In this lesson, students continue to develop their ability to identify, describe, and model relationships with mathematics.
Previously, students worked mostly with descriptions of familiar relationships and were guided to reason repeatedly, which enabled them to see a general relationship between two quantities. Here, students are given tables of values and asked to generalize the relationship between pairs of quantities—by studying the values and looking for patterns (MP8), and by interpreting them in context (MP2). Some of the relationships they encounter here are novel or otherwise require perseverance and careful reasoning to pin down (MP1).
- Identify and describe (orally and in writing) patterns in tables of values and in calculations.
- Use observed patterns to generalize the relationships between quantities and to write equations.
- Let's use patterns to help us write equations.
- I can use words and equations to describe the patterns I see in a table of values or in a set of calculations.
- When given a description of a situation, I can use representations like diagrams and tables to help make sense of the situation and write equations for it.
A limitation on the possible values of variables in a model, often expressed by an equation or inequality or by specifying that the value must be an integer. For example, distance above the ground \(d\), in meters, might be constrained to be non-negative, expressed by \(d \ge 0\).
A mathematical or statistical representation of a problem from science, technology, engineering, work, or everyday life, used to solve problems and make decisions.