SP.1.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

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Formative Assessments
Formative Assessments
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CPALMS: Students are asked to informally fit a line to model the relationship between two quantitative variables and to assess how well that line fits the data.

Line of Good Fit – 1

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CPALMS: Students are asked to informally assess three lines fitted to data to determine which fit is the best.

Three Scatterplots

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CPALMS: Students are asked to informally fit a line to model the relationship between two quantitative variables and to assess how well that line fits the data.
Line of Good Fit – 2
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CPALMS: Students are asked to compare two lines fitted to data to determine which fit is better.

Two Scatterplots

Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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CPALMS: Using this resource, students are able to drag data points and watch the best-fit polynomial curve form instantaly. They can choose the type of fit: linear, quadratic, cubic, or quartic. Best fit or adjustable fit can be displayed.

Curve Fitting

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CPALMS: This helps students in understanding the usefulness of scatter plots when investigating whether there is a relationship between two variables. They could develop a systematic plan for collecting and entering data and set appropriate ranges for the x and y scales.

Scatterplot

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CPALMS: Students can graph a function and a set of ordered pairs on the same coordinate plane. The constants, coefficients, and exponents can be adjusted using slider bars so that they can explore the affect on the graph as the function parameters are changed.

Data Flyer

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CPALMS: This resource introduces students to the difference between univariate and bivariate data and how the two can be represented graphically. It provides links to online graphing applets, as well as suggestions on how to integrate these into lessons.

Univariate and Bivariate Data

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CPALMS: This manipulative allows the student to enter multiple coordinates on a grid, estimate a line of best fit, and then determine the equation for a line of best fit.

Line of Best Fit

Assessment Questions
Assessment Questions
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Multiple Choice
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Videos of Expert Instruction
Videos of Expert Instruction
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This 5-minute video provides an example of how to solve a problem using a trend line to estimate data through a problem called, ``Smoking in 1945.``
Trend Lines (Smoking in 1945)
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Khan Academy tutorial video that demonstrates with real-world data the use of Excel spreadsheet to fit a line to data and make predictions using that line.
Fitting a Line to Data
Use Real Link and Title
Hook/Performance Tasks
Hook/Performance Tasks
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Illustrative Mathematics: Students create scatterplots, and think critically about associations and outliers in data as well as informally fit a trend line. By using spaghetti rather than drawing a line, students can easily make adjustments on placement of the ``line``.

Animal Brains

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Illustrative Mathematics: Students glean contextual information about bird eggs from a collection of measurements organized in a scatter plot. They identify correlation and use it to make interpolative predictions and reason about the properties via the graphical presentation of data.

Birds’ Eggs

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Illustrative Mathematics: This task uses a situation that is familiar to students to solve a problem. The goal is to find and use a linear model to answer the question.

Laptop Battery Charge