Unit 2: Bivariate Data
In this unit students will use functions to model bivariate data. The focus begins primarily with linear and quadratic functions, but other functions are used towards the end of the unit. Students will create models, analyze residuals, and make conclusions about the appropriateness and accuracy of their models. Students also review transformations of parent functions in this unit as it is necessary to master before models can be made.
Prerequisite Units: Unit 1
Materials Needed: Calculator, Computer, CODAP, Desmos (or Geogebra)
Approximately 16- 20 Days needed
Prerequisite Units: Unit 1
Materials Needed: Calculator, Computer, CODAP, Desmos (or Geogebra)
Approximately 16- 20 Days needed
2.1: Review of Linear and Quadratic Functions from Algebra 2
You have options on how you achieve this review goal. You'll find traditional lessons (one for linear and one for quadratic functions) as well as a folder project for each family of functions that I've used in the past. You may decide to bypass section 1 all-together depending on your student population.
Lesson Resources
| Lesson 2.1 Part 1 (Linear) Guided Notes (PDF) |
| Lesson 2.1 Part 2 (Quadratic) Guided Notes (PDF) |
| Lesson 2.1 (Linear and Quadratic) Guided Notes (Word) |
| Problem Set 2.1 |
| Problem Set 2.1 Solutions |
Linear and Quadratic Folder Project
A project is a great alternative way to review these concepts while getting your students to recall their prior knowledge and build examples on their own to refresh their memory.
A project is a great alternative way to review these concepts while getting your students to recall their prior knowledge and build examples on their own to refresh their memory.
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Lesson 2.1 Video (Linear Review)
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2.2: Curve Fitting Using Linear and Quadratic Models
Lesson Resources
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CODAP FILES needed for exploratory activities in Lesson 2.2
Linear Modeling Activity Quadratic Modeling Activity | ||
| Lesson 2.2 Guided Notes (PDF) |
| Problem Set 2.2 (PDF) |
| Problem Set 2.2 Solutions |
Activities and Extra Resources
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| Lesson 2.2 Check for Understanding (PDF) |
Lesson 2.2 Video
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Introduction to Lesson 2.3: Using CODAP to create Models
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To download CODAP file follow the directions below.
1.) Click Unemployment and Crime CODAP FILE link above 2.) In the upper left hand corner click the three lines and upside down triangle. 3.) Select "Create a Copy". A new browser should open in a new window titled the same as the original file with "Copy of ..." in the front. 4.) Click the same three lines and upside down triangle in the upper left corner and select "Save". This should allow you to save the copy you've made in your personal google drive. Once you save the file you can rename it whatever you want and all changes you make will save automatically as you make changes. |
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2.3 Analyzing Bivariate Data with Residuals (Linear Models)
Lesson Resources
| Lesson 2.3 Guided Notes (Word) |
| Lesson 2.3 Guided Notes (PDF) |
| Problem Set 2.3 (Word) |
| Problem Set 2.3 (PDF) |
| Problem Set 2.3 Solutions |
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LINKS TO CODAP FILES - DATA
Vitruvian Man Car MPG vs. Weight Co2 Annual 2000 - 2019 Tried Marijuana Before 13 |
LINKS TO CODAP FILES -ANALYZED
Vitruvian Man Car MPG vs. Weight Co2 Annual 2000 - 2019 Tried Marijuana Before 13 |
Activities and Extra Resources
| Warm Up Exercise or Check for Understanding Lesson 2.3 (Word) |
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Lesson 2.3 Video
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2.4 Analyzing Bivariate Data Using Quadratic Models
Lesson Resources
| Lesson 2.4 Guided Notes (Word) |
| Lesson 2.4 Guided Notes (PDF) |
| Problem set 2.4 (Word) |
| Problem set 2.4 (PDF) |
| Problem Set 2.4 Solutions |
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Activities and Extra Resources
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EXTRA CODAP FILES FOR ADDITIONAL PRACTICE
Crash Involvement Crash Involvement - analyzed Average Global Temperature vs. Year Average global Temperature vs. Year - analyzed | ||||
Lesson 2.4 Video
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2.5: Transformations of Functions
Lesson Resources
| Lesson 2.5 Guided Notes (Word) |
| Lesson 2.5 Guided Notes (PDF) |
Link for Lesson 2.5 DESMOS Activity (to be completed along with guided notes)
| Problem Set 2.5 (Word) |
| Problem Set 2.5 Solutions (PDF) |
| Extra Practice Worksheet (PDF) |
| Extra Practice Worksheet Solutions (PDF) |
Lesson 2.5 Video
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2.6: Toolkit of Functions
Lesson Resources
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| Fluid Math Investigation Worksheet |
| Lesson 2.5-6 Putting it all together (PDF) |
| Problem Set 2.6 |
| Problem Set 2.6 Solutions |
2.7: Using CODAP to Create Models Using Toolkit Functions
Lesson Resources
Choose 2 exercises to do in class together and then assign the rest for homework.
| Lesson 2.7 Guided Notes (Word) |
| Lesson 2.7 Guided Notes (PDF) |
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LINKS TO CODAP FILES - DATA
Homeownership Fetal crown–rump length & gestational age Car MPG vs. Weight Stream Velocity vs. Rock Diameter Light Intensity CD Sales |
LINKS TO CODAP FILES - ANALYZED
Homeownership Fetal crown–rump length & gestational age Car MPG vs. Weight (reprise - reciprocal function) Stream Velocity vs. Rock Diameter Light Intensity CD Sales |
Activities and Extra Resources
| Check for Understanding 2.5 - 7 (Word) |
| Check for Understanding 2.5 - 7 (PDF) |
2.8: The Least Squares Line and the Correlation Coefficient
Lesson Resources
| Lesson 2.8 Guided Notes (Word) |
| Lesson 2.8 Guided Notes (PDF) |
Finding the Linear Regression Line on a TI83 or TI84 Calculator Video
Finding the Linear Regression Line on a TINspire Calculator Video
Finding the Linear Regression Line on a TINspire Calculator Video
| Problem Set 2.8 (Word) |
Activities and Extra Resources
Guess the Correlation Coefficient (Multiple Choice Game) - University of BC
| Least Squares Residual Line (PPT) |
Modeling Project
Students have an opportunity to explore topics that interest them and create a model of their own. They can use any of the toolkit functions to model their data. I introduce the project by spending 20-30 minutes of a class period going through the Death Penalty Fact Sheet. Students are asked to read through the sheet individually and write down what they notice and what they wonder. Then, they are put into pairs to share what they wrote down and come up with two more things together that they notice and wonder. Finally, we have a share session where students share their thoughts and we write lists on the board of what they notice and wonder. Students almost always wonder if they can model the total number of executions throughout the years so I choose that to lead into the next activity where we build an absolute value model for the execution data. The initial CODAP file is below. After we finish I go over the Modeling Project Assignment and Rubric.
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Executions 1976 - 2020 CODAP File
Extra Credit: Listen to More Perfect: Cruel and Unusual episode from Radiolab Podcast | ||
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Websites to Look at Data:
Statista - must have an account (Basic is free). The United States Census Bureau Office of Juvenile Justice and Delinquency Prevention FBI Crime Data Explorer National Oceanic and Atmospheric Administration US Elections Project | ||
Additional Resources
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Problem Sets by Nils Ahbel
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Problem Set Solutions
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