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### Walk the Graph:Algebra I

By: Dawn Gray

Mentor: Dr. Lagoudas and Dr. Davis

PhD Candidate: Parikshith Kumar

REU: Francis Phillips

Objective

- Students will learn how to use the CRB and calculator
- Students will learn rate of change and how it changes the graph
- Students will learn how to calculate velocity
- Students will learn to identify non-linear graphs

Algebra I TEKS

- (a) (5) Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools, and technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to model mathematical situations to solve meaningful problems.
- (b) (A.1) (E) interpret and make decisions, predictions, and critical judgments from functional relationships.
- (A.2) (C) interpret situations in terms of given graphs or creates situations that fit given graphs; and
- (A.11) Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations.

Materials Needed

- CBR or CBL2 with motion detector
- Graphing Calculator (these would work best TI-83, TI-83+, TI-84, TI-84+)
- Massed weights
- SMA spring
- Apparatus (to hang spring and weights)
- 6 volt battery or power source
- 2 leads with alligator clips

http://www.hometrainingtools.com/catalog/general-science/cat_masses-weights.html

http://education.ti.com/guidebooks/datacollection/cbr/cbr-eng.pdf

http://education.ti.com/educationportal/sites/US/productDetail/us_ti84pse.html

http://smart.tamu.edu/

CBR Boundaries

- The CBR has a readable range of .5 meters (about 1.5 feet) to 6 meters (about 19.5 feet). Anything to close or to far away will not be picked up on the CBR correctly. The new CBR 2 has a better forward range. It can read from 15 centimeters (about 6 inches).

Walking the graph

- 2 days at least
- Day 1: CBR Activity – Match the graph

http://education.ti.com/guidebooks/datacollection/cbr/cbr-eng.pdf

Day 2: SMA Activity

Day 1- TI: Match the graph

- Walk the graph activity – distance match
- Students will complete TI activity sheet
- Walk the graph activity – velocity

http://education.ti.com/guidebooks/datacollection/cbr/cbr-eng.pdf

Day 2 – SMA Spring Activity

- Introduce SMA and their applications
- Handout SMA activity worksheet

SMA Activity.doc

- Show a demonstration
- Students work in groups: testing and recording the graphs of different weights

Graphs

- These are examples of graphs that will be displayed
- Graph 1 – has a mass of 47.8 grams and is being heat to bring the spring back to its original shape
- Graph 2 – has a mass of 47.8 grams and is being cooled, the spring is deforming its shape

Pre-calculus

- Students will take the graph and pick out the points and distance
- Students will use the rules (like add-add, and add- multiply) to calculate the type of graph

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