# Lesson 9

Linear Models

### Lesson Narrative

In this lesson, students use linear functions to model real-world situations (MP4). In the candle activity, they are given data for an almost linear relationship and develop a linear model. They use their model to make predictions and discuss the reasonableness of the model. In the shadow activity, it is difficult to tell from the information given if a linear model is appropriate, but when they are given more information, it becomes clear that the relationship is not linear. In the garbage recycling activity, different linear models apply to different time periods.

None of the given data are perfectly fit by a linear function, and students have to determine whether a linear approximation is reasonable and for which values it would be reasonable. Students should start to see both the value of linear models and their limitations. The garbage recycling activity leads into the next lesson, which is about modeling with piece-wise linear functions.

### Learning Goals

Teacher Facing

• Compare and contrast (orally and in writing) different linear models of the same data, and determine (in writing) the range of values for which a given model is a good fit for the data.
• Create a model of a non-linear data using a linear function, and justify (orally and in writing) whether the model is a good fit for the data.

### Student Facing

Let’s model situations with linear functions.

### Student Facing

• I can decide when a linear function is a good model for data and when it is not.
• I can use data points to model a linear function.