The goal of this activity is for students to determine the rate of change for situations. This activity prepares students to interpret the slope of linear models in the associated Algebra 1 lesson. Students have the opportunity to reason abstractly and quantitatively (MP2) when interpreting their answers.

The goal of this activity is for students to practice finding the rate of change in a given scenario. Discuss how students can find the rate of change. Here are sample questions to promote class discussion:

• “How did you determine the rate of change for Andre’s savings account?” (First, I thought about the difference between how much money he had in the beginning and at the end of the situation. Once I determined the difference, then I used the 6 weeks to divide to get the rate of change.)
• “How did you determine the rate of change for Kiran’s checking account?” (First, I thought about the difference between how much money he had in the beginning and at the end of the situation. Once I determined the difference, I set up a proportion to describe what he spent over 4 weeks and to calculate how much that meant he spent each week.)
• “How does rate of change relate to a linear model?” (The rate of change relates to a linear model because linear models show a constant increase, decrease, or no change in the variables. The rate of change tells me how much a variable increases or decreases, or if it does not change at all. Similarly, in a linear model, the slope tells us how much the line increases or decreases, or if it does not change at all. The rate of change and the slope give us the information about how a variable or line changes, respectively.)

The purpose of this activity is for students to think about how to determine if a linear model is a better or worse fit for data displayed in a scatter plot, which allows students to model with mathematics (MP4). Students construct viable arguments and critique the reasoning of others when they decide which model is best (MP3). This activity prepares students to create lines of best fit in the associated Algebra 1 lesson.

The purpose of this activity is for students to learn how to create a linear model that is a good fit to data. Students first determine which scatter plots are best represented by a linear model. Then students create their own linear model that is fit to the data and compare their lines with a partner’s. As students compare their lines, they have the opportunity to construct viable arguments and critique the reasoning of others (MP3).