Tag Archives: Sorting

The Mathematics of the Natural World, Part 1: Attribute Patterns

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I have always been a lover of numbers. Math and science just go together so wonderfully. To me, the idea that most natural phenomena (population growth, diffusion, cell division, plant leaf arrangement, a beautiful vista…) could be explained by a simple mathematical formula or idea, is just mind-boggling and reassuring, at the same time.

This post will provide you, the teacher, with some definitions, establish the relevance of some mathematical ideas to the natural world, and share links to some online resources that will help you plan math connections to your winter study of patterns in nature.

Mathematics in Nature — An Overview

We will review, in brief, a number of mathematical principles in this blog, over the next several weeks. In each post, the concept will be defined, in mathematical terms, then explained as it relates to the natural world. I will share some real-life examples, and then provide helpful links to some classroom tasks to reinforce the idea.

  • patterns
  • order & magnitude
  • symmetry
  • scale & proportion
  • Fibonacci numbers
  • fractals
  • The “Golden Ratio”
  • tessellations

Patterns in the Natural World

When we think of teaching patterns to students, our first thought is usually those patterns we named with letters, back in kindergarten and first grade:




and so on…

In reality, there is much more to the mathematical idea of patternation than this. There are actually three major types of patterns, classified by the basis for the pattern:

  1. Logical patterns
  2. Numerical patterns
  3. Language patterns

All three types can be studied via your science and nature study work, as we will see today.

Logical Patterns

Logical patterns are conceptual patterns based on meaning. There are two main types of logical patterns: attribute patterns and order patterns. Today we will talk about attribute patterns.

Attribute patterns

Children learn, at a very early age, that objects in the real world have qualities, or attributes, some of which can be directly observed (size, shape, color), others which can be determined by the use of simple tools or tests (e.g., floaters and sinkers, magnetism, etc.). When children sort objects into groups based on like attributes, or classify objects into identified groups, they are using attribute patterns as the basis for their work.

Here’s a real-world example of these two types of patterns, based on my son’s homeschool library and room organization. I know that it is easier for children to find things if there is system to organizing them. I have used two different systems over the years, in classroom and homeschool, both successfully. One involves more on my part, one more of the child’s thinking.

Scenario 1: Pre-Determined Classification System (most common)

Before the start of the year, I organize the classroom or homeschool library according to pre-determined categories, based on past experience and curricular needs, label the shelves or explain the system, and guide students to replace materials in the proper category through classification. This is likely the same system most parents use to help kids organize their bedrooms.

I do this based on several attributes, some observable, some based on purpose (not observable). How do you think I organized the two areas in the photos, below?

Logical patterns attributes www.simplesciencestrategies.com

Read below for the criteria by which we sorted my son’s homeschool resources.

Here were our categories, based on use:

  • Encyclopedias and Reference Books (1)
  • History Books (2)
  • Today’s Materials (3)
  • Hats (4)
  • Notebooks (6)
  • Science Books (5)
  • Soccer Stuff (7)

Here is another example, using more obvious attributes…

Logical patterns attributes www.simplesciencestrategies.com

Sorting books based on more obvious attributes.

Scenario 2: Student-originated Organization System (less common)

In some cases, I let the students organize belongings, then tell me their criteria for arranging them. This is the skill of categorization, the flip-side of classification.This requires the adult to let go of the process, and accept the students’ system of organization.

When we did this with the classroom library, it entailed a huge mess (at first), lots of argument, and some rather clever, kid-friendly categories. This is the system my two youngest boys have employed when making sense out of about a million LEGO pieces, as below. (NOTE: My middle son employed a label maker and made category labels for the compartments of an inexpensive hardware storage box):

Logical patterns attributes www.simplesciencsestrategies.com

Form and functionality help the LEGO builder sort bricks.





Logical patterns attributes www.simplesciencestrategies.com

Kindergartners sort and categorize seeds, providing their own categories.

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