1 mathematics sing-along teaching and motivating students through music thomas j. klein, marshall...

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Mathematics Sing-AlongTeaching and Motivating Students Through Music

Thomas J. Klein, Marshall University

Joyce Saxon, Morehead State Univ.

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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

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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

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Mean, Median, Mode (Tune of “3 Blind Mice”)

Mean, median, modeMean, median, modeCentral tendencyCentral tendencyThe mean is the average of what you’ve gotThe median’s the one in the middle spotThe mode is most frequent of the lotThe mean, median, modeMean, median, mode

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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!

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Is This Not 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!

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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!

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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!

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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!

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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!

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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!

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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!

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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!

14

Function Song (Tune of “Bicycle Built for Two”)

Function, function,Give me your rule please do.I’m half crazyTrying 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.

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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 ________.



Oh your rule I will now supply.

x y

3 8

5 10

8 13

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Function Song

Function, function,


I’m half crazy








x y

2 6

7 21

11 33

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Function Song

Function, function,


I’m half crazy








x y

3 1

3 4

3 6

x y

3 1

3 4

3 6

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Triangles Sing This Song (Tune of “Camptown Races”)

Acute triangles sing this songDoodah doodahAcute triangles sing this songOh the doodah dayAll three angles are acuteLess than 90 degreesAcute triangles sing this songOh the doodah day

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Triangles Sing This Song

All right triangles sing this songDoodah doodahAll right triangles sing this songOh the doodah dayOnly one right angleExactly 90 degreesAll right triangles sing this songOh the doodah day

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Obtuse triangles sing this songDoodah doodahObtuse triangles sing this songOh the doodah dayOne angle is obtuseMore than 90 degreesObtuse triangles sing this songOh the doodah day

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Scalene triangles sing this songDoodah doodahScalene triangles sing this songOh the doodah dayAll sides noncongruentNo angles congruent tooScalene triangles sing this songOh the doodah day

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Isosceles triangles sing this songDoodah doodahIsosceles triangles sing this songOh the doodah dayTwo sides (and angles) congruentTwo and maybe threeIsosceles triangles sing this songOh the doodah day

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Equilaterals sing this songDoodah doodahEquilaterals sing this songOh the doodah dayAll three sides congruentThree angles 60 degreesEquilaterals sing this songOh the doodah day

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All triangles sing this songDoodah doodahAll triangles sing this songOh the doodah dayThe sum of two shorter sidesIs longer than the third sideAnd the sum of its three anglesIs 180 degreesAll triangles sing this songOh the doodah day

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Addition—Front End

721260

1293

604020

?4923

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Addition—Compensation

72173

735023

?4923

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Addition—Break-and-Bridge

72963

634023

?4923

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Addition—Compatible Numbers

1143480

802852

?283452

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Subtraction—Compensation

44242

423072

?2872

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Multiplication—Halve & Double

2045

?82

12

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Multiplication—Trailing Zeros

0001800603

1863

?60030

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Division—Trailing Zeros

00590045

5945

?0904500

?9045000

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Let’s Do Mental Math This Minute (Tune of “Letter Home”…Hello Mother, Hello Father)

We’re all mentalWe love mathWe do mentalMath in minutesAll in our headWith slick techniquesSo much fun so let’s do mental math this

minute

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Let’s Do Mental Math This Minute

Let’s do mentalMath additionWith two digitsUsing front endAdd the tens firstThen the ones nextThen you add them both together for the

answer

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Let’s do mentalMath additionAdd two numbersCompensationRound an addendTo the next tenAdd the rounded and the other less the error

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Let’s do mentalMath additionWith two digitsUsing break-and-bridgeAdd one numberTo the tens placeOf the other and then add that number’s

ones place

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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

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Let’s do mentalMath subtractionA two-digitMinus two-digitFront end, break-and-bridgeCompensationAll three methods also work doing

subtraction

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Let’s do mental

Multiplication

Times two numbers

By halve and double

Half one factor

Other double

Multiply these two together for your product

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Let’s do mentalMultiplicationWhen these numbersEnd in zerosDrop end zerosMultiply thenCount the zeros dropped and put them on

your product

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Let’s do mentalMath divisionSame end zerosOff both numbersZeros still leftTake off dividendDisregard these, then divide, add on these

later

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Lots of mentalMathematicsSlick techniques forMath in your headMakes doing mathSo much more funSo let’s do more mental math some other

minute

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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(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.)

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8.by divisible not

is 49578 Therefore

No. 8?by divisible 578 Is

8?by divisible 49578 Is

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(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.)

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7.by divisible is 5243 Therefore

Yes.7?by divisible 35 Is

351651)8(251


5186524)3(2524


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(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.)

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11.by divisible is 275,704 Therefore

Yes.11?by divisible 11 Is

11718

7052

18477

11?by divisible 275,704 Is

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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

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Fraction Operation Song

Let us see how to subtract a fraction by a fraction


Subtract numerators to get your numerator

Write this difference over that same denominator

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Let’s determine how to multiply together fractions

Cancel numerators with either denominator

Multiply the numerators for your numerator

Multiply denominators for denominator

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Let us see how to divide a fraction by a fraction

There’s a couple different methods we could use to do this

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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

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Brahmagupta’s Algorithm

20

9

20

24

24

9

24

20

24

9

6

5

8

320

9

40

18

5

6

8

3

6

5

8

3

:multiply-and-invert using Check

20

9

24

20

24

9

?6

5

8

3

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If we want to use ol’ Brahmagupta’s algorithm


Then divide the numerator of the dividend by

Numerator of divisor to obtain the quotient

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Let us see how to divide or multiply mixed numbers

Rewrite as improper fractions, calculate with these now

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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

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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

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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

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They’re Quadrilaterals (Tune of “Those Were the Days”)

They’re quadrilaterals; they all have four angles.

They have four sides and 360 degrees.



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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.

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70


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.

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72


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.

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74


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.

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76


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.

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I Can Do This Stuff (Tune of “I Shall Not Be Moved”)

I can do this, I can do this stuff.


It may be hard, but with some help and effort,

I can do this stuff.

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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,


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I Can Do This Stuff





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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,


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I Can Do This Stuff





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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.


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I Can Do This Stuff





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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.


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I Can Do This Stuff





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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.


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I Can Do This Stuff





1 mathematics sing-along teaching and motivating students through music thomas j. klein, marshall...

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