Tag Archives: math

Need a boost on the SAT Math section? While our Intensive Classes deliver a full suite of content and strategy for every section of the SAT and ACT in a group setting, our Test Boosts focus exclusively on just one at a time. During this two-hour SAT Math Boost, we’ll run students through a lightning lesson on the arithmetic, algebra, geometry, and trig tested on the exam while providing our innovative strategies for solving math problems as quickly, easily, and accurately as possible. Then, we’ll all work through the Math No Calculator and Calculator sections of an official released SAT to make sure students understand and retain what they’ve learned. Chariot Learning’s Test Boosts are perfect both for students just starting to prep and those in our classes or tutoring programs looking for a little more focused practice for the upcoming SAT. We usually limit enrollment to 10 students, ensuring…

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Happy Pi Day! I can think of no better way to celebrate this magical mathematical holiday than by talking math, specifically the most challenging aspects of one of the most challenging math tests any American student ever takes. Make no mistake: since its most recent revision, the SAT is more of a math test than it’s ever been. If you’re looking for tips on tackling math on the SAT, you already know how much this exam differs from math tests in school. You may already be aware that the SAT tests math from basic arithmetic through advanced topics in algebra 2 and trigonometry. If you’re lucky, you’ve also learned that SAT math focuses heavily on problem solving, particularly through tricky word problems. Still, real success on the SAT Math section requires much more in the way of content knowledge and strategic insight. To speed your progress, I asked a few…

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Life comes with few guarantees, but you can always count on problems. In a long life, you’ll encounter lots and lots of problems, some easy, some hard, but all requiring solutions. In this regard, George Pólya’s How to Solve It: A New Aspect of Mathematical Method doesn’t simply serve as a guide to tackling math problems but also as a handbook for managing challenges in any area. Polya wisely recommends that we always begin by understanding the problem, followed by carefully devising a solution. Unfortunately, the process does not end there. We still have to do the work to implement the solution. “To devise a plan, to conceive the idea of the solution is not easy. It takes so much to succeed: formerly acquired knowledge, good mental habits, concentration upon the purpose, and one more thing; good luck. To carry out the plan is much easier, what we need is…

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“Ignorance more frequently begets confidence than does knowledge: it is those who know little, not those who know much, who so positively assert that this or that problem will never be solved…” Certainty in this complex and confusing conditions can be hard to come by. Sometimes, we cannot know definitively whether we possess sufficient evidence or understanding to make correct choices, yet still we must choose. Such is the uncertain fate of those who tackle standardized test math! Math on exams like the SAT and ACT frustrate test takers for a myriad of reasons, from convoluted word problems to complex or unexpected concepts. Sometimes devising the right solution to a problem seems impossible, while, at other times, we don’t even fully understand the problem. These levels of extreme uncertainly can be considered features of standardized test design, rather than flaws. After all, the test makers channel tremendous knowledge, expertise, and…

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A problem, by definition, needs to be solved. Alas for many, effective solution methods do not include crying, complaining, or ignoring the situation. In fact, problem solving often depends on methods and approaches outside our ordinary routine. Good old George Pólya knew a thing or two about problems and solutions. His masterpiece of mathematical heuristics, How to Solve It: A New Aspect of Mathematical Method, maps out the four essential steps to solving problems. We must always start, of course, by understanding what the problem really is. How else can you solve it? But the second and perhaps most critical step is not, as many believe, to jump right in and start making things happen. Instead, take a moment to come up with a plan about how best to solve the problem: “We have a plan when we know, or know at least in outline, which calculations, computations, or constructions…

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“It is foolish to answer a question that you do not understand. It is sad to work for an end that you do not desire. Such foolish and sad things often happen, in and out of school…” Into every life, it is said, a little rain must fall. Farmers and firefighters may take comfort in the inevitability of precipitation, but most others see an unanticipated deluge for what it is: a problem. Everywhere you look–on tests, in school, throughout life–you find problems. Problems, by their very nature, require solving. Unfortunately, many of us don’t really have a strategy to solve problems apart from painful trial and error. Those who study heuristics, however, have a distinct advantage. A heuristic can be any practical approach to problem solving, learning, or discovery. George Pólya, the Hungarian master of heuristics, systematized problem solving with unparalleled lucidity. His influential work, How to Solve It: A…

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