## Sticker Composition

Create colorful music notation by implementing the concepts of fractions!

### Overview

This is a wonderful, simple activity that combines fractions and music that is especially helpful for students of young ages. Whether students are just beginning to learn fractions or haven't heard of them yet, cutting stickers into equal parts to compose a song gives children a creative, hands-on activity to understand not only what fractions are, but also how to intuitively add, multiple, divide fractions.

To top it off, this great activity transforms an already loved activity of sticker creations into a mathematically, visually, and audibly beautiful work of art!

### Materials

- Different colored stickers (ideally all round; all stickers must be at least the same shape)
- Scissors
- Paper
- At least one marker or pencil
- Optional: extra markers, crayons, etc. for decorating

### Project Background

This project will explore the beats and mathematics in 4/4 time. Don't know what "4/4 time" is? No problem!

Music is written in *measures*. Measures are the building blocks of a song that tell us how many beats we count within each block. For example, count in your head: "1, 2, 3, 4; 1, 2, 3, 4; 1, 2, 3, 4"; each count of "1,2,3,4" is a measure.

The top digit (4) of "4/4" time says that there are 4 beats in a measure. (*"1, 2, 3, 4".*) The bottom digit "4" says that *quarter* notes (*1/4* notes) get the beat. That means that when you are tapping your foot along to the song, no matter how complicated the music notation gets, your foot is tapping on every beat: *1, 2, 3, 4; 1, 2, 3, 4...*.

In this activity,** one whole sticker = 1 beat.** Be sure not to confuse a beat with a note! If you would like to learn more about music notation and beats before getting started with this activity, take a visit to this site: *https://trainer.thetamusic.com/en/content/rhythm-patterns.*

### Project Details: Starting with Just Quarter (1/4) Notes

0. Set-up your "musical staff" strips by taking a piece of regular 8.5x11" paper and cut into four horizontal strips. You can fold your paper in half the "hot dog" way (as opposed to the "hamburger way"!), then fold in half again to get four equal sections. Cut the strips apart.

1. Start by selecting one strip of paper and divide it up into four equal sections with your pencil, drawing lines to show each section. If you want your sections to be equal, try the folding trick again: fold in half and half again, and the creases will create four equal sections!

2. Select 4 round stickers and place them all in a row in the first, left-most section of your strip. You can choose all colors to be the same, or pick each sticker to be a different color!

3. Repeat for the 2nd, 3rd, and 4th (final) section of your strip. Create a pattern of your colors!

4. Try tapping your pattern on a table. (You can use your hand or a pencil as a light drumstick!) Start with a nice, even beat: count in your head, "1, 2, 3, 4; 1, 2, 3, 4;...". Now tap along with one hand, and point to each sticker on your composition sheet. Count along: "1, 2, 3, 4; 1, 2, 3, 4;..."

Your song should sound like this!:

*(Click anywhere on the picture to start. Click the Red Stop Sign to pause. Click the Green Flag to restart.)*

### Project Details: Using 1/8 Notes

1. Let's try a new song. Grab another strip of paper and divide it up into four sections, just like before.

2. Once again, pick four stickers to place in the first section. But this time, cut one of your stickers in half and place both halves down along with your three whole stickers.

3. Repeat the pattern for the remaining measures!

4. Tap along on the table. Point to each sticker with one hand as you tap along with the other. You can count along like musicians do - "1, 2-and, 3, 4; 1, 2-and, 3, 4", or just make your own sound! "Bum, bum-bum, bum, bum".

Your song should sound like this!:

**Let's take a moment to review the math:**

*Remember, we're not just seeing fractions in music, but we are also actively adding, multiplying, and dividing fractions without even realizing it!*

Remember that each sticker is a quarter (1/4) note? Well, what happens when we cut 1/4 in half? That is, what is 1/4 ÷ 2?

We mathematically proved that each orange sticker is a 1/8th note, or "eighth note".

This is the sort of math we see in our final years of elementary school! Does dividing and inverting fractions seem a little scary? Here's an easier way to look at it:

Look at the stickers in your first measure again. Using a pencil, draw a line across each of the three full circles (across the *diameter* of the circle) so that you divide them all in half.

Now count: how many half stickers do you see?

There are eight half-stickers. That means each half sticker is just one 1/8 of the entire 4/4 measure.

What would happen if you re-combined two 1/8 stickers?

(1/8) + (1/8), or 2(1/8) = 2/8 = 1/4. We're right back to one full sticker, which is a quarter (1/4) note!

### Project Details: Using 1/16th Notes

1. Now, what would happen if you took each of those half stickers, and cut them in half again? Grab another strip of paper and select another four stickers. This time, cut one of the stickers in half, then cut the halves into half, giving you four small stickers! Place your stickers in the first measure of your strip of paper.

You took two 1/8 notes and divided each piece by 2. What kind of note is each small orange sticker now?

**Intuitive Way (for 4/4 Time):**

Take your pencil and draw a line across the center (*diameter*) of each remaining full circle from left to right (*horizontally*), then again from top to bottom (*vertically*). Each circle should be divided up into four equal pieces. How many equal pieces are there now in the entire measure?

You should have counted 16! That means every one small orange sticker is one out of a total of 16 equal pieces in a measure. One orange sticker is 1/16 of the 4/4 measure, or a "sixteenth note".

**Algebraic Way:**

Each sticker is a quarter (1/4) note. What happens when we divide 1/4 by 4?

Once again, we show that each new orange sticker is a 1/16th note!

2. Now that you've got the hang of it, finish filling in your song!

3. Don't forget to try tapping the rhythm!

Your song should sound like this!:

### Discussion

Once you've completed the starter song compositions here, try engaging in the following discussion questions:

1. Try creating songs where each measure is different using 1/4 notes and 1/8 notes. What kind of patterns can you create? What if you don't use any patterns? Can you tap along with your new song?

2. Try creating songs where each measure is different using 1/4, 1/8, and 1/16 notes. What kind of patterns can you create? What kind of song can you write with no pattern? Can you tap along with your new song?

3. What kind of songs could you compose in 3/4 time?

"3/4 Time" means that every measure adds up to the fraction 3/4. So if you count the beats in your head, you'll count "1, 2, 3; 1, 2, 3;" and every count is a quarter (1/4) note.

4. Try drawing in your own musical staff, still separating the strip of paper into four equal measures. Use your stickers to now decide what notes you want in addition to the length of the beat. Now you're really composing!

### Supporting Resources

For students ready to take the next step in connecting fractions to music, check out this amazing tool created by Math Engaged's Coding Director for musical and mathematical engagement:

"Beat Maker" was created using Scratch; you can click here to access the app directly.

Looking for another activity combining music and fractions? Check out our Rhythms & Fractions Activity!

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