December 4-7 Math - Repeating Patterns

 

For the last few weeks we have been building our understanding of patterns by looking at patterns and cycles found in our everyday life, creating our own patterns with different elements, extending and translating patterns using a variety of materials.  The following is a summary of the key ideas and concepts we have been learning.

Learning Intentions

I can recognize cycles encountered in daily routines and nature.

I can identify the pattern core, up to four elements, in a cycle.

I can describe change and what stays the same in repeating patterns and cycles.

I can copy a pattern of up to four elements in a different way (translate).

I can extend a pattern.

What Is a Repeating Shape Pattern?

A repeating shape pattern is a sequence of 2-D shapes or 3-D objects where a first set of shapes or objects repeats over and over.

The smallest set of items that repeats is called the core of the pattern.

Since repeating patterns always involve some sort of repetition, knowing the core of a pattern is important. It helps you predict how the pattern will continue.

For example, the core of this pattern is triangle, circle, square.

So, the pattern will continue like this:

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What Types of Repeating Shape Patterns Are There?

Each shape or object in a pattern can be shown with a different letter. The number of letters that repeat tells how many items are in the core. There are many types of repeating patterns.

A pattern with two different items that repeat is called an AB pattern.

A pattern with three different items that repeat is called an ABC pattern.

A pattern with a core made up of one item followed by two identical copies of another item is called an ABB pattern.

A pattern with a core made up of two identical items followed by a different item is called an AAB pattern.

While it can be helpful to name a pattern with letters, it is not critical.

There are many other types of patterns, but in this lesson, we will focus on the four types shown above.

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Continuing a Pattern in Different Ways

A pattern rule tells you how a pattern continues. For example:

Rule: Repeat a cube, a cube, and a cone over and over again.

An important idea for students to understand is that you cannot be sure how a pattern continues unless the person who created the pattern tells you what the core is.

For example, if a pattern begins with a triangle and a circle, it could continue in several ways. For example:

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How We Show a Pattern Continues

We can never show a whole pattern, just the start of it. To show that a pattern continues, people write “…” at the end.

For example,

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What Is a Repeating Number Pattern?

A repeating number pattern is a collection of numbers that are arranged in a specific order that repeats over and over.

Number patterns have the same sort of structures as shape patterns.

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A repeating number pattern has a core just as a repeating shape pattern does.

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A shape pattern can be described using letters. Letters can be used to describe number patterns, too. 2, 4, 2, 4, 2, 4, … is an AB pattern. 3, 7, 3, 7, 3, 7, … is also an AB pattern. 1, 1, 7, 1, 1, 7, 1, 1, 7, … is an AAB pattern. 3, 4, 5, 3, 4, 5, 3, 4, 5, … is an ABC pattern. 4, 6, 6, 8, 4, 6, 6, 8, 4, 6, 6, 8, … is an ABBC pattern. Different letters are used to describe different numbers in the pattern. Pattern Structure The structure of a repeating pattern describes how it repeats. It does not give any information about the items that appear in the pattern. For example, these two patterns have the same structure: Once we identify the structure of a pattern, we can name the pattern with letters. Both patterns above are AAB patterns. When we use different things to create a pattern with the same structure, we say we are translating the pattern. You can translate this ABA pattern made with numbers to get the ABA pattern made with shapes.

Helping Your Child

At home, you can help your child make different types of patterns based on shape, colour, orientation, and sounds.

In terms of shape patterns, you might use various shapes around the house. For example, invite your child to show you the patterns he or she can create using different types of blocks, toys, or stickers. You can also practise making shape patterns on a computer or tablet. You might also have your child observe everyday patterns at home.

For example, you might see these patterns around a table:

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fork, knife, fork, knife, fork, knife, …

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a design repeated around the edge of a plate Creating Number Patterns Creating number patterns is simple. Choose a pattern core and repeat it over and over again. Numbers of any size can be used to create number patterns. For example, these are both ABB number patterns: 2, 3, 3, 2, 3, 3, 2, 3, 3, … 35, 36, 36, 35, 36, 36, 35, 36, 36, … Play a pattern game with your child. Say the first few terms of a repeating number pattern and ask your child, “How do you think this pattern continues?” It can be difficult to find repeating number patterns in day-to-day life. Instead, take opportunities to share visual or sound patterns with your child. Ask your child to name the pattern using letters. For example, you could stamp, clap, clap, stamp, clap, and clap again (which is fun). Your child can join in once he or she recognizes the pattern. Then ask your child to name the pattern (in this case, ABB). You could do the same with colour patterns and shape patterns.