Number and Visual Patterns

The focus of this unit is number patterns and patterns made with shapes or other materials. Much of mathematics involves recognizing, creating, describing, and extending patterns. It is important for students to be able to recognize a pattern and to be able to describe and extend it. 

Topics covered include:

• identifying the core of repeating patterns (grade 2)

• extending repeating patterns (grade 2)

• predicting an element of a repeating pattern (grade 2)

• creating a repeating pattern (grade 2)

• identifying and describing increasing and decreasing patterns (grade 3)

• describing patterns with a pattern rule that includes a starting point and how the pattern continues (grade 3)

• creating increasing and decreasing geometric patterns (grade 3)

• extending patterns to confirm a prediction (grade 3)

• creating an increasing or decreasing pattern from a given pattern rule (grade 3)

• exploring number patterns, including skip counting patterns and patterns on hundreds charts (grade 3)

• identifying errors and missing elements in patterns (grade 3)

• comparing patterns, and describing how they are alike and how they are different

What are Patterns?

Patterns occur when numbers or items are placed in a sequence where the change from one item to the next is predictable and consistent. 

Repeating Patterns (grade 2)

A repeating pattern is one where a certain sequence is repeated over and over. Red, blue, red, blue, red, blue is a repeating pattern because the sequence "red, blue" repeats.  In this case we say that "red, blue" is the core of this pattern, because that is the part that repeats. The core of a pattern can be more than just 2 elements, and students need to be able to look at a pattern and determine its core. 

Increasing and Decreasing Patterns (grade 3)

An increasing pattern is one where the numbers or the objects increase in a predictable way as the pattern continues. For example: 2, 5, 8, 11,... is an increasing pattern, because the numbers increase by 3 each time. Similarly, a decreasing pattern is one where the numbers or objects decrease as the pattern continues. For example: 75, 65, 55, 45... is a decreasing pattern because the numbers decrease by 10.

Pattern Rules (grade 3)

Students need to be able to describe a pattern so that it can be recreated. A pattern rule uses a standard format for describing a pattern. A pattern rule always tells the starting point and how each item in the pattern changes as the pattern continues. For example, this pattern:

X    XX    XXX    XXXX    XXXXX

has a pattern rule of: "Start with 1 X. Add 1 X each time."

This pattern: 75, 65, 55, 45 has a pattern rule of: "Start at 65. Subtract 10 each time."

Extending and Predicting

The whole point of being able to notice and describe patterns is to solve problems. Most mathematics is based on noticing and using patterns to solve problems. When students notice a pattern, they should be able to use the pattern rule to extend the pattern. Sometimes the information we're looking for is further along the sequence than just the next number. 

Think about solving these problems: 

A machine dispenses gum balls in a repeating pattern of yellow, blue, green, red. If each child in line takes only one gum ball, what colour gum with the 14th child get?

Mr. Beals goes for a walk each night. On Monday, he walked 2 km. Tuesday 3 km. Wednesday 4km. If the pattern continues, how far will he walk on Saturday? Students need to be able to notice the pattern and use it to predict what Saturday will look like. That's a lot of walking I did that week!

Some Ways to Practice at Home

• Patterns occur everywhere. Be on the look out for them, and ask your child to notice the pattern and describe it to you. Try to encourage them to tell you the pattern rule. 

• When your child is playing with Lego or other toys, give them a pattern rule and see if they can create the pattern. You could also make a pattern and see if they can extend it.

• Set up riddles or a treasure hunt where your child needs to extend a pattern in order to find the final answer.

• While playing outside, get your child to use natural items to make you an increasing or a decreasing pattern. You could also build a pattern and have them tell you the pattern rule and extend the pattern.