Transformation Unit

For the two week unit my class will be concentrating on the introduction of transformations.

 Arizona Mathematics State Standards 2008

     S4.C2.HS.PO1. Determine whether a transformation of a 2-dimensional figure on a coordinate plane represents a translation, reflection, rotation, or dilation and whether congruence is preserved.

     S4.C2.HS.PO2. Determine the new coordinates of a point when a single transformation is performed on a 2-dimensional figure.

Arizona Academic Content Standards-Mathematics, 2008. http://www.azed.gov/wp-content/uploads/PDF/MathematicsStandard2008.pdf

Arizona Common Core Standards

     G-CO.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

     G-CO.5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

     G-CO.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

NGA Center for Best Practices (NGA Center), Council of Chief State School Officers (CCSSO). (2012). Core Standards for Mathematics: Mathematics Standards for High School. Retrieved August 31, 2012, from Common Core State Standards Initiative: http://corestandards.org/

Learning Goals

1.      Students will be able to identify definitions of transformations and congruence.

2.      Students will be able to identify transformations displayed.

3.      Students will be able to perform transformations.

Measurable Objectives

1.      Given graph paper, students will create a Cartesian plane by correctly labeling the numbers on the x and y axis and identifying the quadrants of the Cartesian plane up to 10 and/or -10 in each direction with less than 5 errors. S4.C2.HS.PO2; G-CO.4.

2.      Given 3 random coordinates, students will plot, label, and translate all coordinates using the proper corresponding letter and prime mark, on a Cartesian plane with less than 3 errors. S4.C2.HS.PO2; G-CO.4.

3.      Given the coordinates of a 2 dimensional shape, students will create the shape on the Cartesian plane by plotting, connecting, and labeling each point, and then translate that shape with less than 5errors. S4.C2.HS.PO2; G-CO.5.

4.      Given 2-dimensional shapes or their coordinates, students will be able to plot and/or reflect and determine their new transformed coordinates given a horizontal or vertical line of reflection with less than 2 errors on each shape. S4.C2.HS.PO2; G-CO.4.

5.      Given two 2-dimensional shapes on a Cartesian plane, students will identify the transformation displayed ¾ times. S4.C2.HS.PO1; G-CO.6.  

6.      Given transformation problems on the post-test, students will be able to use the correct meaning of the definitions of translation, reflection, rotation, and dilation, dilation being the only one not preserving congruence, by correctly identifying or displaying each transformation 7/10 times.   S4.C2.HS.PO1; S4.C2.HS.PO2; G-CO.4; G-CO.5; G-CO.6.

Objective Alignment with Instruction

               Sequentially the measurable objectives above layout exactly what the students are expected to learn. Likewise, for me, the goals for what I am going to be teaching during the lessons of this unit come from the measurable objectives which are based on the state standards. The measurable objectives also are an average of where I want my students to be by the end of the class period and the end of the unit. I would love to have 100% of my students retain and learn 100% of what I teach 100% of the time, but we all know that is not the way it works. Over the school year I get to know my students; I get to learn about the knowledge and the background and the performance levels of my students, and therefore I adjust the percentage rates for the measurable objectives according to what I feel is an obtainable yet challenging goal. Every one of my classes hardly ever has the same percentage goal. If they did then they would have the exact same students in them with the exact same lesson. That is not to say that some of them will not share a percentage goal but I do not teach the same lesson at the same level to all of my classes and expect my lower level class to perform at the same level as my middle or high level classes.

               Each one of the measurable objectives I created has to do with a crucial part of the tasks I want the students to perform by the end of the unit which is a part or in whole the state and/or common core standard. With this unit I have taken into consideration that I only have two weeks to teach this unit, the situation that my classes are all special education classes, and at what level my students are at. With careful consideration I have decided to take the state standard S4.C2.HS.PO1 and modify it to the level of my students and fit it to the time frame we are in and to accommodate the students learning abilities. For translations, I have limited it to simple translations of whole number slides of x and/or y values. For the reflections, I have limited it to horizontal and vertical lines of reflections. For rotations, I have limited it 90 or 180 degrees. For dilations, I have limited it to simply identifying what transformation is displayed.

               My school is on block scheduling. That means a two week period will have five class periods of 90 minutes each. The first week will be Monday, Wednesday, Friday, and the following week will be Tuesday, and Thursday. The first day will consist of a pre-test followed by an introduction of the coordinate plane, graphing points, and then translating points (S4.C2.HS.PO2, G-CO.4.). The second day will consist of plotting 2-dimensional shapes followed by translating those shapes (S4.C2.HS.PO2, G-CO.5.).  The third day will consist of reflecting shapes over a given live of reflection, horizontal or vertical, I will probably stick with the x or y axis for the most part (S4.C2.HS.PO2, G-CO.4). The fourth day will consist of rotations of 90 and 180 degrees on and off a graph, and looking at dilations and how they are different from the other transformations (S4.C2.HS.PO1, G-CO.6). The fifth day will be a review of all the transformations and then the unit test, also known as the post-test (S4.C2.HS.PO1; S4.C2.HS.PO2; G-CO.4; G-CO.5; G-CO.6). This will be the exact same test given as the pre-test so growth can be determined. By the end of the unit the students should be able to identify and/or display each transformation by knowing the definition of each translation, reflection, rotation, and dilation. This is directly related to the two state standards, summarized as, 1) identifying which transformation is used or displayed and 2) identifying the new coordinates for the transformed 2-dimensional shape.

               Part of developing recognition of what something is, sometimes is learning how to create or show it. I have put these two standards together each day and I have intertwined them with being able to determine a transformation on a Cartesian plane by being able to create it or determine the new coordinates of the transformed parts of the 2-dimensional shape. Also, knowing the true definitions of reflection, rotation, translation, and dilation would hold true to knowing if congruence has been preserved. For example, true rotation holds congruence. If there is congruence and dilation, then there are multiple transformations that have transpired not just a rotation.