AN ALTERNATIVE TO PRECALCULUS
  • About
  • Overview
  • Unit 1: Univariate Data
  • Unit 2: Bivariate Data
  • Unit 3: Trigonometry
  • Unit 4: Sequences and Series
  • Unit 5: Exponential and Logarithmic Functions
  • Unit 6: Personal Finance
  • Unit 7: Probability and Simulations
  • Unit 8: The Normal Distribution
  • Contact

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 

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. 
Guided Notes (Word and PDF) for Linear Functions - matches video for flipped classroom opportunity 
WORD
File Size: 2854 kb
File Type: docx
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PDF
File Size: 313 kb
File Type: pdf
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Smart Notebook Review of Linear Functions Lesson 
Guided Notes (Word and PDF) for Quadratic Functions - matches video for flipped classroom opportunity 
WORD
File Size: 136 kb
File Type: docx
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PDF
File Size: 298 kb
File Type: pdf
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Smart Notebook Review of Quadratic Functions Lesson ​
SMART NOTEBOOK FILE
File Size: 62 kb
File Type: notebook
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SMART NOTEBOOK FILE
File Size: 128 kb
File Type: notebook
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Linear and Quadratic Folder Project 
DIRECTIONS
File Size: 1663 kb
File Type: docx
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RUBRIC
File Size: 18 kb
File Type: docx
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PS 2.1 VERSION A
File Size: 110 kb
File Type: docx
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PS 2.1 VERSION C
File Size: 2339 kb
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PS 2.1 VERSION B
File Size: 2208 kb
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PS 2.1 VERSION D
File Size: 1546 kb
File Type: docx
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Problem Set 2.1 
Problem Set 2.1 Solutions 
WORD DOCUMENT
File Size: 213 kb
File Type: docx
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PDF
File Size: 1337 kb
File Type: pdf
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Lesson 2.1 Video (Linear Review) 

Lesson 2.1 Video (Quadratic Review) 


2.2: Curve Fitting Using Linear and Quadratic Models 

Lesson 2.2 Notes (Word) 
WORD
File Size: 1779 kb
File Type: docx
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Lesson 2.2 Notes (PDF)
PDF
File Size: 312 kb
File Type: pdf
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Problem Set 2.2 
WORD DOCUMENT
File Size: 249 kb
File Type: docx
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Problem Set 2.2 Solutions 
PDF
File Size: 805 kb
File Type: pdf
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CODAP FILES needed for exploratory activities in lesson 2.2
Linear Modeling Activity 
Quadratic Modeling Activity 

Lesson 2.2 Video 


Introduction to Lesson 2.3: Using CODAP to create Models

Unemp​​loyment and Crime Data 
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. ​

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)
WORD DOCUMENT
File Size: 442 kb
File Type: docx
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Fathom Files for homework assignment 
FIRE VS. THEFT
File Size: 8 kb
File Type: ftm
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GAS MILEAGE
File Size: 5 kb
File Type: ftm
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FIRE VS. THEFT ANALYZED
File Size: 14 kb
File Type: ftm
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GAS MILEAGE ANALYZED
File Size: 11 kb
File Type: ftm
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2.3 Analyzing Bivariate Data with Residuals (Linear Models)

Guided Notes (Word) ​
Lesson 2.3 Notes
File Size: 1313 kb
File Type: docx
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Guided Notes (PDF) 
Lesson 2.3 Notes
File Size: 539 kb
File Type: pdf
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Powerpoint on Residuals 
POWERPOINT
File Size: 377 kb
File Type: ppt
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Analyze the Data for Bivariate Data (PDF)
ANALYZE THE DATA - BIVARIATE DATA
File Size: 13 kb
File Type: docx
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Problem Set 2.3 
Problem Set 2.3 Solutions (#1-3) 
#4 is left for you to complete on your own. 

WORD DOCUMENT
File Size: 409 kb
File Type: docx
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LINKS TO CODAP FILES - DATA 
WORD DOCUMENT
File Size: 594 kb
File Type: docx
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LINKS TO CODAP FILES -ANALYZED
Vitruvian Man 
Car MPG vs. Weight 
Co2 Annual 2000 - 2019
Tried Marijuana Before 13 
Vitruvian Man
Car MPG vs. Weight 
Co2 Annual 2000 - 2019
Tried Marijuana Before 13
Fathom Files 
VITRUVIAN MAN
File Size: 5 kb
File Type: ftm
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CAR MPG VS WEIGHT
File Size: 5 kb
File Type: ftm
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CO2 ANNUAL 2000-2007
File Size: 5 kb
File Type: ftm
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CRICKETS
File Size: 6 kb
File Type: ftm
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CREDIT CARD DEBT
File Size: 5 kb
File Type: ftm
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MLB AVERAGE SALARIES
File Size: 4 kb
File Type: ftm
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HABITAT FOR HUMANITY
File Size: 9 kb
File Type: ftm
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BATH WATER
File Size: 5 kb
File Type: ftm
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DIVORCES
File Size: 10 kb
File Type: ftm
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MANATEE DEATHS
File Size: 5 kb
File Type: ftm
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RENT PRICES
File Size: 5 kb
File Type: ftm
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PERCENT OF WOMEN LABOR FORCE
File Size: 5 kb
File Type: ftm
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AVERAGE GLOBAL TEMP VS CO2
File Size: 7 kb
File Type: ftm
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Lesson 2.3 Video


2.4 Analyzing Bivariate Data Using Quadratic Models

Guided Notes (Word) ​
Lesson 2.4 Notes
File Size: 14 kb
File Type: docx
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Guided Notes (PDF) 
Lesson 2.4 Notes
File Size: 93 kb
File Type: pdf
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Smart Notebook 2.4 Lesson ​
PDF of Smart Notebook 2.4 Lesson 
SMART NOTEBOOK FILE
File Size: 26 kb
File Type: notebook
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PDF
File Size: 47 kb
File Type: pdf
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Problem Set 2.4 
Problem Set 2.4 Solutions -needs to be updated
WORD DOCUMENT
File Size: 188 kb
File Type: docx
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LINKS TO CODAP FILES - DATA ​
Pig Weight Gain 
Crash Involvement 
Average Global Temperature vs. Year 
Ball Toss 
WORD DOCUMENT
File Size: 235 kb
File Type: docx
Download File

LINKS TO CODAP FILES - ANALYZED
Pig Weight Gain
Crash Involvement 
Average Global Temperature vs. Year 
Ball Toss
Fathom Files
PIG WEIGHT GAIN
File Size: 5 kb
File Type: ftm
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BASEBALL
File Size: 5 kb
File Type: ftm
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DRESS SALES
File Size: 12 kb
File Type: ftm
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MOTORBOAT REGISTRATIONS
File Size: 11 kb
File Type: ftm
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BALL DATA 2
File Size: 5 kb
File Type: ftm
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CRASH INVOLVEMENT
File Size: 5 kb
File Type: ftm
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FEMALE DEER REPRODUCTION
File Size: 4 kb
File Type: ftm
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HAT DROP
File Size: 6 kb
File Type: ftm
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Lesson 2.4 Video


2.5: Transformations of Functions 

Smart Notebook 2.5 Lesson ​
PDF of Smart Notebook 2.5 Lesson ​
SMART NOTEBOOK FILE
File Size: 112 kb
File Type: notebook
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PDF
File Size: 225 kb
File Type: pdf
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Link to Desmos investigation with square root function 
Horizontal Translations Using Abs. Value Function 
https://www.desmos.com/calculator/mqsfyjr9xn
POWERPOINT
File Size: 620 kb
File Type: ppt
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Problem Set 2.5
Problem Set 2.5 Solutions 
WORD DOCUMENT
File Size: 178 kb
File Type: docx
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PDF
File Size: 3036 kb
File Type: pdf
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Lesson 2.5 Video


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. 
https://fluidmath.net/apps/FluidMath/?d=E6A34CFEA75&n=ti1
2.6 GUIDED NOTES
File Size: 315 kb
File Type: docx
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Powerpoint of Toolkit Parent Functions
POWERPOINT
File Size: 99 kb
File Type: ppt
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TRANSFORMATIONS INVESTIGATION
File Size: 234 kb
File Type: pdf
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Problem Set 2.6 
Problem Set 2.6 Solutions 
WORD DOCUMENT
File Size: 218 kb
File Type: docx
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More Practice Worksheet if needed 
WORD DOCUMENT
File Size: 267 kb
File Type: docx
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Jeopardy Review Game 2.1-6 Material
SMART NOTEBOOK FILE
File Size: 344 kb
File Type: notebook
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PDF
File Size: 183 kb
File Type: pdf
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More Practice worksheet solutions 
PDF
File Size: 542 kb
File Type: pdf
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Jeopardy Review Game Solutions 
PDF
File Size: 1600 kb
File Type: pdf
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2.7: Using CODAP to Create Models Using Toolkit Functions

Problem Set 2.7
WORD DOCUMENT
File Size: 340 kb
File Type: docx
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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 
Problem Set 2.7 Solutions - needs to be updated 
PDF
File Size: 57 kb
File Type: pdf
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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 

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 
POWERPOINT
File Size: 986 kb
File Type: ppt
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Problem Set 2.8 
problem_set_2.8.docx
File Size: 340 kb
File Type: docx
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Problem Set 2.8 Solutions 
LINKS TO CODAP FILES - DATA ​​
LINKS TO CODAP FILES - ANALYZED
Manatee Deaths 
Manatee Deaths 
Average Global Temp vs. CO2
Average Global Temp vs. CO2
Car Skids 
Car Skids 

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. 
DIRECTIONS
File Size: 134 kb
File Type: docx
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Samples of Student Work 
RUBRIC
File Size: 112 kb
File Type: docx
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LINEAR - MOTOR VEHICLE DEATHS
File Size: 85 kb
File Type: docx
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QUAD - UNEMPLOYMENT
File Size: 56 kb
File Type: docx
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LINEAR - IPHONE UNIT SALES
File Size: 65 kb
File Type: docx
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LINEAR - HOTDOGS
File Size: 2110 kb
File Type: docx
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LINEAR - BIRTH RATES IN INDIA
File Size: 135 kb
File Type: docx
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QUAD - THOROUGHBREDS IN US
File Size: 61 kb
File Type: docx
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Additional Resources ​

Problem Sets by Nils Abel 
Problem Set Solutions 
PDF
File Size: 514 kb
File Type: pdf
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PDF
File Size: 701 kb
File Type: pdf
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  • About
  • Overview
  • Unit 1: Univariate Data
  • Unit 2: Bivariate Data
  • Unit 3: Trigonometry
  • Unit 4: Sequences and Series
  • Unit 5: Exponential and Logarithmic Functions
  • Unit 6: Personal Finance
  • Unit 7: Probability and Simulations
  • Unit 8: The Normal Distribution
  • Contact