F3 @ T3 (Function Family Fun @ T3)

OAME 2010 Conference

Brock University

St Catherines, ON

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 CurriculumMPM1D AG2.02: identify, through investigation with technology, the geometric

significance of m and b in the equation y = mx + b

MFM1P LR3.05: 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

MPM2D QR2.02: 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

MFM2P LR2.03: identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b

MFM2P QR3.02: 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 CurriculumMCR3U D2.5 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 off(x) =sin(x )and f(x) =cos(x)

MCF3M B2.5 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) = x2

MCF3M C2.6 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

MBF3C A1.3 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 = x2

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 DataPendulumWalk

arounda hula-hoop

WeightedSprings

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 – T3 Regional Instructor

Dwight.stead@rogers.com

Wiki: http://dpcdsb-nspire.wikispaces.com Click on the T3 Conference Link