Activity+Research

= Activity Research Exchange = //Please provide a link or full reference for the activity you found and a brief description of it. Include what tools it uses (if any) and what courses it may be appropriate for. (This is likely all in the first paragraph of what you turned in.)//

Texas Instruments. (2004). Connecting Factors and Zeros (Algebra I). T3 Professional Development Services from Texas Instruments, 1-5. - Students will determine if a quadratic formula is factorable. They have already been introduced to the quadratic formula. If the formula is factorable, they will factor the equation, set each factor equal to zero, and solve for //x//. Students will be able to see from the graphs on their graphing calculators that the factors of an equation, the zeros of a function, and solutions of an equation are all related. When they factor correctly, they should be able to see that the zeros of a function are also the solutions to the equation. This activity is appropriate for Algebra 2 students and any other class which teaches or reviews this content. You really couldn't go wrong.

// Wanko, J. (2005). Tapping into trapezoids. Mathematics Teacher, 99(3), 190-195. (This article has 3 other tasks I do not discuss - also on trapezoids) // Using toothpicks, angle rules and protractors, or GSP to complete the open ended task: Make a list of hypotheses about trapezoids that have three congruent sides and a fourth side twice as long as each of the others. The article calls this a “special isosceles trapezoid”. Hypotheses students may come up with include relationships between triangles created within the trapezoid by adding diagonal and finding the measure of each interior angle, among other things. Most involve dividing the ‘special isosceles trapezoid’ into various triangle configurations.

 Constructing Kites: Schoonover, K. (2008, October 12). //Construction of a Kite and Investigating Its Properties.// Retrieved from http://education.ti.com/calculators/downloads/US/Activities/ Detail?id=11380&ref=%2fcalculators%2fdownloads%2fUS%2fActivities%2fSearch%2fSubject%3fs%3d5022%26sa%3d5024%26t%3d5051%26d%3d9 Using the Cabri Jr. application on the TI-84 plus calculator, students will construct a Kite in a method similar to constructing with a ruler and a compass. Students measure the angles they formed, measures of the angles formed by the diagonals, and the length of the segments. Through this activity they will derive the following properties of kites: (a) angles formed by non-congruent sides are congruent, (b) diagonals are perpendicular, and (c) diagonals bisect each other. The activity also integrates angle-angle-side and side-side-side theorem of triangle congruency.

Transformers (Matrices) Activity: Texas Instruments. (1995). //Transformers (matrices)//. Retrieved from http://education.ti.com/calculators/downloads/US/Activities/Detail?id=8776&ref=%2fcalculators%2fdownloads%2fUS%2fActivities%2fSearch%2fSubject%3fs%3d5022%26sa%3d1010%26t%3d1174%26d%3d9

When a polygon is transformed its vertices change. A transformation is a rule that describes how the coordinates are changed. Students will use a program on the TI-84plus to investigate transformations of squares and triangles using matrices. In the first problem given in the activity students will reflect and rotate a square imprinted with an “F” to show how the orientation of the square changes. Students will explore symmetry groups which are transformations that preserve distance and also line up with the original polygon. In problem two students will look at how multiplying a matrix comprised of the pre-image vertices by a “transformer matrix” yields a matrix comprised of the image vertices. Students will also notice that each reflection is its own inverse. In problem three the students explore the symmetry group of triangles using transformation matrices.