Patterns are everywhere. Exploring and identifying patterns can help children understand our number system, operations, spatial understanding and the foundations of algebra. Mathematics is the study of patterns and exploring them through play can begin mathematical and algebraic thinking in early years. Click here for a downloadable version of this post.

There are several big ideas related to patterns:

1. Patterns exist and occur regularly in the natural and man-made world.
2. Patterns can be recognized, extended and generalized using words and symbols.
3. The same pattern can be found in many different forms – physical objects, sounds, movements and symbols.

The progression of patterns through Saskatchewan Curricula:

When viewing patterns, it is useful to know the following terms:

• Element – an action, object, sound or symbol that is part of a sequence.
• Core – the shortest string of elements that repeats.
• Pattern – a sequence of elements that has a repeating core.

Children will develop their ability to recognize and manipulate patterns differently. Some children will move through the following progression:

Exploring patterns also gives children practice and exposure to other mathematical ideas, including:

• Counting and cardinality – counting the number of items in the unit of a repeating pattern, or how many items are added in an increasing pattern.
• Adding and subtracting – generalizing about an increasing or decreasing pattern – how many more or less.
• Position and spatial properties – which element comes next, which element is between two others, reversing order of elements.

## How might you teach patterns?

As with many mathematical ideas in early years, it is important to connect ideas. Learning is not linear! It is important that children use physical materials from their environment to build and explore patterns rather than relying on drawing and colouring patterns. Buttons, toys, linking cubes and natural materials can all be used to create patterns.

The Measured Mom has a list of fun ways to engage young children in exploring patterns. It is fun to take children outside. Megan Zeni describes how you might have children explore Patterns Outside and in Nature.

## Repeating Patterns

Repeating patterns can be introduced using concrete objects, sounds, body movements or symbols. Exploring with a variety of materials can help children identify what is creating a pattern.

Pattern Strips can be made using any shape or object. Students can work independently or in groups to copy the pattern on a strip using real objects. These patterns can then be extended. Watch whether they are copying each element separately or if they have identified the core of the pattern and are able to place all of the elements of the core at the same time. This might look like:

• If the pattern is red/blue/red/blue – children will place the red and blue at the same time.

A significant step in understanding patterns is when children are able to identify that the same pattern exists even when the materials are different. Using some type of symbol, children are able to code a pattern and compare it to other patterns. If they choose to code the pattern using the alphabet, they might describe it as A-B-A-B or A-A-B-A-A-B. An extension with pattern strips is to create the same pattern with different materials.

Pattern Match can happen in many forms.

• You can give each group a set of different pattern strips, and they find which strips are showing the same pattern.
• Children can work in groups, one child is the pattern caller. They choose 3-4 pattern strips and lay them face up on their table. They then ‘secretly’ choose one of the strips and calls out the pattern code. Their group members try to identify which strip is being read.

## Growing Patterns

In Saskatchewan, children begin to explore increasing patterns in grade 2, and decreasing patterns starting in grade 3.  The beginning of understanding growing patterns is for children to experience building them with concrete objects.

It is important for children to record their observations. A table can help students record the number for each step in the pattern. Using a table, students can predict how many items are needed to create a certain step in the pattern.

## Patterns with Numbers

Number patterns are woven throughout our number system, how we perform operations and the ways we represent numbers. John Van de Walle and LouAnn H. Lovin (Teaching Student-Centered Mathematics K-3, 2006) have created a number pattern activity that has students identify how a number string continues by identifying the pattern present.

### Skip Counting

Skip counting is an excellent source of patterns. We often limit skip counting to small numbers like 2, 3 or 5. We also often start skip counting at 0. Children can explore the patterns that are created when we skip count by larger numbers, changing the start number. It is a great idea to use a calculator, so students don’t get bogged down in computation!

• If we start at 7 and skip count by 5’s, what pattern do we see?
• 7, 12, 17, 22, 27, 32…
• If we start at 7 and skip count by 55’s, what pattern do we see?
• 7, 62, 117, 172, 227, 282, 337, …
• What do we notice about these two patterns?

### Patterns in the Hundreds Chart

#### Start and Jump on the 100s Chart

Using a hundreds chart, have students colour in the pattern created by one of the Start and Jump Numbers sequences given. If different students represent different patterns, what do they notice?

• How do patterns change when
• the start number changes?
• The jump number changes?
• Which skip count numbers create columns?

#### Let’s Build the 100’s Chart

• Using a pocket 100s chart or interactive 100’s chart. Place the following number cards in the pockets:
• 4, 10, 17, 32, 48
• Gather students so they can see the 100’s chart easily.
• Hold up a number related to one of those in the chart, such as 18. Ask “who would like to place this number?”. Explain how you know where to put it.
• Choose numbers to place based on the number concepts you are working on:
• If you are working on adding 10, choose numbers that emphasize that concept.
• If you are working on skip counting, choose numbers that emphasize what you are counting by.

#### Game: Arrow Clues

• Clues can be created on cards or written large enough for all players to play the same clues.
• Arrow clues can look like:
• Differentiation:
• Students can play with or without a 100s chart to refer to.
• Have students describe the impact of each of the types of arrows on the VALUE of the number.

#### Missing Number Puzzles

Using the patterns in the 100’s chart, children can figure out the missing numbers when only a part of the 100s chart is provided.