Data Collection – Linear

On Wednesday, as part of my Innovative Teaching Grant from the Pearland ISD Education Foundation, my students and my subject partner’s students completed their first data collection lab.

Objectives

  • Model data using a linear equation.
  • Interpret the slope and intercept values from a linear model.

Procedure

Case 4 Flipping Coins Instructions

Due to larger than anticipated class sizes, time constraints, and limited 1982 pennies, students worked in groups of three to collect data for one set of pennies (pre-1982, 1982, or post-1982).  In a class of 30, four groups collected data for pre-1982 pennies, two groups collected data for 1982 pennies, and four groups collected data for post-1982 pennies.  After each group collected their data, the data was shared with the class and compared.

Data Lab

Results

Pre-1982

Pre-1982 Pennies

1982

1982 Pennies

Post-1982

Post-1982 Pennies

Students found that pre-1982 pennies were the most dense and post-1982 pennies were the least dense.  Based on their results, they determined that the composition of the penny changed in 1982.

Students interpreted the slope as the “weight” per penny and the y-intercept as the “weight” of the bucket.

For homework, the students completed the Case 4 Flipping Coins Evidence Record.

Case 4 Flipping Coins Evidence Record

Follow-up Questions

Today, I sent the students some follow-up questions using the TI-Nspire Navigator Quick Polls to assess their understanding.

I showed the students the graph below and asked “Which object weighs more?”.

follow-up graph

The results from one class period:

Q1

Almost every student correctly identified the correct answer.  All other periods had similar results.

Then I told the students, “The equation to model Object 1 is y = 0.5x + 0.5.  The equation to model Object 2 is y = 0.7x + 0.5”.  I asked, “What is the weight of the bucket?”.

The results from one class period:

Q2

Every student correctly input the correct answer.  All other periods had similar results.

Finally, to truly test their understanding of the meaning of the slope and y-intercept, I told the students, “You weighed 5 objects and found the weight to be 10 N.  The bucket weighed 0.5 N.”  I asked them to “Write an equation to model the weight of x objects.”.

The results from four class periods:

Q3     Q3

Q3     Q3

The first two classes needed some reteaching regarding slope.  The last two classes did better, but there is still room for improvement.  My last class period did not participate in the follow-up questions due to class orientation meetings during their class period.

Innovative Teaching Grant

In March, I applied for an Innovation Teaching Grant through the Pearland ISD Education Foundation.  The project is described below.

Project Summary

This project will provide the hardware required for real-time data collection by students working in small groups to support three Algebra 2 standards.  Real time data collection and analysis provides the tools to allow students to focus on the collected data and provides the foundation for application of the learning from the Algebra 2 curriculum to Science classes.

Purpose

There are three Algebra 2 standards that apply to data collection:
1.  Predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.
2.  Analyze data to select the appropriate model from among linear, quadratic, and exponential models.
3.  Use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data.

The math department currently has a limited set of hardware which has been used for data collection to support these standards.  With limited equipment, the data collection must be performed by the teacher with the resulting data supplied to the students for analysis.

The purpose of the data collection project is to have students work in small groups to collect their own data, analyze and interpret the data, and predict and make decisions based on the appropriate model. In order for the students to perform the activities, we must have additional data collection equipment.

Objectives

By the end of the school year, all PAP Algebra 2 students will have completed at least three data collection activities (linear, quadratic, and exponential), working in small groups, utilizing the hardware supplied by this grant.

Project Description

The teacher will use pre-made activities from TI’s Math Nspired or Vernier’s websites.  Possible activities include That’s the Way the Ball Bounces – Height and Time for a Bouncing Ball, Chill Out: How Hot Objects Cool, and Making Cents of Math: Linear Relationships between Weight and Quantity.

Research suggests that real-time data collection seems to be the most effective way to connect a graph with real-world experiences. (Lapp, Douglas A., and Vivian Flora Cyrus. “Connecting Research to Teaching: Using Data-Collection Devices to Enhance Students’ Understanding.” Mathematics Teacher 93.6 (2000): 504-10. – National Council of Teachers of Mathematics. Web. 28 Feb. 2015.)

Automated data collection improves the accuracy of the data collected and allows students to focus on the positive educational impact of the development of the mathematical model rather than the methodology of the data collection.

Real-time data collection by the students will supply the foundation for the application of linear, quadratic and exponential models to the analysis of physical measurements made in science curriculum.

Project Evaluation

Students will complete the student pages available through the pre-made activities.  The teacher will use the TI-Navigator to capture screen shots of the student’s data and to send quick polls to assess student’s understanding of concepts learned in each activity.

Budget

3 – Vernier EasyLink adapters – $175.50
3 – TI CBR2 motion sensors – $247.17
9 – Dual-range force sensors – $981.00

Other Funds Secured

For the students to perform their own data collection, working in small groups (4-5 students per group), there must be a total of 10 sets (5 sets per teacher) of data collection hardware.

The math department currently has:
2 – Vernier EasyLink adapters
2 – TI CBR2 motion sensors
6 – Temperature probes (5 personal property of one teacher)
1 – Dual-range force senors (personal property of one teacher)

Separate funding from a PTA grant has been secured for:
5 – Vernier EasyLink adapters – $292.50
5 – Temperature probes – $144.75
5 – TI CBR2 motion sensors – $411.95

Awarded May 28, 2015

grant

Facebook Birthday Posts

My birthday was on Sunday.  Facebook will tell you how many people have posted on your timeline for your birthday.  I started looking back at the history of post to my timeline on my birthday, and it made me curious.  Could I predict how many friends would post to my timeline this year?

I specifically looked for the post that said something like this:

post number

I found data for 2007 – 2014, and created this graph.

all data

Clearly, there were some outliers, so I removed them.

outliers removed

That data sure did look linear, so I added the linear regression.

regression 1

Based on the regression (look at that r^2), I predicted that 53 friends would post to my timeline for my birthday 2015.

And the official Facebook results:

results

I would say I have a pretty good model.  If this trend continues, I am predicting 59 friends will post to my timeline for my birthday 2016.

regression 2

Conic Projects 2015

My favorite project in PAP Algebra 2 is our conics project.  The students must sketch a picture using conics and other functions.  They must write the equations to match their sketch.  Then they enter the equations into a graphing utility.  The final picture is printed by me and then colored by the student.

This project has undergone many changes from the number and type of required equations to the graphing utility.

When I first started this project, we were using TI-84s, so the students had to write a program to create their picture.  It was such a hassle because you had to run the program from the beginning to see what the picture looked like.  It took a long time to run because it graphed the equations in sequential order.  Then if anything was wrong, you had to stop the program at just the right time to correct the mistake.  Syntax mistakes were among the most common.  The printed pictures were very pixelated.

I was so excited when the TI-Nspire came out because the students could enter all the equations on a graph page.  You didn’t have to wait for a program to run to see if an equation was correct.  It was also nice because you no longer had to use “and” for domain restrictions, instead you could enter compound inequalities.  Also, the printed pictures were no longer pixelated, since the resolution on the TI-Nspire was so much better than the TI-84.

This year, we used Desmos to create our pictures.  The student no longer needed to solve for y, and they could restrict the domain, the range, or both.  They could also enter multiple domain or range restrictions for the equations.  Since Desmos is a free website, the students could work on their project from any internet-enabled device.

A PowerPoint slide show of this year’s projects is linked below.

Conic Projects 2015