Susan Cantey has taught mathematics for over thirty years at the high school and college levels. She has been writing songs, mainly Christian themed songs for church, since the 1970's. A few years ago she realized that in addition to visual learning, many students could benefit from auditory learning. That thought birthed her two former CD's: The Tree of Calculus and Pre-Calc! This CD of Algebra songs and it's companion, Algebra Vol. 2, contain songs about almost every conceivable algebra topic. Teachers can use these songs to liven up their classes. Parents can purchase them for their kids to augment studying for exams. There are many styles of music from rap to classical - something for every taste. Susan has worked hard to make the melodies catchy and the lyrics memorable. Hundreds of students are enjoying (and learning with) Susan's Calculus and PreCalculus songs. Algebra is even more important and ubiquitous. Join in the fun! Buy both volumes today. Lyrics: Happy Snappy Algebra by Susan Cantey On the road I often think "How long until I sleep?" Then I see how many miles are left, And divide by my vehicle's speed, But when I'm driving in the car, And junior says "Are we there yet?" If daddy answers "About an hour," He's not doing algebra. Happy snappy algebra, Do it all the time, Happy snappy algebra, It's so fine. Once I needed some cement, So I went to the store, Bags came in many sizes, Forty, eighty pounds or more, So I went back home to measure, Used my calculator, No need to be perturbed, My algebra was superb. (chorus) Let's party! Let's have a pizza party, How many should I buy? (I don't know.) A small one feeds 15, A large, 25. I don't like these cell phone people, They have too many plans, They try to make me pay a lot, What kind of fool do they think I am? So I drew some graphs before I bought, Decided how many minutes I ought To use each day, each month, and then I thought Algebra helps me a lot. (repeat chorus twice) Adding Signed Numbers By Susan Cantey When adding signed numbers, Think of it as cash, Negative, you owe someone, Positive, you have, The answer is the balance Ahead or behind, You're in the black when you're positive, Red's the other kind. Positive plus positive is always positive, Negative plus negative is always negative, But when you're adding one of each, Do yourself a favor, Subtract their magnitudes And keep the sign of the one that's "greater." When adding signed numbers, Never get uptight, Negative moves left, Positive moves right, Always start at zero, Then take one step at a time, You're standing on the answer, When you walk the number line. (chorus) 8 + -6 is 2, Cause 8 has the greater magnitude, -9 + 5 's -4, Cause between the two, 9 is more, -5 + 2 's -3, It quite elementary. Some people only like To memorize the rules, But in my opinion, Rules are rather cruel, If you use a model That makes some sense to you, Then you'll be the master Of signed numbers when you're through. (chorus) Subtracting Signed Numbers by Susan Cantey 8 - 5 is 3, that's easy, 5 - 8 is negative 3, Because you're taking more away than you have, you see, Beginners need to re-write it as addition, And though that could be the tradition, You won't need to do that when you're done. The opposite of opposite is back to positive, I'm not sure why that's not obvious, Like a switch that goes off and on inside your head, When you subtract a negative number, Taking away a negative number, Just like adding a positive value instead. Subtraction, Subtraction, The opposite reaction, Take away a plus and it's a minus, Take away a minus, it's a plus, Subtraction, Subtraction, Opposite reaction, If you know how to add then you can subtract. 12 - -3 's the same as, 12 + 3, so let's be fearless, Two negatives in a row Make a big plus sign, -7 - -2 written, Is -7 + 2; that's a given, And we know that equals negative 5, (chorus) The opposite of opposite is back to positive, I'm not sure why that's not obvious, Like a switch that goes off and on inside your head, When you subtract a negative number, Taking away a negative number, Just like adding a positive value instead. Multiplying Signed Numbers By Susan Cantey Every child can multiply With positives preoccupied, They know their times, four fives and nines, Stay positive and they-re just fine. When you have a negative Times positive; don't ever quit, You know the answer must exist, It's negative, oh yeah, that's it. Now a negative times a negative Is often missed, seems illigit, But if you just submit a list, The pattern goes something like this. -2 times 2 is -4, -2 times 1 is -2, -2 times 0 is zero, each answer is increased by 2, So -2 times -1, it's true, Has to be positive 2, Now let's review. A positive times positive is positive, A negative times positive is negative, A negative times negative is positive, It's a switch with a twist of two opposites. Yo, hello, just go with the flow, All of my knowledge I bestow, I'm preoccupied and fortified; I'll tell you why I'm satisfied, I'm inclined to multiply: I'm a pro, a dynamo. (repeat the first three stanzas) 2 times -3 is -6, 1 times -3 is -3, 0 times -3 is zero; each answer is increased by 3, Are you listening to me? -1 times -3 is positive 3. A positive times positive is positive, A negative times positive is negative, A negative times negative is positive, It's a switch with a twist of two opposites. Commutative Property by Susan Cantey The Commutative Property of addition, That's where the addends change their positions, b + a = a + b, The order doesn't change the answer you see, If a goes west and b goes east, It won't affect the sum in the least. Commutative Property, Switch the numbers as you please. Commutative Property, Switch the numbers as you please. The Commutative Property of multiplication, That's where the factors change their positions, The order doesn't change the answer you see, If a goes west and b goes east, It won't affect the product in the least. (chorus) Instrumental Interlude (chorus) Associative Property by Susan Cantey When the numbers keep their positions, In multiplication or addition, But the parentheses slide to the left or the right, Wrapping around a different quantity, That's the Associative Property. Given 3 + 4 + 5, Should you start at the left or the right? It doesn't matter how you add them, 7 + 5 's the same as 3 + 9, Yes a + b in parentheses, Plus a third number, Let's call it c, Is the same thing that will be, a plus the quantity b plus c. (chorus) Given, Will it really matter any more? The order in which you go, 2 times 12 's the same as 6 times four, Yes a times b in parentheses, Times a third number, Let's call it c, It's the same thing as will be, a plus the quantity b times c. (chorus) Slide, slide the parentheses left, Slide, slide the parentheses right, When you add or multiply, But never when you subtract or divide. (chorus) Distributive Law by Susan Cantey The Distributive Law Applies, Only if you multiply An entire quantity Of addition in parentheses, The Distributive Law is never used With exponents or square roots, Don't participate, just refuse Distributive Law abuse. 6 times the quantity 2w + 3z Is 12w + 18z, Distribute the 6, It's easy to see, That's the well known Distributive Law, But it also works backwards, let's move on. 12w + 18z, Equals 6 times the quantity, 2w + 3z, Factor out the 6; there's no mystery, Forwards and backwards, it goes, When the Distributive Law is known. (chorus) 5 times the quantity 7x - 2z, Is 35x - 10z, Distribute the 5, It's easy to see, That's the well known Distributive Law, But it also works backwards, let's move on. 35x - 10 z Is 5 times the quantity 7x minus 2z, Factor out the 5, no mystery. Forwards and backwards, it goes, When the Distributive Law is known Instrumental Interlude (chorus) Identities By Susan Cantey Identities, identities, They don't change anything, Identities, identities, Everything stays the same. When you add zero to any other number, It will never ever, ever change the sum, That's why zero's often called, yes, it's widely known as The identity element of addition a + 0 is always a, 0 + a is always a; it's always that way. (chorus) When you multiply any number by the number 1 It's never any different when you're done, That is why 1's often called, yes it's widely known as The identify element of multiplication is always a, is always a; it's always that way. (chorus) (chorus) Please Excuse My Dear Aunt Sally by Susan Cantey Please Excuse my dear Aunt Sally! Please Excuse my dear Aunt Sally! Please... Excuse... My dear Aunt Sally! Do what's inside parentheses first, Do something else first and it's gonna hurt, Exponents are second, you've got to be smart, If there's no parentheses, then that's where you start, Third step, multiply and divide, Start on the left then move to the right, You're on the right track, now add and subtract, Left to right again, that's just a fact. Please Excuse my dear Aunt Sally! Please Excuse my dear Aunt Sally! Please Excuse my dear Aunt Sally! Please... Excuse... My dear Aunt Sally! Do what's inside parentheses first, Do something else first and it's gonna hurt, Exponents are second, you've got to be smart, If there's no parentheses, then that's where you start, Third step, multiply and divide, Start on the left then move to the right, You're on the right track, now add and subtract, Left to right again, that's just a fact. Please Excuse my dear Aunt Sally! This Thing Called X by Susan Cantey This thing called x, What could be worse than this thing called x? What will be next? y and z, what can they be? This ever changing, never failing, heart breaking, Breath a-taking, Unstable variable called x. A constant value never changes, Never rearranges, It's always the same, But a variable can't make up it's mind, In one problem it's four, In the next it's nine. (chorus) A fact I must state, That no one debates, Any number rates, They're all candidates, But the values that make the equation true, Are the ones you must find Before you're through. (chorus) Variable (x4) (chorus) Like Terms by Susan Cantey Like terms, we only add like terms, Like terms, we only add like terms, The part that's variable Must match, oh yes it will, The letters must be the same, And their essence will be maintained. 1 + 2 is 3 you see, 2x + 4x, 6x will be, 3xy + 2xy is 5xy, Verified. 2x + 3x is definitely 5x quantifiably, 3 apples, 4 apples, what does that make? 7 apples for your coffee cake. (chorus) Apples and oranges never mix, Can't add x to plain old 6, 3x + 4y can't be simplified, So don't try. 2x + 3x + 4x will be 9x most certainly, If the variable parts are exactly the same, Add them up and keep their name. (chorus) One Step Equations Music by Rossini / lyrics by Susan Cantey To solve a one step equation, To solve a one step equation, To solve a one step equation, Invert the operation. Do the op the op the op the opposite of what you see, Do the op the op the op the opposite of what you see, Use the inverse, the inverse operation, Use the inverse, the inverse operation. If you see addition there, then you must subtract with care, If you see subtraction then, you need an addend, If the x is multiplied, then you know you must divide, If you see division bar, why, you will need to multiply, That's the inverse, the inverse operation, That's the inverse, the inverse operation. (chorus) Solving means you really want to know What the variable equals so, Make the equation true that is our goal, x or y, we simply have to know. (repeat from start) (chorus) Instrumental Interlude (chorus) Do the op the op the op the opposite of what you see, Do the op the op the op the opposite of what you see, Use the inverse, the inverse operation, Use the inverse, the inverse operation. (chorus) Two Step Equations by Susan Cantey ax + b = c, Two operations revealed, What ya gotta do next Is try to reverse, Unravel the mystery, Discover what x has gotta be. Two step equations, Reverse the order, Inverse operations, Two step equations. 3x + 4 is ten, Subtract the 4 and then, 3x = 6, That's an easy fix, Divide by 3, x is 2, That's easy to do. (chorus) x over 4 minus 3, Equals 17, x over 4 equals twenty and no more, Multiply by 4 on both sides, x equals 80, that's right. (chorus) Don't Misuse the Equal Sign Music - traditional French Carol / lyrics by Susan Cantey I love the equal sign, And I know that he is hungry To be used between Two equal quantities, But on the other hand, I surely understand, The sign must be Used appropriately. Don't misuse the equal sign, It's been done too many times, When it's used this is what it states, Two quantities are exactly the same, Equal sign never says, Hello, this is the next step, If you've made any changes, Use an arrow there instead. Equals, what does it mean? Misuse of equals is obscene, Place it between two quantities, Only if they are equal, please. (chorus) Bird Interlude (chorus) Get Your X's on the Same Side By Susan Cantey Get your x's on the same side, Get your numbers on the other side, You can do it by yourself, You don't need nobody else, 'Cause when your x's are on one side, All you got to do is divide, That's the way the problem goes, The way that you can know, What makes the equation true, Check your answer when you're through, And x is by itself on one side. Step 1 simplify parentheses must go bye-bye, Step 2 collect like terms on both sides, Step 3 it's not abstract, you must react, Choose which x's to add or subtract, Soon you will be done, You'll be second to none. (repeat from start) The biggest thing that you must decide, Is to put the x on the left or on the right, Another trick I think you will like, Get rid of fractions, find the LCD and multiply. (repeat first stanza) The Golden Rule of Solving All Equations by Susan Cantey Oh, the golden rule of solving all equations, Is to do unto the right side, Whatever you do to the left side, It's a rule with which you must comply. And you must apply it to everything, Not just one little part of the whole, And it must be a legal operation, Now you can't say that you've not been told. You can rearrange the parts if you like, As long as you don't change the values that's alright, Multiply by one, distribute a multiplier, Add like terms or get a common denominator. (chorus) It's OK to multiply every term on both sides, Add or subtract the very same amount, Once you've got it down to something very easy, You may square or square root all of both sides, you see. (chorus) Monomial By Susan Cantey Let me introduce you To a fellow you will like, He is very ordinary, Lives a simple life, He'll never use a plus sign, No subtraction will you see, One number or one variable Sometimes 2 or 3 Put your monomial in, Put your monomial out, The Distributive Law works both ways, There is no doubt, Put your monomial in, Put your monomial out, We'll have a real good time! Monomial is in the house. Let me introduce you To the family, a and b, h and k, r squared, xyz, 29 and 13mrs or w, 3pq, 4b squared, Just to name a few. (chorus) Instrumental Interlude (chorus) If in every single term You see a 3 or 2, Factor that monomial, y squared or 4z cubed, Sometimes just the opposite, Is what you need to do, Distribute 5 or x or y, Multiply it through. First Outer Inner Last by Susan Cantey (x + 2) times (x + 3), Foiling's elementary, x times x and x times 3, 2 times x and 2 times 3, x plus 3x, 2x plus 6, Only one more thing to fix, Add the middle terms together, x plus 5x, plus 6, yeah, whatever. FOIL, FOIL, FOIL, FOIL, FOIL, FOIL, FOIL, FOIL, First, Outer, Inner, Last, First, Outer, Inner, Last, First, Outer, Inner, Last, First, Outer, Inner, Last, FOIL, FOIL, FOIL, FOIL, FOIL, FOIL, FOIL, FOIL, (3x + 1) times (2x - 5), 3x times 2x minus 3x times 5, 1 times 2x minus 1 times 5, Soon the answer will arrive, 6x minus 15x plus 2x minus 5, And that equals, And this ain't no jive, 6x minus 13x minus 5. (chorus) (a + b) times (c + d), No matter what terms you see, ac plus ad plus bc plus bd, Sometimes like terms can be combined, Gonna do it one more time. (chorus) (x - 2) times (x + 2), A special case, just for you, x times x plus 2 times x, Minus 2x, minus 4, yes, The middle term cancels out, No doubt. (chorus) First, Outer, Inner, Last, First, Outer, Inner, Last. Factor Me by Susan Cantey Factor me, oh, won't you factor me, Factor me, oh, won't you factor me, It's the cry of the trinomial, The cry of the trinomial, Factor me. x + 4x + 3, Let me tell you what you need, Numbers that multiply to 3, But they must also add up to 4, you see, Use your head and think about it, Yeah, 1 and 3, no need to doubt it, x + 1 times x + 3. (chorus) x + 7x + 12, Soon you'll know trinomials well, You need numbers that multiply to twelve, But they must also add up to seven, yeah, Use your head and think about it, Yeah, 3 and 4, no need to doubt it, x + 3 times x + 4, That's swell! (chorus) x - 5x + 4, Yeah, let's do this one, just one more, Numbers that multiply to four, But add to negative five you know, Use your head and think about it, Negative one and negative four don't doubt it, x - 1 times x - 4, (chorus - twice) Factor me! Difference of Squares Music by Johann Strauss Jr. / lyrics by Susan Cantey The difference of squares is something that everybody likes, Always filling us with delight, Recognizing them at once on sight, b - a is the difference of squares, Always factoring the very same way, b + a times b - a. Any time you see two perfect squares separated by a minus, That's the clue that tells us, Factoring is a must, Take the square roots of both the terms And then write two factors, One factor with a plus, the other with a minus. X - y, always factors in the same way, x - y times x + y, You don't need to be a protégée. (repeat the first stanza) x - 9 is x - 3 times x + 3, 16 - z is 4 - z times 4 + z, Even when the squares are quite obscure It's just the very same thing we do, k - 4 uses k plus and minus 2. x - y, always factors in the same way, x - y times x + y, You don't need to be a protégée. Perfect Square Trinomial by Susan Cantey A perfect square trinomial Should be recognized on sight, A perfect square trinomial Should be factored right, Something squared in the front, Something squared at the rear, Twice the product in the middle, The answer's clear., Factors in the following way, a + b in parentheses, Then you square the quantity. (chorus), The x and the 4, Need to be seen, 8x is twice the 4 times the x, x + 4 times itself is next. (chorus) Instrumental Interlude (chorus), If you can see the 2y And the 3, that's fine, 12y is 2 times 6y, 2y - 3 squared this time. (chorus) Factoring Any Trinomial in X Music by Johann Strauss Jr. / lyrics by Susan Cantey How can I explain this in a song, When many children get it wrong? ax + bx + c, Factoring these quadratics isn't easy. But I have a trick up my sleeve, Multiply the a times the c, Then find the factors that will add up to b, Just two more steps, you'll see. Rewrite the middle term with these new factors, Pair terms by two, Take out the largest factors, Now you can conclude the answer quite quickly, By factoring out what's in the parentheses. That's quite a lot to swallow, That's not so easy to follow, So I'll give you an example next With numbers that are easy to digest. 6x + 11x + 4, 6 times 4, that's 24, 2 times 12, no that won't rate, 3 times 8, yes, that looks great, 6x + 3x + 8x + 4, 3x times 2x + 1 and 4 times 2x + 1, Factor out 2x + 1, Times 3x + 4 and you're done. Quadratic Formula Music - Pop Goes the Weasel / lyrics by Susan Cantey There is a formula from algebra we know, That solves, It's called the Quadratic formula, Used when factoring fails, Derived many years ago By completing the square. Write it in your notebook, Or on an index card, Etch it deep into your brain, The quadratic formula. (repeat)
Susan Cantey has taught mathematics for over thirty years at the high school and college levels. She has been writing songs, mainly Christian themed songs for church, since the 1970's. A few years ago she realized that in addition to visual learning, many students could benefit from auditory learning. That thought birthed her two former CD's: The Tree of Calculus and Pre-Calc! This CD of Algebra songs and it's companion, Algebra Vol. 2, contain songs about almost every conceivable algebra topic. Teachers can use these songs to liven up their classes. Parents can purchase them for their kids to augment studying for exams. There are many styles of music from rap to classical - something for every taste. Susan has worked hard to make the melodies catchy and the lyrics memorable. Hundreds of students are enjoying (and learning with) Susan's Calculus and PreCalculus songs. Algebra is even more important and ubiquitous. Join in the fun! Buy both volumes today. Lyrics: Happy Snappy Algebra by Susan Cantey On the road I often think "How long until I sleep?" Then I see how many miles are left, And divide by my vehicle's speed, But when I'm driving in the car, And junior says "Are we there yet?" If daddy answers "About an hour," He's not doing algebra. Happy snappy algebra, Do it all the time, Happy snappy algebra, It's so fine. Once I needed some cement, So I went to the store, Bags came in many sizes, Forty, eighty pounds or more, So I went back home to measure, Used my calculator, No need to be perturbed, My algebra was superb. (chorus) Let's party! Let's have a pizza party, How many should I buy? (I don't know.) A small one feeds 15, A large, 25. I don't like these cell phone people, They have too many plans, They try to make me pay a lot, What kind of fool do they think I am? So I drew some graphs before I bought, Decided how many minutes I ought To use each day, each month, and then I thought Algebra helps me a lot. (repeat chorus twice) Adding Signed Numbers By Susan Cantey When adding signed numbers, Think of it as cash, Negative, you owe someone, Positive, you have, The answer is the balance Ahead or behind, You're in the black when you're positive, Red's the other kind. Positive plus positive is always positive, Negative plus negative is always negative, But when you're adding one of each, Do yourself a favor, Subtract their magnitudes And keep the sign of the one that's "greater." When adding signed numbers, Never get uptight, Negative moves left, Positive moves right, Always start at zero, Then take one step at a time, You're standing on the answer, When you walk the number line. (chorus) 8 + -6 is 2, Cause 8 has the greater magnitude, -9 + 5 's -4, Cause between the two, 9 is more, -5 + 2 's -3, It quite elementary. Some people only like To memorize the rules, But in my opinion, Rules are rather cruel, If you use a model That makes some sense to you, Then you'll be the master Of signed numbers when you're through. (chorus) Subtracting Signed Numbers by Susan Cantey 8 - 5 is 3, that's easy, 5 - 8 is negative 3, Because you're taking more away than you have, you see, Beginners need to re-write it as addition, And though that could be the tradition, You won't need to do that when you're done. The opposite of opposite is back to positive, I'm not sure why that's not obvious, Like a switch that goes off and on inside your head, When you subtract a negative number, Taking away a negative number, Just like adding a positive value instead. Subtraction, Subtraction, The opposite reaction, Take away a plus and it's a minus, Take away a minus, it's a plus, Subtraction, Subtraction, Opposite reaction, If you know how to add then you can subtract. 12 - -3 's the same as, 12 + 3, so let's be fearless, Two negatives in a row Make a big plus sign, -7 - -2 written, Is -7 + 2; that's a given, And we know that equals negative 5, (chorus) The opposite of opposite is back to positive, I'm not sure why that's not obvious, Like a switch that goes off and on inside your head, When you subtract a negative number, Taking away a negative number, Just like adding a positive value instead. Multiplying Signed Numbers By Susan Cantey Every child can multiply With positives preoccupied, They know their times, four fives and nines, Stay positive and they-re just fine. When you have a negative Times positive; don't ever quit, You know the answer must exist, It's negative, oh yeah, that's it. Now a negative times a negative Is often missed, seems illigit, But if you just submit a list, The pattern goes something like this. -2 times 2 is -4, -2 times 1 is -2, -2 times 0 is zero, each answer is increased by 2, So -2 times -1, it's true, Has to be positive 2, Now let's review. A positive times positive is positive, A negative times positive is negative, A negative times negative is positive, It's a switch with a twist of two opposites. Yo, hello, just go with the flow, All of my knowledge I bestow, I'm preoccupied and fortified; I'll tell you why I'm satisfied, I'm inclined to multiply: I'm a pro, a dynamo. (repeat the first three stanzas) 2 times -3 is -6, 1 times -3 is -3, 0 times -3 is zero; each answer is increased by 3, Are you listening to me? -1 times -3 is positive 3. A positive times positive is positive, A negative times positive is negative, A negative times negative is positive, It's a switch with a twist of two opposites. Commutative Property by Susan Cantey The Commutative Property of addition, That's where the addends change their positions, b + a = a + b, The order doesn't change the answer you see, If a goes west and b goes east, It won't affect the sum in the least. Commutative Property, Switch the numbers as you please. Commutative Property, Switch the numbers as you please. The Commutative Property of multiplication, That's where the factors change their positions, The order doesn't change the answer you see, If a goes west and b goes east, It won't affect the product in the least. (chorus) Instrumental Interlude (chorus) Associative Property by Susan Cantey When the numbers keep their positions, In multiplication or addition, But the parentheses slide to the left or the right, Wrapping around a different quantity, That's the Associative Property. Given 3 + 4 + 5, Should you start at the left or the right? It doesn't matter how you add them, 7 + 5 's the same as 3 + 9, Yes a + b in parentheses, Plus a third number, Let's call it c, Is the same thing that will be, a plus the quantity b plus c. (chorus) Given, Will it really matter any more? The order in which you go, 2 times 12 's the same as 6 times four, Yes a times b in parentheses, Times a third number, Let's call it c, It's the same thing as will be, a plus the quantity b times c. (chorus) Slide, slide the parentheses left, Slide, slide the parentheses right, When you add or multiply, But never when you subtract or divide. (chorus) Distributive Law by Susan Cantey The Distributive Law Applies, Only if you multiply An entire quantity Of addition in parentheses, The Distributive Law is never used With exponents or square roots, Don't participate, just refuse Distributive Law abuse. 6 times the quantity 2w + 3z Is 12w + 18z, Distribute the 6, It's easy to see, That's the well known Distributive Law, But it also works backwards, let's move on. 12w + 18z, Equals 6 times the quantity, 2w + 3z, Factor out the 6; there's no mystery, Forwards and backwards, it goes, When the Distributive Law is known. (chorus) 5 times the quantity 7x - 2z, Is 35x - 10z, Distribute the 5, It's easy to see, That's the well known Distributive Law, But it also works backwards, let's move on. 35x - 10 z Is 5 times the quantity 7x minus 2z, Factor out the 5, no mystery. Forwards and backwards, it goes, When the Distributive Law is known Instrumental Interlude (chorus) Identities By Susan Cantey Identities, identities, They don't change anything, Identities, identities, Everything stays the same. When you add zero to any other number, It will never ever, ever change the sum, That's why zero's often called, yes, it's widely known as The identity element of addition a + 0 is always a, 0 + a is always a; it's always that way. (chorus) When you multiply any number by the number 1 It's never any different when you're done, That is why 1's often called, yes it's widely known as The identify element of multiplication is always a, is always a; it's always that way. (chorus) (chorus) Please Excuse My Dear Aunt Sally by Susan Cantey Please Excuse my dear Aunt Sally! Please Excuse my dear Aunt Sally! Please... Excuse... My dear Aunt Sally! Do what's inside parentheses first, Do something else first and it's gonna hurt, Exponents are second, you've got to be smart, If there's no parentheses, then that's where you start, Third step, multiply and divide, Start on the left then move to the right, You're on the right track, now add and subtract, Left to right again, that's just a fact. Please Excuse my dear Aunt Sally! Please Excuse my dear Aunt Sally! Please Excuse my dear Aunt Sally! Please... Excuse... My dear Aunt Sally! Do what's inside parentheses first, Do something else first and it's gonna hurt, Exponents are second, you've got to be smart, If there's no parentheses, then that's where you start, Third step, multiply and divide, Start on the left then move to the right, You're on the right track, now add and subtract, Left to right again, that's just a fact. Please Excuse my dear Aunt Sally! This Thing Called X by Susan Cantey This thing called x, What could be worse than this thing called x? What will be next? y and z, what can they be? This ever changing, never failing, heart breaking, Breath a-taking, Unstable variable called x. A constant value never changes, Never rearranges, It's always the same, But a variable can't make up it's mind, In one problem it's four, In the next it's nine. (chorus) A fact I must state, That no one debates, Any number rates, They're all candidates, But the values that make the equation true, Are the ones you must find Before you're through. (chorus) Variable (x4) (chorus) Like Terms by Susan Cantey Like terms, we only add like terms, Like terms, we only add like terms, The part that's variable Must match, oh yes it will, The letters must be the same, And their essence will be maintained. 1 + 2 is 3 you see, 2x + 4x, 6x will be, 3xy + 2xy is 5xy, Verified. 2x + 3x is definitely 5x quantifiably, 3 apples, 4 apples, what does that make? 7 apples for your coffee cake. (chorus) Apples and oranges never mix, Can't add x to plain old 6, 3x + 4y can't be simplified, So don't try. 2x + 3x + 4x will be 9x most certainly, If the variable parts are exactly the same, Add them up and keep their name. (chorus) One Step Equations Music by Rossini / lyrics by Susan Cantey To solve a one step equation, To solve a one step equation, To solve a one step equation, Invert the operation. Do the op the op the op the opposite of what you see, Do the op the op the op the opposite of what you see, Use the inverse, the inverse operation, Use the inverse, the inverse operation. If you see addition there, then you must subtract with care, If you see subtraction then, you need an addend, If the x is multiplied, then you know you must divide, If you see division bar, why, you will need to multiply, That's the inverse, the inverse operation, That's the inverse, the inverse operation. (chorus) Solving means you really want to know What the variable equals so, Make the equation true that is our goal, x or y, we simply have to know. (repeat from start) (chorus) Instrumental Interlude (chorus) Do the op the op the op the opposite of what you see, Do the op the op the op the opposite of what you see, Use the inverse, the inverse operation, Use the inverse, the inverse operation. (chorus) Two Step Equations by Susan Cantey ax + b = c, Two operations revealed, What ya gotta do next Is try to reverse, Unravel the mystery, Discover what x has gotta be. Two step equations, Reverse the order, Inverse operations, Two step equations. 3x + 4 is ten, Subtract the 4 and then, 3x = 6, That's an easy fix, Divide by 3, x is 2, That's easy to do. (chorus) x over 4 minus 3, Equals 17, x over 4 equals twenty and no more, Multiply by 4 on both sides, x equals 80, that's right. (chorus) Don't Misuse the Equal Sign Music - traditional French Carol / lyrics by Susan Cantey I love the equal sign, And I know that he is hungry To be used between Two equal quantities, But on the other hand, I surely understand, The sign must be Used appropriately. Don't misuse the equal sign, It's been done too many times, When it's used this is what it states, Two quantities are exactly the same, Equal sign never says, Hello, this is the next step, If you've made any changes, Use an arrow there instead. Equals, what does it mean? Misuse of equals is obscene, Place it between two quantities, Only if they are equal, please. (chorus) Bird Interlude (chorus) Get Your X's on the Same Side By Susan Cantey Get your x's on the same side, Get your numbers on the other side, You can do it by yourself, You don't need nobody else, 'Cause when your x's are on one side, All you got to do is divide, That's the way the problem goes, The way that you can know, What makes the equation true, Check your answer when you're through, And x is by itself on one side. Step 1 simplify parentheses must go bye-bye, Step 2 collect like terms on both sides, Step 3 it's not abstract, you must react, Choose which x's to add or subtract, Soon you will be done, You'll be second to none. (repeat from start) The biggest thing that you must decide, Is to put the x on the left or on the right, Another trick I think you will like, Get rid of fractions, find the LCD and multiply. (repeat first stanza) The Golden Rule of Solving All Equations by Susan Cantey Oh, the golden rule of solving all equations, Is to do unto the right side, Whatever you do to the left side, It's a rule with which you must comply. And you must apply it to everything, Not just one little part of the whole, And it must be a legal operation, Now you can't say that you've not been told. You can rearrange the parts if you like, As long as you don't change the values that's alright, Multiply by one, distribute a multiplier, Add like terms or get a common denominator. (chorus) It's OK to multiply every term on both sides, Add or subtract the very same amount, Once you've got it down to something very easy, You may square or square root all of both sides, you see. (chorus) Monomial By Susan Cantey Let me introduce you To a fellow you will like, He is very ordinary, Lives a simple life, He'll never use a plus sign, No subtraction will you see, One number or one variable Sometimes 2 or 3 Put your monomial in, Put your monomial out, The Distributive Law works both ways, There is no doubt, Put your monomial in, Put your monomial out, We'll have a real good time! Monomial is in the house. Let me introduce you To the family, a and b, h and k, r squared, xyz, 29 and 13mrs or w, 3pq, 4b squared, Just to name a few. (chorus) Instrumental Interlude (chorus) If in every single term You see a 3 or 2, Factor that monomial, y squared or 4z cubed, Sometimes just the opposite, Is what you need to do, Distribute 5 or x or y, Multiply it through. First Outer Inner Last by Susan Cantey (x + 2) times (x + 3), Foiling's elementary, x times x and x times 3, 2 times x and 2 times 3, x plus 3x, 2x plus 6, Only one more thing to fix, Add the middle terms together, x plus 5x, plus 6, yeah, whatever. FOIL, FOIL, FOIL, FOIL, FOIL, FOIL, FOIL, FOIL, First, Outer, Inner, Last, First, Outer, Inner, Last, First, Outer, Inner, Last, First, Outer, Inner, Last, FOIL, FOIL, FOIL, FOIL, FOIL, FOIL, FOIL, FOIL, (3x + 1) times (2x - 5), 3x times 2x minus 3x times 5, 1 times 2x minus 1 times 5, Soon the answer will arrive, 6x minus 15x plus 2x minus 5, And that equals, And this ain't no jive, 6x minus 13x minus 5. (chorus) (a + b) times (c + d), No matter what terms you see, ac plus ad plus bc plus bd, Sometimes like terms can be combined, Gonna do it one more time. (chorus) (x - 2) times (x + 2), A special case, just for you, x times x plus 2 times x, Minus 2x, minus 4, yes, The middle term cancels out, No doubt. (chorus) First, Outer, Inner, Last, First, Outer, Inner, Last. Factor Me by Susan Cantey Factor me, oh, won't you factor me, Factor me, oh, won't you factor me, It's the cry of the trinomial, The cry of the trinomial, Factor me. x + 4x + 3, Let me tell you what you need, Numbers that multiply to 3, But they must also add up to 4, you see, Use your head and think about it, Yeah, 1 and 3, no need to doubt it, x + 1 times x + 3. (chorus) x + 7x + 12, Soon you'll know trinomials well, You need numbers that multiply to twelve, But they must also add up to seven, yeah, Use your head and think about it, Yeah, 3 and 4, no need to doubt it, x + 3 times x + 4, That's swell! (chorus) x - 5x + 4, Yeah, let's do this one, just one more, Numbers that multiply to four, But add to negative five you know, Use your head and think about it, Negative one and negative four don't doubt it, x - 1 times x - 4, (chorus - twice) Factor me! Difference of Squares Music by Johann Strauss Jr. / lyrics by Susan Cantey The difference of squares is something that everybody likes, Always filling us with delight, Recognizing them at once on sight, b - a is the difference of squares, Always factoring the very same way, b + a times b - a. Any time you see two perfect squares separated by a minus, That's the clue that tells us, Factoring is a must, Take the square roots of both the terms And then write two factors, One factor with a plus, the other with a minus. X - y, always factors in the same way, x - y times x + y, You don't need to be a protégée. (repeat the first stanza) x - 9 is x - 3 times x + 3, 16 - z is 4 - z times 4 + z, Even when the squares are quite obscure It's just the very same thing we do, k - 4 uses k plus and minus 2. x - y, always factors in the same way, x - y times x + y, You don't need to be a protégée. Perfect Square Trinomial by Susan Cantey A perfect square trinomial Should be recognized on sight, A perfect square trinomial Should be factored right, Something squared in the front, Something squared at the rear, Twice the product in the middle, The answer's clear., Factors in the following way, a + b in parentheses, Then you square the quantity. (chorus), The x and the 4, Need to be seen, 8x is twice the 4 times the x, x + 4 times itself is next. (chorus) Instrumental Interlude (chorus), If you can see the 2y And the 3, that's fine, 12y is 2 times 6y, 2y - 3 squared this time. (chorus) Factoring Any Trinomial in X Music by Johann Strauss Jr. / lyrics by Susan Cantey How can I explain this in a song, When many children get it wrong? ax + bx + c, Factoring these quadratics isn't easy. But I have a trick up my sleeve, Multiply the a times the c, Then find the factors that will add up to b, Just two more steps, you'll see. Rewrite the middle term with these new factors, Pair terms by two, Take out the largest factors, Now you can conclude the answer quite quickly, By factoring out what's in the parentheses. That's quite a lot to swallow, That's not so easy to follow, So I'll give you an example next With numbers that are easy to digest. 6x + 11x + 4, 6 times 4, that's 24, 2 times 12, no that won't rate, 3 times 8, yes, that looks great, 6x + 3x + 8x + 4, 3x times 2x + 1 and 4 times 2x + 1, Factor out 2x + 1, Times 3x + 4 and you're done. Quadratic Formula Music - Pop Goes the Weasel / lyrics by Susan Cantey There is a formula from algebra we know, That solves, It's called the Quadratic formula, Used when factoring fails, Derived many years ago By completing the square. Write it in your notebook, Or on an index card, Etch it deep into your brain, The quadratic formula. (repeat)