Generalizing and Representing a Quadratic Relationship
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 number of gray stones in a cobblestone pattern. They apply and then generalize Amir’s method using algebra.
Episode 1: Making Sense
ET and Haleemah make sense of the cobblestone context and think about how another student, Amir, is seeing the stones in a cobblestone pattern of a certain Size Number.
Episode 2: Exploring
The students apply Amir’s method to a new Size Number and use their calculation to explain how Amir is seeing the stones.
Episode 3: Repeating Your Reasoning
The students apply Amir’s method to find the number of gray stones for another Size Number and connect their calculations to the cobblestone context.
Episode 4: Exploring
Haleemah and ET generalize Amir’s method that relates an unknown Size Number and the number of gray stones in the cobblestone pattern.
Episode 5: Reflecting
They use their general equation for another Size Number and reflect on their equation by connecting each part to their drawing.
Episode 6: Reflecting
Haleemah and ET explain what each symbol and operation of their general equation means in the cobblestone context.