Clip 20/29: Standard 1: Making Sense and Perseverance Using Rate of Change Part 1A
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals.
Antoinette Villarin begins her lesson on graphing constant rates of change by reviewing the learning goals and mathematical practices, naming Standards for Mathematical Practice 1, 3, 6, and 7. She notes that it is important that her students understand how to build a mathematical argument, and she shares sentence frames and key vocabulary that the students will use as they build their arguments.
Antoinette presents a model of two bottles attached to each other so that fluid can flow between them, and she asks her students to make sense of the problem by describing what they see happening.
Students share that as the amount of fluid in the top container/prism decreases, the amount in the bottom container/prism increases.
This clip also relates to standard 3 (construct viable arguments & critique the reasoning of others), standard 4 (model with mathematics), standard 6 (attend to precision), and standard 7 (look for and make use of structure).