Super Bowl Ad Costs vs. Engagement: A Linear Model
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Super Bowl Ad Costs vs. Engagement: A Linear Model

Grade 8Math1 days
In this project, eighth-grade students explore the relationship between Super Bowl advertisement costs and viewer engagement by constructing linear models. Through activities like creating scatter plots and calculating rate of change, students gain a deeper understanding of linear functions and their application in analyzing real-world data. By interpreting these mathematical models, students learn to predict future advertising trends, enhancing their appreciation for the role of mathematics in real-world scenarios. The project involves hands-on experience as marketing executives, further solidifying students’ skills in data analysis and critical thinking.
Linear ModelSuper Bowl AdsViewer EngagementData AnalysisMathematicsTrend PredictionScatter Plots
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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we create a mathematical model to evaluate the relationship between Super Bowl advertisement costs and viewer engagement, and what insights can this model provide about advertising trends?

Essential Questions

Supporting questions that break down major concepts.
  • How can we use mathematics to determine the effectiveness of Super Bowl advertisements based on cost and viewer engagement?
  • In what ways can the relationship between advertisement costs and viewer engagement rates be represented using a linear function?
  • What is the significance of the rate of change and initial value in a linear function when analyzing Super Bowl ad data?
  • How can data from Super Bowl ads be used to predict future trends in advertising?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:
  • Students will be able to construct a linear function model representing the relationship between advertisement costs and viewer engagement for Super Bowl ads.
  • Students will understand and explain the concepts of rate of change and initial value within the context of Super Bowl advertisement data.
  • Students will be able to create and interpret scatter plots to analyze the relationship between two quantitative variables, such as ad costs and engagement rates.
  • Students will critically analyze and predict future advertisement trends based on historical data of Super Bowl ad costs and engagement.

Common Core Standards

8.F.B.4
Primary
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.Reason: The project involves creating a mathematical model to evaluate the relationship between Super Bowl advertisement costs and viewer engagement, which requires understanding the rate of change and initial value in a linear function.
8.SP.A.1
Secondary
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities.Reason: Students will need to create scatter plots to visually represent and analyze the relationship between advertisement costs and viewer engagement.
8.SP.A.2
Supporting
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.Reason: This standard supports the use of straight lines to model the relationship between advertisement costs and viewer engagement when analyzing data points for trends.

Entry Events

Events that will be used to introduce the project to students

Design Your Super Bowl Ad

Students take on the role of marketing executives tasked with designing a Super Bowl ad. They'll need to consider cost, target audience, and engagement strategies. Once created, they simulate launch and track potential viewer engagement metrics.
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Portfolio Activities

Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.
Activity 1

Linear Function Construction Workshop

Students will learn to construct a linear function model based on the data they studied. They will calculate the rate of change and identify the initial value to solidify their understanding of linear relationships.

Steps

Here is some basic scaffolding to help students complete the activity.
1. From previously organized data, choose two years' data points to focus on.
2. Determine the rate of change using the slope formula (change in engagement/change in ad cost).
3. Identify and interpret the initial value from the data.
4. Write the equation of the line in slope-intercept form (y = mx + b).

Final Product

What students will submit as the final product of the activityA written linear function representing the relationship between advertisement costs and viewer engagement.

Alignment

How this activity aligns with the learning objectives & standardsMeets 8.F.B.4 standard by guiding students to construct and interpret a linear model concerning rate of change and initial value.
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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Linear Function and Data Analysis Rubric

Category 1

Linear Function Construction

Assessment of students' ability to create a linear function model, including determining rate of change and initial value.
Criterion 1

Rate of Change Calculation

Measures accuracy and understanding in determining the slope or rate of change between the given data points.

Exemplary
4 Points

Accurately calculates and explains the rate of change using the slope formula, providing comprehensive insights into its significance.

Proficient
3 Points

Correctly calculates the rate of change with a clear explanation of its relevance.

Developing
2 Points

Calculates the rate of change with some errors and provides a basic explanation of its relevance.

Beginning
1 Points

Struggles to calculate the rate of change accurately and provides little to no explanation.

Criterion 2

Initial Value Identification

Evaluates ability to identify and interpret the initial value in the context of the data.

Exemplary
4 Points

Accurately identifies and thoroughly interprets the initial value with detailed context understanding.

Proficient
3 Points

Correctly identifies the initial value and provides a clear contextual explanation.

Developing
2 Points

Identifies the initial value with some inaccuracies and a limited explanation.

Beginning
1 Points

Struggles to identify the initial value and provides minimal explanation.

Criterion 3

Equation Formulation

Assess the student's ability to correctly formulate the linear equation using y = mx + b.

Exemplary
4 Points

Formulates an accurate and well-explained equation that reflects a deep understanding of slope-intercept form.

Proficient
3 Points

Accurately formulates the equation with a clear understanding of slope-intercept form.

Developing
2 Points

Formulates the equation with some errors or misconceptions.

Beginning
1 Points

Struggles to formulate the equation accurately and demonstrate understanding.

Category 2

Data Interpretation and Analysis

Evaluates students' abilities to interpret data patterns and predict trends from the given advertisement datasets.
Criterion 1

Scatter Plot Creation and Analysis

Assessment of students' ability to create and analyze scatter plots for data patterns and linear associations.

Exemplary
4 Points

Creates precise scatter plots and provides a thorough analysis of data patterns with clear predictions.

Proficient
3 Points

Creates accurate scatter plots and offers a clear analysis of data patterns.

Developing
2 Points

Creates scatter plots with minor inaccuracies and provides limited analysis.

Beginning
1 Points

Struggles to create accurate scatter plots and analyze data patterns meaningfully.

Criterion 2

Trend Prediction and Explanation

Evaluates the student's ability to predict future trends using historical data and support their predictions with logical explanations.

Exemplary
4 Points

Predictively analyzes trends with excellent rationale and comprehensive support from data.

Proficient
3 Points

Provides reasonable trend predictions with clear and relevant data support.

Developing
2 Points

Offers basic predictions with limited rationale and minimal data support.

Beginning
1 Points

Struggles to predict trends or support predictions with appropriate data.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning
Question 1

Reflect on how the process of constructing a linear function helped you understand the relationship between Super Bowl advertisement costs and viewer engagement rates.

Text
Required
Question 2

On a scale from 1 to 5, how confident are you in your ability to use math to analyze real-world data, like Super Bowl ads?

Scale
Required
Question 3

Which aspect of creating and interpreting scatter plots and linear models did you find most challenging?

Text
Required
Question 4

In your opinion, how do the rate of change and initial value in a linear function help in predicting future advertising trends? Select the statement that best matches your view.

Multiple choice
Required
Options
They provide a precise prediction model for future ad performance.
They offer insight but must be combined with other data for accurate predictions.
They are mainly useful for analyzing past trends, less so for predicting future trends.
I am unsure of their significance in trend prediction.
Question 5

Describe how your perspective on the importance of mathematics in real-world situations has evolved over the course of this project.

Text
Optional