Practice tests for each grade level of the assessment are available below for you to use to familiarize yourself with the kinds of items and format used for the Mathematics MCAS assessment. ... Fourth grade . Which number sentence represents n, the total number of pictures in 1 day? How much change did she get? How many cups of cooking oil did Bobby have altogether. It took 4 hrs and 35 minutes to cook a turkey. You It can help students feel more relaxed when they take the actual test. The math assessments measure student mastery of the Tennessee Academic Standards and require students to demonstrate a deep conceptual understanding of mathematics, number sense, fluency, problem … This is a test that should be used to decide weather to move your 4th grader into 5th grade math or not. Upon completion of a practice test, you are given a detailed summary of your results. 4th Grade Math Benchmark Practice. 4 1 The difference between 76,423 and 29,876 is bestdescribed as closest to — A 60,000 B 50,000 C 40,000 D 30,000 2 is closestto — F 100 G 600 H 1,000 J 1,800 53 18× The Assessment Materials page provides information and resources for the Grades 3-8 Oklahoma School Testing Program (OSTP) assessments. The Practice Test may be used at home or at school for students to become familiar with the LEAP test they will take in spring 2013. Which units are reasonable for measuring the perimeter? Department of Defense Education Activity. Removing question excerpt is a premium feature. After reviewing the results at the end of the Fourth Grade Mathematics full-length practice test, you may be interested in having a look at how much time was spent on answering each question. F 12 feet G 24 feet H 36 feet I 66 feet 10 Benchmark: MA.4… Grade 4 FSA Mathematics Practice Test Questions The purpose of these practice test materials is to orient teachers and students to the types of questions on paper-based FSA tests. Grade Gmade. Long Island University-Brooklyn Campus, Masters, Special Education. Improve your math knowledge with free questions in "Benchmark fractions" and thousands of other math skills. Benchmark Test Grade 3 Math - Displaying top 8 worksheets found for this concept.. O.16 Benchmark fractions. By taking advantage of Varsity Tutors’ Learning Tools, you can customize your learner’s educational experience by isolating the areas that need the most work. Tonya is saving money for a new bike. Associated Files. Each test is categorized into a number of components, including geometry, measurement, fractions, and algebraic thinking. 14 square units B. Amy and Curtis have the same probability of winning. Take F G H J 19. The clues for the numbers are:1. Test preparation help and review questions, study guide, and flashcards. When you make full use of the free Common Core Fourth Grade Mathematics study material available on the Varsity Tutors’ website, you are using resources that can help build test-taking confidence in your learner. student AR JC MT FR GS TB LM SG RT AL JS DC GN CL JN hours 4 5 4 5 4 2 1 4 0 2 5 4 3 2 1 6 5 4 3 2 1 0 0-2 3-4 … University of North Carolina at Chapel Hill, Current Undergrad, Mathematics. Environmental Studies Quiz: 4th Grade Trivia! It took 1 hour and 18 minutes to cook soup. PDF • 1.87 MB. LUS. On the other hand, Grade 8 students must pass the exam to move onto Grade 9. A. 4th Grade Place Value Test Identify the place value of digits in large numbers (up to a billion). We would like to extend a special "Thank You" to all the teachers that have contributed to this wonderful collection of tests and quizzes. A chalkboard eraser is most likely a _____ . Each roll of film has 24 pictures. This resource is related to: Accountability Services; EOG; Released Tests; Last updated: Feb 10, 2020. Another excellent feature that may help your learner’s Common Core Fourth Grade Mathematics preparation is the full-length practice tests. Intro to place value: Place value Writing whole numbers in expanded form: Place value … These released practice tests are available through the STAAR Online Testing Platform. Each carton costs $.75. After throwing a 6-sided cube with 5 sides colored red, blue, yellow, green, and black, the following results happened:Toss 1: blueToss 2: yellowToss 3: blueToss 4: redToss 5: greenToss 6: blueToss 7: black...What color is most likely to be on the 6th side? After completing the practice tests online, you have the ability to efficiently and effectively improve your student’s Common Core Fourth Grade Mathematics review by examining your learner’s test results. (Hint: 1 pint = 2 cups.). Expand. The following practice tests are currently available: FSA ELA Writing Grade 8. What is the probability of picking tile C? They need more practice! One of the most useful features of Varsity Tutors’ Learning Tools are the free Common Core Fourth Grade Mathematics Practice Tests. STAAR Mathematics Grade 4 Practice Questions. How much space is there between the top of his hat and the top of the entrance. On the following pages are passages and multiple-choice questions for Grade 4 Reading Practice Test, a practice opportunity for the Nebraska State Accountability (NeSA). If he or she passes this test, you should ask to move your child up to 5th grade math. FREE Mississippi Academic Assessment Program (MAAP) practice tests and sample questions for Math and Language Arts (ELA). This math assessment resource contains a 9-page math benchmark assessment with 54 questions covering ALL of the 4th Grade common core math standards and the sub-standards. The online practice tests are not available for printing or scoring. A photographer used 32 rolls of film in 1 day. 17 square units C. 10 square units × 11 D. 16 square units 28. They need more practice! Varsity Tutors’ Common Core Learning Tools give elementary learners the opportunity to access a wide range of study materials. SKIP TO CONTENT. Grade Test Forms Answer Keys Item Rationales ... 4. Saint Thomas University, Bachelors, Education. His hat adds 5 inches to his total height. 4th Grade Math Practice Test consists of questions for NYST, which provides homework help to students, helps parents with homeschooling and Teachers with lesson plans.. The time allotted for each subpart and the total time for math is similar to last year. There are many different free Fourth Grade Common Core Math practice tests online that cover important Common Core Fourth Grade Mathematics concepts. There are many different free Fourth Grade Common Core Math practice tests online that cover important Common Core Fourth Grade Mathematics concepts. This is a high stakes exam because Grade 4 students have to pass the LEAP test to proceed to Grade 5. If he or she fails, keep them at 4th grade math! Janet wants to find the total weight of the recycled cans she has collected.The bags of cans weigh 24 3/4 pounds, 21 7/8 pounds, and 19 1/2 pounds. Which expression can be used to find the fraction of flowers in the vase that are daisies or tulips? Our grade 4 math worksheets help build mastery in computations with the 4 basic operations, delve deeper into the use of fractions and decimals and introduce the concept of factors. Place value. Passing is a 75/100 just in case you were wondering. Amy rolls a cube with the numbers 0, 1, 2, 7, 8, and 9 on it.Curtis rolls a cube with the numbers 1, 2, 3, 4, 6, and 8 on it.The player who rolls a number less than 4 is the winner.Both players roll their cube.Which statement is true? Draw a bar graph to summarize the information. Round to the nearest 100, then estimate how much water is left in the tank. Try it now! If he or she passes this test, you should ask to move your child up to 5th grade math. Curtis has a higher probability of winning. Bobby added 1 cup of cooking oil to 2 pints of cooking oil. How much longer did it take to cook the turkey than the soup? NWEA's 4th Grade MAP Test is an adaptive, computerized test that focuses on the student's abilities in language usage, reading, and math. Comparing Fractions Choose whether a fraction is larger, smaller, or equivalent to another. A. Our completely free Common Core: 4th Grade Math practice tests are the perfect way to brush up your skills. share to google . Track your scores, create tests, and take your learning to the next level! concepts you understand and which ones require your ongoing attention. What is the standard form for 80,000,000 + 7,000,000 + 600,000 + 20,000 + 400 + 30 + 2? Bob has 32 cards, and Christina has double that. These are the specific skills that 4th graders in the Grandview C4 district will be working on for the 2014 - 2015 school year. Then answer each question carefully by choosing the best answer. 4 4 + 5 5 6 15 + 5 15 4 15 + 5 15. Which of these could be the polygon Hayden drew? By using these materials, students will become familiar with the types of items and response formats On the first day, she saved $1.00. help you identify your strengths and weaknesses. When you visit the Learning Tools’ website, you will see the vast array of resources available to help your elementary learner maximize his or her Common Core Fourth Grade Mathematics preparation time. Share skill. Hayden drew a polygon that has exactly two right angles. 6 3/4 is greater than 7 1/2 is greater than 7 3/4, 7 3/4 is greater than 7 1/2 is greater than 7 1/4, 8 1/2 is greater than 8 1/4 is greater than 8 3/4, 9 1/2 is greater than 9 3/4 is greater than 9 1/4. If the real man is 6 feet tall, how tall is the picture of the man on the billboard? Draw 2 congruent shapes and 2 similar shapes in the space below: 30. End-of-the-Year Test Grade 4 This test is quite long, so I do not recommend that your child/student does all of it in one sitting. On the second day, she saved $2.00 more than the first day. Each Common Core: 4th Grade Math problem is tagged down to the core, underlying concept that is being tested. The number of each kind of flower in a vase is shown. For all questions: † … A number divisible by 2, 3, and 5 will always be divisible by _____________ . Some of the worksheets for this concept are Grade 3 mathematics, Grade 3 math practice test, Introduction, End of the year test, Grade 3 mathematics, Grade 4 mathematics practice test, 2018 texas staar test grade 3 math, Assessment for the california mathematics standards grade 3. On the third day, she saved $2.00 more than on the second day. An excellent way for elementary students to become accustomed to Fourth Grade Mathematics is by using the free Common Core Fourth Grade Mathematics study material. Each test is categorized into a number of components, including geometry, measurement, fractions, and algebraic thinking. Please talk to your teacher for more information on IXL. This document contains a Practice Test that shows what each part, or session, of an actual grade 4 transitional math assessment is like. What is the total weight of the bags? Kim has 18 cards less than Christina. Grade 4 and Grade 8 students sit for this exam which covers key subjects of Mathematics, English Language Arts (ELA), Social Studies and Science. Sally has 31 cards more than Bob.Who has the most cards? This exam allows parents and teachers to better understand students' academic needs and areas of growth throughout the school year. Released test forms that were administered online are released as practice tests. These tests are aligned with the Texas Essential Knowledge and Skills (TEKS), the state-mandated curriculum standards. All worksheets are printable pdf files. Information and resources for the Grade 11 assessments can be found on our College- and Career-Readiness Assessments page. American Career College of Education, Masters, Curriculum and Instruction. The math assessments will be administered in three subparts, the first of which is without a calculator. Benchmark Test : Grade 4 Math ©1999-2011 Progress Testing Page 1 Name Date Class/Grade Benchmark: MA.4.A.4.2 Mrs. Rivers' fourth-grade class is taking a field trip to a strawberry farm. NNAT3 Each session included: Twenty-one common items, including multiple-choice, short-answer, and open-response questions. This test can also be used for extra practice on 6th or 7th grade work. When accessing the Common Core study help material, you have flashcards, daily questions, and the full course curriculum at your disposal. Which expression could be used to find the total cost of the juice that was sold? 18. By using these practice tests, you can not only help your learner revise, but potentially help him or her develop valuable study skills that will assist them in their future academic career. There were 827 gallons of water in Center City's water tank. Benchmark Test : Grade 4 Math ©1999-2011 Progress Testing Page 4 Benchmark: MA.4.A.1.2 On a billboard, a picture of a man is 6 times as large as the real man it depicts. Grade 4 Mathematics EOG Released Items . ***This could even be used a the beginning of 5th grade to assess where your students are … You are also given a percentile ranking that lets you know where your learner ranks among other test-takers. For all questions: † Read each passage. Click to share with specific Email friends via direct message. Pick one of our Common Core: 4th Grade Math practice tests now There are 100 gumballs in a machine:30 red25 yellow20 green15 white10 blueWhat is the probability of getting a green gumball from the machine? On the following pages are multiple-choice questions for the Grade 4 Practice Test, a practice opportunity for the Nebraska State Accountability–Mathematics (NeSA–M). 29. These tools are just one way that you can engineer a comprehensive study plan that helps your leaner study efficiently. There is not enough information given to answer the question. In this summary, each problem is accompanied with an in-depth explanation which is aimed at helping students better understand how to apply their knowledge. What is 351.24 rounded to the nearest tenth? These free Common Core Fourth Grade practice tests are also organized by difficulty, which is great when pinpointing which areas your learner should spend more time reviewing. The Common Core Fourth Grade Mathematics exam, which your state uses to evaluate Common Core curriculum mastery, evaluates students on a number of math-related concepts that fourth graders should be proficient in, including multiplication, number values up to 1,000,000, adding and subtracting fractions, and more complex geometry. Varsity Tutors. Free Printable STAAR Practice Tests 4th Grade- Math and Reading If your child is a 4th grade student at a Texas public or charter school, you’ve probably heard of STAAR (State of Texas Assessments of Academic Readiness). The mystery number is less than 100.Which statement below is true? Each skill is linked to IXL practice problems in which your child will need an account. Worksheets > Math > Grade 4. First published: Nov 12, 2019. Two friends are playing The Mystery Number Game. Use your judgment. Grade 4 Mathematics EOG Released Items . These common items are the items on which each student’s 2016 MCAS Mathematics … This is a test that should be used to decide weather to move your 4th grader into 5th grade math or not. Download. Math - 4th grade Practice Test Suzy Skelton Fourth Grade Mathematics 13 Test. Grade 4 math worksheets from K5 Learning. Kareen put a fence around the perimeter of a baseball field. Rochelle bought 3 packs on gum for $.79 each and a pen for $2.49. Tales Of The Fourth Grade Nothing Novel Quiz. Includes standards-aligned tech-enhanced questions update for 2019-2020 year that mirror MAAP testing items. Grade 4 Mathematics EOG Released Items . These testlets were created using the the Georgia CRCT Online program maintained by Measured Progress during the school year 2002-2003. The Common Core: 4th Grade Math diagnostic test results highlight how you performed on each area of the test. There are 26 letter tiles, one for each letter of the alphabet, in a bag. Daisies Roses Tulips. What quantity does not have the same value as the other three? one of our many Common Core: 4th Grade Math practice tests for a run-through of commonly asked questions. These are the number of hours students did homework over the weekend. During the past 2 weeks, a total of 378 cartons of juice were sold in the school cafeteria. If all morgs are red and have 3 eyes, and Trug is red with 2 eyes, which statement is true? Assessment For The California Mathematics Standards Grade 4 S 1.1 18. 60 is less than the mystery number.2. Choose your grade 4 … The practice tests contain sample items for specific grade-level/subject tests. The town used 287 gallons of water. You can then utilize the results to create a personalized study plan that is based on your particular area of need. This is to be used as a diagnostic test. If he or she fails, keep them at 4th grade math! Each question will ask you to select an answer from among four choices. The spring 2016 grade 4 Mathematics test was made up of two separate test sessions. 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Sep 9, 2017 - 8:59 PM
in reply to sueycr
I'm afraid the only way to tell is to do the math as explained in the 3th link of my previous post. If you don't mind buying tickets for all trips the Swiss Half Fare Card is certainly an option, but whether you actually save more money than with a Swiss Travel Pass depends on your day trips. Study the maps of what's included carefully and do the calculations based on all trips you expect to make, and museums you expect to visit (the Swiss Travel Pass includes most museums). All details, including the maps, can be found through the links I gave you.
Last modified on Sep 9, 2017 - 9:00 PM by Arno


Date: January 4 2021
Summary: A brief overview on what arithmetic series are and some of its underlying math.
Keywords: ##zettel #arithmetic #sums #series #proof #archive
An arithmetic sequence is one which the difference between one term and the next only differs by a constant. One example is this:
where the difference between each proceeding term is the constant value, 1.
An arithmetic series is one in which values in an arithmetic sequence are summed together:
This is a visual proof of the Arithmetic Series algorithm:
A formalization of the above is:
which is equivalent to:
The latter formalization is somewhat more common and it works as gives the same values as what the size of the sequence is which is . From the visual proof, the constant comes from halving the size of each region.
(Thanks to Mark Kittisopikul, Yingbo Ma, and Benoit Pasquier for these explanations)
Zelko, Jacob. Arithmetic Sums & Series. https://jacobzelko.com/01052021044121-arithmetic-series. January 4 2021.


BLOG: Relational Modeling with Unknown Objects
BLOG by Milch et al. provides a language which help us model random functions and probabilistic properties of unknown objects. Going beyong Herbrand Universe. This mainly reviews the key contributions and limitations of that paper. Written as part of the Statistical Relational Learning course by Prof.Sriraam Natarajan.
Most of the First-Order Logic Models we have seen till now like Bayesian Logic Programs or MLNs works with an assumption that we are given a fixed set of objects, a Herbrand Universe and we have a possible world, Herbrand Interpretation on which we build our BLP model or MLN Network. However, in many practical problems we do not have a fixed Herbrand Universe, or we do not know how many objects are there in the universe. This paper introduces BLOG (Bayesian LOGic) which can perform inference even when the objects are unknown. BLOG is a representation language which can generate objects for such an unknown universe and create a Bayesian network which can then be used for inference. BLOG model describes a stochastic process which creates a world by generating objects in an order. The existence of a generated object is governed by the unknown number of objects in the universe and by the random functions defined in the model. The key idea here is that any property of the newly created object depends only on the objects that are already created. Using this and the concept of context specific independence, BLOG generates a countably infinite Bayesian network in which each node has finite set of parents. The finite set of parents and prior knowledge about the distribution makes the inference possible.
According to me, the key contribution of this paper is the representation language. This language helps us model random functions and probabilistic properties of unknown objects. Consider the Balls in Urn example provided in the paper. We do not know the number of balls in the urn and we randomly draw balls and put it in. We have no way to identify if the same ball was drawn twice. We can only detect the color of the ball and that too has false detection probability of 0.2. With this information, we are supposed to find out number of balls in the urn. Most other models will give up at the first step itself. BLOG provides a simple language which can model such a stochastic scenario by using just 6 kinds of statements: Type Declarations, Random Function Declarations, Non-random Function Definitions, Guaranteed Object Statements, Dependency Statements, Generating Functions, and Number Statements. Once we have the model, we can represent any possible instantiation of the world.
As BLOG creates a Random Variable for every function and object type, we potentially get a Bayesian Network with exponential number of Random Variables. Although context specific independence assumption helps us do the inference, it is computationally impossible to work with a such huge Bayesian Network. This makes the whole development less viable in practical scenarios as the purpose of the model was to provide inference over unknown or non-finite universe.
Representation can have unnecessary variables. For example, if we have the evidence that balls drawn in Draw1 and Draw2 are equal, model creates a new constant for that. Also, we would still have all random variables for both
ObsColor[Draw2]. So, there will be 2n extra random variables where n is the number of functions for Draw object.
To make the Bayesian network inferable, BLOG makes the context specific independence assumption. But this assumption is not straight forward. For instance, in the aircraft example, a blip at time t is dependent on the state of all the aircraft at time t. To make it dependent only on its source aircraft, we would need evidence or prior knowledge about the source of the blip.
As the BLOG assumes that any newly created object depends only on the already existing object, it is assuming the universe to be acyclic and objects have topological order.
The model cannot learn any prior distributions. It assumes that it has all the prior distributions from the domain expert.
As each object is stored as a tuple, they can expand to considerable size. For example, in the aircraft model each blip is represented as (Blip, (Source, (Aircraft, 2)), (Time, 8), 1), if the object blip had k properties the tuple size would increase further.
- The examples of the stochastic world taken are motivating. The paper provides a beautiful explanation on the difference between conditioning on the constant versus conditioning on the existence.
- These new constants resemble Skolem constants, but conditioning on assertions about the new constants is not the same as conditioning on an existential sentence. For example, suppose you go into a new wine shop, pick up a bottle at random, and observe that it costs USD 40. This scenario is correctly modeled by introducing a new constant Bottle1 with a Uniform CPD. Then observing that Bottle1 costs over USD 40 suggests that this is a fancy wine shop. On the other hand, the mere existence of a USD 40+ bottle does not suggest this, because almost every shop has some bottle at over USD 40.”
- The paper represents the model, functions, worlds, etc,. in mathematical expressions but doesn’t provide strong mathematical proof/explanation for the unique joint distribution.
- There is inconsistency in the models. For instance, Aircraft example has a number function for creating the blip which assigns the source and time simultaneously. However, in the Ball example, true color of balls is not assigned when it is created using number function. Similarly, the number function of Publication assigns Author but the generating function for author is missing. Hence, it appears that there can be multiple models to represent the same scenario. However, there is no explanation if different representation would result in same joint distribution.
- Paper doesn’t put forward enough experimental evidence. The experiment conducted asserts that 10 balls were drawn and all appeared blue. The query was made about number of balls in the urn. Results showed that when the prior for the number of balls is uniform over 1, . . . , 8, the posterior puts more weight on small numbers of balls. And this experiment was validated by saying ”this makes sense because the more balls there are in the urn, the less likely it is that they are all blue”. Few more experiments would have helped.
- Brian Milch, Bhaskara Marthi, Stuart Russell, David Sontag, Daniel L. Ong and Andrey Kolobov, BLOG: Relational Modeling with Unknown Objects, IJCAI 2005
- Lise Getoor and Ben Tasker, Introduction to Statistical Relational Learning, (Adaptive Computation and Machine Learning), The MIT Press.


Synonyms / Related
Definitions of order of magnitude:
- noun: a number assigned to the ratio of two quantities; two quantities are of the same order of magnitude if one is less than 10 times as large as the other; the number of magnitudes that the quantities differ is specified to within a power of 10
- noun: a degree in a continuum of size or quantity
Example: "An explosion of a low order of magnitude"
Search for order of magnitude at other dictionaries: OneLook, Oxford, American Heritage, Merriam-Webster, Wikipedia
Use in a sentence...


Fast Division Quiz Online allows you to enjoy the quiz right away without any registration or login function.
Learn division with our free quiz game app! features a ranking function for each course.
The ranking is based on how quickly and accurately you can answer the division quiz.
Fast Division Quiz Online offers the following four types of division quiz courses.
In the beginner level, you will be asked 10 division quiz questions with no remainder.
The difficulty level is relatively easy, making this course ideal for those who are just beginning to learn division.
Next, in the Intermediate level, there will be a 20-question quiz on division with remainders.
The difficulty level is the same as the beginner level, but the quizzes require the student to find the exact remainder.
In the advanced level, the difficulty level is raised a little so that questions are given on division formulas with up to three digits.
Finally, in the "Most Difficult Master Division Quiz Course," there will be 100 division questions that are not limited to the number of digits or remainders.
This is the most difficult course because the number of digits has increased significantly, and the division answer may or may not have a remainder.
Please try to answer all the questions correctly and earn the title of the most difficult master divider.
Fast Division Quiz Online has a "My Page" where you can view your history of quiz challenges you have played so far.
In this My Page, you can see
the number of correct answers and the time, the best time for each course, and the ranking position.
In particular, since you can see the number of correct answers and times in your play history, you can use this page as a learning record to keep track of how well you have improved your division.
If you have any suggestions for improvement after using the quiz, please contact us through this URL.
You can check this url too.
Fast Division Quiz Online(Microsoft store)
Amazon Appstore is here.
Please play as many times as you like and try to become good at division.


In broadcasting, the only basis for planting is the total seeding rate usually expressed in the weight of seeds per unit area. Example: 50-100 kg per hectare for lowland rice. There are no rows and uniform plant-to-plant distances are not considered.
It is possible to calculate the total plant population and the average number of plants per unit area upon germination if the average weight and the germination percentage of seeds are known. A replicated sampling of stand count per square meter or any sample area can also give a good estimate of the total population.
In both the hill and drill methods of planting by direct seeding, there is a desired row-to-row spacing. Take mungbean, for example. The distance between adjacent rows maybe 60 cm.
If planted by hill, 12 seeds may be sown in 4 hills 25cm apart in each linear meter in a row at 3 seeds per hill. Otherwise, if planting is by drill, the 12 seeds will just be dispersed in one linear meter without considering uniformity in plant-to-plant spacing within the row. With 12 seeds per linear meter (1m = 100cm), the mathematical, but not actual, average for the plant-to-plant distance will be 8.3cm (i.e., 100cm ÷ 12 = 8.3cm).
But if broadcasted, no reference to any distance nor spatial arrangement is necessary. For uniformity, however, the average seeding rate should be 20 seeds per square meter or 12 seeds in every 0.6-sq m ground area. In all these planting methods, the total seeding rate is constant at 200,000 seeds per hectare.
In the hill method, the hills are either occupied by a single plant or any multiple numbers of plants and spaced uniformly within each row. Therefore the row distance, hill distance, and the number of plants (or seeds) per hill are always given or otherwise computed from a given plant population density.
In contrast, there is no uniform spacing between plants within the row in the drill method. Instead, seeds are released over the intended row in uniform seed weight or the number of plants per linear meter.
To illustrate further, here are some calculated results:
In Broadcasting. If the required seeding rate is 100 kg per hectare, the seeds have to be broadcated at an average rate of 0.01 kg or 10 g per sq meter. Assume further that the crop to be grown is rice and the seeds to be used for planting have an average weight at 14% moisture content of 30 grams per 1000 grains (equivalent to about 33,333 grains per kilogram). This will be equivalent to an average seeding rate of about 333 grains per sq. meter or a total seeding rate of 3,333,333 grains per hectare. If seed germination is 100%, the same figures will apply to seedling emergence.
In Hill Planting. Assuming that the recommended planting distance for corn is 75cm x 25cm, this means a spacing of 75 cm between rows and 25 cm between hills. If the planting rate is 1 seed per hill, the computed total seeding rate per hectare will be 53,333.3 seeds. The decimal point indicates that this value is just an estimated average. Formula:
PD (or TSR) = [A ÷ (Dr x Dh)] x NPh where: PD = total plant population density (no. of plants) TSR = total seeding rate (no. of seeds) A = area to be planted (m²) Dr = distance between rows (m) Dh = distance between hills (m) NPh = number of plants (or seeds) per hill
In Drill Planting. Given the same assumptions under broadcasting, i.e., a seeding rate of 100 kg (=100,000 g) per hectare and 1,000-grain weight= 30 grams but planting the seeds in drill: If the rows are 20 cm apart, the calculated average seeding rate per linear meter in the row will be 2 grams. With a 1000 grain weight of 30 grams for rice, this is equivalent to an average seeding rate of about 66.7 seeds per linear meter. But if the row distance is widened to 25 cm, the average seeding rate will increase to 2.5 grams or 83.3 seeds per linear meter. Formula:
PD (or TSR) = (A ÷ Dr) x Nplm where: PD = total plant population density (no. of plants) TSR = total seeding rate (no. of seeds) A = area to be planted (m²) Dr = distance between rows (m) Nplm = no. of plants (or seeds) per linear meter
Calculations for the above given assumptions under broadcasting:
1. To calculate the average seeding rate (ASR) in the weight of seeds (grains) per square meter, divide the recommended seeding rate by the area to be seeded. This is the desired amount of seeds that should be broadcasted per square meter for uniformity throughout the crop area.
ASR (i.e., weight of seeds/m²) = recommended seeding rate (kg) ÷ area (m²) = seeding rate per hectare (kg) ÷ area of 1 hectare (m²) = 100 kg/ha ÷ 10,000 m²/ha = 0.01 kg/m² or 10 g/m²
2. To calculate the average weight of a single seed (grain), divide the weight by the given number of grains. Here we have presumed that we have data providing that 1000-grain weight is 30 g.
Ave. Seed Weight (g/grain) = Weight of seeds ÷ no. of seeds = Weight of 1000 grains (g) ÷ 1000 grains = 30 g ÷ 1000 grains = 0.03 g per grain
3. To calculate the average seeding rate (ASR) in the number of seeds (grains) per square meter, divide the ASR (weight of seeds/m²) by the average seed weight.
ASR (i.e., no. of seeds/m²) = ASR (g/m²) ÷ Ave. seed weight (g/grain) = 10 g/m² ÷ 0.03 g/grain = 333.3 grains per sq meter
4. To calculate the total seeding rate (TSR) in the number of seeds (grains) per hectare, divide the required (or recommended) seeding rate per hectare by the average seed weight or, given the ASR in a number of seeds per sq. meter (no. 3), multiply it by 10,000, the area of a hectare. Make the necessary conversion to the same units of measurement. The result will also be the total perfect plant population if germination of the broadcasted seeds and plant establishment is 100 percent.
TSR (no. of seeds/ha) = Seeding rate per hectare (g/ha) ÷ Ave. seed weight = 100 kg/ha ÷ 0.03 g/grain = 100,000 g/ha ÷ 0.03 g/grain = 3,333,333.3 grains per hectare


Updated Mi-STAR Academy Included in Free NGSS Workshops for Michigan Science Teachers
Thursday, January 12, 2017
Science teachers from across Michigan can now enroll in an updated version of the online Michigan Science Teaching and Assessment Reform (Mi-STAR) Academy.
The academy is a self-paced, online course that helps teachers deepen their understanding of the new Michigan Science Standards and Next Generation Science Standards. Modules address topics such as the structure of the standards; understanding science and engineering practices, crosscutting concepts and disciplinary core ideas; engineering in K-12 science classrooms; and how the standards can be applied to curriculum and assessments.
Mi-STAR Academy will be provided free to approximately 1,200 teachers participating in the five-day Next Generation Science Exemplar (NGSX) professional development series, which is being funded by the SMILE program. Science, Math Integrating Literacy and Engineering (SMILE) is a project of the Michigan Mathematics and Science Center Network, funded by a Mathematics and Science Partnership through the Michigan Department of Education.
The five-day NGSX sessions combine face-to-face work in a study group format and a web-based environment. Participants receive training in the NGSS and gain the skills to help other teachers implement the standards in their classrooms. Teachers also receive credit toward professional recertification.
“We needed professional development to get teachers up to speed in the NGSS, and the Mi-STAR Academy was a good fit,” said Shawn Oppliger, director of the Western U.P. Center for Science, Math and Environmental Education, one of 33 centers offering the NGSX workshops.
Mi-STAR Academy format allows teachers to pick and choose what parts to cover, based on their prior knowledge of the NGSS. The usual $25 fee will be waived for those participating in the NGSX sessions.
“We’re excited that the Mi-STAR Academy has been chosen to be part of SMILE,” said Brenda Bergman, Mi-STAR director of operations. “Teachers who participated in the Academy through Mi-STAR gave us great feedback, which inspired us to develop this version for all Michigan teachers.” Mi-STAR is developing an NGSS-aligned curriculum for the middle grades.
To participate in NGSX Workshops, Michigan science teachers should contact their local Math and Science Center. Web links to local Math and Science Centers can be found on the Michigan Math and Science Center Network website. To register for Mi-STAR Academy, see the application form here. For more information on Mi-STAR Academy, contact Marianne Semones at email@example.com.
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Mi-STAR was founded in 2015 through generous support provided by the Herbert H. and Grace A. Dow Foundation. Mi-STAR has also received substantial support from the National Science Foundation, the MiSTEM Advisory Council through the Michigan Department of Education, and Michigan Technological University.
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|Statement||Mark A. Pinsky.|
|LC Classifications||QA374 .P55 1984|
|The Physical Object|
|Pagination||x, 326 p. :|
|Number of Pages||326|
|LC Control Number||83018724|
This introductory text explores the essentials of partial differential equations applied to common problems in engineering and the physical sciences. It reviews calculus and ordinary differential equations, explores integral curves and surfaces of vector fields, the Cauchy . This book has been widely acclaimed for its clear, cogent presentation of the theory of partial differential equations, and the incisive application of its principal topics to commonly encountered problems in the physical sciences and engineering. It was developed and tested at Purdue University over a period of five years in classes for advanced undergraduate and beginning graduate students 4/5(4). ing partial diﬀerential equations, has become commonly available and is currently used in all practical applications of partial diﬀerential equations. Therefore, a modern introduction to this topic must focus on methods suit-able for computers. But these methods often rely . Note: If you're looking for a free download links of Partial Differential Equations: An Introduction to Theory and Applications Pdf, epub, docx and torrent then this site is not for you. tonyasgaapartments.com only do ebook promotions online and we does not distribute any free download of ebook on this site.
Partial differential equations also play a toward both their numerical analysis and the qualitative theory. This book provides an introduction to the basic properties of partial dif-ferential equations (PDEs) and to the techniques that have proved useful in * What is . used textbook “Elementary differential equations and boundary value problems” c ). Many of the examples presented in these notes may be found in this book. The material of Chapter 7 is adapted from the textbook “Nonlinear dynamics and chaos” by Steven H. Strogatz (Perseus Publishing, c ). 8 Partial differential equations Jan 13, · Definitely the best intro book on ODEs that I've read is Ordinary Differential Equations by Tenebaum and Pollard. Dover books has a reprint of the book for maybe dollars on Amazon, and considering it has answers to most of the problems found. He is the author of over papers published in major scientific research journals as well as 4 other books, including the definitive Springer graduate text, Applications of Lie Groups to Differential Equations, and another undergraduate text, Applied Linear Algebra.
Introduction to Ordinary and Partial Differential Equations. This note covers the following topics: Classification of Differential Equations, First Order Differential Equations, Second Order Linear Equations, Higher Order Linear Equations, The Laplace Transform, Systems of Two Linear Differential Equations, Fourier Series, Partial Differential Equations. Introduction PDE Motivations and Context The aim of this is to introduce and motivate partial di erential equations (PDE). The section also places the scope of studies in APM within the vast universe of mathematics. What is a PDE? A partial di erential equation (PDE) is an equation involving partial deriva-tives. Introduction Ordinary and partial diﬀerential equations occur in many applications. An ordinary diﬀerential equation is a special case of a partial diﬀerential equa-tion but the behaviour of solutions is quite diﬀerent in general. It is much more complicated in . “This introduction to partial differential equations is addressed to advanced undergraduates or graduate students . an imposing book that includes plenty of material for two semesters even at the graduate level. The author succeeds at maintaining a good balance between solution methods, mathematical rigor, and tonyasgaapartments.com: Springer International Publishing.


We can think of a tension in a given rope as T = (m × g) + (m × a), where “g” is the acceleration due to gravity of any objects the rope is supporting and “a” is any other acceleration on any objects the rope is supporting.
When a rope supports the weight of an object that is at rest, the tension in the rope is equal to the weight of the object: T = mg.
The only horizontal force acting on mass 1 is the pull coming from the tension in the rope. Therefore the tension T is given by T=m1*F/(m1+m2) (again, the acceleration is the same because of the rope and the lack of friction, I think).
Calculate the tension in the rope using the following equation: T = M x A. Four example, if you are trying to find T in a basic pulley system with an attached mass of 9g accelerating upwards at 2m/s² then T = 9g x 2m/s² = 18gm/s² or 18N (newtons).
For example, where R=10 pounds per inch, P=20 pounds and T=1.5 inches, you can find the pounds of force for your spring’s initial tension. Simply multiply 10 by 1.5 and subtract from 20 to get 5 pounds of force (5lbf).
After we have found the acceleration of the system, we can use Newton’s Second Law of Motion again to calculate the system’s rope or string tension. To do this, multiply the acceleration by the mass that the rope is pulling.
Tension Formula. The tension on an object is equal to the mass of the object x gravitational force plus/minus the mass x acceleration. T = mg + ma. T = tension, N, kg-m/s2.
1 : the act of straining or stretching : the condition of being strained or stretched I adjusted the strap’s tension. 3 : a state of unfriendliness There was tension between the two groups.
The tension in the rope is constant if its force does not have to be used to accelerate anything else, including itself. Therefore, if it has negligible mass and is held taut between two points, the tension will be considered constant throughout.
The correct amount of initial tension is equal to two (2) times the load achieved at (L1) minus the load at (L2). As an example: If an extension has a load of 10 pounds when it is extended .
Since we observe that a tense rope is stationary and completely still then it must be that every small piece of the rope has a zero net force. Thus, the pull on the left will propagate, without loss, through the length of the rope. And the tension is thus the same everywhere.
Pulley: A pulley serves to change the direction of a tension force, and may also (in the case of multiple-pulley systems) change its magnitude. … The tension of an “ideal cord” that runs through an “ideal pulley” is the same on both sides of the pulley (and at all points along the cord).
No. The rope has mass, so tension varies, as one bit has to carry the other bits.
The only way for the object to undergo uniform circular motion as depicted is if the net force on the object is directed towards the center of the circle. … If the string is under tension, the force of tension will always be towards the center of the circle.
To conclude, the total belt tension as calculated above is usually expressed as a unit tension for reference against various information tables. This is done by dividing the total calculated tension by the belt width. Therefore Unit Tension = Belt tension (N) / Belt width (mm) giving units of N/mm width.
how to find tension in a rope with mass and angle
how to find tension in a rope with acceleration
how to find tension in a rope on an incline
tension formula with angle
tension formula with length
tension formula with acceleration
calculating tension in a string over a pulley


A meta-analysis of 242 articles assessing the math skills of 1,286,350 people found no difference between the two sexes. This was confirmed in an analysis of the data from several large surveys of American adolescents (the National Longitudinal Surveys of Youth, the National Education Longitudinal Study of 1988, the Longitudinal Study of American Youth, and the National Assessment of Educational Progress).
(2010). New trends in gender and mathematics performance: A meta-analysis..
Psychological Bulletin. 136(6), 1123 - 1135.


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The surgery equalities immediately lead to the existence of corresponding Lagrangian cobordisms. Note that in case 1 , a similar cobordism construction was established in  using Lefschetz fibrations independently. Remark 1. We also include a detailed discussion on gradings involved in Lagrangian surgeries. This benefits us in two aspects: we use a grading assumption to exclude bubblings in immersed Floer theory Section 7.
But we emphasize the grading is a vital part of the foundation of Lagrangian surgeries for an intrinsic reason. Consider the simple case when all involved Lagrangians are Z-graded and embedded, according to the cone relation proved in , the algebra instructs a surgery happen only at degree zero cocycles. This principle was noticed first by Paul Seidel . Such a principle interprets several known phenomena in a uniform way. When the resolved intersections have mixed degrees, in many cases this leads to obstructions in Floer theory, as exemplified in [12, Chapter 10].
In better situations when resolved intersections have zero degree mod N, the surgery at least results in collapse of gradings, which can also be checked directly on the Maslov classes. As for our applications, we extend this principle to clean surgeries. This matches well with predictions from homological algebra dictated by Lagrangian Floer theory with clean intersections .
It also extends the surgery exact sequence to clean intersection case. In another direction, since our construction holds for arbitrary symplectic manifolds, when combined with the general framework due to Fukaya-Oh-Ohta-Ono , it yields a proof of Seidel s exact sequence in arbitrary symplectic manifold.
This is part of an ongoing work . As a consequence of the cone relations in functor categories, we also consider the auto-equivalences of AutpFukpW qq, for W a Milnor fiber of ADE-type singularities The generalization of the result from A-type singularities to DE-type singularities was suggested to us by Ailsa Keating. In  it was proved that FukpW q is split generated by the vanishing cycles.
Moreover, in  it is shown that there is a braid group embedded into Symp c pw q when W is an A n -Milnor fiber induced by Dehn twists along the standard vanishing cycles. It is natural to ask whether this braid group indeed is the whole mapping class group, i. On the other hand,  5. As a consequence, we turn to a categorical reduction of the problem.
In other words, we consider Question 1.
Pseudo-Isotopies of Compact Manifolds
We are able to prove a weaker version of Question 1. As Seidel discovered the long exact sequence associated to a Dehn twist along spheres, the spherical twists, as the mirror autoequivalences, also received much attention . Also, such a cone relation on the A-side has become a foundational tool in the study of homological mirror symmetry, especially in the Picard-Lefschetz theory .
It has long been curious since that, what the auto-equivalence corresponding to the Dehn twists along a rank-one symmetric space is.
Pseudo-Isotopies of Compact Manifolds
On the B-side, Huybrechts-Thomas  defined P n -objects on derived categories of smooth algebraic varieties, as well as a corresponding new auto-equivalence called the P n -twist. They then conjectured the P n - twist is exactly the mirror auto-equivalence of the one induced by a Dehn twist along Lagrangian CP n on the Fukaya categories.
Richard Harris studied the problem in A 8 contexts and formulated the corresponding algebraic twist on A-side . The only missing link to the actual geometry of Lagrangian submanifolds, remains unproved for years. As an application of the surgery equalities in Theorem 1.
Catalog Record: Pseudo-isotopies of compact manifolds | HathiTrust Digital Library
Then Huybrechts-Thomas conjecture is true up to determination of connecting maps. The proof of Theorem 1. These are 6. A family version of projective twist is also given, see Theorem 9.
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While it is not difficult to find examples of Lagrangian RP n in problems in symplectic topology , the search of interesting examples of Lagrangian CP n is more intriguing. In  the authors suggested several sources of P n -objects in derived categories. While the role of P n objects on either side of mirror symmetry remains widely open so far, it is interesting to know whether such objects split generate either side of mirror symmetry.
In a different direction, the P n -cone relation should be interested in understanding some basic problems in symplectic topology, such as mapping class groups of a symplectic manifold and the search of exotic Lagrangian submanifolds. For instance, while a Lagrangian CP n -twist is always smoothly isotopic to identity, it is usually not Hamiltonian isotopic to identity. A simplest model result along this line is to generalize Seidel s twisted Lagrangian sphere construction : in the plumbing of three T CP n, the iterated Dehn twists along CP n in the middle should generate an infinite subgroup in the symplectic mapping class group.
With Theorem 1. The only difference between the formulas is the grading shift of the first term, as specified in Theorem 9.
Therefore, the iterated cone relation can be packaged into a long exact sequence without invoking the immersed Floer theory. The idea follows largely that of  and . For the case at hand, we have restricted ourselves to the exact setting for simplification, and mostly followed Alston-Bao s exposition . The upshot is as expected, that the existence of an immersed Lagrangian cobordism incurs a quasi-isomorphism between certain mapping cones coming from Floer theory.
However, the actual proof is far from straightforward. The key issue is the cleanness of self-intersections of the immersed cobordisms, which is required for the well-behaviors of moduli spaces of pseudo-holomorphic curves. It is not hard to establish a cobordism theory naively following Biran-Cornea s definition in embedded categories and assume the required geometric transversality, but this will not even cover the simplest application at hand. L is given by the cotangent fiber at a point, and we assume it passes through the unique immersed point of S.
The cobordism can be constructed so that it naively satisfies Biran-Cornea s definition, i. However, it is evident that the self-intersection cannot be clean since they form a ray. In general any surgery process involving resolution of an immersed point will suffer from the same caveat. Therefore, we need a modification for the Floer theory to be well-defined. Although we only deal with Donaldson-Fukaya categories in our setting, considerable amounts of new issues need to be addressed since most of our curves cannot actually be projected, which is also the main catch to prove statements on the A 8 level.
This will appear independently in the future. Using Theorem 1. A bonus point of this alternative approach is we could compute the connecting maps which is difficult for general Lagrangian cobordisms. The immersed formalism along with a simple algebraic trick extract enough information to determine almost all relevant mapping cones up to quasi-isomorphisms we covered in this paper, see Section 8.
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In particular, when 8. A note on coefficients. Using characteristic zero coefficients is possible up to checking orientations for the general framework on Lagrangian cobordisms for [6, 7]. Acknowledgement This project was initiated from a discussion with Luis Haug, and have benefited significantly from conversations with Octav Cornea, who suggested the key idea of bottleneck among many other invaluable inputs. We thank both of them for their help and interests over the whole period when this paper was being prepared.
All Lagrangians are assumed to be proper, and non-compact exact Lagrangian embeddings are assumed to have cylindrical end, unless specified otherwise. We identify T S with T S by g and switch freely between the two. The following lemma is well-known. Lemma 2. To define Dehn twist, we need to introduce an auxiliary function. We first consider the case when S is not diffeomorphic to a sphere. Example 2. As usual, one may globalize the model Dehn twist.
Definition 2. A Dehn twist along S in M is a compactly supported symplectomorphism defined by the model Dehn twist as above in a Weinstein neighborhood of S and extended by identity outside. Let apsq, bpsq P R. The main property of an admissible curve can be rephrased as follows. We will frequently use the two equivalent descriptions of admissibility interchangeably.
As a consequence, we have Corollary 2. Now, we present an new approach of performing Lagrangian surgery which also motivates the definition of Lagrangian surgery along clean intersections. The conclusion follows. Under the assumption in Lemma 2. Cerf showed that a one-parameter family of functions between two Morse functions can be approximated by one that is Morse at all but finitely many degenerate times.
For the purposes of intuition, here is an analogy. Notice that in stratified spaces, the co-dimension 0 open stratum is open and dense. For notational purposes, reverse the conventions for indexing the stratifications in a stratified space, and index the open strata not by their dimension, but by their co-dimension. In the case of. Cerf's one-parameter theorem asserts the essential property of the co-dimension one stratum. Alexander in Igusa's theorem, Topology 39 MR g Gajer, Riemannian metrics of positive scalar curvature on compact manifolds with boundary, Ann.
MR 89m Gromov and H. Lawson, Jr. MR 81h MR 85g Hatcher and J. Igusa, Higher singularities of smooth functions are unnecessary, Annals of Mathematics, 2nd Ser. MR 85k Igusa, On the homotopy type of the space of generalized Morse functions, Topology 23 , MR 86m Igusa, The space of framed functions, Trans.
Joyce, Compact 8-manifolds with holonomy Spin 7 , Invent. MR 97d Lichnerowicz, Spineurs harmoniques , C.


A magician has a spectator select one card
and memorize it. Now the wonderworker introduces transparent
plastic cards that a single number printed
on each card. The magi states that he will find out the
selected card by using those numbered cards.
Now our conjurer retrieves 3 cards, number
3, 4, and 5. He says the selected card
should match with one of three... The
answer is..... "NO"..
In fact, it was totally impossible from the
very beginning… The selected card is “Queen
It appears that the magician’s attempt has
ends up in failure….However, the magician
STILL says that these three cards are the
chosen card--- By adding the three numbers
(3, 4, and 5), the total is 12, which equals
Queen….. But it wasn’t a BIG surprise. Now
the three cards are placed inside the box
and shaken.. The numbers transform into “Q"(ueen).
Next, the remaining cards are also placed
and shaken…. The numbers transforms into
Ton Onosaka's Miracle Number


That's an *old* clip of my Princess (one month ago).
I started her on multiplication when we got to Florida. In about 1.5 months she's just about mastered the basics (1-10 tables).
All I did was make her fill out that homemade multiplication table - every single day. That's about it!
Though now we're working on her *speed* with Math Rider - which I've found very good for creating an urgency that my kids don't experience on account of not being in a conventional school with its quizzes, tests, and whatnot. I will have a full review of that product shortly. But so far, the Princess is doing very well with it.
Today my son is participating in his first *math competition*.
He's doing World Math Day in the 4-7 year old division.
It's an internet event. He squares off in 100 one minute rounds against kids from all over the globe -although the winners will be determined by aggregate score, by who answers the most most questions correctly. Contestants have 48 hours to play their *games* between today and tomorrow.
Anyone ages 4-18 can sign up just click the link above. And hurry!
So far my son is on his 25th game or so. The first 20 were simple math questions like "8+2" and "10+0". But now the questions are getting tougher.
I'm ashamed to admit that I gave my son an earful when two blokes from Ireland beat him in one round. He was goofing around and not concentrating!
Ooh I do hope that I don't turn into a math version of the stereotypical *hockey dad*...


I'm Soham Chowdhury, a functional programmer interested in compilers, programming-language theory, and expressive type systems.
I'm also a student of mathematics interested in algebraic and arithmetic geometry and in number theory; a self-taught guitarist (and nearly omnivorous consumer of music); a fan of a lot of good writing; an occasional speedcuber; and an enthusiast for unexplained analogies in and around mathematics, physics, and computer science.
This is my personal site and blog.
A near-complete implementation of the Sound and Complete type system from Dunfield and Krishnaswami (2016), which describes a minimal ML-like language with GADTs, existential types, and coverage-checked pattern-matching.
A set of Nix scripts for reproducible, predictable Haskell development environments supporting custom package-sets and native dependencies.
A numeric programming framework for Haskell featuring highly polymorphic algebraic structures and custom deriving strategies to build complex algebraic behaviors from simpler ones.


Knowledgebase: Microsoft Excel
Finding the Relative Position of Numbers within a String
Posted by - NA - on 20 March 2006 08:47 AM
List1 (column A) consists of strings composed of numbers and characters.
Numbers may appear at the beginning or the end of the string, but not in the middle.
For each of the strings, we want to determine whether the numbers appear at the beginning or the end
Use the ISNUMBER, RIGHT, and LEFT functions as shown in the following formula:


When I was writing my personal statement, I was really tempted to include a few endearing stories about how I came to love math. It was hard for me to take the advice of others, like the other advice offered here, that graduate schools didn't care about when I first learned to calculate compound interest, or how much I loved my first calculus class.
Personal Statement:Mathematics 20 At first sight, what a mathematician does may seem small, but it is the closest one can come to achieving permanence. The possibility of producing or creating anything that is even slightly permanent is what drives me to study mathematics.
At middle school, I represented my school to participate in the national Mathematics Olympics Competition to win a second-class award. As soon as I had access to computer in the senior middle school, I became enchanted with the computer programs that possessed equal logical beauty as the mathematics vocabulary and language.
Personal statement examples. Degrees Maths degree courses. Online degrees Online maths degree courses. CV templates CV examples (over 300 professionally written samples) Graduate CV templates. Student resources Essay writing Graduate internships Introduction to graduate fasttrack schemes Revision timetable Revision tips Student accommodation.
I have some questions regarding my personal statement for graduate school in math. I hope this is not the wrong place to ask. My question(s) are comprehensive and long, as the title suggests, thus I have numbered and sub-numbered the questions.
In addition to this, I taught at an elementary school in the Philippines and volunteered at a local state school, teaching Mathematics to young children. I managed to introduce them to new concepts in such a way that they understood the subject. For example, rather than just telling them angles in a triangle add up to 180 degrees, I showed them.
Personal Statement. of mathematics while at North Carolina State University confirmed my intent to purse further study of mathematics at the graduate level. A number of other experiences have helped me develop skills that I believe will help me succeed in graduate school. For example, I have help train other students in multimedia, desktop.
The Personal Statement of Purpose for Graduate Study in Statistics, Masters, PHD. Statistics is the study of the collection, organization, analysis, interpretation and presentation of data.This includes the planning of data collection in terms of the design of surveys and experiments.


Code Snippets »
C/C++ Code Snippets
C program to find sum of all digits until sum is not in single digit
This program is asked by kalyani shevale through comment on 18/12/2016.
I want one program code
input is an only integer value and output will be displayed only one digit in c
input int a=8999
Here, we are writing this code to calculate sum of all digits until sum is not in single digit in c programming language.
If number is 8999 the sum will be 8+9+9+9 = 35 = 3+5 = 8
This program is implementing by using recursion function, the function calculateDigits() is calling recursively until sum is not less than 10.
int calculateDigits(int num)
printf("Enter any positive integer number: ");
printf("Sum of digits is: %d\n",sum);
Enter any positive integer number: 8999
Sum of digits is: 8
Enter any positive integer number: 12345
Sum of digits is: 6
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Well, not really, of course. But I've been keeping a walking log for years, and just went from page 24 to page 25, which means that it was time to add up my miles and see how far I'd walked.
Yup, I've walked over 3,500 miles. New York to London is 3,471 miles, so if there wasn't a pesky little ocean in the way, I could have walked to London from the house I grew up in. If I can multiply that number of total miles walked by 7 before I die, I'll have walked around the circumference of the earth.
If I average 300 miles a year, that means it would take me just over 83 years to walk around the earth. I probably have over 60 years to go at this rate, and I don't know if I'll be able to walk 300 miles a year when I'm over 100 (which is where I'll be in 60 years). I'd better start walking more!


It is well known that India has given the lead to the world in the field of Mathematics and has produced several mathematicians of eminence like Ramanujan. The value of zero and the use of decimals were made known to the world by Indian mathematicians and these laid the foundation of complex mathematical calculations for scientific technology and development of computers.
It is however less known that the use of mathematics and mathematical calculations is an ancient scientific proven asset found in the Vedas and the Sutras. The author has made an in-depth study of these ancient scriptures and brought to our knowledge details of mathematics expounded in our old literature. The book clearly highlights simple steps incorporated in the Vedas of solving complex mathematical problems in an easier, logical and interesting manner. The Book presents a very sound theoretical exposition with numerous illustrative problems and explanatory notes for easier understanding of critical mathematical problems detailed in the Sutras. Wherever necessary charts have been given to enrich the knowledge. Chapters are logically set and graded to cover the whole of Vedic mathematics thereby facilitating readersto grasp the subject. Students will find chapters in this book containing simple and useful tips for easy and very interesting calculations. The unified approach to teaching of mathematics, outlined in the book as based on Vedic Mathematics is therefore most welcome and is of great relevance even today.
About the Author:
Mahesh Maheshwari (Tawani) is a Fellow member of the Institute of Charted Accountants of India. He has done Oracle and D2K course. He is mapping requirements and is providing customized software selection of appropriate technique, for various MIS reports, analyzing on system and co-ordinating with system design, integration and implementation. Application, maintenance and technical support of ERP like SAP are his main concerns. He has over 20years of experience of Finance and Software development in Audit, Media, Projects and Steel Ind.
Drawing sketches is one of his interests. He has conducted exhibition of sketches of Lord Ganesha, and Sri Hanumanji.
He has conducted seminars on Vedic Maths in Schools, Colleges, companies and other institutions.
As efforts based on his vast experience have been made to solve problems and perform calculations in a very interesting manner it would encourage minds for learning maths and it will not be a bugbear for the learners.


plotExpectedType1Error creates a plot showing the expected type 1 error as a function of standard error.
plotExpectedType1Error( logRrNegatives, seLogRrNegatives, seLogRrPositives, alpha = 0.05, null = NULL, xLabel = "Relative risk", title, showCis = FALSE, showEffectSizes = FALSE, fileName = NULL )
A numeric vector of effect estimates of the negative controls on the log scale.
The standard error of the log of the effect estimates of the negative controls.
The standard error of the log of the effect estimates of the positive controls.
The alpha (nominal type 1 error) to be used.
An object representing the fitted null distribution as created by the
fitNull function. If not provided, a null will be fitted before
If showing effect sizes, what label should be used for the effect size axis?
Optional: the main title for the plot
Show 95 percent credible intervals for the expected type 1 error.
Show the expected effect sizes alongside the expected type 1 error?
Name of the file where the plot should be saved, for example 'plot.png'.
See the function
ggsave in the ggplot2 package for supported file
A Ggplot object. Use the
ggsave function to save to file.
Creates a plot with the standard error on the x-axis and the expected type 1 error on the y-axis. The red line indicates the expected type 1 error given the estimated empirical null distribution if no calibration is performed. The dashed line indicated the nominal expected type 1 error rate, assuming the theoretical null distribution.
If standard errors are provided for non-negative estimates these will be plotted on the red line as yellow diamonds.
data(sccs) negatives <- sccs[sccs$groundTruth == 0, ] positive <- sccs[sccs$groundTruth == 1, ] plotExpectedType1Error(negatives$logRr, negatives$seLogRr, positive$seLogRr)


Dual Credit via PSU
Length/Credit(s): 2 semester/1.0 credit
Grade(s): 11, 12
PSU Course Title: Introduction to Probability and Statistics, 8.0 quarter credits
Course Codes: STAT 243 and STAT 244
Cost: Each semester costs $220 for a total of $440 for the full year.
A basic sequence in statistical analysis including presentation of data probability, probability distributions, sampling distributions, estimation, tests of significance, experimental design and analysis of variance, regression and correlation, nonparametric statistics, selected topics, applications, and use of statistical computer program packages.


Shift-modulation invariant spaces on LCA groups
A $(K,\varLambda )$ shift-modulation invariant space is a subspace of $L^2(G)$ that is invariant under translations along elements in $K$ and modulations by elements in $\varLambda $. Here $G$ is a locally compact abelian group, and $K$ and $\varLambda $ are closed subgroups of $G$ and the dual group $\hat G$, respectively.
We provide a characterization of shift-modulation invariant spaces when $K$ and $\varLambda $ are uniform lattices. This extends previous results known for $L^2(\mathbb R^d)$. We develop fiberization techniques and suitable range functions adapted to LCA groups needed to provide the desired characterization.


Today, we celebrated the wonderful world of mathematics with our maths puzzle day. Our focus for the day was mathematical reasoning, fluency and problem solving, with an emphasis on using the language of maths. These areas are highlighted in the 2014 Maths Curriculum as being of vital importance in supporting children to become confident mathematicians.
Throughout the day, the children were engaged in a variety of activities designed to get them thinking logically and problem solving collaboratively. It was wonderful to see the creativity with with the children approached the puzzles and the extent to which all children were focussed and engaged with the activity. The day was a great success and we hope to do something similar in the not too distant future.
Click here to read more


CARMA Research Group
Mathematical Modelling and Industrial Applications
Leader: Mike Meylan
The mathematical modelling and industrial applications group works on the application of mathematics to solving real-world problems. We have particular expertise in the implementation of differential equations to modelling complex problems in fluid dynamics and other processes. Our research can be broadly grouped into the following areas.
1) Mathematical Modelling. We have wide-ranging experience in modelling including extensive applications in fluid flows, material science, and biological processes.
2) Nanostructures and their applications in nanotechnology, includeing modelling electrorheologicalflui ds, the mechanics of carbon nanostructures, nanomaterials used in biology and medicine and protein and other polymer chain structures using the calculus of variations.
3) Electromaterials in energy applications such as solar cells and energy storage and modelling interactions between cells.
4) Finite element methods and numerical solution of complex equations, including Mixed and Hybrid Finite Element Methods, Domain Decomposition Methods, Non-conforming Discretization Techniques, Nearly Incompressible Elasticity, Approximation Theory, Subset Selection & Variational Methods in Image Processing..


This calculator can be used to calculate an odds ratio (OR) which can inform the application of the ACMG PS4 criterion for variants in genes related to autosomal dominant disorders. This calculator is not intended to be used in the context of autosomal recessive disorders.
The OR is the ratio of the odds of a disease / phenotype in exposed versus non-exposed individuals. In genetic terms, it is an approximation for the relative risk (RR) of developing a disease / phenotype associated with having a particular genotype or allele as compared with not having that genotype or allele. An OR of >1 indicates an increased risk; an OR of <1 indicates decreased risk.
Inputting case and control data
The calculator accepts either genotypes
When inputting genotypes
users should add the total number of cases or controls with the variant (heterozygous or homozygous) and the total number of cases or controls tested.
When inputting alleles
users should add the total variant allele count (AC) and total allele number (AN) for cases or controls. Please note, this option does not make a distinction between heterozygous or homozygous counts and therefore assumes occurrences are heterozygous.
6 out of 10,000 individuals in a case cohort are heterozygous for a variant.
The allele count (AC) for that variant in gnomAD is 4 and the allele number (AN) is 120,000.
Calculating the Odds ratio with confidence intervals
The calculator converts the input data to genotype counts to generate the following values in a 2×2 table (which can viewed by clicking ‘Show 2×2 table’):
a = Number of cases with the variant
b = Number of cases without the variant
c = Number of controls with the variant
d = Number of controls without the variant
The OR is calculated as follows:
OR = (a / b) / (c / d)
An OR should always be interpreted in the context of confidence intervals (CIs). The calculation of an odds ratio is based on a sample of cases and a sample of controls, and confidence intervals provide an indication of the likely range of the ‘true’ value of an OR in an entire population (rather than just the sample). Confidence intervals are calculated according to the following formula:
Upper CI = e [log(OR) + z * √(1/a + 1/b + 1/c + 1/d)]
Lower CI = e [log(OR) - z * √(1/a + 1/b + 1/c + 1/d)]
In this formula, the value of z determines the level of confidence calculated. For 95% confidence intervals, z = 1.96. For 90% confidence, z = 1.645, and for 99% confidence, z = 2.576.
An OR should only be considered to represent a significant increase in risk if the lower confidence interval is greater than 1.
Selecting levels for PS4 criterion
The application of PS4 at various strength levels should be determined by the calculated value of the lower confidence interval
. Users can select OR thresholds for each criterion level ‘Strong’, ‘Moderate’ or ‘Supporting’, and the % confidence interval (CI) they wish to use.
In the ClinGen guidelines for variants detected in sarcomeric genes in the context of inherited cardiomyopathy, it has been proposed that PS4 can be applied at supporting, moderate, or strong level if the 95% lower confidence interval
is ≥5, ≥10, or ≥20 respectively.
6 in 6,000 case genotypes vs 2 in 60,000 control genotypes gives an odds ratio of 30.03 (95% CI = 6.06-148.81).
The lower bound 95% CI is greater than 5 (95% CI = 6.06). Therefore, PS4 is set to PS4_Supporting
Created by: M. Bowman, Oxford Regional Genetics Laboratory, UK.


Alien invasion began, and scary man-eating aliens are establishing their bases all over the country. You are only safe on the places that are sufficiently far away from all current alien bases. You need to quickly write a program to help you determine where to move.
The input contains at most $25$ instances, each of them consisting of several lines. The first line of each instance contains integers $N$ ($1 \leq N \leq 10\ 000$), $M$ ($0 \leq M \leq 100\ 000$), $A$ ($0 \leq A \leq N$) and $K$ ($1 \leq K \leq 100$) separated by spaces, giving the number of towns in the country, the number of roads between them, the number of bases that the aliens are going to build, and the minimum safe distance from alien bases, respectively. The towns are assigned numbers $1, \ldots , N$.
The following $M$ lines describe the roads; each of them contains integers $T_1$, $T_2$ ($1 \leq T_1 < T_2 \leq N$) and $D$ ($1 \leq D \leq 100$) separated by spaces, where $D$ is the length of the road between towns $T_1$ and $T_2$. There is at most one direct road between any two towns. All roads can be used in both directions.
The following $A$ lines describe the positions of alien bases; the $i$-th of them contains the number $B_ i$ ($1 \leq B_ i \leq N$) of the town where the aliens build their $i$-th base.
The last instance is followed by a line containing four zeros.
The output for each input instance consists of $A$ lines. On $i$-th line, write the number of towns that are safe after the aliens build their $i$-th base. The town is safe if its distance from any of the towns $B_1, B_2, \ldots , B_ i$ is at least $K$.
Print one empty line after each instance.
|Sample Input 1||Sample Output 1|
7 6 3 3 1 2 1 1 3 1 2 5 1 3 6 1 1 4 1 4 7 2 2 1 4 1 0 1 1 1 0 0 0 0
2 1 0 0


High School Math Workshops
Anshe Sfard Hall, 1370 45th Street, 2nd Floor, Brooklyn, New York 11219
The mornings of August 1st and 5th will have repeated content. Please register for one or the other.
- August 1: Math Lesson Structures + Preview of Revised NYS Standards for Grades 5-8 Math
- August 5: Math Lesson Structures + Algebra I Yearly Check-In (includes Review of June Regents)
- August 8 : Geometry + Algebra 2 + Preview of Revised NYS Standards for Grades 9-11
Time: 9:30 AM to 4:30 PM
This workshop is open to General Studies teachers in New York City only due to being funded by Title IIA.
Please note, once you have registered, we cannot refund your order.
Workshop located at:
Anshe Sfard Hall
1370 45th Street
Brooklyn NY 11219
To promote a richer variety of mathematics learning experiences for their students, participants will analyze the following three lesson structures, one at a time:
- Inquiry-Based Lessons, including Hands-On lessons
- “Conscious” Practice Sessions
- Problem Solving Workshops
With each of these three lesson structures, participants will:
- Critique examples either via video, in-person simulations, or print
- Examine the role of core instructional practice elements (objective, varieties of interactions, end of lesson formative assessment, etc.)
- Determine how each supports each of the 8 NCTM Math Teaching Practices.
- Consider their own use of that lesson structure
Participants will also either review a Regents Exam from June, distilling the implications for our teaching OR make a preview of the Revised NYS Standards for Grades 5-8 Math, which we need to be ready to use in Fall 2020.
Dennis Desormier meets thousands of teachers each year in his workshops through Catapult Learning. His professional experience includes years of teaching, curriculum design, and instructional design for several organizations. However, his greatest love in the education field is professional development for teachers in the areas of mathematics and assessment. He has written (or cowritten) most of the mathematics and assessment workshops currently presented by Catapult staff around the country. His passion for rigorous but lighthearted teaching and learning comes through in every workshop he presents.
If you have any questions, please email Sloane Gray.
A Cholov Yisroel meal will be served with each workshop.
Please note that photographs and footage will be taken throughout High School Math Workshops. These will be used by The Jewish Education Project for marketing and publicity.


Google Drive How To Video
This is a great site for basic math skills like multiplication tables, addition and subtraction facts, division facts, fractions, decimals and more. The site also has Literacy links which I will post more about soon.
Here is a PDF file with discussion questions for the ESL classroom. I have used similar lists by displaying the PDF through a projector or Doc Camera to the Board and giving students 3 minutes to interview a partner with the questions. After 2 minutes they switch. It is a good warm up or wake up activity when the students are looking a little bored.
This site is jam packed with ESL resources, technology for the classroom and technology tools for school. Take a look at the site and discover the world of educational technology for ESL and non-ESL students and teachers.


When taking account of superstructures which have sloping
end bulkheads, in the calculations of freeboards, such superstructures
should be dealt with in the following manner:
1 When the height of the superstructure, clear
of the slope, is equal to or smaller than the standard height, the
length (S) should be obtained as shown in figure 4.
Figure 4 Height of superstructure equal to or smaller than the standard height
2 When the height is greater than the standard,
the length (S) should be obtained as shown in figure 5.
Figure 5 Height of superstructure greater than the standard height
3 The foregoing should apply only when the slope,
related to the base line, is 15°, the configuration should be
treated as sheer.
When the height of the superstructure, clear of the slope
is less than the standard height, its effective length (E)
should be its length (S), as obtained from paragraph
1 above, reduced in the ratio of its actual height to the standard
When a poop or forecastle has sloping end bulkheads, and
sheer credit may be allowed on account of excess height, the formula
given in regulation 38(12) should be used,
the values for y and L' being as shown in figure 6.
Figure 6 Sheer credit (s) for excess height


Next: Convergence criteria Up: Types of analysis Previous: Turbulent Flow in Open Contents
The solution of the three-dimensional Navier-Stokes equations has been implemented following the Characteristic Based Split (CBS) Method of Zienkiewicz and co-workers ,. The present implementation does give reasonable answers for a lot of problems (e.g. the lid-driven cavity), however, the accuracy is not sufficient for industrial use of solutions for compressible media. The problems are:
- The accuracy for compressible flow is not satisfactory. In particular, the variation of the total temperature in airfoil calculations is too strong.
- Without the smoothing effect of the shock capturing technique compressible flow problems do not converge.
Further research is going on to locate the reason for these problems.
Fluid problems are of a quite different nature than structural problems. What we particularly noticed in fluid problems is that
- The solution can be mesh dependent, i.e. the fluid flow sometimes follows the element edges although this may be wrong. This is particularly true for coarse meshes.
- Coarse meshes may produce a solution which is completely wrong. Taking this solution as starting point for gradually finer meshes frequently leads to the right solution.
- If the boundaries of the mesh are too close to the area of interest the solution may not be unique. For instance, turbulent flow may lead to an undefined reentry at the exit of your mesh. Consequently, the boundaries of your mesh must be far enough away.
The CBS Method transforms a transport equation of the form
where C stands for the convective term, D for the diffusion term and F for the external forces, into
Here and are the shape functions. The first, second and third term on the right hand side correspond to convection, diffusion and external forces, respectively. The fourth and fifth terms are the stabilization terms for convection and external forces, while the last term is the area term corresponding to diffusion. It is the result of partial integration. The stabilization terms were obtained through partial integration too. In agreement with the CBS Method the corresponding area terms are neglected. Furthermore, third-order and higher order terms are neglected as well (particularly the stabilization terms corresponding to diffusion).
This method is now applied to the transport equations for mass, momentum and energy. Furthermore, the resulting momentum equation is split into two parts (Split scheme A in ), one part of which is calculated at the beginning of the iteration scheme. Subsequently, the conservation of mass equation is solved, followed by the second part of the momentum equation. To this end the correction to the momentum in direction is written as a sum of two corrections:
This results in the following steps:
Step 1: Conservation of Momentum (first part)
The partial differential equation reads:
Applying the CBS method to all terms except the pressure term leads to:
is the momentum, is the diffusive stress and is the Reynolds stress multiplied by (only for turbulent flow), all evaluated at time t. is the gravity acceleration at time . The diffusive stress satisfies
whereas is defined by
Here, is the turbulent viscosity and is the turbulent kinetic energy. What is lacking in equation (153) to be equivalent to the momentum transport equation is the pressure term.
Step 2: Conservation of mass
The partial differential equation reads:
Applying Galerkin, this leads to:
In agreement with  the following approximation was made:
leading to the last term in equation (157). The velocity in the mass conservation equation is calculated at time , whereas the pressure in the momentum transport equation is expressed at time ( ). If the scheme is called explicit, else it is semi-implicit (in the latter case it is not fully implicit, since the diffusion term in the momentum equation is still expressed at time t). For compressible fluids (gas) an explicit scheme is taken. This means that the second term on the left hand side of equation (157) disappears and the only unknowns are . For incompressible fluids the density is constant and consequently the first term is zero: the unknowns are now the pressure terms .
An additional difference between compressible and incompressible fluids is that the left hand side of equation (157) for incompressible fluids (liquids) is usually not lumped: a regular sparse linear equation solver is used. For compressible fluids it is lumped, leading to a diagonal matrix. Lumping is also applied to all other equations (momentum,energy..), irrespective whether the fluid is a liquid or not.
Step 3: Conservation of Momentum (second part)
This equation takes care of the pressure term in the momentum equation, which was not covered by step 1:
Notice that for compressible fluids the second term on the right hand side disappears ( ). Consequently, is not needed for gases. This is good news, since only is known at this point (conservation of mass).
Step 4: Conservation of Energy
The governing differential equations runs:
where is the total internal energy per unit of volume, is the conduction coefficient, are the external forces and represents volumetric heat sources. satisfies
Straightforward application of the CBS method yields
For turbulent flows has to be complemented by . For liquids the energy equation is uncoupled from the other equations, unless the temperature leads to motion due to differences in the density (buoyancy). For gases, however, there is a strong coupling with the other equations through the equation of state:
where is the specific gas constant.
Step 5: Turbulence
The turbulence implementation closely follows the equations in . There are basically two extra variables: the turbulent kinetic energy and the turbulence frequency . The governing differential equations read
For the meaning of the constants the reader is referred to . The turbulence equations are in a standard form clearly showing the convective, diffusive and external force terms. Consequently, application of the CBS scheme is straightforward.
Because of the problems occurring for laminar flow, the turbulence step has not been activated yet.
Notice that the unknowns in the systems of equations in all steps are the conservative variables , (or for liquids) and . The physical variables the user usually knows and for which boundary conditions exist are , and . So at the start of the calculation the initial physical values are converted into conservative variables, and within each iteration the newly calculated conservative variables are converted into physical ones, in order to be able to apply the boundary conditions.
The conversion of conservative variables into physical ones can be obtained using the following equations for gases:
and . For liquids is a function of the temperature T and the first equation has to be replaced by
since . T in all equations above is the static temperature. For gases the total temperature and Mach number can be calculated by:
where . Notice that the equations for the static temperature are nonlinear equations which have to be solved in an iterative way, e.g. by the Newton-Raphson procedure.
The semi-implicit procedure for fluids and the explicit procedure for liquids are conditionally stable. For each node a maximum time increment can be determined. For the semi-implicit procedure it obeys:
is the Prandl number, and for the explicit procedure it reads
is the speed of sound. In the above equations is the smallest distance from node i to all neighboring nodes. The overall value of is the minimum of all nodal 's.
Feasible elements are all linear volumetric elements (F3D4, F3D6 and F3D8). The Navier-Stokes procedure as not been tested yet for quadratic elements.
For gases a shock capturing technique has been implemented following . This is essentially a smoothing procedure. To this end a field is determined for each node i as follows:
where the sum is over all neighboring nodes and p is the static pressure. It can be verified that for a local maximum and if the pressure varies linearly. So is a measure for discontinuous pressure changes. The smoothing procedure is such that the smoothed field is derived from the field by
is the left hand side matrix for the variable involved, is the lumped matrix (i.e. the matrix [M] where all values in each row are summed and put on the diagonal, all off-diagonal terms are zero) and is a parameter between 0 and 2. The bigger , the stronger the smoothing. This procedure was elaborated in on . After the regular calculation of , and , the temperature and the pressure are calculated, the field is determined and all conservative variables are smoothed. This leads to new values after which the boundary conditions for the velocity, the static pressure and static temperature are enforced again. If no convergence is reached, a new iteration is started.
It is important to note that for CFD calculations adiabatic boundary conditions have to be specified explicitly by using a *DFLUX card with zero heat flux. This is different from solid mechanics applications, where the absence of a *DFLUX or *DLOAD card automatically implies zero distributed heat flux and zero pressure, respectively.
Finally, it is worth noting that the construction of the right hand side of the systems of equations to solve has been parallelized (multithreading). Therefore you need the lpthread library at linking time. By setting the OMP_NUM_THREADS environment variable you can specify how many CPUs you would like to use (see Section 2).
Next: Convergence criteria Up: Types of analysis Previous: Turbulent Flow in Open Contents guido dhondt 2012-10-06


Month: March 2021
Tutor Reflection & Tips
Each Math Motivators tutor brings a unique style to make a positive difference.
The Actuarial Foundation Announces the Finalists for the 2021 Modeling the Future Challenge
SCHAUMBURG, IL (March 23, 2021) – The Actuarial Foundation is proud to announce the finalists in the 2020-2021 Modeling the Future Challenge, a national scholarship…


CPI% v Fixed 3%
At The Lease Bureau we see the results of a lot of lease negotiations and lately we’ve noticed a trend towards fixed percentage Rent reviews as opposed to the traditional CPI % review.
So, we did some number crunching to compare the outcome based on the last 10 years figures.
I found the outcome interesting and I’m sure you will as well.
We assumed an initial annual Rent of $30,000 in 2009 and using the March Quarter CPI, here’s how it looks: –
Although it doesn’t look like much of a difference, consider this.
If we assume an 8% Yield, this means that a Property that was worth $375,000 in 2009 has gone up in value in 2019 to: –
$459,662 (using a CPI% Review method)
$503,963 (using a Fixed 3% Review method).
Quite a difference really.
As always if you have any questions, please give me a call.


Measurement and Geometry - Position is an approx. 1.5 hr mathematics incursion using environmental and outdoor themes to enrich and strengthen mathematics learning outcomes, specifically ‘Position’ MAG-17MG - using simple maps and grids to represent position and follow routes, including using compass directions.
Students will use GPS devices, compasses, school maps and orienteering games to extend their understanding of the 'Position' outcome of the mathematics syllabus in a fun and interactive way.
- Use simple maps and grids to represent position and follow routes.
- Determine the directions N, S, E, and W; NE, NW, SE, and SW given one of the directions.
- Describe the location of the object on a simple map using coordinates or directions.
Key syllabus outcomes
- uses simple maps and grids to represent position and follow routes, including using compass directions MA2-17MG
The Cross Curriculum Priorities area of ‘Sustainability’ is also a feature of this program.
During the program, students will develop knowledge and skills in:
- Using a key or legend to locate specific objects
- using given directions to follow a route
- using coordinates on simple maps to to describe position
- using a compass to find compass points
- using compass directions to describe the location of an object on a simple map
- working mathematically to discuss the use of grids in the environment
- use computer software involving maths position and paths
- create a simple map or plan using computer tools/software
- use simple coordinates in games.
On the day activities:
During the incursion, students will:
- Learn about the concept of 'position' using a compass and basic school map.
- Use school maps and compasses to take part in a playground orienteering challenge to strengthen their understanding of 'Position'.
- Use a GPS device to learn about the concept of Global Positioning System.
- Use Google MyMaps to create an individual orienteering challenge for classmates.
Pre visit and follow up resources
Pre visit activities
Activities prior to the delivery of the program will help prepare students for the day as well as link the program to the class program.
These could include:
- Watch YouTube Giving Directions
- Watch YouTube Co-Ordinates
Follow up activities
Pre and post vist resources PDF 99KB
- DoE - $10 per student (GST free).
- Non Government School $15 per student (GST free). Minimum cost of $600.
Incursion program downloads
Download these documents to help with your incursion planning:
- Program and teachers checklist (DOCX 1MB)
- Risk assessment plan (DOC 64KB)
- Measurement and Geometry - Position