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Patterns you can hear and move

Patterns and sequences · level 1, lesson 2 of 6

A question to start

Listen to a drum. It goes:

boom, tap, tap, boom, tap, tap, boom, tap, tap...

Can you turn that sound into a row of beads? And can you turn it into a dance with your body?

Here is the surprising part. The drum, the beads and the dance can all be the same pattern, even though one is a sound, one is a thing you can hold and one is a way of moving. In this lesson you will find out what "the same pattern" really means.

The idea

Patterns you can hear

A pattern does not have to be something you can see. You can make a pattern with sounds.

Try this. Clap your hands, then stamp your foot twice:

clap, stamp, stamp, clap, stamp, stamp, clap, stamp, stamp

What is the core? The part that repeats is clap, stamp, stamp. It is 3 sounds long.

Sound patterns are everywhere. A clock goes tick, tock, tick, tock: that is an AB pattern. A song often has a part that comes back again and again (grown-ups call it the chorus). A skipping rhyme has a beat that goes on and on, and your feet land in time with it.

Patterns you can move

You can also make a pattern with your body. Try this:

jump, turn, turn, jump, turn, turn, jump, turn, turn

Many dances and games are movement patterns. When you skip, your feet go hop-step, hop-step. When you swim, your arms go left, right, left, right. When you march, you go left, right, left, right. A grown-up may count "one, two, one, two" to help everyone stay together.

The same pattern in different clothes

Now here is the big idea of this lesson. Look at these four rows.

sounds clap stamp stamp clap stamp stamp beads moves jump turn turn jump turn turn letters A B B A B B
  • The sounds go clap, stamp, stamp.
  • The beads go orange, blue, blue.
  • The moves go jump, turn, turn.

They look and sound very different. But in every row, the first thing in the core is one kind, and the next two are another kind, twice. So we can give all three the same letter name: ABB.

That is what "the same pattern" means. The pattern is not the claps or the beads or the jumps. The pattern is the rule: one of the first kind, then two of the second kind, and repeat. You can dress that rule up in sounds, in colours, in shapes or in moves. It is like a person wearing different clothes. The clothes change, but it is the same person underneath.

A good way to check is to write the letters:

  1. Call the first thing A.
  2. Each time something new comes, give it the next letter: B, then C.
  3. Each time something you have seen before comes again, use its old letter.

If two patterns get the same letters, they are the same pattern.

Why the letters work

Why can we swap claps for beads and still have the same pattern? Because the rule only cares about two things:

  • How long the core is. Here, 3.
  • Where the repeats are inside the core. Here, the 2nd and 3rd are the same, and the 1st is different.

The rule never says "it must be a clap" or "it must be blue". So you can pick any two things, as long as you use one of them where the A goes and the other where the B goes.

This idea, finding the same thing underneath two things that look different, is one of the most powerful ideas in all of mathematics. Mathematicians do it all the time. When you know that 2 apples and 3 apples make 5 apples, you also know that 2 cars and 3 cars make 5 cars. The things change, the counting stays the same.

Silence counts too

In a sound pattern, a rest is a beat where you make no sound. It is still part of the pattern! Try this:

clap clap rest clap clap rest clap clap rest

Say it: clap, clap, (shh), clap, clap, (shh). The core is clap, clap, rest: 3 beats long, an AAB pattern. If you forget the rest, you get clap, clap, clap, clap, which is a different pattern.

So when you turn a sound pattern into beads, the rest needs a bead too. You could use an empty space, or a white bead.

Turning a sound into a picture

Back to the drum: boom, tap, tap. Let us draw it. Use a big blue square for boom and a small orange circle for tap.

boom tap tap boom tap tap boom tap tap

Now you can see the sound. And you can play it back by looking at the picture: every blue square is a boom, every orange circle is a tap. Musicians do something like this. They write music down with marks on paper, so other people can play the same tune.

To turn it into a dance, choose a move for boom (maybe a big jump) and a move for tap (maybe a little clap). Then: jump, clap, clap, jump, clap, clap. Same pattern, third set of clothes.

Worked examples

Example 1. From sound to colours. Turn clap, clap, snap into a pattern of red and yellow blocks.

  1. Find the core: clap, clap, snap. It is 3 long.
  2. Give letters: clap is A, clap is A, snap is B. So it is AAB.
  3. Choose a colour for A (red) and a colour for B (yellow).
  4. The blocks go: red, red, yellow, red, red, yellow, red, red, yellow.

You could also choose yellow for A and red for B: yellow, yellow, red. That is still AAB, so it is still right.

Example 2. Which two match? Which two rows are the same pattern?

(a) (b) (c)
  1. Row (a): green, green, orange. Green is A, green is A, orange is B: AAB.
  2. Row (b): triangle, square, square. Triangle is A, square is B, square is B: ABB.
  3. Row (c): orange, blue, orange, blue: AB.
  4. None of them have the same letters! So no two match. Row (a) and row (b) both have a core 3 long, but the pair is in a different place. In (a) the pair comes first; in (b) the pair comes last.

That was a trick question, and it shows why the letters help. Rows (a) and (b) look alike (both use two shapes, both have cores of 3), but they are different patterns.

Example 3. A long movement pattern. The pattern is touch your head, touch your toes, again and again. What do you touch on the 9th move? On the 10th?

  1. The core is head, toes. It is 2 long. Toes is last in the core.
  2. Toes comes on 2, 4, 6, 8, 10, ... (counting by 2s).
  3. So the 10th move is toes. The 9th move is not in the count by 2s, so it is head.

Example 4. A rest in a pattern. A drummer plays boom, rest, boom, rest, boom, rest. Is this an AB pattern?

  1. Boom is A. Rest is something different (no sound), so it is B.
  2. Boom is A, rest is B... The letters go A B A B. Yes, it is an AB pattern, the same as orange, blue, orange, blue. The rest takes the place of the blue bead.

Try it

  1. Clap this pattern out loud: clap, clap, stamp, clap, clap, stamp. What is the core? What is the letter name?
  2. Turn tick, tock, tick, tock into a pattern of circles and squares.
  3. Turn the bead pattern green, orange, orange, green, orange, orange into a movement pattern. (Choose your own moves.)
  4. Which pattern is the odd one out?
    • (a) clap, snap, clap, snap
    • (b) red, blue, red, blue
    • (c) hop, hop, sit, hop, hop, sit
    • (d) up, down, up, down
  5. Give the letter name of snap, clap, stamp, snap, clap, stamp.
  6. A pattern goes clap, rest, rest, clap, rest, rest. How many claps are there in the first 12 beats?
  7. A dance goes step left, step right, jump, again and again. What is the 7th move? What is the 12th?
  8. Make up a sound pattern that is ABB, and a movement pattern that is the same ABB pattern.
Answers
  1. The core is clap, clap, stamp. Clap is A, clap is A, stamp is B: AAB.
  2. Tick is A and tock is B: AB. For example circle, square, circle, square. (Square, circle, square, circle is right too.)
  3. Green is A, orange is B: ABB. For example jump, wave, wave, jump, wave, wave. Any moves are fine, as long as the first move is different and the next two are the same.
  4. (c) is the odd one out. (a), (b) and (d) are all AB patterns. (c) is AAB: hop is A, hop is A, sit is B.
  5. Snap is A, clap is new so B, stamp is new so C: ABC.
  6. The core is 3 beats long and has 1 clap. 12 beats is 4 cores (3, 6, 9, 12), so there are 4 claps. They come on beats 1, 4, 7 and 10.
  7. The core is 3 long, and jump is last: jumps come on 3, 6, 9, 12. So the 12th move is jump. The 6th move is a jump too, so the 7th starts a new core: step left.
  8. Many answers. For example: sound stamp, clap, clap and movement sit, wave, wave. Check that both give the letters A B B.

Common mistake

Thinking a pattern changes when its things change. Clap, stamp, stamp and red, blue, blue are the same pattern, ABB, even though one is loud and one is colourful. Write the letters to check.

Thinking two patterns match because they use the same number of things. Green, green, orange and triangle, square, square both have a core of 3, but one is AAB and the other is ABB. The order matters, not just the count.

Where it leads