Objectives

• Record the successive maximum heights for a bouncing ball.
• Model the bounce height data with an exponential function.

Procedure

Bounce Back

Groups of three students used a motion detector to collect the height of a bouncing ball for 5 seconds.

Analysis

An example of one group’s data collection.

Students determined the maximum height of five successive bounces.  They put the data in a List & Spreadsheets Page.

The data for the first and fourth bounce was used to mathematically determine an exponential model that would fit the data.  They plotted their data and model on a Data & Statistics Page.

Then they had the calculator find the exponential regression for their data.

Results

Most groups found their model and the exponential regression to be very similar.

Today, as part of my Innovative Teaching Grant from the Pearland ISD Education Foundation, my students completed their third data collection lab.

Objectives

• Record temperature versus time for a cooling object.
• Model the temperature of an object as it cools.

Procedure

How Cool It Is

I had a crock pot of hot water.  Each group of three students were given a cup of the hot water.  They placed the temperature probe in the hot water for about 30 seconds, then removed the temperature probe and allowed it to cool.  The calculator collected the temperature data for three minutes.

Analysis

An example of one group’s data collection.

Students determined that an exponential model should fit the data.  They had the calculator graph the exponential regression for their data.

The exponential model did not appear to be a very good fit.  They determine that the exponential model should have an asymptote at room temperature.  So they adjusted the collected temperature values by subtracting the room temperature.  Then they sent the data to a Data & Statistics page for further analysis.

The data for 20 seconds and 160 seconds was used to mathematically determine an exponential model that would fit their adjusted temperature data.  They plotted their model, then compared their model to the exponential regression using the adjusted temperature data.

Results

Most groups found their model and the exponential regression to be very similar.

On Friday, as part of my Innovative Teaching Grant from the Pearland ISD Education Foundation, my students completed their second data collection lab.

Objectives

• Record height versus time data for a bouncing ball.
• Model a single bounce using both the vertex and standard forms of a parabola.

Procedure

That’s the Way the Ball Bounces Instructions

Since my subject partner’s classes were not participating in the data collection, we had ten CBR2 to share among all students in the class.  With several students out for a pep rally, students were able to work with a partner, and each student collected his/her own data.  Students dropped a racquetball below the CBR2 motion detector.  The CBR2 collected data for position vs time for 5 seconds.

Analysis

An example of one student’s data collection.

Students chose one bounce to model.  They selected the bounce and struck the outside data.

Then they sent the data to a Data & Statistic page to analyze the bounce.

They traced along the scatterplot to find the coordinates of the vertex.  They used the coordinates of the vertex to plot a function in vertex form.  Students had to change the value of a until they found the best fit for their data.

Then they expanded the vertex form to get the equation in standard form.  This student’s equation was .

Next they had the calculator find the quadratic regression for their bounce.

Students compared the expanded vertex form equation to the standard form from the regression.  They found that the vertex form equation they had plotted was very similar to the standard form equation from the regression.

Students answered the questions on the record sheet.

That’s the Way the Ball Bounces Record Sheet

Conclusion

More than one student commented, “That was fun.”

Some of the juniors mentioned that they wished the had the TI-Nspire in Physics class.  They had recently done an experiment using the TI-84s with the motion detector to see how long it takes objects of differing masses to hit the ground.  They commented that it was easier to use the motion detector with the TI-Nspire.

 

 

 

 

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.

Results

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?”.

The results from one class period:

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:

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:

    

    

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.