well throughout college. It is capable of solving all of the financial calculations required as a note investor, such as time-value-of-money, cash flow analysis, amortization schedule generation, Internal Rate of Return (IRR) and Net Present Value (NPV). The BA II Plus operates most closely to simple function calculators, so it should be easier to familiarize yourself.
My personal go to calculator is the HP-12C. Like the BA II Plus, it performs all necessary financial calculations that would be desired from a real estate note investor. Uniquely, the HP-12C computations are in Reverse Polish Notation (RPN), which may lead to some confusion when first using the calculator. Aesthetically the HP-12C feels premium and refined compared to the BA II Plus, which is reflected in the slightly higher price. For the higher price, I feel that it is justified the premium craftsmanship alone.
The links on this page are affiliate links, which means that purchasing/signing up with any of the recommended resources through the links above will give NoteVestment.com a small commission (though the price you pay is no higher). If you end up using an affiliate link above, you are directly supporting NoteVestment.com. All being said, if you do choose to use them, thank you.


I enjoyed meeting you during the Parent Teacher Interviews! It was nice to actually sit down and chat with you. 🙂
I promised some parents I would post a few links to some of the learning songs we do in class!
Jolly Phonics song about the sounds of each letter- https://www.youtube.com/watch?v=ei0iFs5uF6w
Letters start at the top- https://www.youtube.com/watch?v=um096Twf3lQ or with children singing it– https://www.youtube.com/watch?v=tcAYnrh6fdw
This week in KB:
Sight word- GO
Math- #6 and part part whole activities (PPW)
What is Part Part Whole? Part part whole relationships (PPW) involve seeing numbers as being made of two or more parts. Many researchers have said this is the major conceptual achievement of the early years. A strong understanding of PPW has been shown to increase understanding of subsequent work with place value, number concepts, and word problems.
After students learn to count, they need to work on part part whole relationships before beginning addition and subtraction. The Hands On Math program follows this order.
As in the other number relationships, students use counting as a scaffold to form their ideas about PPW. When students are exploring parts of a number, they need to work with one number in a variety of ways and with a variety of concrete materials. We also want to use a multisensory approach, which requires visualization and begins to move students away from relying on their counting skills.
Christmas Families and Spirit Day Fundraiser – Our students will be involved in a spirit day fundraiser to support our Christmas families. We are asking parents who would like to do one cash donation to our Christmas Family Program to send their contributions to the school before December 15.
Hers’s the list of Spirit Days!
November 24th-PJ Day
December 1st Crazy Hair/Hat day
December 8th Red, Green and White Day
December 15th Backwards Day /Bubble gum day (I will be giving them bubblegum to chew in class)
December 22nd Christmas/Winter Sweater Day! (no donations)


Exceedance (shown) and non-exceedance (not shown) growth curves can be plotted when their respective radio buttons are selected. The recurrence interval is plotted on the x-axis on a log scale while the variable of interest is plotted on the y-axis; the data for the selected site are plotted as a gray growth curve. In addition, growth curves for all selected distributions are plotted using various colors. There are 13 standard distributions included within the current version of Hydro-FIT. The user can plot or remove any of the distributions from the exceedance and non-exceedance graphs by clicking the checkbox(es) adjacent to the desired distribution(s).


If you are launching a new site, calculating your bandwidth is difficult to determine.
The best approach is to keep careful track of your website's activity for the first few months after it goes live so you can determine your actual monthly usage, and adjust the required bandwidth accordingly.
For more established sites, calculating your estimated bandwidth goes as follows:
- Estimate the average page size of your site, in kilobytes (KB).
- Multiply this value by the monthly average number of visitors.
- Multiply the result from step 2. by the average number of pageviews per visitor.
Keep in mind that your calculations must include every one of your sites hosted on the server.
If you run twelve domains on the same VPS account, take the time to add up the page sizes, visitors and pageviews across all domains.
These simple calculations should give you an idea of how much bandwidth you can expect to use, but some math is required.
Basing your usage allotment solely on these rough estimates will not give you the entire picture.


A lot of misconceptions students have about linear algebra stem from an incomplete understanding of this core concept. Now since I want you to leave this chapter with a thorough understanding of linear algebra we will now review—in excruciating detail—the notion of a basis and how to compute vector coordinates with respect to this basis.
1. Prove the projection matrix formula involving the double angle. That is, start with Apr 12, 2009 In the chapter on linear algebra you learned that the projection of w onto x is projection M(d) is that it violates the structure given in Equation 2 Homework Statement That is the question. The answer on the bottom is incorrect Homework Equations I believe that is the formula that is Feb 16, 2011 Math 19b: Linear Algebra with Probability. Oliver Knill, Spring If we combine a projection with a dilation, we get a rotation dilation. Rotation.
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Minstakvadratmetoden har en linjär och en icke-linjär variant beroende på om Vid varje iteration approximeras lösningen med en linjär lösning, varför de Linear Algebra and its Applications, David C. Lay ISBN 978-1-292-09223-2 Sensor Resource Management driven by threat projection and priorities. Information Structural Equation Modeling techniques are used to evaluate dependencies variable in one such matrix and those of any other matrix. The ROC Risk In such cases, a clear understanding of the connection between shaft rotation and corresponding linear displacement, as well as system mechanical tolerances Algebra. Verktyg.
Learn the basics of Linear Algebra with this series from the Worldwide Center of Mathematics. Find more math tutoring and lecture videos on our channel or at
Properties of the dot product.
is orthogonal to vj for all j, it is orthogonal to any linear combination of them c1v1 + . (a) Write a formula for the orthogonal projection P : R2 → V. (b) What is: i)
A linear transformation is defined by equations a11x1. + a12x2. + + a1nxn It gives the orthogonal projection of point (x, y) onto the x-axis.
First, we must realize that when we are minimizing the SSE, This shadow corresponds to the projection of b Exercise 3.3.17. Find the projection matrix that projects vectors in onto the line . Answer: The vector is a basis for the subspace being projected onto, which is thus the column space of Using the formula we have so that and … Continue reading → Our journey through linear algebra begins with linear systems. Row Reduction We row reduce a matrix by performing row operations, in order to find a simpler but equivalent system for … Linear Algebra is a type of mathematics that is used in advanced game development, statistical programming, mathematical programming, and more. It is also a required class in many college degrees.
We have released a 20-hour Linear Algebra course on the freeCodeCamp.org YouTube channel. The course is taught by Dr.
Projection, Linear Algebra 4th - Jim Hefferson | All the textbook answers and step-by-step explanations. Ask your homework questions to teachers and professors, meet other students, and be entered to win $600 or an Xbox Series X
Linear Algebra is an app to solve some of the mathematical problems on the go. Here in this app, you need to enter the value and click the Calculate button to get the result.
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Linear regression is commonly used to fit a line to a collection of data. The method of least squares can be viewed as finding the projection of a vector. Linear algebra provides a powerful and efficient description of linear regression in terms of the matrix A T A .
In Figure 2-9, we have two vectors and and we want to know (the component of in the direction of ). Again we can form a right triangle with the two vectors and we find the following where is the angle between the two vectors: many videos ago we introduced the idea of a projection and in that case we dealt more particularly with projections onto lines that went through the origin so if we had some line let's say L and let's say L is equal to the span of some vector V or you could say alternately you could say that L is equal to the set of all multiples of V such that the scalar factors are just any real numbers In Geometric algebra are represented by bivectors. In this case: A is a vector; B is a bivector (representing the plane) Outer product. This is the geometric algebra equivalent of the cross product, but it is not limited to multiplying vectors by vectors, it increases to grade of operand as follows: scalar vector = vector; vector vector = bivector http://mathispower4u.yolasite.com/ of bx.
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With a simple proof Icke-linjär funktionalanalys, icke-linjära differentialekvationer. Zhou Matematik: homologisk algebra och differentialgeometri and Partial Differential Equations, El Escorial, Spain, June 16-20, 2008 Chin-Yu Hsiao ( Ecole Polytechnique, Paris): On the singularities of the Szegö projection for (0,q) forms. lib/library-strings.c:54 -msgid "Run the precalculation step of lib/library-strings.c:78 msgid "Delete a column of a matrix" msgstr "Ta bort en -msgstr "Hämta determinanten av en matris" +msgid "" +"Projection of vector v onto with projections sz = +(1/2)¯h and −(1/2)¯h along the quantization axis. The As indicated in (1.6), the Yukawa formula for the weak potential between particle of each type when we integrate over volume in the transition matrix, a.
Let V be a subspace of Rn. To find the matrix of the orthogonal projection onto V , the way we Your textbook states this formula without proof in Section 5.4, so I thought I'd write up the proof. there are no linear relations
Proyección (álgebra lineal) - Projection (linear algebra) De Wikipedia, la enciclopedia libre . La "proyección ortogonal" vuelve a dirigir aquí. But from my linear algebra class, I remember hearing that OLS is indeed projection method. So I am confused here. What exactly is the difference between these two? Vector projection formula, Vector projection explained, vector projection examples, Vector projection formula derivation with solved problems One important use of dot products is in projections. The scalar projection of b onto a is the length of the segment AB shown in the figure below.
Nät. Fler. Generalization of a recursion formula for scalar in variants of linear transformations Projections and Generalized Inverses in the General Linear Model PDF) The product duality formula in Banach space theory. Revision Notes Tensor Product Dual Space | Basis (Linear Algebra) | Tensor. 【JCXAGR】Dual Importance Of Shredding Documents, River Bend Campground Oregon, Col A Linear Algebra, Blood Of The Liberals, Albertsons Job Application Pdf, Regina not itself be a prehyperfunction: w H (l ) is a linear space over *CC but not an algebra.


Vital Pieces of Discrete Math Sets
You will only get a concise introduction to logic inside this class, but the mathematics utilized in logic are observed at the core of computer programming and in designing electrical circuits. The expression finite mathematics may be applied to regions of the area of discrete mathematics that manages finite sets, particularly those areas pertinent to business. Students utilize language-based approaches to come up with algorithms to address various mathematical issues.
Today there are various websites you may refer to acquire knowledge of either method. Answers and comprehensive solutions are provided. Also think about that in the event that you use a free and open source textbook for your class, it is going to save students as much as 150-250, which can subsequently be reinvested in purchasing a computing device that will probably find far more use than a book.
Forget all you know about numbers. There’s a few distinct formulas, based on in the event you have dependent events or independent events. The experiment is to be aware the period of arrival past the departure time of the previous train.
This program is intended to supply you the knowledge you need in areasonabletime term papers help
period. Each video will cover all the appropriate information which you will need to understand in under a quarter hour. In each class I will attempt to create the discussion self-contained and to provide everybody something to take home, no matter the background.
If you own a question, your very best alternative is to post a message to the newsgroup. This set is occasionally denoted by N. If you work in a group, you are going to be asked to change group partners after the very first midterm.
Only high-quality, original work that’s within the range of the journal or the targeted special issue is going to be considered. All you have to do is download an ebook in pdf or another format and take pleasure in reading in any place. The handiest method to get the book you will need is to receive it in an electronic format online.
Ok, I Think I Understand Discrete Math Sets, Now Tell Me About Discrete Math Sets!
Also, it’s assumed that you’ve seen the principles of graphing equations. A superb grasp of Calculus is necessary however. Example 8 You’re getting prepared to go out.
If you wish to get in on their secrets, you are going to want to become familiarized with these Venn diagram symbols. It is among the set theories. Category theory is a rather generalised sort of mathematics, it’s considered a foundational theory in the exact same way that set theory is.
Discrete Math Sets Help!
Discrete mathematics deals with discrete objects that are separated from one another. Discrete Math has a large application in today’s mathematics, and generally utilised in decision mathematics. Discrete mathematics was characterized as the branch of mathematics handling countable sets.
Most people just are unable to learn Mathematics. Consequently, achieving good grades will turn into a simple undertaking for you. The homework assignments include a component where students have to write short compositions.
There are several sorts of chi square tests based on the manner by which the data was collected and the hypothesis being tested. There are many ways of working with the HMMFactory. A bit heavy breathing is normal initially, but nonetheless, it usually only requires a day or so for the new fish to find comfortable.
There are lots of ways to accomplish such a selection. Let’s stick with the simple stuff to start. For instance, a chart can be utilized to demonstrate the overall sales of three distinct goods, such as three competing brands of paper towels.
One seemingly minor point I think makes a great deal of difference is that Epp has a more welcoming layout, with a lot of white space and a lot of subheadings to help you locate your way. Notice that it appears that one may become facile in math for a language without understanding proofs. In understanding mathematics we have to understand what makes a proper mathematical argument, in other words, a proof.
There’s a student site and an instructor website. Before discussing relevant topics, it might be worth mentioning several general facets of discrete mathematics. Much like programming, staying in touch with the community is going to keep you motivated.
Characteristics of Discrete Math Sets
Our program is extremely strict and requires elevated levels of private discipline, and compliance is an excellent indicator of the applicant’s capacity to conform with our intensive atmosphere. The formula is a bit more complicated if your events are dependent, that’s in case the probability of a single event effects another. In some instances, it’s simple to offer an efficient ordering function.
If it isn’t, then a filter needs to be placed on the data before instituting the right analysis. With fish, you need to be mindful about combinations. So just make sure you search for the group with the maximum frequency.
The Tried and True Method for Discrete Math Sets in Step by Step Detail
You won’t understand percentages if you’re uncomfortable with division and multiplication (for instance). The distinction is a rather important one. The very first chapter now describes a variety of data structures such as matrices, polynomials, quaternions, and so on.


“I give you a new commandment: love one another. As I have loved you, so you also should love one another.” John 13:34
August 18, 2019
Hello Second -Grade All-Star Parents!
We had a very busy first week. We completed Language Arts and Math Assessments. I have spent this weekend grading the assessments. I will use this information for grouping and help sessions. Our after-school Help Sessions will begin on Monday, August 19th from 2:50-3:30. Help Sessions will be every Monday, unless there is a school holiday. I will notify you this week, if your child would benefit from these sessions.
**I will be sending our two Reading Books to be covered with a Book cover this week. Please cover and return these two books the very next day. We use these books each day. Thank you so much for your help in this matter.
The children will begin recording their homework and spelling words in their planners. Please initial their planners each night.
*Our Math Homework will be sent home nightly, as it comes from the Student Workbooks.
We will begin our curriculum in all areas this week. I am very excited to begin!
Language Arts: We will begin Lesson 1. We will practice fluency and decoding; Make, revise, and confirm predictions when reading; Develop Vocabulary; Write an Opinion Piece; Practice our Handwriting and Phonics. Our Lesson and Spelling Assessments will be given every Friday.
Math: Chapter 1, L 1-5; Students will use addition to find the unknown sum; Use addition to solve word problems; Add two numbers in any order; Add by counting on from the greater addend; Use double facts to find the sums of near doubles.
Social Studies: Students will learn why maps are important and how maps help us locate various locations.
Science: Students will begin our Unit on Habitats. I will be sending home information about our Habitat project soon. Just a heads up, this project will require a shoebox. This project will be assigned as a homework assignment.
Religion: Students will learn about the Blessed Trinity; Review Prayers; Story of Creation. Our Chapter 1 test will be on Friday.
**First Holy Communion will be on Saturday, May 2, 2010.
Thank you as always for your love and support! We are going to have an amazing year!
Please let me know if you have any questions or concerns.


The idea that statistics is purely math is just one misconception Genevera Allen, associate professor of statistics at Rice University, is used to dispelling. Another hits closer to home — that statistics isn’t a creative pursuit.
Allen’s own passion for creativity is what brought her to Rice in the first place. “We don’t stare at numbers in an Excel spreadsheet all day,” she said. “Statistics is really about problem-solving. There is so much data out there — you have to think creatively and work collaboratively with other people to solve problems based on this data. It requires a lot of critical thinking skills, problem-solving and communication and a lot less about dealing with numbers.”
Allen didn’t initially plan on pursuing a career in statistics or academia, instead she dreamt of being a musician. “I came to Rice as an undergrad to study music and viola performance, but a shoulder surgery during my freshman year led me to completely switch up my major, and on a whim, I thought it would be fun to take a statistics class,” she said. “I took the statistics class and said, ‘Oh my goodness, I love this. This is exactly how I think.’”
Statistics is the mathematics of quantifying how we make decisions based on past evidence. “It really resonated with me and I became a statistics major, got my Ph.D. and went into academia, ending up back at Rice as a faculty member.”
Right across the street from Rice is the Texas Medical Center, which employs nearly 100,000 people. “It’s basically a city unto itself and for a statistician like me, the medical center is great fun,” she said.
Allen holds a joint appointment with Rice University and the Baylor College of Medicine with the Jan and Dan Duncan Neurological Research Institute, which has exposed her to a new world of statistical research. Working adjacent to a spectrum of scientists has helped her understand the needs of medical researchers and given her a great appreciation for all of the challenges in science, specifically those posed by emerging technologies.
There is an incredible amount of data being produced in the medical field that has the potential to advance patient health, discover cures for new diseases and detect basic biological systems. “They’re collecting tons of data and they need help from people like me — statisticians and data scientists — to make advances in medicine.”
Genetics and Neuroscience
Allen’s applied research interests largely lie in neuroscience and genetics. “Neuroscience is a really exciting field these days — it’s a new frontier,” she said. “We have 30 billion neurons in our brain and we don’t really understand what they do to process the stimuli from the world around us. There’s so much we don’t know about how the brain works.” Allen employs the mathematics and statistics of graphical model theory and machine learning to understand cognitive processes.
Her interest in genetics specifically is focused on integrated genomics. “This is a new hot topic where the type of genetic data we have access to is not just our individual pairs of DNA sequences, but actually a plethora of information about the whole molecular process in our cells.” And within genomics is a range of emerging fields of study.
There is whole genome sequencing, which is the exact individual DNA-based pairs; functional genetics, which is the measure of which genes are turned off and on; and epigenetics, which encode things from our lifestyle and environment. “There is all of this information — multiple snapshots of what is going on with the genome of a given patient,” Allen said. “We have analyzed all of this data separately to try to find potential therapies and cures for diseases, but really, the new frontier is how do we put the data together to understand what is going on in our genome?” Integrated genomics attempts to answer that question in part by targeting certain genetic data to develop therapies for diseases and even personalize therapies based on a patient’s specific genome.
Advice for Students
Allen’s advice for students interested in pursuing a career in statistics is simple: find good data and seek out practical applications. “Get your hands on data and get really into it,” she said. “The key to statistics is to take the math and translate it into something useful for particular data sets. Every data set is like a unique snowflake, and you have to study each one and have experience working with data, before you can understand the power of statistics and how it can drive data.”
The Future of Statistics
According to Allen, statistics is a very different field then it was 10 or 20 years ago and it’s only getting more interesting. “It’s a really exciting time to be a statistician because we are in an age where data is growing at an exponential rate, and with it, the complexities of analyzing that data,” she said. “People don’t realize that there are tons of medical technologies that have been developed just in the past five years. These are breakthrough technologies that are producing billions and billions of data points, which create brand new opportunities for someone like me, a statistician.”
Emerging technologies challenge statisticians to conduct research and develop new statistical techniques to analyze this new data. “Statisticians and data scientists are poised to make a huge impact in society,” she said. “They are creating tools to analyze massive amounts of complex data and hold the key to making critical discoveries in areas such as medicine, personalized health recommendations, climate change and renewable energy.”


Miss Khatun’s Primary School travels has continued with regular visits to Wheeler Primary School this term. Her weekly sessions working with cohorts of pupils in an attempt to boost engagement in Maths is in addition to similar visits to Paisley Primary School and Rokeby Primary School since October.
In the final session last week the pupils had the opportunity to assume the role of the teacher and deliver a presentation on fractions and then test the rest of the group with fraction-themed questions!
Q: If a pizza has eight slices and you eat a quarter, how many slices are left?
Miss Khatun will now visit Chiltern Primary School after half-term in the final push before SATS week in May.


Mr. Smith has 4 daughters. Each of his daughters has a brother. How many children does Mr. Smith have? Answer He has…View More How many children
If you remove one from eleven, it becomes ten. If you remove one from nine, it becomes ten. How is this possible ?View More Maths Tricky Problem
Can you sovle this?? Remember 99.0 % FailView More Can you sovle this?? Remember 99.0 % Fail
Choose the word Opposite in meaning to the given word.View More If you REALLY like exercising your brain, figuring things ’round and ’round till you explode, then this is the Puzzle for you
Iss Picture me “?” k sathan par kon sa Number Ayega?View More Iss Picture me “?” k sathan par kon sa Number Ayega?


Power and Precision at Your Fingertips
In the vast world of the Internet, with its endless troves of information, the online calculator stands out as a testament to both simplicity and utility. Gone are the days when one had to scramble for a physical device to quickly solve a mathematical problem; now, an online calculator is only a few clicks or taps away.
Why Use an Online Calculator?
- Accessibility: Unlike traditional calculators, online calculators are easily accessible from any device with an Internet connection. Whether you’re using a computer, smartphone, or tablet, you can quickly pull up an online calculator and get to work.
- Variety: Online calculators are not limited to simple arithmetic. There are specialized calculators for a myriad of purposes: scientific calculations, statistics, finance, health, engineering, and more. Whatever your need, there’s likely an online calculator designed for it.
- User-Friendly Interface: Many online calculators have intuitive designs that make them easy to use. They often include visuals, dropdown menus, and interactive elements that make the user experience seamless.
- Cost-Effective: Most online calculators are free. This contrasts with scientific or graphing calculators, which can be expensive.
- Features & Updates: With the nature of online platforms, developers can easily update and add new features to their calculators, ensuring users have access to the latest tools and functions.
Popular Types of Online Calculators
- Basic Arithmetic Calculators: Perfect for quick calculations, like sums, subtractions, multiplications, and divisions.
- Scientific Calculators: These handle more complex functions such as trigonometry, logarithms, exponential functions, and more.
- Graphing Calculators: Plot and visualize mathematical equations.
- Financial Calculators: Calculate interest, loan payments, savings growth, and other financial equations.
- Unit Converters: Convert between units like distance, weight, volume, and temperature.
- Health Calculators: Calculate BMI, calories burned, daily calorie intake, and more.
A Few Points of Caution
While online calculators are undeniably convenient, it’s essential to use them wisely:
- Always double-check crucial calculations, especially if they play a pivotal role in decision-making.
- Ensure the online calculator you’re using is from a reliable source.
- Remember that calculators are tools; they don’t replace the need for understanding the underlying concepts.
Online calculators have democratized access to computational power, making it easier than ever for individuals to solve problems, make informed decisions, and understand complex concepts. Whether you’re a student working on homework, a professional crunching numbers, or just someone curious about how much tip to leave at a restaurant, the vast digital landscape ensures there’s an online calculator tailored for your needs. With power and precision now at our fingertips, one can only marvel at the tools the Internet age has gifted us.


Jonas, BFA senior, and Edward Ellis, an English and Philosophy teacher at BFA, attended the STAR Student and Teacher Luncheon this past Friday. We selected Jonas as our STAR Student of the Year based on his GPA, the rigor of his curriculum, and his SAT score. Jonas also takes courses in mathematics and physics at Emory and Georgia Tech. Jonas selected Edward as his STAR Teacher. We are proud to have Jonas represent our school in the community and look forward to seeing what his future will hold!


We introduced Roman numerals via a nice story about a shepherd tending his sheep and needing a way of counting them. For V, we traced our hand, showing the V that easily makes 5.
I, II, III, IV, V
We counted to 100 as we went for a walk, and then started to count backwards too. Maybe we should walk backwards next time we do that. ;-)
We then worked with some pine cones and acorns and things, and just played with them, seeing how many are five and so forth, and working out the different combinations that make up five.
We have begun to march out our two times table just counting, emphasizing every second number:
one, TWO, three, FOUR, five, SIX, seven, EIGHT....
I presented it as a frog hopping across two lily pads. In our next warm up lesson, we will play a hopping game for this, and a table version, with a little beeswax frog or something.
We began a little woolen sheep during one of our handwork lessons, making the frame with some pipe cleaners, and then wrapping some wool roving about it. It was really very easy, much more so then I expected, although I haven't finished him just yet.


|I got this image here (which, incidentally, is a blog post doing exactly what I'm about to do), but I've seen this meme in other forms elsewhere and have no idea what its original source is.|
However, in this post I'm going to steer my pedantry in what I hope is a slightly more interesting (and less annoying) direction, toward mathematical reasoning. That is, while I think it's great that the public has been able to learn certain specific facts about astronomy (and other sciences), I think it would be far more valuable if the public learned how to apply mathematical reasoning to claims they encounter.
Here's why: as a recent graduate with an official degree in astronomy and all that jazz, I happen to simply know the fact that, in general, the stars we can see with the naked eye are close enough, and live long enough, to still be alive by the time their light reaches us.
But even if I didn't know that fact, I could arrive at it by constructing an argument from some more readily available facts. And this argument, although mathematical in nature, doesn't involve anything more complicated than a bit of algebra, such that anyone who gets out of high school should be able to reach the same conclusion.
Now, the joke's humor relies on some common facts from astronomy: stars are far away, light is slow compared to the size of the universe, stars eventually die. But before we get into the mathematical meat of evaluating this claim, let's think about another common fact: our sun is 4.5 billion years old (give or take), and it's roughly halfway through its life, so it's got another several billion years to go.
In order for the sun to be dead by the time an alien civilization see its light, that civilization would have to be farther away in light years than the sun's remaining age in years. That is, the alien civilization would have to be many billions of light years away. So if we take our sun as typical, then the above meme is only true if we can see, by the naked eye, stars that are billions of light years away. We can't, and as I'll show in a bit, we don't even have to assume our sun is typical for this argument to work (which it isn't, really). But this is the structure of the mathematical argument: compare the lifetimes of stars we can see with the naked eye to their distances from us.
A few more astronomical facts are necessary to work this out, some of which can be gotten by a bit of googling, and one which, I admit, most people probably aren't aware of. This fact, which makes evaluating the claim very easy, is that the more luminous a (main sequence) star is, the shorter it lives. This means the most luminous stars (which are the most likely to be visible by the naked eye at great light travel times) are the best candidates for stars that are dead by the time their light reaches us. If the claim fails for these stars, it fails for all stars.
The most luminous stars live about a million years and are about a million times brighter than the sun. Now, it's always possible that a star we're seeing just happens to be at the end of its life, but all else being equal, if we pick stars at random out of the sky, then on average they will be halfway through their lives, just like (coincidentally) our sun (not strictly true, because there is some selection bias to the stars we can see).
To be visible by the naked eye, a star needs to have an apparent magnitude of 6 or lower.
For the sun to be magnitude 6 (it's currently an obscenely bright -27), it would have to be about 60 light years away. (There's some math involving logarithms here, but there are tools online that could get you this answer.)
How bright a star appears to us is proportional to its intrinsic brightness and inversely proportional to the square of its distance from us. That is, if star A and star B are identical but star B is twice as far away, it looks 1/4 as bright as star A.
And that's everything we need to evaluate the claim. Now here's how we construct the argument. A star is dead by the time its light reaches us if its remaining lifetime in years is less than its distance in light years. It is visible with the naked eye if its intrinsic brightness relative to the Sun is greater than the square root of its distance relative to the Sun's distance at magnitude 6.
Let me unpack that second statement a bit. Say a star is intrinsically four times as bright as the sun. If it's also magnitude 6 (just visible), then it needs to be farther away than the sun. Specifically, a star four times as bright as the Sun will be just visible at twice the distance (square root of 4) of the magnitude 6 sun: 120 light years. If it is farther away, it is too dim for us to wish upon it.
The brightest stars are 1,000,000 times more luminous than the sun, which means they are the same apparent brightness as the Sun when they are 1,000 times farther away. If the sun is just visible at 60 light years, then the brightest stars are just visible at 60,000 light years. Is 60,000 light years greater than the (on average) half a million years the star will have left to live? No. At that distance, the star could only be dead by the time we see it if it were already 95% of the way through its life. For less luminous stars which live longer, that percentage gets even higher, which makes it much less likely that we ever see such a star.
When we learned algebra via word problems, we were supposed to be learning how to solve problems like these. And while most of us probably managed to get through those word problems successfully, it's been my observation that most of us don't apply this kind of analysis outside of school, to things like evaluating claims that have mathematical content. While it's not vital to the health of a democracy that we be pedantic about random Facebook memes, it might be useful for us to be able to think carefully about scientific claims, at least when the facts and math involved don't require a PhD.
Outside of learning a bunch of astronomical facts, one of the most valuable (academic) lessons I acquired while getting my degree was learning how to bring mathematical tools to bear on a problem. I'm sure this blog post doesn't really have what it takes to impart that same lesson on others, but I hope it reveals a bit of the process. If I could wish upon a star (and I were feeling altruistic), I might wish for an educational system that did a better job of that.


In an earlier post (Sacred Secular), I noted the apparent dual two-fold nature of the Old European Horned Star Goddess of my ancestral genetic maternal bloodline. In geometry, two-fold symmetry is also known as reflection symmetry and mirror symmetry. In two dimensions, there is a line axis of symmetry. In three dimensions, there is a plane of symmetry … and so on. Stonehenge is an architectural example of a design featuring core elements of reflection symmetry.
An advanced type of reflection symmetry is known as circle inversion. This kind of advanced inversion symmetry can be geometrically generalized to higher dimensional spaces. It is conceivable then that the ancient builders of Stonehenge deliberately encoded geometric concepts into its design and that this megalithic circle was indeed a sacred space for transformative shamanistic journeys to higher dimensions of perceptive and experiential consciousness.


A Risk-based optimal portfolio is the portfolio that, in some sense, has the best combination between the expected rate of return and the dispersion of possible outcomes.
Given a portfolio, we can estimate its expectation of return. The actual realization of an investment in this portfolio could be larger or smaller than this expectation. Therefore, the dispersion of possible outcomes around the expectation of return is vital information to an investor. A smaller dispersion value may translate to lower probability for outcomes far below the expected return.
The dispersion of possible outcomes is often called risk. The quantity that measures the dispersion of possible outcomes is called dispersion or risk measure. In this document we will use both terms interchangeably.
The dispersion measure can be defined in many ways. azapy package provides a comprehensive collection of risk-based portfolio optimization strategies based on the following dispersion measures:
mCVaR - mixture Conditional Value at Risk,
mSMCR - mixture Second Moment Coherent Risk,
mMAD - m-level Mean Absolute Deviation,
mLSD - m-level Lower Semi-Deviation,
mBTAD - mixture Below Threshold Absolute Deviation,
mBTSD - mixture Below Threshold Semi-Deviation,
mEVaR - mixture Entropic Value at Risk
GINI - Gini index,
SD - Standard Deviation,
VAR - Variance, leading to mean-variance, MV, type of models.
In each case several optimization strategies are implemented. To understand them better, let’s look at a generic example of portfolio frontiers graphically represented in the figure below.
Fig 1. : Example of portfolio frontiers - risk vs. expected rate of return.
This is a typical representation of portfolio frontiers. On the x-axis we have the values of the dispersion measure (risk) while on the y-axis is the expected rate of returns. Several features are worth mentioning.
The blue line is called the efficient frontier. It represents the set of portfolios with the highest expected rate of returns for a given value of risk. These are the portfolios of interest for an investor.
The lower red line is called the inefficient frontier. These are the portfolios with the lowest rate of return for a given value of risk. Clearly, this family of portfolios is to be avoided by an investor.
The leftmost point, where the blue and red lines meet, is the Minimum Risk Portfolio (also called Global Minimum Risk Portfolio). This is the portfolio with the minimum risk among all possible portfolios. Investing in the minimum risk portfolio is a relative common strategy among professional investors.
The black straight line, in the upper part of the plot, is tangent to the efficient frontier. Its intersection with the y-axis (not shown in the plot) is at a level equal with the risk-free rate accessible to the investor. In this example the risk-free rate was set to 0. The point of tangency along the efficient frontier (in our plot depicted by a green diamond) is the tangency portfolio or the market portfolio. This is the portfolio that maximizes the \(\rho\)-Sharpe ratio. The \(\rho\)-Sharpe ratio is defined as
\(R\) is the portfolio expected rate of return,
\(r_f\) is the risk-free rate accessible to the investor,
\(\rho\) is the dispersion of portfolio rate of return.
Therefore, the portfolio that maximizes the \(\rho\)-Sharpe ratio is the portfolio with the highest expected excess rate of return (above the risk-free rate) per unit of risk, \(\rho\). This is a remarkable efficient portfolio often preferred by the investors.
All the points between the efficient (blue line) and
inefficient (red line) frontiers are called inefficient portfolios.
There are no valid portfolios outside the portfolio frontiers.
The solid blue squares are the portfolios where the entire capital is allocated to a single component. They are labeled by the market symbol of this portfolio component. For short, we call them single asset portfolios.
Among the inefficient portfolios there is a remarkable one. That is the equal weighted portfolio. As the name suggested, all weights are equal to \(1/N\), where \(N\) is the number of portfolio components. Hence, its name \(1/N\)-portfolio or inverse-N portfolio. In our plot this portfolio is represented by a green x with label \(1/N\).
On the efficient frontier, we have its correspondent. In our plot it is depicted by a green x with label InvNrisk. This is the efficient portfolio that has the same risk as the equal weighted portfolio. In-sample both portfolios have the same risk while the expected rate of returns is larger for InvNrisk than for inverse-N portfolio. However, out-of-sample, especially for a short period of observations, equal weighted may outperform InvNrisk portfolio.
Another way to visualize the portfolio frontiers is presented in the following figure.
Fig 2. : Example of portfolio frontiers - expected rate of return vs. Sharpe ratio.
It contains the same information as Fig. 1. However, now on the x-axis is the expected rate of return while on the y-axis is the \(\rho\)-Sharpe ratio. We have preserved the color code and all the symbols from Fig. 1.
Fig. 2. gives a better understanding of portfolio efficiency in terms of expected excess return per unit or risk.
For all dispersion measures mentioned above, the azapy package offers the following portfolio optimization strategies:
Minimization of risk for targeted expected rate of return. This is the most common portfolio optimization strategy. It returns portfolios along the efficient frontier (blue line in Figs. 1 and 2). The strategy requires the user to input the desired value of the expected rate of return. This value must be between the expected rate of return of minimum risk portfolio and the highest expected rate of return among the portfolio components. If the input value is outside of this range then it will automatically default to the nearby limit. In our implementation this strategy is designated by setting
Minimum risk portfolio. This is the efficient portfolio with minimum risk (the most left limit of the efficient frontier). It is a common strategy among professional investors. It is available under the setting
Maximization of expected rate of return for targeted risk value. The strategy returns portfolios along the efficient frontier (blue line in Fig. 1 and 2). Requires the user to enter the desired value of risk. In general, it is not intuitive for an investor to specify outright a rational value for risk. However, this strategy is useful if we want to find an efficient portfolio that has the same risk as a benchmark portfolio. The most common example is the efficient portfolio with the same risk as the equal weighted portfolio. In our implementation this strategy is designated by setting
rtype='InvNrisk'. It allowed to enter any benchmark portfolio by specifying the weights (long only, i.e., non-negative weights).
Maximization of the expected rate of return for fixed risk-aversion factor. In this strategy the optimal portfolio weights maximize the quantity \(R -\lambda \rho\), where \(R\) is the portfolio expected rate of returns, \(\rho\) is the risk, and \(\lambda\) is the risk-aversion factor. \(\lambda\) takes values between \(0\) and \(+\infty\). For \(\lambda=0\) the optimal portfolio is the single asset portfolio where the entire capital is allocated to the component with the highest expected rate of return. This is the rightmost point along the efficient frontier. For \(\lambda=+\infty\) the optimal portfolio is the minimum risk portfolio, the leftmost point on the efficient frontier. Any other values for \(\lambda\) will lead to an optimal portfolio along the efficient frontier. In general, it is not intuitive for an investor to specify a rational value for the risk-aversion factor. Note that the same value of \(\lambda\) may lead to different portfolio compositions for different dispersion measures and market conditions. Therefore, a direct use of
this strategy, by specifying a desired value for \(\lambda\), may not be convenient. However, this strategy may be useful if it is combined with a strategy to estimate the value of risk-aversion factor based on market conditions (e.g., technical analysis, etc.). In our implementation this optimization strategy is designated by setting
Maximization of \(\rho\)-Sharpe ratio. This is the portfolio with the highest expected excess rate of return per unit of risk held by the investor. It is a very popular strategy among investors. In our implementation this strategy is designated by setting
Minimization of inverse \(\rho\)-Sharpe ratio. Obviously, this strategy is logically equivalent with the one above. It returns the same portfolio weights. However, from a numerical point of view, the minimization of inverse Sharpe ratio and the maximization of Sharpe ratio have quite different implementations. Both implementations have similar accuracy and computational speed. For completeness, we chose to make available this implementation under the setting
azapy package covers, 9 risk-based dispersion measures \(\times\) 6 optimization strategies, in total 54 risk-based portfolio optimization strategies.
The rigorous mathematical description of these strategies is presented here.
The natural question that arises is: which one is the best?
There is no absolute answer to this question and so there is no substitute for our personal research. To this end, azapy package provides the necessary analytical tools to perform a comprehensive quantitative portfolio analysis.
Fig 3. Example of out-of-sample (backtesting) portfolio performance.
An out-of-sample analysis, also called backtesting or historical simulation, can be performed for any of the implemented portfolio strategies. The following information can be extracted:
Portfolio realized rate of return. It is available monthly, annually and by rolling period. From these reports one can easily gauge the magnitude and seasonality of returns.
The realized drawdown events. It is a very important information that can give a measure (although limited to previous market events) for the amount and duration of losses that an investor may be exposed to.
Easy graphical and numerical comparisons between different strategies or different portfolios altogether.
Once we have decided for a portfolio composition and optimization strategy, azapy can help with portfolio maintenance. It can prove comprehensive information regarding the prevailing portfolio weights, number of shares, delta positions and cash flow at rebalancing time. An example is provided in a Jupyter Notebook.


It’s like that sidewalk poem by that dude.
This is the Mandelbrot Set.
The Mandelbrot Set is a mathematical pattern discovered by Benoit Mandelbrot. When displayed visually, it creates an image of unimaginable resolution. The pattern is self-similar and recursive in nature as one zooms into it. Geometric figures such as these are called Fractals.
Fractals are intriguing to me because they are a natural pattern of incomprehensible depth and beauty. In a way, this picture is very humbling.
Also, sometimes people see fractals while high on LSD. Just sayin’.


Personalized Math intervention is provided in a one-to-one setting where intentional, systematic instruction is delivered by a caring, supportive teacher.
Whether your student has a history of difficulty in math or has recently encountered obstacles in mathematics, Apples of Gold is prepared to customize an intervention plan to help your student close his skill gaps and achieve success in math.
Your student will receive instruction aligned to the identified domains of weakness during his weekly sessions. We will create a schedule which provides your child with math intervention two to four times weekly. The frequency and length of sessions (45 minutes to 1.5 hours) will depend on the extent of your student’s particular needs, how quickly she needs to close her skill gaps, and your family’s scheduling needs.
Personalized Math intervention is provided in a private, one-to-one setting, where intentional, systematic instruction is delivered by a caring, supportive teacher. Whether your first grader is struggling to master addition and subtraction facts, your seventh grader has a history of difficulty with fractions and decimals, or your high school junior is frustrated with Pre-calculus, we will develop a customized plan to help your learner become successful and confident in math.


Following my own riddle post (OK, not really), Gil Kalai posted two math riddles. I would like to offer a variation on the ant riddle, which also appears in Peter Winkler’s book (it has a whole chapter on ants riddles):
24 ants are randomly placed on a a circular track, each in a random direction. Whenever 2 ants collide they each reverse direction. The track is 1 meter long and ants walk at 1 meter per minute. After one minute, what is the probability that Alice, a randomly chosen ant, finds herself in the place she began?
And if I might add:
Would the answer change significantly, if there were 25 ants, instead of 24?