Mathematics Sing-AlongTeaching and Motivating Students Through Music : 1 Mathematics Sing-AlongTeaching and Motivating Students Through Music Thomas J. Klein, Marshall University
Joyce Saxon, Morehead State Univ.
I Love M-A-T-H(Tune of “I Am C-H-R-I-S-T-I-O-N”) : 2 I Love M-A-T-H(Tune of “I Am C-H-R-I-S-T-I-O-N”) Oh I love M
Love M-A-T-H
Love M-A-T-H-E-M-A-T-I-C-S
I love to do M-A-T-H
Love N-U-M-B-E-R-S
G-E-O-M-E-T-R-Y
And problems S-O-L-V-E
Know, Know, Know Your Math (Tune of “Row, Row, Row Your Boat”) : 3 Know, Know, Know Your Math (Tune of “Row, Row, Row Your Boat”) Know, know, know your math
It will make you cool
Problem solving, problem solving
Math your biggest tool
Mean, Median, Mode (Tune of “3 Blind Mice”) : 4 Mean, Median, Mode (Tune of “3 Blind Mice”) Mean, median, mode
Mean, median, mode
Central tendency
Central tendency
The mean is the average of what you’ve got
The median’s the one in the middle spot
The mode is most frequent of the lot
The mean, median, mode
Mean, median, mode
Is This Not a Polygon?(Tune of “Twinkle, Twinkle, Little Star”) : 5 Is This Not a Polygon?(Tune of “Twinkle, Twinkle, Little Star”) Is this not a polygon?
Yes this is a polygon!
Is this not a triangle?
Yes this is a triangle!
Count the sides, and see, there’s three!
Count the angles, also three!
(Count the diagonals, half zero times three.)
(The angles add up to 180 degrees.)
Is this not a triangle?
Yes this is a triangle!
Is This Not a Polygon? : 6 Is This Not a Polygon? Is this not a polygon?
Yes this is a polygon!
Is this not a quadrilateral?
Yes this is a quadrilateral!
Count the sides, and see, there’s four!
Count the angles, also four!
(Count the diagonals, half one times four.)
(The angles add up to 360 degrees.)
Is this not a quadrilateral?
Yes this is a quadrilateral!
Is This Not a Polygon? : 7 Is This Not a Polygon? Is this not a polygon?
Yes this is a polygon!
Is this not a pentagon?
Yes this is a pentagon!
Count the sides, and see, there’s five!
Count the angles, also five!
(Count the diagonals, half two times five.)
(The angles add up to 540 degrees.)
Is this not a pentagon?
Yes this is a pentagon!
Is This Not a Polygon? : 8 Is This Not a Polygon? Is this not a polygon?
Yes this is a polygon!
Is this not a hexagon?
Yes this is a hexagon!
Count the sides, and see, there’s six!
Count the angles, also six!
(Count the diagonals, half three times six.)
(The angles add up to 720 degrees.)
Is this not a hexagon?
Yes this is a hexagon!
Is This Not a Polygon? : 9 Is This Not a Polygon? Is this not a polygon?
Yes this is a polygon!
Is this not a heptagon?
Yes this is a heptagon!
Count the sides, and see, there’s seven!
Count the angles, also seven!
(Count the diagonals, half four times seven.)
(The angles add up to 900 degrees.)
Is this not a heptagon?
Yes this is a heptagon!
Is This Not a Polygon? : 10 Is This Not a Polygon? Is this not a polygon?
Yes this is a polygon!
Is this not a octagon?
Yes this is a octagon!
Count the sides, and see, there’s eight!
Count the angles, also eight!
(Count the diagonals, half five times eight.)
(The angles add up to 1080 degrees.)
Is this not a octagon?
Yes this is a octagon!
Is This Not a Polygon? : 11 Is This Not a Polygon? Is this not a polygon?
Yes this is a polygon!
Is this not a nonagon?
Yes this is a nonagon!
Count the sides, and see, there’s nine!
Count the angles, also nine!
(Count the diagonals, half six times nine.)
(The angles add up to 1260 degrees.)
Is this not a nonagon?
Yes this is a nonagon!
Is This Not a Polygon? : 12 Is This Not a Polygon? Is this not a polygon?
Yes this is a polygon!
Is this not a decagon?
Yes this is a decagon!
Count the sides, and see, there’s ten!
Count the angles, also ten!
(Count the diagonals, half seven times ten.)
(The angles add up to 1440 degrees.)
Is this not a decagon?
Yes this is a decagon!
Is This Not a Polygon? : 13 Is This Not a Polygon? Is this not a polygon?
Yes this is a polygon!
Count the sides, and see, there’s n!
Count the angles, also n!
(Count the diagonals, half (n - 3) times n.)
(The angles add up to 180 times (n – 2) degrees.)
Is this not a polygon?
Yes this is a polygon!
Function Song (Tune of “Bicycle Built for Two”) : 14 Function Song (Tune of “Bicycle Built for Two”) Function, function,
Give me your rule please do.
I’m half crazy
Trying to figure out you.
The input is called the domain.
The output is called the range.
I input “x” and out comes “y.”
Oh your rule I will now supply.
Function Song : 15 Function Song Function, function,
Give me your rule please do.
I’m half crazy
Trying to figure out you.
The input is called the domain.
The output is called the range.
I input ________ and out comes ________.
I input ________ and out comes ________.
I input ________ and out comes ________.
Oh your rule I will now supply.
Function Song : 16 Function Song Function, function,
Give me your rule please do.
I’m half crazy
Trying to figure out you.
The input is called the domain.
The output is called the range.
I input ________ and out comes ________.
I input ________ and out comes ________.
I input ________ and out comes ________.
Oh your rule I will now supply.
Function Song : 17 Function Song Function, function,
Give me your rule please do.
I’m half crazy
Trying to figure out you.
The input is called the domain.
The output is called the range.
I input ________ and out comes ________.
I input ________ and out comes ________.
I input ________ and out comes ________.
Oh your rule I will now supply.
Triangles Sing This Song (Tune of “Camptown Races”) : 18 Triangles Sing This Song (Tune of “Camptown Races”) Acute triangles sing this song
Doodah doodah
Acute triangles sing this song
Oh the doodah day
All three angles are acute
Less than 90 degrees
Acute triangles sing this song
Oh the doodah day
Triangles Sing This Song : 19 Triangles Sing This Song All right triangles sing this song
Doodah doodah
All right triangles sing this song
Oh the doodah day
Only one right angle
Exactly 90 degrees
All right triangles sing this song
Oh the doodah day
Triangles Sing This Song : 20 Triangles Sing This Song Obtuse triangles sing this song
Doodah doodah
Obtuse triangles sing this song
Oh the doodah day
One angle is obtuse
More than 90 degrees
Obtuse triangles sing this song
Oh the doodah day
Triangles Sing This Song : 21 Triangles Sing This Song Scalene triangles sing this song
Doodah doodah
Scalene triangles sing this song
Oh the doodah day
All sides noncongruent
No angles congruent too
Scalene triangles sing this song
Oh the doodah day
Triangles Sing This Song : 22 Triangles Sing This Song Isosceles triangles sing this song
Doodah doodah
Isosceles triangles sing this song
Oh the doodah day
Two sides (and angles) congruent
Two and maybe three
Isosceles triangles sing this song
Oh the doodah day
Triangles Sing This Song : 23 Triangles Sing This Song Equilaterals sing this song
Doodah doodah
Equilaterals sing this song
Oh the doodah day
All three sides congruent
Three angles 60 degrees
Equilaterals sing this song
Oh the doodah day
Triangles Sing This Song : 24 Triangles Sing This Song All triangles sing this song
Doodah doodah
All triangles sing this song
Oh the doodah day
The sum of two shorter sides
Is longer than the third side
And the sum of its three angles
Is 180 degrees
All triangles sing this song
Oh the doodah day
Addition—Front End : 25 Addition—Front End
Addition—Compensation : 26 Addition—Compensation
Addition—Break-and-Bridge : 27 Addition—Break-and-Bridge
Addition—Compatible Numbers : 28 Addition—Compatible Numbers
Subtraction—Compensation : 29 Subtraction—Compensation
Multiplication—Halve & Double : 30 Multiplication—Halve & Double
Multiplication—Trailing Zeros : 31 Multiplication—Trailing Zeros
Division—Trailing Zeros : 32 Division—Trailing Zeros
Let’s Do Mental Math This Minute (Tune of “Letter Home”…Hello Mother, Hello Father) : 33 Let’s Do Mental Math This Minute (Tune of “Letter Home”…Hello Mother, Hello Father) We’re all mental
We love math
We do mental
Math in minutes
All in our head
With slick techniques
So much fun so let’s do mental math this minute
Let’s Do Mental Math This Minute : 34 Let’s Do Mental Math This Minute Let’s do mental
Math addition
With two digits
Using front end
Add the tens first
Then the ones next
Then you add them both together for the answer
Let’s Do Mental Math This Minute : 35 Let’s Do Mental Math This Minute Let’s do mental
Math addition
Add two numbers
Compensation
Round an addend
To the next ten
Add the rounded and the other less the error
Let’s Do Mental Math This Minute : 36 Let’s Do Mental Math This Minute Let’s do mental
Math addition
With two digits
Using break-and-bridge
Add one number
To the tens place
Of the other and then add that number’s ones place
Let’s Do Mental Math This Minute : 37 Let’s Do Mental Math This Minute Let’s do mental
Math addition
With two digits
Those compatible
Add first addends
With sums that are
Multiples of ten and then add on the others
Let’s Do Mental Math This Minute : 38 Let’s Do Mental Math This Minute Let’s do mental
Math subtraction
A two-digit
Minus two-digit
Front end, break-and-bridge
Compensation
All three methods also work doing subtraction
Let’s Do Mental Math This Minute : 39 Let’s Do Mental Math This Minute Let’s do mental
Multiplication
Times two numbers
By halve and double
Half one factor
Other double
Multiply these two together for your product
Let’s Do Mental Math This Minute : 40 Let’s Do Mental Math This Minute Let’s do mental
Multiplication
When these numbers
End in zeros
Drop end zeros
Multiply then
Count the zeros dropped and put them on your product
Let’s Do Mental Math This Minute : 41 Let’s Do Mental Math This Minute Let’s do mental
Math division
Same end zeros
Off both numbers
Zeros still left
Take off dividend
Disregard these, then divide, add on these later
Let’s Do Mental Math This Minute : 42 Let’s Do Mental Math This Minute Lots of mental
Mathematics
Slick techniques for
Math in your head
Makes doing math
So much more fun
So let’s do more mental math some other minute
The Divisibility Song (Tune of “Polly Wolly Doodle”) : 43 The Divisibility Song (Tune of “Polly Wolly Doodle”) Oh I want to know, yes I want to know, is this integer divisible by two?
Oh I want to know, yes I want to know, is this integer divisible by two?
Could the last digit be a zero, eight, six, four, or two?
If it is a zero, eight, six, four, or two, yes this integer’s divisible by two.
The Divisibility Song : 44 The Divisibility Song Oh I want to know, yes I want to know, is this integer divisible by three?
Oh I want to know, yes I want to know, is this integer divisible by three?
Find the sum of the digits; is this sum divisible by three?
If this sum is a multiple of three, yes this integer’s divisible by three.
The Divisibility Song : 45 The Divisibility Song Oh I want to know, yes I want to know, is this integer divisible by four?
Oh I want to know, yes I want to know, is this integer divisible by four?
Do the last two digits form an integer divisible by four?
If these two digits form a multiple of four, yes this integer’s divisible by four.
The Divisibility Song : 46 The Divisibility Song Oh I want to know, yes I want to know, is this integer divisible by five?
Oh I want to know, yes I want to know, is this integer divisible by five?
Could the last digit be equal to a zero or five?
If the last digit is a zero or five, yes this integer’s divisible by five.
The Divisibility Song : 47 The Divisibility Song Oh I want to know, yes I want to know, is this integer divisible by six?
Oh I want to know, yes I want to know, is this integer divisible by six?
What if this integer is divisible by two and three?
If this integer is divisible by these, yes this integer’s divisible by six.
The Divisibility Song : 48 The Divisibility Song Oh I want to know, yes I want to know, is this integer divisible by nine?
Oh I want to know, yes I want to know, is this integer divisible by nine?
Find the sum of the digits; is this sum divisible by nine?
If this sum is a multiple of nine, yes this integer’s divisible by nine.
The Divisibility Song : 49 The Divisibility Song Oh I want to know, yes I want to know, is this integer divisible by ten?
Oh I want to know, yes I want to know, is this integer divisible by ten?
Could the last digit be equal to only zero?
If the last digit equals a zero, yes this integer’s divisible by ten.
The Divisibility Song : 50 The Divisibility Song (Oh I want to know, yes I want to know, is this integer divisible by eight?
Oh I want to know, yes I want to know, is this integer divisible by eight?
Do the last three digits form an integer divisible by eight?
If these three digits form a multiple of eight, yes this integer’s divisible by eight.)
Slide 51: 51
The Divisibility Song : 52 The Divisibility Song (Oh I want to know, yes I want to know, is this integer divisible by seven?
Oh I want to know, yes I want to know, is this integer divisible by seven?
Does the integer represented without its units digit minus twice the units digit form an integer divisible by seven?
If a multiple of seven is formed this way, yes this integer’s divisible by seven.)
Slide 53: 53
The Divisibility Song : 54 The Divisibility Song (Oh I want to know, yes I want to know, is this integer divisible by eleven?
Oh I want to know, yes I want to know, is this integer divisible by eleven?
Does the sum of the digits in the places that are even powers of ten minus the sum of the digits in the places that are odd powers of ten form an integer divisible by eleven?
If a multiple of eleven is formed this way, yes this integer’s divisible by eleven.)
Slide 55: 55
Fraction Operation Song (Tune of “Yankee Doodle”) : 56 Fraction Operation Song (Tune of “Yankee Doodle”) Let’s determine how to add a fraction and a fraction
Rewrite both the fractions with the same denominator
Add the numerators up for your numerator
Write your sum with this over that same denominator
Fraction Operation Song : 57 Fraction Operation Song Let us see how to subtract a fraction by a fraction
Rewrite both the fractions with the same denominator
Subtract numerators to get your numerator
Write this difference over that same denominator
Fraction Operation Song : 58 Fraction Operation Song Let’s determine how to multiply together fractions
Cancel numerators with either denominator
Multiply the numerators for your numerator
Multiply denominators for denominator
Fraction Operation Song : 59 Fraction Operation Song Let us see how to divide a fraction by a fraction
There’s a couple different methods we could use to do this
Fraction Operation Song : 60 Fraction Operation Song If we want to use invert-and-multiply to do this
Calculate reciprocal of fraction that’s divisor
Then you multiply divisor’s inverse by the dividend
Use the rule for multiplying fractions then to do this
Brahmagupta’s Algorithm : 61 Brahmagupta’s Algorithm
Fraction Operation Song : 62 Fraction Operation Song If we want to use ol’ Brahmagupta’s algorithm
Rewrite both the fractions with the same denominator
Then divide the numerator of the dividend by
Numerator of divisor to obtain the quotient
Fraction Operation Song : 63 Fraction Operation Song Let us see how to divide or multiply mixed numbers
Rewrite as improper fractions, calculate with these now
Fraction Operation Song : 64 Fraction Operation Song Let’s determine how to add mixed number and mixed number
Rewrite as improper fractions, calculate with these or
Do addition with the fractions, carry if you need to
Then add up whole numbers, then combine for your mixed number
Fraction Operation Song : 65 Fraction Operation Song Let us see how to subtract mixed number by mixed number
Rewrite as improper fractions, calculate with these or
Do subtraction with the fractions, borrow if you need to
Then subtract whole numbers, then combine for your mixed number
Fraction Operation Song : 66 Fraction Operation Song Let’s determine how to do a fraction operation
When there is a mixed number and whole number or fraction
We adapt the rule for operating two mixed numbers
And we use this rule to complete our calculation
They’re Quadrilaterals (Tune of “Those Were the Days”) : 67 They’re Quadrilaterals (Tune of “Those Were the Days”) They’re quadrilaterals; they all have four angles.
They have four sides and 360 degrees.
They’re quadrilaterals; they all have four angles.
They have four sides and 360 degrees.
They’re Quadrilaterals : 68 They’re Quadrilaterals A kite has pairs of adjacent sides congruent.
Its diagonals are perpendicular to each other.
At least one diagonal bisects the other.
And also bisects nonconsecutive angles.
They’re Quadrilaterals : 69 They’re Quadrilaterals They’re quadrilaterals; they all have four angles.
They have four sides and 360 degrees.
They’re quadrilaterals; they all have four angles.
They have four sides and 360 degrees.
They’re Quadrilaterals : 70 They’re Quadrilaterals A trapezoid has exactly two sides parallel.
One pair of opposite sides is not congruent.
If the other pair of opposite sides is congruent.
Then this trapezoid is what we call isosceles.
They’re Quadrilaterals : 71 They’re Quadrilaterals They’re quadrilaterals; they all have four angles.
They have four sides and 360 degrees.
They’re quadrilaterals; they all have four angles.
They have four sides and 360 degrees.
They’re Quadrilaterals : 72 They’re Quadrilaterals A parallelogram has pairs of opposite sides parallel.
Its pairs of opposite angles are congruent.
Its pairs of opposite sides are also congruent.
And its diagonals bisect each other in two.
They’re Quadrilaterals : 73 They’re Quadrilaterals They’re quadrilaterals; they all have four angles.
They have four sides and 360 degrees.
They’re quadrilaterals; they all have four angles.
They have four sides and 360 degrees.
They’re Quadrilaterals : 74 They’re Quadrilaterals A rhombus is a parallelogram with four congruent sides.
Its diagonals are also perpendicular.
They also bisect each pair of opposite angles.
The rhombus reminds you of a diamond.
They’re Quadrilaterals : 75 They’re Quadrilaterals They’re quadrilaterals; they all have four angles.
They have four sides and 360 degrees.
They’re quadrilaterals; they all have four angles.
They have four sides and 360 degrees.
They’re Quadrilaterals : 76 They’re Quadrilaterals A rectangle is a parallelogram with right angles.
Its diagonals are congruent to each other.
And if all of its sides are congruent to each other,
Then this rectangle is what we call a square.
They’re Quadrilaterals : 77 They’re Quadrilaterals They’re quadrilaterals; they all have four angles.
They have four sides and 360 degrees.
They’re quadrilaterals; they all have four angles.
They have four sides and 360 degrees.
I Can Do This Stuff (Tune of “I Shall Not Be Moved”) : 78 I Can Do This Stuff (Tune of “I Shall Not Be Moved”) I can do this, I can do this stuff.
I can do this, I can do this stuff.
It may be hard, but with some help and effort,
I can do this stuff.
I Can Do This Stuff : 79 I Can Do This Stuff I might make it harder than it is.
I might make it harder than it is.
But if I think, and use my intuition,
I can do this stuff.
I Can Do This Stuff : 80 I Can Do This Stuff I can do this, I can do this stuff.
I can do this, I can do this stuff.
It may be hard, but with some help and effort,
I can do this stuff.
I Can Do This Stuff : 81 I Can Do This Stuff I won’t always do it rapidly.
I won’t always do it rapidly.
But with some time and extra perseverance,
I can do this stuff.
I Can Do This Stuff : 82 I Can Do This Stuff I can do this, I can do this stuff.
I can do this, I can do this stuff.
It may be hard, but with some help and effort,
I can do this stuff.
I Can Do This Stuff : 83 I Can Do This Stuff If I do get stuck and can’t go on,
If I do get stuck and can’t go on,
It is okay to ask for help from someone.
I can do this stuff.
I Can Do This Stuff : 84 I Can Do This Stuff I can do this, I can do this stuff.
I can do this, I can do this stuff.
It may be hard, but with some help and effort,
I can do this stuff.
I Can Do This Stuff : 85 I Can Do This Stuff If I ask I’ll get the help I need.
If I ask I’ll get the help I need.
I’ll understand, and I’ll continue working.
I can do this stuff.
I Can Do This Stuff : 86 I Can Do This Stuff I can do this, I can do this stuff.
I can do this, I can do this stuff.
It may be hard, but with some help and effort,
I can do this stuff.
I Can Do This Stuff : 87 I Can Do This Stuff I did math I didn’t know I could.
I did math I didn’t know I could.
My confidence increases when this happens.
I can do this stuff.
I Can Do This Stuff : 88 I Can Do This Stuff I can do this, I can do this stuff.
I can do this, I can do this stuff.
It may be hard, but with some help and effort,
I can do this stuff.