Grade by Grade
C. Algebra · Patterns, Equality and Coding

Making and Translating Patterns

C1.2About 30 minutes
Learning goals
  • I can make a pattern with movements, sounds, objects, shapes, letters and numbers.
  • I can translate a pattern: show the same pattern in a different way.
  • I can use letters like AB or AAB to name a pattern.

Words to know

create
To make something new.
translate
To show the same pattern using different things. The things change, but the rule stays the same.
AB pattern
A pattern whose core has two different parts, like clap, stomp, clap, stomp.
AAB pattern
A pattern whose core is the first thing twice, then a different thing, like leaf, leaf, snowman.
ABC pattern
A pattern whose core has three different parts, like red, yellow, blue.

Clap, stomp, clap, stomp!

Stand up and try this: clap, stomp, clap, stomp, clap, stomp.

You just made a pattern with your body! Patterns are not only pictures. You can make patterns with:

  • movements: clap, jump, wave, touch your head
  • sounds: beep, boop, drum, whistle
  • objects: spoon, fork, spoon, fork
  • shapes: circle, square, circle, square
  • letters: A B A B
  • numbers: 1 2 1 2

Naming patterns with letters

Math helpers use letters to name the core of a pattern.

  • The first kind of thing gets the letter A.
  • A new, different kind of thing gets the letter B.
  • Another new kind of thing gets C.

So 🍎 🍌 🍎 🍌 is an AB pattern.

🍎 🍎 🍌 🍎 🍎 🍌 is an AAB pattern.

🍎 🍌 🍇 🍎 🍌 🍇 is an ABC pattern.

PatternCoreLetter name
clap, stomp, clap, stompclap, stompAB
🐟 🐟 🐻 🐟 🐟 🐻🐟 🐟 🐻AAB
red, yellow, blue, red, yellow, bluered, yellow, blueABC
jump, wave, wave, jump, wave, wavejump, wave, waveABB
Naming patterns with letters

Translating a pattern

To translate a pattern means to show the same pattern using different things.

The things change. The rule stays the same.

Look at this shape pattern:

circle, triangle, triangle, circle, triangle, triangle, circle, triangle, triangle. This is an ABB pattern.
Way to show itThe same ABB pattern
Shapescircle, triangle, triangle, circle, triangle, triangle
LettersA B B A B B
Movementsjump, clap, clap, jump, clap, clap
Soundsboom, ding, ding, boom, ding, ding
Objectsspoon, fork, fork, spoon, fork, fork
Numbers1 2 2 1 2 2
One pattern translated six ways. Every row follows the rule ABB.
Worked example

Translate a pattern into actions

Translate this pattern into movements:

🍁 🍁 ⛄ 🍁 🍁 ⛄ 🍁 🍁 ⛄

  1. Find the core: 🍁 🍁 ⛄.
  2. Name it with letters: leaf is A, snowman is B. The core is A A B.
  3. Choose a movement for A: pat your knees.
  4. Choose a different movement for B: clap.
  5. Do it: pat, pat, clap, pat, pat, clap, pat, pat, clap.

pat, pat, clap, pat, pat, clap, pat, pat, clap. It is still an AAB pattern. Only the things changed.

Worked example

Translate into numbers and letters

Translate this sound pattern into letters and into numbers: beep, boop, buzz, beep, boop, buzz

  1. The core is beep, boop, buzz. It has 3 different parts.
  2. Letters: beep = A, boop = B, buzz = C. So it is A B C A B C.
  3. Numbers: give each part a number. beep = 1, boop = 2, buzz = 3.

Letters: A B C A B C. Numbers: 1 2 3 1 2 3.

Check your translation

Put your new pattern under the old one. Each thing in the old pattern should match one thing in the new pattern. Same thing in the old one? Same thing in the new one!

coreShapesLettersNumbersMovesA1jumpB2clapB2clapA1jumpB2clapB2clap
One ABB pattern shown four ways. Read down any column: a circle is always A, 1 and jump, and a triangle is always B, 2 and clap. The dashed box is the core.

Your turn

1

Name this pattern with letters: 🐶 🐱 🐶 🐱 🐶 🐱

2

Name this pattern with letters: 🔺 🔺 🟩 🔺 🔺 🟩

3

Name this pattern with letters: snap, clap, stomp, snap, clap, stomp

4

Translate A B A B A B into a movement pattern.

5

Translate red, red, blue, red, red, blue into numbers.

6

Sam says 1 2 2 1 2 2 and A B A B A B are the same pattern. Is he right?

7

Make your own AABB pattern using objects from your kitchen.

Just for fun

Knock, knock.

Who's there?

Clap.

Clap who?

Clap, stomp, clap, stomp, clap... you know what comes next!

Hands-on activity

Pattern band

You need: a pot and a wooden spoon, or just your hands and feet.

  1. A grown-up makes a sound pattern, like drum, drum, clap.
  2. You copy it.
  3. Now translate it! Use movements instead: jump, jump, spin.
  4. Then translate it again with objects. Line up toys: car, car, block, car, car, block.
  5. Write the letters under your toys: A A B A A B.
  6. Switch jobs: you make a pattern and your grown-up translates it.

Math talk

Ask: How are these two patterns the same? How are they different? (They have the same rule, but use different things.)

More practice: warm-up

1

Name this pattern with letters: 🐝 🌼 🐝 🌼 🐝 🌼

2

Name this pattern with letters: hop, hop, spin, hop, hop, spin

3

Name this pattern with letters: 🟢 🔵 🔵 🟢 🔵 🔵

4

True or false? 1 2 1 2 1 2 is an AB pattern.

5

Which movement pattern is an A B A B pattern?

  • a) clap, clap, jump, clap, clap, jump
  • b) clap, jump, clap, jump, clap, jump

More practice: on your own

1

Translate 🍁 ⛄ ⛄ 🍁 ⛄ ⛄ into letters and into numbers.

2

Translate this sound pattern into shapes: ding, dong, ding, dong, ding, dong

3

Name this pattern with letters: 🚗 🚌 🚲 🚗 🚌 🚲

4

Translate A A B B A A B B into things from your backpack.

5

Which two patterns are the same pattern?

  • a) 🐶 🐶 🐱 🐶 🐶 🐱
  • b) red, blue, red, blue, red, blue
  • c) 5 5 9 5 5 9

Challenge

1

Find the mistake! Nora translated 🦆 🦆 🐟 🦆 🦆 🐟 into movements:

clap, clap, stomp, clap, stomp, stomp

What did she do wrong? Fix it.

2

Ben says 1 2 3 1 2 3 is an AB pattern because it only uses numbers. Is he right? Explain.

3

Name this pattern with letters: jump, jump, clap, wave, jump, jump, clap, wave. How many parts are in the core?

Check your understanding

Quiz

1.

What does it mean to translate a pattern?

2.

Which letters name this pattern? jump, jump, clap, jump, jump, clap

3.

Which is a translation of 🍎 🍌 🍎 🍌?

4.

Which pattern is an ABC pattern?

5.

Which letters name this pattern? 🍓 🍓 🥕 🥕 🍓 🍓 🥕 🥕

6.

Which is a translation of jump, clap, clap, jump, clap, clap?

For parents and teachers

Translating a pattern shows that your child understands the structure (the rule), not just the pictures. This is an early step toward algebra, where letters stand for things.

Common mistakes

  • Changing the rule while translating (for example, turning AAB into AB). Line the two patterns up one under the other and check each pair.
  • Thinking the letters must match the first letter of the word (B for banana). Explain that A just means the first kind of thing.
  • Making a "pattern" that only shows the core once. A pattern should show the core at least 3 times so others can see the rule.

How to help

  • Make sound and movement patterns in the car, at bath time or while waiting in line.
  • Use toys, cutlery, socks, LEGO or pasta to make object patterns.
  • Take turns: one person makes a pattern, the other translates it.