Linear Models (IM Algebra 1 - Unit 3, Lesson 4)
Task
Lesson Purpose In this lesson, students analyze the slope and intercept of a linear model to make sense of it in context. They also use the model to predict what might be expected for other values in the same context. When students articulate things they notice and things they wonder about a scatter plot and the accompanying linear model, students have an opportunity to attend to precision in the language they use to describe what they see (MP6). Students reason abstractly by making sense of slope and intercept in context (MP2). How Tuva Enhances the lesson Illustrative Mathematics notes that this activity works best when students can use a digital tool to estimate a line of best fit dynamically. Tuva supports this work by giving students a clear, visual, and interactive way to create scatter plots and model data. Students can add a line of best fit, undo and redo changes, and use color options to distinguish their model from the data points. A summary view of the best-fit line highlights key components of the linear equation, making it easier for students to analyze the slope and vertical intercept in the context of the situation. Because the data and model remain available, students can return to the same scatter plot in later lessons to refine their thinking, compare models, and deepen their understanding of linear relationships. Tuva also supports vocabulary development by helping students connect visual features of the graph to terms such as scatter plot, slope, intercept, and linear model. Overall, Tuva makes the modeling process more accessible and efficient, allowing students to focus on interpreting the mathematics rather than managing the mechanics of graphing.
Notice and Wonder: Crowd Noise Before we start today’s task, let’s warm up! Mathematical language you might use: scatter plot, linear model, slope, intercept
Topics and standards: HSS-ID-C-7, HSS-ID-B-6-A, HSS-ID-B-6, Algebra I, Illustrative Math & Tuva