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 [Algebra]  [Arithmetic]  [Geometry]  [Metrics]  [Special No.]  [Stat]  [Trig]  Algebra absolute value inequalities by Alan Androski ```From: Alan Androski To: Teacher2Teacher Public Discussion Date: 1 Nov 00 15:14:30 -0500 (EST) Subject: math tricks When solving absolute value inequalities: if the absolute value is greater than a number you must use the conjunction OR, when the absolute value is less than a number you must use the conjunction AND. To remember this just remember two words "GOR"-"LAND," which translate into "G(greater)OR" and "L(less than)AND." When I introduce this topic I tell students that we are about to enter "GOR-LAND." (no political implications intended) ``` equation solving by Greg Smith ```From: GREG SMITH To: Teacher2Teacher Public Discussion Date: 14 Jun 99 22:19:15 -0400 (EDT) Subject: MATH TRICKS FOR PRE-ALGEBRA & ALGEBRA I use many SMATHism's in class. Here are several: In equation solving, I emphasize that we always do "things" in pairs to maintain equality in mathematices. In equation solving, I emphasize that we need only perform one opposite to "get rid of" something. For equation solving when we want to undo something, we use B. S. well actually double B. S. to determine where to perform the operation the Back Side of Both Sides of the equation, or the Bottom Side of Both Sides of the equation. When you substitute, always substitute as a quantity. The verb always becomes the equal sign in equations. Formulas: A=(pi)r^2 Apple pies r square A=(pi)r*r Apple pies r round C = (pi)d Cherry pie delight I = p r t I "am" p-r-t pronounced I am pretty rt = d rt are d pronounced retard The three s's of equation solving: Substitute, simplify, solve I also teach equation solving by using equation solving cycle. I've not seen this anywhere else. An analogy in science would be the water cycle. One continuous repetitive cycle. < < < < < < < < < < < < < < < < < < < S First symbols of inclusion Last E I Second exponents 3rd V M Third multiplication and division 2nd L P Fourth addition and subtraction First O L > > > > > > > > > > > > > > > > S I F Y ``` factoring a trinomial with a lead coefficient by Lyle O'Neal ```From: Lyle O'Neal To: Teacher2Teacher Public Discussion Date: 2 Mar 00 14:16:07 -0500 (EST) Subject: re: math tricks >The "3R" Method (for factoring a trinomial with a lead coefficient: 1. "R"emove the lead coefficient, but don't throw it away. Multiply the constant with the lead coefficent. 2. Factor the remaining trinomial 3. "R"eplace the lead coefficent you removed. Put it in front of both x's. 4. "R"educe! Reduce the numbers in each set of parenthesis, as you would a fraction, to lowest terms. 5. Optional - use the FOIL method to check and see that I am right. *note: if the three numbers in the trinomial have a common factor it must be factored out in the beginning for the "3R" method to work. ``` factoring sum or difference of two cubes by Claudia Carter ```One trick that I have created is for factoring sum or difference of two cubes. x^3+y^3 = (x+y) then, we SOPPS the binomial to get the trinomial factor. S(quare) O(pposite sign) P(roduct) P(lus) S(quare) (x+y)(x^2 - xy + y^2) -Claudia, for the Teacher2Teacher service ``` quadratic formula by Beth Phillips ```From: Beth To: Teacher2Teacher Public Discussion Date: 6 Nov 00 23:02:39 -0500 (EST) Subject: The Quadratic Formula The quadratic formula can be a tricky equation to memorize when students first encounter it in Algebra. I rely on a favorite old song to help my students remember. Try singing the following lyrics to the tune of "Pop Goes the Weasel" x is equal to negative b plus or minus the square root of b squared minus 4ac ALL over 2a Twelve years ago I was taught this song, and I STILL hear the tune every time I use the quadratic formula! ``` quadratic formula by Kay Wilson ```From: Kay To: Teacher2Teacher Public Discussion Date: 11 Jan 00 15:22:38 -0500 (EST) Subject: Remember the quadratic formula To teach students to remember the quadratic formula, teach them to sing it to the tune of "PoP! Goes the Weasel" "X equals a negative b Plus or Minus the square root, Of b squared minus four a c All over 2 a" ``` quadratic formula by Lyle O'Neal ```From: Lyle O'Neal To: Teacher2Teacher Public Discussion Date: 2 Mar 00 14:16:07 -0500 (EST) Subject: re: math tricks >Quadratic Formula (sung to the tune of pop-goes-the-weasle: "x is equal to negative b, plus or minus the square root, of b squared minus 4ac, all over 2a" ``` solving inequalities involving absolute value by Greg Smith ```From: GREG SMITH To: Teacher2Teacher Public Discussion Date: 14 Jun 99 22:19:15 -0400 (EDT) Subject: MATH TRICKS FOR PRE-ALGEBRA & ALGEBRA When solving inequalities involving absolute value, the students and I have developed the following phrases to determine whether the two solution sets contain the word "and" or "or" in them: |x+5|> 6 "great OR" |x - 2| < 3 "less th AND" |x + 2| = 4 "equat OR" ``` [top] Arithmetic 9 times table by Alicia ```From: Alicia To: Teacher2Teacher Public Discussion Date: 29 Nov 00 13:36:47 -0500 (EST) Subject: Re: 9 times table and 11 times table tricks Another trick for the 9 times table up to 9x10 is to write the numbers 0-9 down the left hand side: 0 1 2 3 4 5 6 7 8 9 Then, repeat the process of writing the numbers 0-9, this time going UP the right side: 09 18 27 36 45 54 63 72 81 90 Now you have your 9's times table: 9 x 1 = 09 9 x 2 = 18 9 x 3 = 27 9 x 4 = 36 9 x 5 = 45 9 x 6 = 54 9 x 7 = 63 9 x 8 = 72 9 x 9 = 81 9 x 10 = 90 Have fun! ``` 9 times table by Jody Underwood ```From: Jody Underwood To: Teacher2Teacher Public Discussion Date: 17 Nov 00 10:56:56 -0500 (EST) Subject: 9 times table and 11 times table tricks I love math tricks. I remember learning these in the 5th grade from my student teacher, Miss Ansell. 9 times table: (This is hard to explain in words, but I'll try.) Open both your hands and face them to you. Put down your left thumb. This represents 9 x 1 = 9. (Notice there are 9 fingers in one "group". The groups will become more obvious in a minute.) Lift your thumb, and put down the pointer finger of your left hand. there's 1 finger on the left of the "down" finger, and 8 on the right. That represents 18, or 9 x 2. The 2 comes from the second finger. Raise all your fingers again, and put down the middle finger of your left hand. This gives you 2 fingers to the left of the down (third) finger, and 7 to the right of it. 9 x 3 = 27. Get it? It only works up until 9 x 10 = 90. I've shared this with adults who say they're lousy at their multiplication tables, and they are upset they didn't learn it in the 5th grade, too! -Jody ``` 11 (multiplication by) by Noorali Jiwaji ```From: Noorali Jiwaji To: Teacher2Teacher Public Discussion Date: 4 Nov 00 21:51:28 -0500 (EST) Subject: Multiplying by 11 MULTIPLICATION BY 11 For 2 digit numbers: Add the two digits and keep the answer in between the two digits. If the addition comes to more than 10 then carry over and add to the left hand digit. E.g. 68 x 11 = 6 (6+8) 8 = 6 (14) 8 =6+1 (4) 8 = 7 4 8 = 748 For more than two digits: Keep the extreme digits on their respective extreme sides, then pair off digits starting from the left and add the pairs from the right keeping the answer in their respective positions, carrying over if required. E.g. 7964 x 11 = 7 (7+9) (9+6) (6+4) 4 = 7 (16) (15) (10) 4 = 7 (16) (15+1) (0) 4 = 7 (16) (16) 0 4 = 7 (16+1) (6) 0 4 = 7 (17) 6 0 4 =7+1 (7) 6 0 4 = 8 7 6 0 4 = 87604. Quite amazing and satisfying, especially for large numbers! Dr. Noorali Jiwaji ``` 11 times table by Jody Underwood ```From: Jody Underwood To: Teacher2Teacher Public Discussion Date: 17 Nov 00 10:56:56 -0500 (EST) Subject: 9 times table and 11 times table tricks Here's one for the 11 times table: This only works (simply) for 11 times two-digit numbers. Let's say you want to multiply 11 by 23. Write down the 23, but with a space between the two numbers: 2 3 Add them up and put that number in the middle. 253 That's 11 x 23. If you have a carry, you have to add it into the left number, so it's not as clean as you would want, but it's still cute and fun for kids. You can extend this for 3 and more digit numbers, but carry overs get more complicated. I found it a lot of fun as a kid, and continued to play with it to extend it as far as I could. -Jody ``` change a mixed numeral to an improper fraction by Greg Smith ```From: GREG SMITH To: Teacher2Teacher Public Discussion Date: 14 Jun 99 22:19:15 -0400 (EDT) Subject: MATH TRICKS FOR PRE-ALGEBRA & ALGEBRA In class to change a mixed numeral to an improper fraction, I use the chant: the bottom times the side plus the top. ``` divisibility by Brenda Barrow ```From: Brenda Barrow To: Teacher2Teacher Public Discussion Date: 6 Jul 00 09:15:34 -0400 (EDT) Subject: Re: math tricks needed in Southern California I know you needed some math tricks before now but maybe you can use these for the future. To find out if a number is divisible by 9 you can add the digits of the number and if you get a multiple of 9 it is divisible by 9. As a matter of fact if you keep adding the digits of the numbers you get you will eventually get to a sum of 9. Ex. 459 Add the digits. 4+5+9 = 18 18 is a multiple of 9, so 458 is divisible by 9. If you add the 1 and the 8 in 18 you get 9. This also works for numbers that are divisible by 3 or 6 except you can get a sum of 3, 6 or 9. Of course the number has to be an even number in order to be divisible by 6. When you actually work with students have them make these discoveries instead of just telling them. It is very exciting for them and when they discover it they usually remember it. Also if students have a large number that they want to know if it is divisible by 9 they can try finding sums of 9 within the number and they will know it is divisible by 9. Ex. Is 853,164 divisible by 9? A student can see that 5+4 =9 and 6+3=9 and 8+1=9, so 853,164 must be divisible by 9. It's also divisible by 3 and 6. If I switched the last 3 digits around to make them 641 instead of 164 the number would no longer be divisible by 6 because all numbers that are divisible by 6 must be even numbers. That is not to say that all even numbers are divisible by 6, but that all numbers that are divisible by 6 must be even. This kind of thinking helps students develop number sense. I am a math resource teacher and math lead teacher at Monroe Elementary School in Norfolk, Va. Since I am a resource teacher I have the opportunity to work with 3rd, 4th and 5th graders most of the time. I do a lot of motivational things in math for the whole school so that our students feel that they are immersed in math. We are math lovers and not math phobics. Are you planning to teach? If I can be of assistance let me know. I wish you the best. Brenda ( < : } ``` division by Greg Smith ```From: GREG SMITH To: Teacher2Teacher Public Discussion Date: 14 Jun 99 22:19:15 -0400 (EDT) Subject: MATH TRICKS FOR PRE-ALGEBRA & ALGEBRA For division, I tell the students to put the "top-in's" and "left-overs" inside the refrigerator i.e., whatever is on top of the fraction or whatever is over on the left of the division sign is placed inside the long division symbol (dividend). This strategy also works with the calculator. ``` equivalent fractions by Robert Mehigan ```From: rob To: Teacher2Teacher Public Discussion Date: 17 Aug 00 02:35:14 -0400 (EDT) Subject: Re: math tricks needed in Southern California A student only today told me of a maths trick his Dad had passed on to him. (Good on you,parents!) Re: Equivalent fractions 1/2 = 3/x Say "3 divided by 1, times 2 = x" Simple and end of story. There is no playing around with guess and check methods, nor the hassle of setting up cross multiplication, nor more formal multiplying both sides. So what about x/2= 4/8 ? Well I figured out what to do...... Say "4 times 2, divided by 8 = x" The methods are a kind of shorthand that has to be learned, which may be ideal for the students who are weaker in conceptualising the more formal methods. Hope this helps. ``` fraction to a decimal by Cheryl Ireland ```From: Cheryl Ireland To: Teacher2Teacher Public Discussion Date: 13 Oct 00 12:45:34 -0400 (EDT) Subject: changing a fraction to a decimal When teaching students to change a fraction, 3/4 to a decimal, I tell them to associate the denominator with "dog" and the numerator with "Nancy." Denominator dog stays outside the house (the bracket) and Numerator Nancy goes inside the house. ``` mixed numbers to improper fractions by Amy Standring ```From: Amy Standring To: Teacher2Teacher Public Discussion Date: 16 Oct 00 18:37:41 -0400 (EDT) Subject: A Trick for changing MIXED NUMBERS to fractions To teach changing mixed numbers to improper fractions, I use the "LOOP" idea. The students make a "loop" by multiplying the whole number by the denominator, adding it to the numerator and placing all that over the denominator again. I use an arrow going around the mixed number to illustrate the idea. When i tell the kids to "make their loop" they know exactly what to do!! (Much more so than if i said "change to an improper fraction...") ``` percentage of change by Kimberley Girard ```You might be interested in a mnemonic device developed by my freshmen students for remembering how to do this type. They used "(new - old)/ old". This gives a decimal form which can easily be written as a percentage. Old refers to the original price (in your problem); new refers to the current price. A positive answer means there was a percentage of increase, a negative means a percentage of decrease. -Kimberley, for the T2T service ``` squares of numbers ending with the digit 5 by Anjali Poonia ```From: anjali To: Teacher2Teacher Public Discussion Date: 20 Oct 00 12:25:53 -0400 (EDT) Subject: SQUARES OF NUMBERS ENDING WITH DIGIT 5 THIS IS AN INTERESTING TRICK TO FIND SQUARES OF NUMBERS ENDING WITH THE DIGIT 5 e.g. 25*25= first digit(first digit+1)second digit*second digit =2(2+1)25=2(3)25=625. This is an example of two digit number. Here we have just miltiplied the first digit with the first digit added to one.Units &tens place will always be taken by the digit 25. The result of the product of the tens digit &its successor will always take hundreds or thousands place.Similarly we can find squares of numbers having more than two digits,but the thing to remember is that leaving the number in the units place the rest of the number is considered as a single number.Here too the units &the tens place will betaken by the digit 25 &the resultant product will take hundreds or thousands place depending on how big is the digit. Another e.g. with three digit 325.square of 325 will be 325*325=32(32+1)25=32(33)25=(1056)25=105625. 6125*6125=612(612+1)25=? ``` what to do with a zero in a fraction by Alan Androski ```From: Alan Androski To: Teacher2Teacher Public Discussion Date: 1 Nov 00 15:14:30 -0500 (EST) Subject: math tricks A great trick that a student taught me for remembering what to do with a zero in a fraction- it's called the happy and the sad man. Imagine two stick men created with a zero, a fraction bar and the number symbol. first one (drawing below): this is the happy man because he is standing upright. He is also happy because he can divide and get an answer. It is equal to zero. O - # second one (drawing below): this is the sad man because he is upside- down. He is also sad because he cannot divide. It is not equal to anything, it is undefined. # - O ``` [top] Geometry isosceles triangles by Dr. A.V. Manohara ```From: Dr.A.V.Manohara sharma To: Teacher2Teacher Public Discussion Date: 9 Aug 99 12:46:47 -0400 (EDT) Subject: coordinate geometry to see which triangle the three given lines form observe whether the slopes of the lines are like m, 1/m and 1 OR m, 1/m and -1 then the triangle should be isosceles ex. the lines 2x+3y+6=0, 3x+2y-1=0 and x-y+4=0 for and isosceles triangle as the slopes here are -2/3 , -3/2 and 1. ``` measure of the special segments of a circle by Deborah ```From: deborah To: Teacher2Teacher Public Discussion Date: 1 Jul 00 01:03:14 -0400 (EDT) Subject: Re: Circle theorems To teach finding the measure of the special segments of a circle we have a song to the tune of "Row, row your boat" It goes like this: Chord is part*part = part *part Secant is outside all = outside all Chord is part * part = part * part (chorus) Tangent squared = secant segment * outside I can usually teach this in a day and the students know how to apply the song to problems by the end of the class period. I demonstrate the problems along with the song and then the class sings and demonstrates. ``` supplementary and complimentary angles by Lynne Jacobsen ```From: Lynne To: Teacher2Teacher Public Discussion Date: 2 Sep 00 13:01:18 -0400 (EDT) Subject: Supplementary and Complimentary Angles I teach middle school students. My students know that supplementary and complimentary angles are angles that equal 90 degrees and 180 degrees, but they get confused as to which is which. They also know that 90 degree angles are right angles. So I tell them that a compliment is the right thing to do, and right angles equal 90 degrees, therefore complimentary angles are two angles that equal 90 degrees. Then they know that 180 degrees is the other one, supplementary. ``` supplementary and complimentary angles by Mary MacNeil ```From: Mary MacNeil To: Teacher2Teacher Public Discussion Date: 9 Nov 00 18:55:07 -0500 (EST) Subject: Re: Supplementary and Complimentary Angles "Complementary" - early in the alphabet, so = 90 degrees. "Supplementary" - later in the alphabet, so = 180 degrees. My middle school students show me 90 degrees with their arms (straight up, straight out - I'm fussy), then estimate various acute and obtuse angles with their arms. It's fun to do quickly - they look like they're going to fly. This also helps them to choose the appropriate scale on the protractor. Simple kinesthetic. ``` triangle names by Lynn Greenwade and students ```From: Lynn Greenwade To: Teacher2Teacher Date: Oct 23, 2006 at 16:19:27 Subject: triangle names My adult GED students jumped on the mnemonic PEMDAS, and they want one for remembering the names of triangles. In particular, isosceles and scalene give them trouble. Here is what we came up with: Equilateral triangles have 3 sides and 3 angles equal. Isosceles triangles have 2 sides and 2 angles equal. Scalene triangles have 0 sides and 0 angles equal. So, to remember them in that order, EIS, "Eat ice slowly". ``` two given lines cut the coordinate axes in four concyclic points or not by Dr. A.V. Manohara ```From: Dr.A.V.Manohara sharma To: Teacher2Teacher Public Discussion Date: 9 Aug 99 12:53:33 -0400 (EDT) Subject: coordinate geometry to see whether the two given lines cut the coordinate axes in four concyclic points or not just see whether the product of coefficients of x in both the equations is equal to that of coefficients of y. if the given lines are ax+by+c=0 and bx+ay+d=0 they cut the axes in concyclic points. ``` [top] Metric Measurement metric conversions by Errol LaGuerre ```From: Errol LaGuerre To: Teacher2Teacher Public Discussion Date: 21 Jun 99 01:45:26 -0400 (EDT) Subject: Conversions in metric my milli cat centi died deci unusually unit drinking deca hot hecta ketchup kilo e.g. Convert 10 decameters to centimeters. Set up the columns as shown below so that the ones column comes under deca. Move the decimal point to the right of the column with centi. Add zeros until you are under centimeters. That is your answer. kilo hecta deca unit deci centi milli 1 0 kilo hecta deca unit deci centi milli 1 0 0 0 0 i.e. 10 dam = 10 000 cm Try, as an exercise, to convert from small units to larger units. ``` metric conversions by Jim Wenk ```From: Jim Wenk To: Teacher2Teacher Public Discussion Date: 26 Jul 00 02:26:04 -0400 (EDT) Subject: Re: Conversions in metric Another play on the metric conversions is: "King Henry Died Monday Drinking Chocolate Milk" Km Hm Dam M Dm Cm Mm To convert... 3.75 Hm = ______ Cm It's 4 jumps to the right from Hm to Cm, simply move the decimal 4 jumps to the right. 3.75 Hm = 37,500. Cm To convert... 0.59 Dm = _______ Hm It's 3 jumps to the left from Dm to Hm, simply move the decimal 3 jumps to the left. 0.59 Dm = 0.00059 Hm ``` metric systems by Dawn ```From: Dawn To: Teacher2Teacher Public Discussion Date: 13 Nov 00 17:52:43 -0500 (EST) Subject: metric conversion This is just another way to remember the order to convert in the metric systems, and it gets away from just using meters. Kahn's kilo Hot hecto Dogs deca Uses units (meter, liter, or grams) Dead deci Cow centi Meat milli ``` [top] Special Numbers e to 15 decimal places by Matt Collins ```From: Matt Collins To: Teacher2Teacher Public Discussion Date: 2 Aug 00 10:50:09 -0400 (EDT) Subject: Remembering e to 15 decimal places Here's a cool way to remember e to 15 decimal places: e=2.718281828459045... Andrew Jackson was the 7th president, elected in 1828 to two terms. Then tack on the 45-90-45 right triangle. Feel free to share with history teachers in your school. Matt ``` feet in a mile by Bob Stanarrow ```From: Bob Stanarrow To: Teacher2Teacher Public Discussion Date: 7 Mar 01 17:38:50 -0500 (EST) Subject: How to remember how many feet in a mile I figured out a way to remember how many feet are in a mile. Just say to yourself 5 tomatoes. Really there are 5,280 feet in a mile, so you can remember that by saying 5 tomatoes. 5 to mat oes ( 5 ) ( 2 )( 8 )( 0 ) ``` pi - first eight digits of by Alan Androski ```From: Alan Androski To: Teacher2Teacher Public Discussion Date: 1 Nov 00 15:14:30 -0500 (EST) Subject: math tricks To get the first eight digits of pi, count the number of letters in each word of this phrase: May(3) I(1) have(4) a(1) large(5) container(9) of(2) coffee(6)? ``` [top] Statistics Central tendencies by Nancy Patrizio ```From: Nancy To: Teacher2Teacher Public Discussion Date: 3 Mar 00 22:11:53 -0500 (EST) Subject: Central tendencies To help my middle grade students remember range, mean, median and mode- Range - I tell the them to think of a gas range that has high and low temperatures. This helps them to remember to subtract the lowest from the highest number. Mean - the "a" in mean stands for the average or my students like to think of it as "the mean teacher gives you your average of your grades"!. Median - think "mid" - the number or numbers in the middle. Mode - think "most" - the number or numbers that occur the most. It sounds so simple but it works! is/of works wonders when working with percentages When multiplying or dividing numbers by 10, 100, 1000,...,use MR DL(Mister Doll) ;when multiplying, move the decimal to the right; when dividing, move the decimal to the left. When multiplying or dividing numbers by.1, .01, .001,...,use DR ML(Doctor Mole) ;when multiplying, move the decimal to the left; when dividing, move the decimal to the right. ``` [top] Trigonometry definition of a logarithm by Marielouise Derwent Date: Oct 23, 1998 at 15:04:14 Subject: Re: Math Tricks ```One of the ideas that I have used for a long time is for the definition of a logarithm: If (base)^(Exponent) = (Number) then, log (Number) to the (base) = Exponent b^E = N, if log N to the b = E. When doing transformations of functions remember: RST! Do your Reflections first, then your Size changes of compressing or stretching and then your Translations of sliding up, down, right and left. This helps students when they are trying to decide what the equation of a transformation is when looking at a graph. They then do the RST in reverse order: Translate first, then change sizes and then reflect over x-axis or y- axis. -Marielouise, for the Teacher2Teacher service ``` positive trig. values in the quadrants by Maree McCarthy ```From: Maree To: Teacher2Teacher Public Discussion Date: 25 Oct 00 10:07:03 -0400 (EDT) Subject: Trigonometry For the positive trig. values in the quadrants, All Sexy Tom Cats works great - if you do not mind the giggles! ```

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