function modeling in algebra 1 with nspire and cbr2 cc-212a 2011 t 3 international conference san...
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Function Modeling in Algebra 1Function Modeling in Algebra 1with Nspire and CBR2with Nspire and CBR2
CC-212A CC-212A 2011 T3 International ConferenceSan Antonio, TXSaturday, February 26th
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: FunctionsConstruct 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 abct = 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.
http://www.corestandards.org/the-standards/mathematics/high-school-functions/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 DataPendulumWalk around a hula-hoopWeighted SpringsOthers?
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
www.edugains.ca/ and click on Math Gains
For more information, please contact me: Dwight Stead – T3 Regional Instructor
Wiki: http://dpcdsb-nspire.wikispaces.com Click on the T3 Conference Link