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A worksheet is a sheet of paper, or on a computer, on which problems are worked out or solved and answers recorded.
Students in a school may have 'fill-in-the-blank' sheets of questions, diagrams, or maps to help them with their exercises. Students will often use worksheets to review what has been taught in class. A worksheet generator is a software program that generates problems, particularly in mathematics or numeracy. Such software is often used by teachers to make classroom materials and tests.
In accounting a worksheet often refers to a loose leaf piece of stationery from a columnar pad, as opposed to one that has been bound into a physical ledger book. From this, the term was extended to designate a single, two-dimensional array of data within a computerized spreadsheet program. Common types of worksheets used in business include financial statements, such as profit and loss reports. Analysts, investors, and accountants track a company's financial statements, balance sheets, and other data on worksheets.
In the Microsoft spreadsheet program Excel, a single document is known as a 'workbook' and by default each workbook contains three arrays or 'worksheets'. One advantage of such programs is that they can contain formulae so that if one cell value is changed, the entire document is automatically updated, based on those formulae.
Math wars is the debate over modern mathematics education, textbooks and curricula in the United States that was triggered by the publication in 1989 of the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM) and subsequent development and widespread adoption of a new generation of mathematics curricula inspired by these standards.
While the discussion about math skills has persisted for many decades, the term "math wars" was coined by commentators such as John A. Van de Walle and David Klein. The debate is over traditional mathematics and reform mathematics philosophy and curricula, which differ significantly in approach and content.
Advocates of reform
The largest supporter of reform in the US has been the National Council of Teachers of Mathematics.
One aspect of the debate is over how explicitly children must be taught skills based on formulas or algorithms (fixed, step-by-step procedures for solving math problems) versus a more inquiry-based approach in which students are exposed to real-world problems that help them develop fluency in number sense, reasoning, and problem-solving skills. In this latter approach, conceptual understanding is a primary goal and algorithmic fluency is expected to follow secondarily.
A considerable body of research by mathematics educators has generally supported reform mathematics and has shown that children who focus on developing a deep conceptual understanding (rather than spending most of their time drilling algorithms) develop both fluency in calculations and conceptual understanding. Advocates explain failures not because the method is at fault, but because these educational methods require a great deal of expertise and have not always been implemented well in actual classrooms.
A backlash which advocates call "poorly understood reform efforts" and critics call "a complete abandonment of instruction in basic mathematics" resulted in "math wars" between reform and traditional methods of mathematics education.
Critics of reform
Those who disagree with the inquiry-based philosophy maintain that students must first develop computational skills before they can understand concepts of mathematics. These skills should be memorized and practiced, using time-tested traditional methods until they become automatic. Time is better spent practicing skills rather than in investigations inventing alternatives, or justifying more than one correct answer or method. In this view, estimating answers is insufficient and, in fact, is considered to be dependent on strong foundational skills. Learning abstract concepts of mathematics is perceived to depend on a solid base of knowledge of the tools of the subject.
Supporters of traditional mathematics teaching oppose excessive dependence on innovations such as calculators or new technology, such as the Logo language. Student innovation is acceptable, even welcome, as long as it is mathematically valid. Calculator use can be appropriate after number sense has developed and basic skills have been mastered. Constructivist methods which are unfamiliar to many adults, and books which lack explanations of methods or solved examples make it difficult to help with homework. Compared to worksheets which can be completed in minutes, constructivist activities can be more time consuming. (Reform educators respond that more time is lost in reteaching poorly understood algorithms.) Emphasis on reading and writing also increases the language load for immigrant students and parents who may be unfamiliar with English.
Critics of reform point out that traditional methods are still universally and exclusively used in industry and academia. Reform educators respond that such methods are still the ultimate goal of reform mathematics, and that students need to learn flexible thinking in order to face problems they may not know a method for. Critics maintain that it is unreasonable to expect students to "discover" the standard methods through investigation, and that flexible thinking can only be developed after mastering foundational skills.
Some curricula incorporate research by Constance Kamii and others that concluded that direct teaching of traditional algorithms is counterproductive to conceptual understanding of math. Critics have protested some of the consequences of this research. Traditional memorization methods are replaced with constructivist activities. Students who demonstrate proficiency in a standard method are asked to invent another method of arriving at the answer. Some teachers supplement such textbooks in order to teach standard methods more quickly. Some curricula do not teach long division. Critics believe the NCTM revised its standards to explicitly call for continuing instruction of standard methods, largely because of the negative response to some of these curricula (see below).
Examples of reform curricula introduced in response to the 1989 NCTM standards and the reasons for initial criticism:
- Mathland (no longer offered)
- Investigations in Numbers, Data, and Space is criticized for not containing explicit instruction of the standard algorithms
- Core-Plus Mathematics Project, initially accused of placing students in remedial college math courses, a report that was later challenged.
- Connected Mathematics, criticized for not explicitly teaching children standard algorithms, formulas or solved examples
- Everyday Math , criticized for putting emphasis on non-traditional arithmetic methods.
Critics of reform textbooks say that they present concepts in a haphazard way. Critics of the reform textbooks and curricula support traditional textbooks such as Singapore Math, which emphasizes direct instruction of basic mathematical concepts, and Saxon math, which emphasizes perpetual drill.
Reform educators have responded by pointing out that research tends to show that students achieve greater conceptual understanding from standards-based curricula than traditional curricula and that these gains do not come at the expense of basic skills. In fact students tend to achieve the same procedural skill level in both types of curricula as measured by traditional standardized tests. More research is needed, but the current state of research seems to show that reform textbooks work as well as or better than traditional textbooks in helping students achieve computational competence w
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Answers:Hey, some people are just mean and shortsighted, but we live in a free country and they are free to express an opinion. But the rest of us are free to wholly ignore (recommended) or disagree. I say ignore, because often some will post something ugly in order to start an argument. They get off on the conflict. I try not to feed them. Life's too short for that kind of silliness. He strikes me as being one of those navel-gazing keyboard jockeys looking for a following or a fight. Such self-involved types write on forever about pretty much nothing at all and insult anyone who disagrees with them. If he thinks he's smart, let him enjoy his delusion. No one's going to convince him otherwise, anyway! ;>) Honestly, he's NOT worth your time!
Answers:always (by definitions of square, rectangle and rhombus) --------------------------------------- sorry can't understand what you want --------------------------------------- sometimes (the opposite angles of a rhombus are equal thus only if it is a square) ---------------------------------------- sometimes (always congruent but perpendicular only if it is a square) ---------------------------------------- never (the diagonals of a rhombus bisect each other perpendicularly so for the diagonals, the side is 13cm) ---------------------------------------- you have AE = 9 cm (as the diagonals bisect each other perpendicularly) and angle ABE = 42 deg (the diagonals bisect the angles between two subsequent sides) thus the side = 9 / cos 42 = 12.1 -------------------------------------------- AC = 10 cm so BD = 10 cm (as the diagonals of a rectangle are congruent) so by Pythagoras theorem, 10^2 = (x + 2)^2 + (x + 4)^2, thus x = -3 + (89)^(1/2) or -3 - (89)^(1/2) which is rejected. thus the answer is EC + ED + CD = 5 + 5 + 1 + (89)^(1/2) = 11 + (89)^(1/2) i have triple checked my answer. check if you have typed the question correctly this is the method though. ------------------------------------------- AC = 20 BC = AD = 12 = 2x + y by Pythagoras theorem, you get 3x - y = 12 thus x = 4.8 and y = 2.4 ------------------------------------------ I'll tell you how to proceed as the value of RC is not typed. the subsequent angles at the point of intersection of the diagonals are supplementary. draw the perpendicular bisectors of the sides, they bisect the angles at the center X. let them intersect RE, EC, CT and RT at L, M, N and O now, RX = EX = CX = TX = RC/2 and angle RXO = 30 deg and angle RXL = 60 deg Use trigonometry to find RO (=RX cos30) and RL (=RX cos60). RT = 2 RO = EC RE = 2 RL = CT I will deal the same problem using the property of parallel lines (this is faster) after drawing the perpendicular bisectors, LN and MO you see that they are parallel to sides EC and CT respectively, and by corresponding angle property of parallel lines and transverse lines, angle RXO = angle RCT = 30 and angle RCE = 60 deg by complementary angle property of angles RCT and RCE again using trigonometry, RT = EC = RC cos30 and RE = CT = RC cos60 you may use pythagoras theorem in some places, but trigonometry is easier. ------------------------------------------------- the side of the square = diagonal / cos45 = 2^(1/2) * 18 thus the perimeter = 72 * 2^(1/2) = 101.8 as for the rhombus, draw the diagonal RO, they bisect perpendicularly at X. now angle RHX = 30 deg thus RH = HX / cos30 = 2 * 9 / 2^(1/2) = 6 * 3^(1/2) thus the perimeter = 24 * 3^(1/2) = 41.5 clearly the rhombus has the smaller perimeter.
Answers:Typically tests like these are timed tests. You may get 5 minutes to answer as many questions as possible and there may be 150 of them. And usually they are low level math with some minor algebra. Examples: 4+3-5=? 5=6-? (5)6=? You don't need to finish it all. What they are looking for is the amount you get done and the accuracy of your answers. These are called in my book "i'm not an idiot tests". They aren't looking you to show your math genius, just making sure you are somewhat educated and not going to mess up the simplest procedure.
Answers:You hit the nail on the head - faith. Faith is the issue that makes people delusional, ignorant and in severe cases causes airplanes to fly into buildings. The world would be a much better place if people did not have strong faith in books that contain so much evil as the Bible and Quran do. @Esther - you are either ignorant, uneducated or hiding from the truth. Your logic that the Bible is true thus evolution is false such an illogical statement. Maybe I am wrong and you have some amazing new evidence for the following: 1 - Plenty of evidence of the Bible being the real word of God - please provide (real evidence, not the typical generalizations or prophesies from before the Bible was written). Please realize what evidence really is. 2 - Proof of Creationism 3 - Explanation to show all the real evidence of evolution false. All the fossils, DNA evidence and tons of scientific backing proving evolution as a fact much be refuted by real scientists(people educated in biology to the PhD level). Also your comments: It is not uneducated to believe in something that you don't believe in. It is uneducated to pitch a fit because people believe something differently than you do. - The comments that you stated were uneducated. Anyone with a basic biology education knows that it is a FACT that you are uneducated in biology. You may be educated in other subjects, but you are very uneducated in biology and evolution and logic. (Unless of course you provide new revolutionary evidence to the contrary that has just been discovered - but I doubt you are on the leading edge of science...just a guess) Also if the Bible is the true word of God, please explain why you worship a child killer? 2 Kings 2 : 23-24. There is no excuse for this and proves how delusional or ignorant followers are. And this is just one example of many.