Using Algebra to Express a Generalization (Method 2)
Haleemah and ET create a new method for finding the number of tiles in the border of a swimming pool. Then they apply their method to pools of different sizes and generalize their method. Finally, they write an algebraic equation to express their generalization and explain what each part of the equation means in the pool context.
Episode 1: Making Sense
ET and Haleemah make sense of their previous solution and think of a way to correct their answer, creating a new method for finding the number of tiles in the border of the pool.
Episode 2: Repeating Your Reasoning
The students apply their method for finding the number of tiles in the border to swimming pools of different sizes.
Episode 3: Exploring
Haleemah and ET generalize their method and write an algebraic equation that shows the relationship between a border with any number of tiles on one side and the total number of tiles in the border.
Episode 4: Reflecting
The students work to explain what each symbol in their equation means in the pool context and encounter a challenge.