Clip 4/7: Standard 4: Model with Mathematics Using Rate of Change Part 1A
Overview
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.… They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense….
Antoinette Villarin begins her lesson on graphing constant rates of change, 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 1 (make sense of problems and persevere in solving them), standard 3 (construct viable arguments & critique the reasoning of others), standard 6 (attend to precision), and standard 7 (look for and make use of structure).