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 (or Fathom), Desmos (or Geogebra)
Approximately 20 Days needed
Prerequisite Units: Unit 1
Materials Needed: Calculator, Computer, CODAP (or Fathom), Desmos (or Geogebra)
Approximately 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.
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Guided Notes (Word and PDF) for Linear Functions - matches video for flipped classroom opportunity
Smart Notebook Review of Linear Functions Lesson
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Guided Notes (Word and PDF) for Quadratic Functions - matches video for flipped classroom opportunity
Smart Notebook Review of Quadratic Functions Lesson
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Linear and Quadratic Folder Project
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Problem Set 2.1
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Problem Set 2.1 Solutions
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Lesson 2.1 Video (Linear Review) |
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Lesson 2.1 Video (Quadratic Review) |
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2.2: Curve Fitting Using Linear and Quadratic Models
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Lesson 2.2 Notes (Word)
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Lesson 2.2 Notes (PDF)
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Problem Set 2.2
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Problem Set 2.2 Solutions
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CODAP FILES needed for exploratory activities in lesson 2.2
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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Introduction to Lesson 2.3: Using Fathom to create Linear and Quadratic Models
(skip if you are using CODAP)
Using Fathom to Create Linear and Quadratic Models (Word Document)
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Fathom Files for homework assignment
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2.3 Analyzing Bivariate Data with Residuals (Linear Models)
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Guided Notes (Word)
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Guided Notes (PDF)
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Powerpoint on Residuals
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Analyze the Data for Bivariate Data (PDF)
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Problem Set 2.3
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Problem Set 2.3 Solutions (#1-3)
#4 is left for you to complete on your own. |
LINKS TO CODAP FILES - DATA
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LINKS TO CODAP FILES -ANALYZED
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Fathom Files
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Lesson 2.3 Video |
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2.4 Analyzing Bivariate Data Using Quadratic Models
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Guided Notes (Word)
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Guided Notes (PDF)
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Smart Notebook 2.4 Lesson
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PDF of Smart Notebook 2.4 Lesson
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Problem Set 2.4
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Problem Set 2.4 Solutions -needs to be updated
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LINKS TO CODAP FILES - DATA
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LINKS TO CODAP FILES - ANALYZED
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Fathom Files
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Lesson 2.4 Video |
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2.5: Transformations of Functions
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Smart Notebook 2.5 Lesson
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PDF of Smart Notebook 2.5 Lesson
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Link to Desmos investigation with square root function
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Horizontal Translations Using Abs. Value Function
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Problem Set 2.5
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Problem Set 2.5 Solutions
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Lesson 2.5 Video |
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2.6: Toolkit of Functions
2.6 Guided Notes using Fluid Math - I usually put students in groups of two to do these notes as a partner exercise since it is a review of Alg. 2 functions. Students need to do the first set of 2.6 notes first (review of the toolkit functions) before they do the transformations investigation. The link below takes you through the notes and transformations investigation.
Powerpoint of Toolkit Parent Functions
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Problem Set 2.6
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Problem Set 2.6 Solutions
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More Practice Worksheet if needed
Jeopardy Review Game 2.1-6 Material
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More Practice worksheet solutions
Jeopardy Review Game Solutions
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2.7: Using CODAP to Create Models Using Toolkit Functions
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Problem Set 2.7
LINKS TO CODAP FILES - DATA
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Problem Set 2.7 Solutions - needs to be updated
LINKS TO CODAP FILES - ANALYZED
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2.8: The Least Squares Line and the Correlation Coefficient
I have not taught this lesson yet, but will be adding it to the materials officially in the 2020-2021 school year. Below are Nils' materials.
Lesson 2.8
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Problem Set 2.8
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Problem Set 2.8 Solutions
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LINKS TO CODAP FILES - DATA
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LINKS TO CODAP FILES - ANALYZED
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Modeling Project
I have done this modeling project with my students for the past three years. I limited it this past year so that students could only use a linear or quadratic model (because we missed so many days due to hurricanes) and I was able to sneak this project in after section 2.5. The project outline is easy to edit though and you can open it up as much as you want. I have also included the rubric that you can edit. My kids always find some really neat stuff for this project - the majority choose to work with linear models.
Samples of Student Work
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Additional Resources
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Problem Sets by Nils Abel
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Problem Set Solutions
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