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UC MAT Technology

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UC MAT Technology is the "official" Wiki for the 2008 University of Cincinnati MAT Technology summer course. I am trying to post as much stuff that I use in class as I can here on this page. Please visit the other wiki to see what the teachers in the class have done (and leave comments there!).

A bit of History about the UC MAT!

The Department of Mathematical Sciences of the University of Cincinnati has offered a Master of Arts for Teachers of Mathematics (MAT) for over a quarter of a century. This program for high school teachers runs during the summer. The Technology course is charged with providing support for the Geometry course and Linear Algebra course (being run concurrently) as well as creating materials for other teachers to use. This support and materials will be in the form of Dynamic Worksheets.

Contents

Dynamic Worksheets used in Class

Composing Two Dilations

When you Htm.gifCompose two Dilations, the centers are collinear and the product of the individual scale factors is the the scale factor of the composition.

Finding the Center of Dilation

In Htm.gifFinding the Center of Dilation, you are given a pre-image triangle and several dilation images. You are to use the properties of dilations to find the center, and if possible, find the scale factor.

Coordinates of a Point

Htm.gifThis worksheet is used to reinforce the idea that the coordinates of a point do not change when subjected to a linear transformation, but remain the same when derived from the transformed axis.

Images of F

It is a little easier to see the result of a linear transformation when you look at an Htm.gifimage of F. There is an associated pdf worksheet that goes with it. You can also use the Images of Dr. Minda worksheets: pdf and word.

Linear Transformation with Two Grids

Nothing fancy here, but Htm.gifthis worksheet illustrates linear transformations using a domain and codomain. Drag the basis vectors and see the matrix.

Inverse on Two Grids

Htm.gifThis worksheet is a modified version of the Htm.gifLinear Transformation with Two Grids worksheet, allowing the user to study the inverse transformation.

Transforming Quadrilaterals

The purpose of this worksheet is to reinforce the idea of parallelograms being mapped to other parallelograms by non-singular linear transformations. With Htm.gifTransforming Quadrilaterals, you will investigate how you can transform a given quadrilateral (say, a non-square rectangle) into other quadrilaterals (say, a square or a rhombus). There is an associated pdf and word worksheet.

Images of Dr. Minda

Professor Minda has been teaching the Linear Algebra course for the first four weeks. Htm.gifImages of Dr. Minda allowed the teachers to manipulate column vectors in a matrix and observe the resulting changes in Dr. Minda's picture! There is an associated pdf and word worksheet.

Parallelogram Target Practice

With a (non-singular) linear transformation, parallel lines are mapped to other parallel lines. Therefore, parallelograms are mapped to other parallelograms. In Htm.gifParallelogram Target Practice, this idea is reinforced. In this worksheet, your task is to map the blue square to different parallelograms. This is accomplished by changing the size of the square, moving the square, and changing the column vectors.

Vector Equation of a Line Through Two Points

Teachers have been studying lines of this form in the Linear Algebra class for the MAT program. The Htm.gifVector Equations file illustrates lines of the form X=\left(1-t\right)A+tB.

Dot Product Equation of a Line

The teachers in the MAT have just started working with the dot product of two vectors. The idea of Htm.gifDot Product Lines is to develop an understanding of how the collection of all vectors whose dot product with a given vector is a constant is just a line. So for example, 2x + 3y = 5 can viewed as a dot product statement [2,3]\cdot[x,y]=5.

Function Families

Many of the teachers in the MAT are interested in function families. The Htm.gifFunction Families file illustrates another way to show function families (actually, function forms) using the SEQUENCE[] command, check boxes, and sliders.

Command Constructions

To learn about some of the command features of GeoGebra, you can work through some simple commands in the file Htm.gifCommand Constructions. Study the commands and try to predict what each will do.

Vector Fun

In the Dynamic Worksheet Htm.gifVector Fun, you are given three fixed vectors and three points. Using vector arithmetic rules, you are given different challenges, like make two perpendicular vectors whose tails are at one of the given points.

What's My Rule?

Htm.gifWhat's My Rule? is modeled after a TI-Nspire activity. The idea is to reveal a mystery point that moves in response to a given point A. Your task it to determine the movement rule for the mystery point.

Constructions with NO Toolbar

Can you construct a Htm.gifParallelogram with no toolbar, only using the algebra input line? Use what you know about vectors and have at it!

Constructions with a Limited Toolbar

Can you construct a Htm.gifKite with a limited toolbar? What about a Htm.gifParallelogram with a limited toolbar or a different Htm.gifParallelogram with a different limited toolbar? Try your hand at them! These construction emphasize using transformations to perform the constructions. Thanks to Chris Sangwin's article How Does This Button Work? for this idea of a "limited toolbar."

Angle Bisector

Can you construct an angle bisector without using the Mode angularbisector 32.gif button? Try your hand at it by constructing an Htm.gifAngle Bisector using a limited toolbar. Thanks to Chris Sangwin's article How Does This Button Work? for this idea.

Parallel Line

Can you construct a parallel line without using the Mode parallel 32.gif button? Try your hand at it by constructing a Htm.gifParallel Line using a limited toolbar. Thanks to Chris Sangwin's article How Does This Button Work? for this idea.

Drag Test

What does it mean to "Pass the Drag Test?" Htm.gifDrag Test illustrates this concept using squares and kites.

Vector Operations

Htm.gifVector Operations illustrates some of the vector concepts Dr. Minda discussed in the Linear Algebra class on Monday.

Centroid Curiosity

Htm.gifCentroid Curiosity was created to illustrate a dynamic worksheet and to preview a concept to be introduced in the Linear Algebra course.

Other Examples of Dynamic Worksheets

Here are some examples of worksheets used in my classes this past year. Simply examples so you know what you are getting yourself into.

Practice Dynamic Worksheets

Below you will find the UC MAT Technology Class' "first attempts" at turning GeoGebra files into Dynamic Worksheets. Not only did we make Dynamic Worksheets, we learned how to upload our files into the UC MAT directory and link them to our Wiki. These products were produced after two classes (or three hours) working with GeoGebra.