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# Tiling Pools

Use for CMP2 and CMP3, Problem 1.1 Tiling Pools

Students develop several equations to model a linear relationship. The focus is on students talking to each other about equivalent expressions and the implied understanding of equivalence.

The video concludes with the teacher reflecting on the student understandings during the lesson and how she uses that information to plan.

Real time was 1.5 class periods.

As you view the video, consider the following:

- What is the evidence of students’ understanding and reasoning? What prior understandings do you see students using or building upon?
- What is the evidence of students’ understanding and reasoning? What prior understandings do you see students using or building upon?
- What is the evidence of students’ use of the mathematical practices from the Common Core State Standards? To what extent are students growing in their sophistication of their use of the practices?
- Were there any “aha moments” in the video?
- How is the teacher facilitating the development of students’ understanding and reasoning?
- As a teacher, how would you use the information from this lesson to plan the next lesson?

- Full Length (27:36)
- Problem 1.1 Tiling Pools
- CMP2 Goals for Investigation
- Model situations with symbolic statements
- Interpret expressions in a given context
- Interpret the information equivalent expressions represent in a given context
- Review the Distributive Property
- Write equivalent expressions using the Distributive Property
- Determine if two or more expressions are equivalent in a variety of ways including using the
- Distributive Property and other properties of real numbers.

- Goals for CMP3 Problem 1.1 Tiling Pools
- Equivalence Develop understanding of equivalent expressions and equations.
- Model situations with symbolic statements
- Recognize when two or more symbolic statements represent the same context
- Use the properties of real numbers, such as the Distributive Property, to write equivalent expressions
- Determine if different symbolic expressions are mathematically equivalent
- Interpret the information that equivalent expressions represent in a given context
- Determine the equivalent expression or equvation that is most helpful in answering a particular question about a relationship
- Use algebraic equiations to describe the relationship among the volumes of cylinders, cones, and spheres that have the same height and radius
- Solve linear equations involving parentheses
- Determine if a linear equation has a finite number of solutions, an infinite number of solutions or no solution
- Develop understanding and some fluency with factoring quadratic expressions
- Solve quadratic equations by factoring
- Recognize how and when to use symbols, rather than tables or graphs, to display relationships, generalizations, and proofs

- Equivalence Develop understanding of equivalent expressions and equations.
- Video Transcript
- Suggestions for organizing Professional Development