This resource asks students to describe how they see a pattern growing. Adapted from: https://www.youcubed.org/tasks/squares-upon-squares/

Start by asking students “How do you see the shapes growing?” Ask that they make their answer visual, and to forget about counting and numbers. Color coding is often a great tool for this.

Once students share how they see the growth in the pattern, proceed to the numerical and algebraic questions. Having looked at the pattern growth visually opens up the ways of thinking about the pattern to answer the question about the 100th and the nth case. It also shows students how we all see math differently even in a question that has a single numerical answer.

As an extension of this task, you can ask students to come up with algebraic expressions that match the different visual ways of seeing the pattern grow. This might give rise to a question like “Since the number of squares is the same in each way of seeing why do the algebraic representations look different?” and it might lead into a conversation about equivalent algebraic expressions and simplification. Discussions about this idea and question bridge the visual and algebraic ways of thinking and exercise the connections between different parts of the brain.