Finding the Pattern Core and Predicting What Comes Next - First Grade Mathematics

Every repeating pattern has a beating heart: a small, secret rhythm unit called the pattern core! If you know the core of a pattern, you hold the master key to the entire sequence. You do not just know what comes next; you know what the 10th shape, the 20th shape, or even the 100th shape will be! Finding the pattern core is like discovering the secret code of a mystery. In this chapter, you will master isolating the pattern core, testing it to make sure it repeats without errors, and predicting what comes next in any sequence.

How to Find the Pattern Core

To find the pattern core, look for the moment when the pattern starts over again from the beginning!

Isolating the Core:
Look at:  Circle, Triangle, Square, Circle, Triangle, Square, Circle...
            (O)       /\       [#]  |   (O)       /\       [#]  |  (O)
Start:     (O)
Next:      /\
Next:      [#]
Wait! Look: Here is (O) again! That is our starting shape!
Draw a divider line right before the (O)!

The Three Steps to Isolate the Core:

Step 1: Identify the very first item (the leader). Step 2: Scan forward until you see that exact leader appear again. Step 3: Check if the items following that leader match the beginning! If they do, put brackets [ ] around the first group. That chunk is your PATTERN CORE!

Testing the Core: The Repeat Check

Never assume you have found the core until you test it against the rest of the pattern!

Testing: Red, Blue, Blue, Red, Blue, Blue, Red, Blue, Blue

Candidate Core: [ Red, Blue, Blue ] (Length = 3)
Test Chunk 1:   Red, Blue, Blue   (Matches!)
Test Chunk 2:   Red, Blue, Blue   (Matches!)
Test Chunk 3:   Red, Blue, Blue   (Matches!)
The Core is VERIFIED: Red, Blue, Blue (ABB)!

The Incomplete Core Trap

What if someone looks at Red, Red, Blue, Red, Red, Blue and thinks the core is just Red, Red? Test it: After Red, Red comes Blue, NOT Red, Red! The core failed the test. The true core must be Red, Red, Blue!

Predicting What Comes Next

Once your core is verified, predicting the missing pieces is simple:

Predicting the Missing Pieces:
Pattern: Triangle, Star, Star, Triangle, Star, [ ? ], [ ? ]
Core:    [ Triangle, Star, Star ]

Look at the third chunk:
It starts with: Triangle
Next must be:   Star
Next must be:   Star
The missing pieces are: Star, Star!

Practice Exercises

Exercise 1: Circle or write down the pattern core for this sequence: Heart, Diamond, Star, Heart, Diamond, Star, Heart, Diamond, Star.

Exercise 2: Find the core and write the next two shapes for this pattern: Square, Circle, Circle, Square, Circle, Circle, Square, , .

Exercise 3: A student looks at this pattern: Up, Up, Down, Up, Up, Down, Up, Up. What is the pattern core, and what word comes next?

Exercise 4: Explain why you must check the second and third repetitions of a pattern before you can be sure you found the true pattern core.

Solutions and Explanations

Solution to Exercise 1: The pattern core is "Heart, Diamond, Star" (an ABC pattern of 3 items).

Solution to Exercise 2: The pattern core is "Square, Circle, Circle" (an ABB pattern). The next two shapes are Circle, Circle.

Solution to Exercise 3: The pattern core is "Up, Up, Down" (an AAB pattern). The next word is Down (completing the third core repetition).

Solution to Exercise 4: You must check subsequent repetitions to ensure the pattern is truly repeating consistently. If you only look at the first two items, you might mistake an AAB or ABC pattern for an AB pattern. Testing multiple repetitions verifies that the rule holds true.