Welcome to the World of Patterns!

Have you ever noticed the stripes on a zebra, listened to the steady beat of a drum, or watched leaves unfold along a stem? If so, you are already thinking like a mathematician! Patterns are everywhere around us, from the music we hear to the games we play and the natural world outside our window.

In this chapter, we will explore patterns in everyday situations. We will discover how patterns work through sounds, actions, objects, and nature. We will also learn the two main ways patterns behave: they can repeat, or they can grow.

Note: Later chapters explore number-based rules, such as odd and even numbers or skip counting, but here our focus is on observing, identifying, extending, and creating patterns in daily life!

What Is a Pattern?

A pattern is an arrangement of things—such as sounds, shapes, movements, or objects—that follows a clear, predictable order or sequence. Because it follows an order, a pattern helps us predict what comes next.

When we explore patterns in mathematics, we go through three exciting steps:

1. Constructing meaning: We build our understanding by using our senses, handling real objects, clapping beats, or looking at nature.
2. Transferring meaning into symbols: Once we understand the pattern in real life, we can draw pictures, make diagrams, or use letters and symbols to record it.
3. Applying with understanding: We can spot patterns independently and use them to solve real-life puzzles and create our own designs!

Part 1: Repeating Patterns

A repeating pattern has a specific part that happens again and again in the exact same order. This repeating part is called the core or the repeating unit.

Repeating Patterns Around Us

Repeating patterns do not just live on paper; we experience them every single day:

• Sounds: A drum rhythm that goes boom, tap, tap, boom, tap, tap, boom, tap, tap.
• Actions: A dance routine like clap, stomp, jump, clap, stomp, jump.
• Objects: Setting a dinner table with fork, plate, spoon, fork, plate, spoon.
• Nature: The regular cycle of day and night, or the bands of colour on a caterpillar.

Finding the Repeating Core

To understand a repeating pattern, always ask yourself: "What part keeps happening over and over?"

Let's look at an example using fruit on a tray:
Apple, Banana, Apple, Banana, Apple, Banana...

• The core is: Apple, Banana.
• Once you spot the core, you can easily tell what comes next: another Apple!

We often use letters to describe the structure of a repeating core:

• AB Pattern: clap, tap, clap, tap, clap, tap... (The core is two items long: \(A, B\))
• AAB Pattern: red, red, blue, red, red, blue... (The core is three items long: \(A, A, B\))
• ABC Pattern: triangle, square, circle, triangle, square, circle... (The core is three items long: \(A, B, C\))

Quick Takeaway: In a repeating pattern, the core never changes its size—it simply repeats itself in the exact same order over and over.

Part 2: Growing Patterns

Not all patterns stay the exact same size. Some patterns change systematically at each step. These are called growing patterns (or changing patterns).

In a growing pattern, each step or stage is related to the one before it by an increase or a predictable change. Things get bigger, taller, longer, or more numerous!

Growing Patterns Around Us

Where can we see growing patterns in real life?

• Nature: A plant sprouting new leaves. On day one it has \(1\) leaf, on day two it has \(2\) leaves, on day three it has \(3\) leaves.
• Objects: Building a staircase with wooden blocks. Step one is \(1\) block high, step two is \(2\) blocks high, step three is \(3\) blocks high.
• Sounds: A rhythm that gets progressively longer: \(1\) clap, pause, \(2\) claps, pause, \(3\) claps, pause!

Understanding How a Pattern Grows

Don't worry if growing patterns seem a bit trickier than repeating patterns! You just need to be a pattern detective and look for what is being added at each stage.

Imagine building towers with snap cubes:

• Stage 1: A tower of \(2\) cubes.
• Stage 2: A tower of \(4\) cubes.
• Stage 3: A tower of \(6\) cubes.

Ask yourself: "What changed between Stage 1 and Stage 2?"
We added \(2\) cubes!
"Did the same change happen between Stage 2 and Stage 3?"
Yes, we added \(2\) more cubes!
Because \(2\) cubes are added every single time, we know that Stage 4 will have \(6 + 2 = 8\) cubes.

Quick Takeaway: In a growing pattern, the elements do not simply repeat the same cycle. Instead, they change from one step to the next in a regular, predictable way.

How to Work with Patterns: The Four Key Skills

To master patterns in everyday situations, practice these four essential skills:

1. Identifying Patterns

Look and listen carefully. Spot whether the sequence repeats the exact same unit or if it grows larger at each step.

2. Describing Patterns

Use clear words to explain what you see or hear. For example:
• "This is a repeating pattern. The core is blue bead, yellow bead, yellow bead."
• "This is a growing pattern. Each row has one more block than the row before it."

3. Extending Patterns

Use the rule you found to continue the pattern into the future.
• If a repeating pattern ends on hop, step, and the rule is hop, step, jump, the next movement must be jump.
• If a staircase grows by \(1\) block each step (\(1, 2, 3, 4\)), the next step will have \(5\) blocks.

4. Creating Patterns

Now it's your turn to be the designer! You can make your own patterns using buttons, drawings, body percussions (like snapping and clapping), or natural items like pebbles and leaves.

Common Mistakes to Watch Out For

• Stopping the core too early: In a pattern like circle, circle, star, circle, circle, star, make sure you don't call the core just circle, star. Look at the whole repeating unit: it is circle, circle, star!
• Confusing repeating with growing: Always check if the stages are getting bigger. If the number of items stays the same in every cycle, it is a repeating pattern. If each stage has more items than the stage before, it is a growing pattern.
• Rushing past the rule: Before trying to extend a pattern, always pause and double-check your rule on at least two full steps to make sure it works consistently.

Quick Review

• Patterns are regular, predictable arrangements found in sounds, actions, objects, and nature.
• Repeating patterns repeat an unchanging unit called the core (like \(A, B, A, B\)).
• Growing patterns change predictably from stage to stage (like adding \(1\) more each time).
• We can identify, describe, extend, and create patterns in our everyday environment!