How to number talk using visual patterns

Naomi Dupre-Edelman, assistant director of math leadership programs at Mount Holyoke College, shares how to incorporate some of her favorite “mathy” thinking activities — visual patterns! — into lessons.

How to number talk

Visual patterns

Visual patterns are some of my favorite “mathy” thinking activities. They feel like puzzles. With visual patterns, you can incorporate ideas around counting, multiplying, adding, creating input/output tables and writing expressions — many of the Standards of Mathematical Practice (SMPs).

How to use visual patterns

In my experience, visual patterns take very little planning. You might need to prepare manipulatives suitable for your students’ grade level and aligned with the topics you’re covering. But the students really do the “hard work.”

Start by finding a developmentally and content-appropriate visual pattern and display it for your class. Then, you can ask questions like “What do you notice? What do you wonder?” Encourage your students to think about the pattern.

Visual Patterns - Pattern #329 - from Fawn Nguyen

Grab a pencil, and let’s try it.

Pattern #329 the webpage Visual Patterns [Credit: Fawn Nguyen]

Take a minute to jot down answers to the questions above. You can then think of other questions, such as, What will be the next in the pattern? How do you know? Then, try to come up with an expression that correlates with the visual representation.

Before presenting to your class, you could bring this to a professional learning circle or casual meeting with your grade-level or content-based team. Compare your strategies, talk about the math and use the questions below to help you along the way.

Questions to ask:

  • What do you notice?
  • What do you wonder?
  • Can you tell me more about your thinking?
  • Can someone say that in a different way?
  • What is changing?
  • How is it changing?
  • How would you describe the pattern?
  • What comes after the [100th/nth] figure?
  • What would the [100th/nth] figure of this pattern look like?
  • How would this pattern continue?
  • What is the pattern’s rule? Write an expression for this pattern.

Links to Standards of Mathematical Practice

Number talks are great opportunities to link back to SMPs. The pattern above highlights these SMPs:

  1. SMP 7: Look for and make use of structure 
    In this number talk, students will look at the visual representations and try to make sense of the pattern. I can’t think of a better way than visual patterns to help them grapple with SMP 7
  2. SMP 2: Reason abstractly and quantitatively 
    Deep questions that ask students to think abstractly about the relationship between each step in a pattern and to represent the pattern symbolically with numbers and variables are geared toward upper elementary students and older. We can begin to ask questions such as “How would you describe the pattern?” Or we can ask them to write an expression for the pattern.

Where to find them

Patterns are everywhere. Just look around. You can even ask students to make patterns with manipulatives or to take pictures of patterns they see.

Here are a couple of websites to get you started:

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