Students work with visual patterns and real-world situations to notice and apply relationships. They generalize those relationships and represent them using algebraic expressions and equations. Students relate each algebraic symbol and term to what they mean in a context. They also explore a velocity applet in a scooter context, which allows them to explore the types of numbers that algebraic letters can take on: negative, fractional, and decimal values.
Lesson 1: Using Algebra to Express a Generalization (Method 1)
Haleemah and ET create a 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.
Lesson 2: 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.
Lesson 3: Simplifying Algebraic Equations
ET and Haleemah explore a new situation of three friends purchasing game apps for a phone or iPad. They come up with a method for finding how much the friends spend altogether, then apply their method for apps of different prices. They generalize their first method, then create a different, shorter method. Finally, they compare their methods and explain why the equations are equal.
Lesson 4: Using Negatives and Decimals as Values for Algebraic Symbols
Haleemah and ET work to model a scooter trip by relating the scooter’s start location, trip time, velocity, and end location. Using this context, they begin to think about the different kinds of values that an algebraic symbol can take on.
Lesson 5: 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.
Lesson 6: Comparing Quadratic Relationships Using Visual Patterns
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.