Unit 8: Developing Algebraic Reasoning through Visual Patterns

This unit in the CUNY HSE Math Curriculum Framework offers two lessons for presenting  algebra through the use of visual patterns.

  • LESSON I: Introduction to Visual Patterns & A Scaffolded Approach to the Arch Problem This lesson plan begins with some activities to introduce patterns in general. It then models a scaffolded approach to visual patterns with a selection of questions to build towards the development of linear equation(s) that describe the relationship between the number of squares and the figure number. The lesson makes explicit how each question can be used to develop specific algebraic content and reasoning. This lesson is meant to serve as an introduction for students that can be repeated using different visual patterns.
  • LESSON II: An Open-Ended Exploration of Pattern #141 This lesson plan models an open approach to using visual patterns. As with the arch problem, the activity and questions can be used with almost any visual pattern. Using the open-ended activity described here will not only help students develop their algebraic thinking, but it will give them opportunities to revise and improve their precision in mathematical communication. Since students are creating their own problems and choosing which ones to work on, this activity works especially well with a mixed-level class. Everyone is working from the same visual patterns, but at their own pace.

One thought on “Unit 8: Developing Algebraic Reasoning through Visual Patterns

  1. I just filled in for an ESOL teacher today last minute, not knowing what in the world I was going to do. So, I brought in manipulatives and The Arch Problem. They seamlessly discovered the recursive and explicit rules that represent the pattern and were able to express their thinking to the rest of the class using English to explain how they arrived at their conclusions.

    Math is, after all, a universal language and patterns are what the human brain searches for in all languages and cultures. I had so much fun with the group and I think they did too, if all the thank yous that I received are any indication:)

    With the new emphasis on math in the ESOL classroom I was very intrigued with how this class answered the math challenge. I never thought about it until after the class, but I remember seeing that some of the CUNY Curriculum is available in Spanish. However, we got by very well using the English version. Very fun.

    Happy Math Adventures,


Add Your Comment