The Secret to Teaching Math Facts: Number Bonds Below you will see why I think teaching math basics with number bonds is the best way for your homeschoolers to learn math. Over our last four years of homeschooling, I have used several different math curricula. Some I liked better the others, but they all had their own strengths and weaknesses. One of the strengths of one particular curriculum we use, Singapore Math, is their method of teaching basic math facts. Now, I realize this is just my unprofessional opinion, but as a self-professed math geek, I truly believe number bonds are (likely) the best ways to teach math facts. Why? They're simple. How Number Bonds Work If you're not familiar with what number bonds are, allow me to illustrate. As in the example for addition on the left, the student is taught to recognize that the number 7 is made of 3 and 4. If you'd like to teach your children number bonds, you can download my Number Bond Chart and Worksheet set here. Number Bond Flashcards Teaching Algebraic Thinking
Eureqa | Cornell Computational Synthesis Laboratory Eureqa is a breakthrough technology that uncovers the intrinsic relationships hidden within complex data. Traditional machine learning techniques like neural networks and regression trees are capable tools for prediction, but become impractical when "solving the problem" involves understanding how you arrive at the answer. Eureqa uses a breakthrough machine learning technique called Symbolic Regression to unravel the intrinsic relationships in data and explain them as simple math. Using Symbolic Regression, Eureqa can create incredibly accurate predictions that are easily explained and shared with others. Over 35,000 people have relied on Eureqa to answer their most challenging questions, in industries ranging from Oil & Gas through Life Sciences and Big Box Retail. Eureqa One Page Overview (.pdf) »Visit the Eureqa Community » Eureqa utilizes a machine learning technique called Symbolic Regression to distill raw data into non-linear mathematical equations.
Adding Signed Numbers - Lesson 101 Video Adding Signed Numbers - Lesson 101 Hi, I’m Larry. This is the video from Lesson 101 on my website, adding signed numbers. I you have difficulty understanding this lesson you will have trouble with all the materials that follows because it builds up on this lesson especially when we get to Algebra we’re going to be using the skill again and again, so make sure that you don’t have any difficulty with it whatsoever. Up until now I’ve been working with adding positive numbers and we haven’t any trouble with that. Now, very often students say something like, “Wow! Now, I like to think of negative numbers as a debts or how much money I owe, so if I say negative three I’ll think of that as I owe $3.00. For this example I’d like to add 3 + -5. Here’s how I like to teach you. Okay, so the situation is I have $3.00 but I owe you $5.00. I still owe you $2.00 and the way I will show that is by writing a -2 the negative meaning I owe you money, I still owe you money.
What does 0^0 (zero raised to the zeroth power) equal? Why do mathematicians and high school teachers disagree? « Ask a Mathematician / Ask a Physicist Clever student: I know! Now we just plug in x=0, and we see that zero to the zero is one! Cleverer student: No, you’re wrong! You’re not allowed to divide by zero, which you did in the last step. which is true since anything times 0 is 0. Cleverest student : That doesn’t work either, because if then is so your third step also involves dividing by zero which isn’t allowed! and see what happens as x>0 gets small. So, since = 1, that means that High School Teacher: Showing that approaches 1 as the positive value x gets arbitrarily close to zero does not prove that . is undefined. does not have a value. Calculus Teacher: For all , we have Hence, That is, as x gets arbitrarily close to (but remains positive), stays at On the other hand, for real numbers y such that , we have that That is, as y gets arbitrarily close to Therefore, we see that the function has a discontinuity at the point . but when we approach (0,0) along the line segment with y=0 and x>0 we get Therefore, the value of that will make the function ! . as
Integer Number Line In this lesson,we will look at integers and the number line. Related Topics: More Lessons on Integers Integer Worksheets Integer Games Integers Integers consist of negative integers, zero and positive integers. Example: 0 is an integer but is neither positive nor negative. Negative numbers have a ‘–’ sign before them. Example: –3 is read as “negative three” +6 or 6 is read as “positive six” or “six” Opposite of a Number The opposite of a number is the number with the sign changed. The opposite of 4 is –4 The opposite of –6 is 6 Since 0 is neither positive nor negative, the opposite of 0 is also 0. Number Line Integers can be represented on the number line. An integer on the horizontal number line is greater than the number on its left and less than the number on its right. Example: –1 is greater than –2 and less than 0. We can also write it as –1 > –2 and –1 < 0. Recall that “>” means greater than and “<” means less than. On the number line, moving to the right is positive. OML Search
Quotes « Let ε < 0. The four branches of arithmetic — ambition, distraction, uglification and derision. (Lewis Caroll, Alice in Wonderland) As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality. (Albert Einstein) If you can’t explain what you are doing to a nine-year-old, then either you still don’t understand it very well, or it’s not all that worthwile in the first place. Only two things are infinite: the universe and human stupidity, and I’m not sure about the former. The two most common things in the Universe are hydrogen and stupidty. I’ve heard that the government wants to put a tax on the mathematically ignorant. Old mathematicians never die; they just lose some of their functions. I turn away with fear and horror from this lamentable plague of functions which do not have derivatives. Mathematics is a game played according to certain simple rules with meaningless marks on paper. Physics is much too hard for physicists.
s Math Resources - Integers: Operations with Signed Numbers Have you ever been to a party like this? Everyone is happy and having a good time (they are ALL POSITIVE). Suddenly, who should appear but the GROUCH (ONE NEGATIVE)! The grouch goes around complaining to everyone about the food, the music, the room temperature, the other people.... What happens to the party? Everyone feels a lot less happy... the party may be doomed!! But wait... is that another guest arriving? What if another grouch (A SECOND NEGATIVE) appears? Now that the two grouches are together the rest of the people (who were really positive all along) become happy once again. The moral of the story is that (at least in math, when multiplying or dividing) the number of positives don't matter, but watch out for those negatives!! To determine whether the outcome will be positive or negative, count the number of negatives: If there are an even number of negatives -and you can put them in pairs- the answer will be positive, if not... it'll be negative:
The Narrow Road » If We Taught English the Way We Teach Math Imagine that your only contact with “English” as a subject was through classes in school. Suppose that those classes, from elementary school right through to high school, amounted to nothing more than reading dictionaries, getting drilled in spelling and formal grammatical construction, and memorizing vast vocabulary lists — you never read a novel, nor a poem; never had contact with anything beyond the pedantic complexity of English spelling and formal grammar, and precise definitions for an endless array of words. You would probably hate the subject.You might come to wonder what the point of learning English was. In response perhaps the teachers and education system might decide that, to help make English relevant to students, they need to introduce more “Applied English”. This means teaching English students with examples from “real life” (for varying degrees of “real”) where English skills are important, like how to read a contract and locate the superfluous comma.
The Thirty Greatest Mathematicians Click for a discussion of certain omissions. Please send me e-mail if you believe there's a major flaw in my rankings (or an error in any of the biographies). Obviously the relative ranks of, say Fibonacci and Ramanujan, will never satisfy everyone since the reasons for their "greatness" are different. Following are the top mathematicians in chronological (birth-year) order. Earliest mathematicians Little is known of the earliest mathematics, but the famous Ishango Bone from Early Stone-Age Africa has tally marks suggesting arithmetic. Early Vedic mathematicians The greatest mathematics before the Golden Age of Greece was in India's early Vedic (Hindu) civilization. Top Thales of Miletus (ca 624 - 546 BC) Greek domain Thales was the Chief of the "Seven Sages" of ancient Greece, and has been called the "Father of Science," the "Founder of Abstract Geometry," and the "First Philosopher." Apastambha (ca 630-560 BC) India Pythagoras of Samos (ca 578-505 BC) Greek domain Tiberius(?)
Online texts Professor Jim Herod and I have written Multivariable Calculus ,a book which we and a few others have used here at Georgia Tech for two years. We have also proposed that this be the first calculus course in the curriculum here, but that is another story.... Although it is still in print, Calculus,by Gilbert Strang is made available through MIT's OpenCourseWare electronic publishing initiative. Here is one that has also been used here at Georgia Tech. Linear Methods of Applied Mathematics, by Evans Harrell and James Herod. Yet another one produced at Georgia Tech is Linear Algebra, Infinite Dimensions, and Maple, by James Herod.
Math Help An Engineers Quick References to Mathematics Algebra Help Math SheetThis algebra reference sheet contains the following algebraic operations addition, subtraction, multiplication, and division. It also contains associative, commutative, and distributive properties. There are example of arithmetic operations as well as properties of exponents, radicals, inequalities, absolute values, complex numbers, logarithms, and polynomials. Calculus Integrals Math Sheet This calculus integral reference sheet contains the definition of an integral and the following methods for approximating definite integrals: left hand rectangle, right hand rectangle, midpoint rule, trapezoid rule, and Simpson’s rule.
OSWINS - Mathematics Content: calculators , graphs , computational tools , math games , algebra , courses , tutorials and problem solving Quotes "The understanding of mathematics is necessary for a sound grasp of ethics." - Socrates "Mathematicians do not study objects, but relations between objects. "I will not define time, space, place and motion, as being well known to all." - Sir Isaac Newton "So far as the theories of mathematics are about reality, they are not certain; so far as they are certain, they are not about reality." - Albert Einstein "The creator of the universe works in mysterious ways. (GPL) (Free) (Free, Geogebra License) (GPL) (Artistic License) (Free) (Free) (Free) (GPL) (GPL)