F T 3 (Function Family T 3 ) OAME 2010 Conference Brock University St Catherines, ON

Nspire Self-Assessment  Please self assess you experience with Nspire:  1 finger indicates no prior experience  2 fingers indicates only using 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

Big Ideas in Secondary Math  According to Marian Small’s new book: “Big Ideas from Dr. Small: Grades 9-12” one big idea is Transformations:  By focusing on the “Big Ideas”, teachers will enable and encourage students to use mathematical reasoning throughout their lives  Using technology to investigate transformations of functions is a theme that runs from grade 9 to12

Transformations across the Grades 9&10 Curriculum MPM1DAG2.02: identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b MFM1PLR3.05: describe the meaning of the rate of change and the initial value for a linear relation arising from a realistic situation, and describe a situation that could be modeled by a given linear equation MPM2DQR2.02: explain the roles of a, h, and k in y = a(x – h ) 2 + k, using the appropriate terminology to describe the transformations, and identify the vertex and the equation of the axis of symmetry MFM2PLR2.03: identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b MFM2PQR3.02: solve problems by interpreting the significance of the key features of graphs obtained by collecting experimental data involving quadratic relations

Transformations in the Grade 11 Curriculum MCR3UD2.5 determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y =a f(k(x – d)) + c, where f(x) =sin(x) or f(x) =cos(x) with angles expressed in degrees, and describe these roles in terms of transformations on the graphs of f(x) =sin(x )and f(x) =cos(x) MCF3MB2.5 determine, through investigation using technology, the roles of a, h, and k in quadratic functions of the form f (x) = a(x – h) 2 + k, and describe these roles in terms of transformations on the graph of f(x) = x 2 MCF3MC2.6 determine, through investigation using technology, the roles of the parameters a, c, and d in functions in the form f(x) = a sin(x), f(x) = sin(x) + c, and f(x) = sin(x – d), and describe these roles in terms of transformations on the graph of f(x) = sin(x) with angles expressed in degrees MBF3CA1.3 determine, through investigation using technology, the roles of a, h, and k in quadratic relations of the form y = a(x – h) 2 + k, and describe these roles in terms of transformations on the graph of y = x 2

Function Modeling  Nspire makes function modeling accessible to every student using only handhelds and CBR2’s  Linear modeling in grades 9 &10  Quadratic modeling in grade 10 &11  Periodic (Sinusoidal) modeling in grade 11  Collecting data improves student engagement and comprehension

Auto Launch Window  Since OS v1.6, Nspire (CAS and non-CAS) allows “Plug N Play” with data collection devices  To begin, you 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

Linear Data Modeling Demo  The Nspire teacher edition allows you to model data collection and linear modeling  You will need a mini- USB adapter available from Vernier  Lets see a demo ….

Experiments to Gather Data for Modeling: Linear Data  Walk 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 must have members with at least two different coloured poker chips  Assign roles (Operator, Tech Support, Coach)  Your group will complete all 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)

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 Texas Instruments booth for more information

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