Repeating Patterns (AB, AAB, ABB, ABC) - First Grade Mathematics

Have you ever tapped your foot to the steady rhythm of your favorite song: clap, stomp, clap, stomp, clap, stomp? That catchy beat is a pattern! In mathematics, a pattern is an orderly arrangement of shapes, colors, sounds, or numbers that repeats according to a predictable rule. Patterns are everywhere in nature: the stripes on a zebra, the rings on a raccoon's tail, and the alternating day and night cycle. In this chapter, you will master repeating patterns, learn how to label them using letter codes like AB, AAB, ABB, and ABC, and predict what comes next.

What Is a Repeating Pattern?

A repeating pattern is a sequence where a specific chunk of elements repeats over and over in the exact same order without changing.

The Core Rhythm of an AB Pattern:
Circle, Square, Circle, Square, Circle, Square...
  (O)     [#]     (O)     [#]     (O)     [#]
   A       B       A       B       A       B

The Pattern Core

The shortest part of the pattern that repeats is called the PATTERN CORE. In the pattern above, the core is (O) [#], or A B. Once you identify the core, you can extend the pattern as far as you want into the future!

Letter Coding: Naming Patterns with A, B, and C

Mathematicians use letters of the alphabet to label and compare different patterns, no matter what objects are being used!

The Four Classic Repeating Patterns:

1. AB Pattern (Two alternating items):
   Red, Blue, Red, Blue, Red, Blue...
   A     B     A     B     A     B

2. AAB Pattern (First item repeats twice):
   Star, Star, Moon, Star, Star, Moon...
   A      A     B     A      A     B

3. ABB Pattern (Second item repeats twice):
   Triangle, Circle, Circle, Triangle, Circle, Circle...
      A         B       B        A        B       B

4. ABC Pattern (Three completely different items):
   Red, Yellow, Blue, Red, Yellow, Blue...
    A     B       C    A     B       C

Transferring Patterns

Here is the beauty of letter codes: If one pattern is: Apple, Banana, Apple, Banana... (AB) And another is: Clap, Stomp, Clap, Stomp... (AB) And a third is: Red block, Blue block, Red block, Blue block... (AB) Even though the objects are totally different, all three share the EXACT SAME MATHEMATICAL STRUCTURE: they are all AB patterns!

Extending and Completing Repeating Patterns

To find what comes next in a pattern: Step 1: Read the pattern aloud with rhythm! Step 2: Circle the repeating core each time it appears. Step 3: Continue the core from where it left off!

Extending an ABC Pattern:
Pattern: [Triangle] [Square] (Circle) | [Triangle] [Square] (Circle) | [Triangle] [ ? ]
Core is: Triangle, Square, Circle!
After Triangle comes: SQUARE!
Next shape: [Square]!

Practice Exercises

Exercise 1: What is the pattern core in this repeating pattern: Dog, Cat, Dog, Cat, Dog, Cat? What letter code describes this pattern?

Exercise 2: Identify the letter code (AB, AAB, ABB, or ABC) for each of these patterns: Red, Red, Blue, Red, Red, Blue: _ Circle, Triangle, Square, Circle, Triangle, Square: _ Apple, Orange, Orange, Apple, Orange, Orange: ____

Exercise 3: Look at this pattern: Up, Down, Up, Down, Up, ____. What comes next in the sequence?

Exercise 4: Explain what the mathematical term "pattern core" means.

Solutions and Explanations

Solution to Exercise 1: The pattern core is "Dog, Cat." The letter code that describes this pattern is AB.

Solution to Exercise 2: Red, Red, Blue, Red, Red, Blue is an AAB pattern. Circle, Triangle, Square, Circle, Triangle, Square is an ABC pattern. Apple, Orange, Orange, Apple, Orange, Orange is an ABB pattern.

Solution to Exercise 3: The next word is Down. The pattern is an alternating AB pattern (Up, Down).

Solution to Exercise 4: The pattern core is the shortest sequence or chunk of items that repeats continuously to create the entire pattern.