Comparing Quadratic Relationships Using Visual Patterns
Haleemah and ET explore the context of cobblestone patterns from the Czech Republic. They make sense of another student, Amir’s, way of seeing the relationship between a Size Number and the Haleemah and ET are given another way of seeing a pattern in a cobblestone figure, this time starting with an algebraic equation. Given Nicole’s algebraic equation, the students will work to make sense of how she may have been seeing the relationship between the size number and the number of gray stones. Then, they will compare and explore the equality between Amir and Nicole’s methods.
Episode 1: Making Sense
ET and Haleemah make sense of the cobblestone context and think ET and Haleemah make sense of Nicole’s algebraic and arithmetic equations and create a drawing that they believe describes how she was seeing the pattern.
Episode 2: Exploring
The students apply Nicole’s method for finding the total number of gray cobblestones for a new Size Number.
Episode 3: Reflecting
ET and Haleemah reflect on their generalized algebraic expression and make sense of each portion of their expression in the cobblestone context in two ways.
Episode 4: Exploring
Haleemah and ET explore the equality between Amir and Nicole’s methods by discussing the similarities and resolving the differences between the two methods.
Episode 5: Reflecting
The students look at someone else’s reasoning about a key difference between Amir’s and Nicole’s methods. They use this to explain what parts of the algebra equations mean in the cobblestone pattern.