Function Modeling in Algebra 1 with Nspire and CBR2 CC-212A 2011 T 3 International Conference San Antonio, TX Saturday, February 26 th

Where I’m from

Session Goals  Design experiments to collect distance-time data using a CBR2  Choose an appropriate function model (linear, quadratic, sinusoidal)  Create a curve of best fit using transformations  Connect the parameters in the curve of best fit to the data collection experiment

Nspire Self-Assessment  Please self assess your experience with Nspire:  1 finger indicates no prior experience  2 fingers indicates only using it at workshops  3 fingers indicates using the handheld in your class  4 fingers indicates downloading and using pre-made activities in you class  5 fingers indicates creating your own activities in your class and being an expert at your school

Common Core Standards: Functions Construct and compare linear, quadratic, and exponential models and solve problems. 1. Distinguish between situations that can be modeled with linear functions and with exponential functions. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 3. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 4. For exponential models, express as a logarithm the solution to ab ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. Interpret expressions for functions in terms of the situation they model. 5. Interpret the parameters in a linear or exponential function in terms of a context. linear-quadratic-and-exponential-models/

Function Modeling in Ontario  The Ontario secondary Mathematics curriculum has a function modeling theme that runs from grades 9 to 12  Nspire makes function modeling accessible to every student using only handhelds and CBR2’s  Linear modeling in grade 9  Quadratic modeling in grade 10  Periodic (Sinusoidal) modeling in grade 11  Collecting data to model functions improves student engagement and comprehension

Auto Launch Window  Nspire (CAS and non-CAS) allows “Plug N Play” with data collection devices  To begin, simply open a new document and add a blank notes page  Next, connect the CBR2, or Vernier probe, and an Auto Launch window appears.

Data Collection Console  Once you select the type of page to collect data onto, a split screen appears with the data collection console at the bottom  The data collection console controls the beginning and end of data collection  To change the frequency and duration of the data collection use the Experiment menu  To retry the data collection use the Data menu  The data collected is stored into variables dc01.time, dc01.dist1, dcc01.vel1 and dc01.acc1

Vernier Data Probes for Nspire  Vernier offers four products for data collection EZ-Temp Probe (connects to Handheld and collects real time temperatures), P/N EZ-TMP, $59 Go-Link (connect CBL2 probes to PC), P/N GO- LINK, $85 Easy Link (connect CBL2 probes to Nspire), P/N EX-LINK, $89 Mini USB Adapter (Connect EZ-Temp or CBR2 to PC), P/N MINI-USB, $7.50  Visit the Vernier booth for more information

Linear Data Modeling Demo  The Nspire teacher edition software allows youto quickly collect data and easily create function models  We will collect distance- time data using a CBR2  (You will need a mini-USB adapter available from Vernier)  Lets see a linear demo ….

Experiments to Gather Data for Modeling: Linear Data  Walk at a constant rate  Roll a car or can at a constant rate  Others? Quadratic Data  Ball bounce  Roll a can up a ramp  Pillow toss  Others? Sinusoidal Data  Pendulum  Walk around a hula-hoop  Weighted Springs  Others?

It’s Your Turn …  Form a group of 3 or 4. Your group should have a variety of Nspire experience levels  Assign roles (Operator, Experimenter, Coach)  Your group will complete three activities: Modeling Linear Data (Violet sheet) Modeling Quadratic Data (Light green sheet) Modeling Sinusoidal Data (Buff coloured sheet)  For extra support refer to: Data Collection with TI Nspire (Bright Green sheet) Manually Manipulating Functions on TI-Nspire (Pink Sheet)

Math GAINS in Ontario  Check out the Ministry of Education web site and click on Math Gains

For more information, please contact me:  Dwight Stead – T 3 Regional Instructor   Wiki: Click on the T3 Conference Link