The Beauty of Number Patterns

The world around us provides virtually limitless  ways to teach number patterns to children. I found that our local place of worship, the mall, the park, and our public swimming pool were all wonderful places to investigate number patterns. We visited each place so my son could copy the pattern of the floor tiles, mosaics, and stained glass windows. We found that using graph paper made it easier for him to draw the patterns he saw. Having these visual representations in front of us, made it easy to calculate the number patterns they each contained. Also, the repetition within the patterns gave us a great opportunity to practice multiplication tables. Since my son was essentially making scale drawings, this led to a discussion of architecture. We pondered how each place could be improved upon, in terms of space, seating, and lighting. We shared our ideas with our local homeschooling group. As a group, we created plans for improving some of the venues. Next, we sent a letter to our local government outlining our ideas and explaining the reasoning behind them. When we went to the park to draw patterns, we were also able to combine math and health. We measured and recorded our heartbeats at rest, then again after walking, hopping, and running. Later, at home, we made a graph of ascending and descending number patterns according to how vigorously we had exercised.

Investigating Functions

In addition to the more concrete number patterns, we also looked at abstract, symbolic representations, such as input-output function machines, which are a stepping stone to algebra. These are not actual machines, of course, but are often drawn as computers where numbers go in and come out. They can be an enjoyable way to introduce children to relationships between numbers. Each machine has three main areas: input, rule, and output. Once the rule has been established, e.g. “+2“, the child inputs a number (e.g. “2“), follows the rule (“+2“), then calculates the output (“4“). Once your child is familiar with how function machines work, you can give him the input and output numbers, having him figure out the rule. Here is an example of a basic  input-output function machine. 

Making Predictions Using Number Patterns

You can base input-output function machines on anything you like. Because we live near the ocean, and are subject to hurricanes, we collected data from our immediate environment. We looked online at predicted wave surge heights for different categories of hurricane. Next, we based our machine on average wave height (input), storm surge (rule), and post-hurricane wave height (output). We calculated input-rule-output for several nearby towns. We projected our forecast according to the strength of the hurricane and the distance and elevation of each town from the shore. While it makes sense that the further a town lies inland, the safer it is from the effects of a hurricane, it was interesting to confirm this hypothesis by calculating it mathematically. 

Number Pattern lesson plans:

Visual and Number Patterns

Students describe, extend, and create their own patterns based on numbers, attributes, and geometry.

Explore Number Patterns using a Hundreds Chart

Students explore six different number patterns within a hundreds chart.

Patterns and Possibilities

Discover patterns using a variety of methods, including videos and hands-on activities.

Guess My Rule

Using patterns, functions, and Algebra, this lesson plan provides great ideas and worksheets for teaching and practicing math patterns. It can be adjusted for desired grade level