1 Mathematics Sing-Along Teaching and Motivating Students Through Music Thomas J. Klein, Marshall University Joyce Saxon, Morehead State Univ.

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

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

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

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!

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!

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!

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!

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!

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!

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!

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!

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!

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.

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 ________. Oh your rule I will now supply. xy

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 ________. Oh your rule I will now supply. xy

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 ________. Oh your rule I will now supply. xy xy

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

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

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

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

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

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

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

25 Addition—Front End

26 Addition—Compensation

27 Addition—Break-and-Bridge

28 Addition—Compatible Numbers

29 Subtraction—Compensation

30 Multiplication—Halve & Double

31 Multiplication—Trailing Zeros

32 Division—Trailing Zeros

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

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

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

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

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

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

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

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

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

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

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? 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.

44 The Divisibility Song 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.

45 The Divisibility Song 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.

46 The Divisibility Song 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.

47 The Divisibility Song 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.

48 The Divisibility Song 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.

49 The Divisibility Song 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.

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.)

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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.)

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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.)

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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

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

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

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

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

61 Brahmagupta’s Algorithm

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

63 Fraction Operation Song Let us see how to divide or multiply mixed numbers Rewrite as improper fractions, calculate with these now

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

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

78 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.

79 I Can Do This Stuff I might make it harder than it is. But if I think, and use my intuition, I can do this stuff.

80 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.

81 I Can Do This Stuff I won’t always do it rapidly. But with some time and extra perseverance, I can do this stuff.

82 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.

83 I Can Do This Stuff If I do get stuck and can’t go on, It is okay to ask for help from someone. I can do this stuff.

84 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.

85 I Can Do This Stuff If I ask I’ll get the help I need. I’ll understand, and I’ll continue working. I can do this stuff.

86 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.

87 I Can Do This Stuff I did math I didn’t know I could. My confidence increases when this happens. I can do this stuff.

88 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.