Standard #: MAFS.8.SP.1.3 (Archived Standard)


This document was generated on CPALMS - www.cpalms.org



Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.


General Information

Subject Area: Mathematics
Grade: 8
Domain-Subdomain: Statistics & Probability
Cluster: Investigate patterns of association in bivariate data. (Supporting Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    Assessment Limits :

    Numbers in items must be simple rational numbers (e.g., begin mathsize 11px style 1 half end stylebegin mathsize 11px style 1 fourth end style , to the 10th). Data are required for all items. In all items requiring a line of best fit, the equation of that line should be given.

    Calculator :

    Neutral

    Context :

    Required



Sample Test Items (2)

Test Item # Question Difficulty Type
Sample Item 1

The slope of the line of best fit for the data shown is approximately 1.5.

What is the meaning of 1.5 in terms of the context?

N/A MS: Multiselect
Sample Item 2

The amount of money Alan earns as a plumber after x hours is modeled by the equation y = $25x + $50.

What is the meaning of $25 in this model?

N/A OR: Open Response


Related Courses

Course Number1111 Course Title222
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))


Related Resources

Formative Assessments

Name Description
Tuition

Students are asked to use a linear model to make a prediction about the value of one of the variables.

Stretching Statistics

Students are asked to interpret a specific solution and the y-intercept of a linear equation that describes a context.

Foot Length

Students are asked to interpret the line of best fit, slope, and y-intercept of a linear model.

Developmental Data

Students are asked to interpret the slope of a linear model.

Lesson Plans

Name Description
Sea Ice Analysis Grade 8

The changing climate is an important topic for both scientific analysis and worldly knowledge. This lesson uses data collected by the National Snow and Ice Data Center to create and use mathematical models as a predictive tool and do critical analysis of sea ice loss.

Shipwrecked Pirates

In this lesson, students will take the role of shipwrecked pirates. Working in groups, they will have to use the concepts of force, speed, scatter plots, and literal equations to come up with a way of getting one student to a nearby sister island so that they will both have enough food to survive.

Steel vs. Wooden Roller Coaster Lab

This lesson is a Follow Up Activity to the Algebra Institute and allows students to apply their skills on analyzing bivariate data. This STEM lesson allows students the opportunity to investigate if there is a linear relationship between a coaster's height and speed. Using technology the students can determine the line of best fit, correlation coefficient and use the line for interpolation. This lesson also uses prior knowledge and has students solve systems of equations graphically to determine which type of coaster is faster.

Height Scatterplot Lab

This lesson is a Follow Up Activity to the Algebra Institute and allows students to apply their skills on analyzing bivariate data. This STEM lesson allows students the opportunity to investigate if there is a linear relationship between a person's height and foot length. Using technology the students can determine the line of best fit, correlation coefficient and use the line for interpolation.

Scattering Plots

Students will find the slope of the line of regression in a scatter plot. Students will interpret the line of regression in context to a real-world situation involving bivariate data.

Scatter Plots at Arm's Reach

This lesson is an introductory lesson to scatter plots and line of best fit (trend lines). Students will be using m&m's to represent different associations in scatter plots, and measure each other's height and arm span to create their own bivariate data to analyze. Students will be describing the association of the data, patterns of the data, informally draw a line of best fit (trend line), write the equation of the trend line, interpret the slope and y-intercept, and make predictions.

Linear Statistical Models

In this lesson, students will learn how to analyze data and find the equation of the line of best fit. Students will then find the slope and intercept of the best fit line and interpret the meaning in the context of the data.

Spaghetti Bridges Students use data collection from their spaghetti bridge activity to write linear equations, graph the data, and interpret the data.
Graphing Equations on the Cartesian Plane: Slope The lesson teaches students about an important characteristic of lines: their slope. Slope can be determined either in graphical or algebraic form. Slope can also be described as positive, negative, zero, or undefined. Students get an explanation of when and how these different types of slope occur. Finally, students learn how slope relates to parallel and perpendicular lines. When two lines are parallel, they have the same slope and when they are perpendicular their slopes are negative reciprocals of one another. Prerequisite knowledge: Students must know how to graph points on the Cartesian plane. They must be familiar with the x- and y- axes on the plane in both the positive and negative directions.

Original Student Tutorials

Name Description
Scatterplots Part 6: Using Linear Models

Learn how to use the equation of a linear trend line to interpolate and extrapolate bivariate data plotted in a scatterplot. You will see the usefulness of trend lines and how they are used in this interactive tutorial.

This is part 6 in 6-part series. Click below to open the other tutorials in the series.

Scatterplots Part 5: Interpreting the Equation of the Trend Line

Explore how to interpret the slope and y-intercept of a linear trend line when bivariate data is graphed on a scatterplot in this interactive tutorial.

This is part 5 in 6-part series. Click below to open the other tutorials in the series.

Perspectives Video: Professional/Enthusiast

Name Description
Slope and Deep Sea Sharks

Shark researcher, Chip Cotton, discusses the use of regression lines, slope, and determining the strength of the models he uses in his research.

Download the CPALMS Perspectives video student note taking guide.

Problem-Solving Tasks

Name Description
You and Michael

In this problem solving task, students will test Marcus Vitruvius"s theory that a person"s height is approximately equal to their arm span (wingspan). Students will test this theory via collection, recording, graphing and analysis of data.

US Airports

In this resource, real-world bivariate data is displayed in a scatter plot. The equation of the linear function which models the relationship between the two variables is provided, and it is graphed on the scatter plot. Students are asked to use the model to interpret the data and to make predictions.

Unit/Lesson Sequences

Name Description
Linear Functions and Slope This session on linear function and slope contains five parts, multiple problems and videos, and interactive activities geared to help students recognize and understand linear relationships, explore slope and dependent and independent variables in graphs of linear relationships, and develop an understanding of rates and how they are related to slopes and equations. Throughout the session, students use spreadsheets to complete the work, and are encouraged to think about the ways technology can aid in teaching and understanding. The solutions for all problems are given, and many allow students to have a hint or tip as they solve. There is even a homework assignment with four problems for students after they have finished all five parts of the session.
Direct and Inverse Variation "Lesson 1 of two lessons teaches students about direct variation by allowing them to explore a simulated oil spill using toilet paper tissues (to represent land) and drops of vegetable oil (to simulate a volume of oil). Lesson 2 teaches students about inverse variation by exploring the relationship between the heights of a fixed amount of water poured into cylindrical containers of different sizes as compared to the area of the containers' bases." from Insights into Algebra 1 - Annenberg Foundation.

Video/Audio/Animations

Name Description
Linear Equations in the Real World

Linear equations can be used to solve many types of real-word problems. In this episode, the water depth of a pool is shown to be a linear function of time and an equation is developed to model its behavior. Unfortunately, ace Algebra student A. V. Geekman ends up in hot water anyway.

Fitting a Line to Data

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.

Virtual Manipulatives

Name Description
Graphing Lines

Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.

Equation Grapher

This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s).

Line of Best Fit

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

Student Resources

Original Student Tutorials

Name Description
Scatterplots Part 6: Using Linear Models :

Learn how to use the equation of a linear trend line to interpolate and extrapolate bivariate data plotted in a scatterplot. You will see the usefulness of trend lines and how they are used in this interactive tutorial.

This is part 6 in 6-part series. Click below to open the other tutorials in the series.

Scatterplots Part 5: Interpreting the Equation of the Trend Line :

Explore how to interpret the slope and y-intercept of a linear trend line when bivariate data is graphed on a scatterplot in this interactive tutorial.

This is part 5 in 6-part series. Click below to open the other tutorials in the series.

Problem-Solving Task

Name Description
US Airports:

In this resource, real-world bivariate data is displayed in a scatter plot. The equation of the linear function which models the relationship between the two variables is provided, and it is graphed on the scatter plot. Students are asked to use the model to interpret the data and to make predictions.

Video/Audio/Animations

Name Description
Linear Equations in the Real World:

Linear equations can be used to solve many types of real-word problems. In this episode, the water depth of a pool is shown to be a linear function of time and an equation is developed to model its behavior. Unfortunately, ace Algebra student A. V. Geekman ends up in hot water anyway.

Fitting a Line to Data:

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.

Virtual Manipulatives

Name Description
Graphing Lines:

Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.

Equation Grapher:

This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s).

Line of Best Fit:

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



Parent Resources

Problem-Solving Task

Name Description
US Airports:

In this resource, real-world bivariate data is displayed in a scatter plot. The equation of the linear function which models the relationship between the two variables is provided, and it is graphed on the scatter plot. Students are asked to use the model to interpret the data and to make predictions.

Video/Audio/Animation

Name Description
Fitting a Line to Data:

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.

Virtual Manipulative

Name Description
Graphing Lines:

Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.



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