The Rhythm Name Game! (Xs and Os) Measuring, LCM, Ratios and Reciprocals Part 1: Measuring Music (20 Minutes) Ask: What is rhythm? Rhythm can be thought of as measured motion or repeating patterns. There are many kinds of rhythm that appear in nature and in everyday life: the Earth rotates every 24 hours, and revolves around the sun every year; a train chugging along the tracks; the sound of footsteps while walking down the street; even waking up each morning to get ready for school! Ask: What are some other examples of rhythm? Take a finger or two and see if you can feel a pulse in your wrist or neck. Another example of rhythm in nature! In music, the pulse is the feel of a song, and is typically what your foot is tapping along to. In music, rhythm is measured with a basic unit of time called a beat, or a count. Clap a steady beat, have the class join in. If the class has a problem with speeding up, try having them clap randomly first, like an audience, them have them synch up with you by watching your hands. It might take a little practice! Try counting to two, three or four along to the claps, beginning at one again. 1-2-3-1-2-3-1-2-3 or 1-2-3-4-1-2-3-4-1-2-3-4 It helps to clap beat one a bit louder than the others. This is called an accent. 1-2-3-1-2-3-1-2-3 or 1-2-3-4-1-2-3-4-1-2-3-4 You can feel the difference. Most music you hear on the radio, whether it s rock, hip-hop, country, jazz, etc. is divided into 4 beats. This is called common time. Music divided into three beats is also common however, and is the rhythm for a well-known type of dance, the waltz.
The Name Game Write your name on the board, and place an x under each consonant, and an o under each vowel. You can leave the initial capitalized: Ex: T e d X o x Clap for each x Pat knees for each o Try clapping the pattern once, then several times in a row. When you write it out multiple times, it starts to resemble a music score, as well as a ruler or number line. You can place a bar between each name to separate each measure (the space between two bars), and count the number of beats in each measure. Ex: 1 2 3 1 2 3 1 2 3 1 2 3 T e d T e d T e d T e d X o x X o x X o x X o x clap-pat-clap, clap-pat clap, clap-pat-clap In a large circle, write each student s name on the board one at a time, writing Xs and Os underneath. Have the class take turns clapping each other s names. As the class gets the hang of the activity, try adding a stomp on the initial to the pattern.
Part 2: LCM, Ratios, and Reciprocals (25 Minutes) Once students get the hang of it, you can try dividing the class in two to clap two names at once. Let s try the above example but with one half of the class clapping the name John. This name has four letters instead of three. Hearing two patterns at once makes this a bit tricky, like rubbing your stomach and patting your head at the same time. Try having students focus only on what they are clapping at first. Keeping a steady beat is also important, so start slow! Try adding in stomps on the initials (indicated by a dash). How many times will it take to clap each name (measure) before we hear the whole class stomp together again? 1 2 3 4 5 6 T e d T e d T e d T e d T e d T e d 1 2 3 4 5 _ J o h n J o h n J o h n J o h n J o h n If we count each instance of Ted we get 4 complete measures (with the 5 th lining up with the beginning of John again. If we count the instances of John, we get 3 complete measures. This gives us a ratio of 3:4, or: 4 Ted measures 3 John measures Using Least Common Multiple to find repeating patterns Since each name has its own number of letters, each measure will have a fixed number of beats. There are three letters (beats) in the name Ted and four in John. We can use Least Common Multiple to find how many beats it will take for each name to begin at the same time again. 3: 3, 6, 9, 12, 15 4: 4, 8, 12, 16, 20 Notice that if we count the above pattern, the initials line up again on the 13 th beat, not the 12 th. That s because the pattern itself is 12 beats long, and would begin again on the next beat, beat 13. Using the Reciprocal to find repeating patterns
We can also take the ratio of beats in each name and multiply it by its reciprocal to get the number of beats it takes for the entire pattern to repeat: 4 Ted measures = 3 beats x 4 measures = 12 beats 3 John measures = 4 beats x 3 measures = 12 beats 3 x 4 = 12 4 3 = 12 Let s try with another example, this time with the names Jim and Tabitha : 1 2 3 4 5 6 7 8 9 _ J i m J i m J i m J i m J i m J i m J i m J i m J i m 1 2 3 4 T a b i t h a T a b i t h a T a b i t h a T a b i t h a Jim has three letters and Tabitha has seven. Listing out multiples of each and finding the LCM will tell us how many beats there are in the entire pattern. 3: 3, 6, 9, 12, 15, 18, 21, 24 7: 7, 14, 21, 28, 35 In this example, it will take 21 beats for the pattern to repeat. Multiplying by the reciprocal will give us the same answer: 7 Jim measures = 3 beats x 7 measures = 21 beats 3 Tabitha measures = 7 beats x 3 measures = 21 beats
Making Music with Straws Math Objectives Measuring Multiplication with Ratios Mixed Fractions Rational Approximation Music Objectives Knowledge of how sound works Pitch, and how they can be arranged to form a scale Reading music with simple notation Collaboration through ensemble playing Performance practice and etiquette Activity Description (for the teacher) In this lesson, we will make a kind of musical instrument called a pan flute, or panpipes, that can be used to play all kinds of songs. The pipes are made of straws of different lengths which each produce their own pitch (how high or low the note sounds). Students will cut eight straws, one for each note in a scale. If you ve ever heard anyone sing, Do Re Mi Fa So La Ti Do, before, that is the major scale, and is the basis for so much of the music we hear everyday. Optional: Watch a video of the song, Do Re Mi from Rodgers and Hammerstein s The Sound of Music to help explain the scale. Each note gets it s own ratio, the smallest of which is! for the octave, the eighth! and final note in the scale. You can see how size matters when it comes to producing sound in an orchestra; the violin is much smaller and produces a higher sound, while the bigger cellos and basses make a lower, deeper sound. The same is true if you were to look at the strings of a harp or a piano; the lower strings are longer, and the higher strings are shorter. A pipe organ is another great visual example.
You will have to measure and cut straws to the appropriate length for the songs to sound right. To do this we will have to multiply the length of the first straw (20 cm), by each ratio. We can set up an equation: 20 cm ratio = length We know the first straw is 20 cm, but what about the rest? Let s try finding the length of the straw for the second note in the scale, Re, by plugging in its ratio. 20 cm!! = length 20 8 = 160 160 9 = 17 R 7, or 17 7 9 cm
If we start with 20 cm for our first straw, we will get the following lengths for the whole scale: Scale Note Equation Note Length Do 20 cm!! Re 20 cm!! Mi 20 cm!! Fa 20 cm!! So 20 cm!! La 20 cm!! Ti 20 cm!!" Do 20 cm!! 20 cm 17 7 cm 9 16 cm 15 cm 13 1 cm 3 12 cm 10 2 cm 3 10 cm Rational Approximation The notes, Re, So, and Ti pose a bit of a problem. Measuring 1 3 cm or 177 9 cmdoesn t make much sense since the ruler won t have those markings. Instead we can compare ratios and ask which is bigger to get an approximate answer. Student s will probably need some help with this! Ask, Which do you think is bigger, 1 2 or 1 3? Ask, How much? 0 1 2 1 2 3 4
Do the same with 1 2 and 2 3. 0 1 2 1 2 3 4 Finally, with 1 2 and 7 9. 0 1 2 1 2 3 4 Make sure students know to add the fraction to the larger number. For example: 10 and!! cm.
Make Music With Straws Part 1: The Construction What You'll Need 8 straws scissors a ruler tape markers plastic sandwich bag for storage What to Do (WARNING: We ll need to use some math!) To make the flutes, we need to know how long each straw should be. Our first straw will be 20 centimeters. To find the length remaining straws, we will have to multiply the length of our first straw by each note s ratio: 20 cm note ratio = length Solve the problems in the chart on the next page, and write your answer in the right column. Use scratch paper if needed.
Scale Note Equation Note Length Do 20 cm 1 1 20 cm Re 20 cm 8 9 Mi 20 cm 4 5 Fa 20 cm 3 4 So 20 cm 2 3 La 20 cm 3 5 Ti 20 cm 8 15 Do 20 cm 1 2
Once you know the lengths of the straws, you can start measuring and cutting! Carefully line up the end of the straw with the zero line of the ruler. Mark the length on the straw with a marker. Do this for all 8 straws. Help! I can t find those weird fractions on my ruler! That s because they re not there! You ll have to approximate! Tape the straws together from longest to shortest. Cut your scraps into about one-inch pieces to use as spacers between the longer straws. This makes our panpipes easier to play. With a marker, number the straws 1 through 8, from longest to shortest.
Part 2: The Performance Hold the panpipe vertically below your lips. Blow across the tops of the straws as though you are blowing across the top of a soda bottle. Try playing one of the songs below, or make up your own songs. Remember: 1 is the longest straw and 8 is the smallest. Twinkle, Twinkle Little Star 11 55 66 5-44 33 22 1-55 44 33 2-55 44 33 2-11 55 66 5-44 33 22 1 Jingle Bells 333-333- 35123-4444 433 3355421 Mary Had a Little Lamb 3212333-222- 355-3212333- 22321 Ode to Joy 3345 5432 1123 3 22-3345 5432 1123 2 11 Star Wars 1 5 4328 5 4328 5 4342--- 1 5 4328 5 4 28 5 4342--- What's Happening? As you blow across a straw, the air in the straw vibrates. These vibrations travel outward and reach our ears sounding like the notes of a scale. You can change the pitch (the highness or lowness of a sound) by changing the length of the straw. A long straw produces a low note. A short straw produces a high note.