A. Learning Goals

A1. Learning Goal 1

Wyoming Common Core 7G5

“Students use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.” (Wyoming Department of Education, 2012)

A1a. Measurable Objective 1:

Students will write and accurately solve equations for an unknown angle in a segmented straight angle 4 out of 5 times on a worksheet.

A1b. Measureable Objective 2:

Students will write and accurately solve simple equations for an unknown angle in a segmented right angle 4 out of 5 times on a worksheet.

A1c. Measureable Objective 3:

Students will write and accurately solve simple equations for an unknown angle in a figure including supplementary, complementary and vertical angles 3 out of 5 times on a worksheet.

A2. Learning Goal 2

Wyoming Common Core 8G5.

“Students use informal arguments to establish facts about the angles created when parallel lines are cut by a transversal.” (Wyoming Department of Education, 2012)

A2a. Measurable Objective 1:

Using a graphic organizer, students will state the relationships of the angles formed when transversals cross parallel lines with 100% accuracy.

A2b. Measureable Objective 2:

Given the measure of one angle, students will be able to find the measure of all other angles formed by a transversal when it crosses parallel lines with 100% accuracy on a worksheet.

A2c. Measureable Objective 3:

Given the diagram of parallel lines, cut by a transversal, students will be able to identify congruent angles 5 out of 6 times on a worksheet.

A3. Learning Goal 3

Wyoming Common Core 8G3.

“Students describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.” (Wyoming Department of Education, 2012)

A3a. Measurable Objective 1:

Students graph given transformations of line segments and triangles with 80% accuracy on a worksheet.

A3b. Measureable Objective 2:

Students identify translations, rotations and reflections in a diagram with 80% accuracy on a homework book assignment.

A3c. Measureable Objective 3:

Students sketch translations and reflections along a given line of a diagram with 80% accuracy on a worksheet.

      B. Alignment to Unit of Instruction

            The unit of instruction that I taught was Plane Geometry in a Pre-Algebra class consisting of 9^th-10^th graders.  The purpose of high school Pre-Algebra is to lay a foundation so that students will be successful in later grades when students study the topics more in-depth. 

            The plane geometry unit first reviews concepts that should have been covered in earlier grades and then moves on to more abstract ideas about angles, lines and triangles.  Understanding of these concepts is instrumental in studying Algebra and especially Geometry.  This unit is a kind of bridge between the elementary operations to a more complex understanding of the relationships between geometric figures.

            The goals of the unit reflect this transition period.  Most of the goals are below grade level which is at the level of the material to be learned.  The first learning goal is using supplementary, complementary, vertical and adjacent angles in multi-step problems to write and solve simple equations from an unknown angle.  Students first reviewed all necessary prerequisite knowledge to lead to the point of discussing supplementary, complementary and vertical angles.  This is connecting the prior knowledge of points, segments, lines and rays into a new idea of supplementary, complementary and vertical angles.  Students have solved equations but now are required to use their understanding to write and solve equations.

            Objective A1a measures student understanding of supplementary angles and the angles that have the potential to create them.  Similarly objective A1b measures student understanding of right angles.  These two objectives lead to objective A1c which combines the knowledge of supplementary, complementary and vertical angles to solve multi-step problems from a diagram that contains one or more of the types of angles being studied.  These objectives lead to a further understanding of the relationships between angles.

Learning Goal 2

            This knowledge of angles is all prerequisite to understanding angles formed when parallel lines are cut by a transversal.  Students first used a graphic organizer and a diagram to test hypotheses regarding the relationships between angles.  Students had to use the knowledge measured in learning goal 1 in order to successfully complete the organizer in objective A2a.  Several different methods could be utilized, but all related to the previous learning goal.  The objective was set at 100% because of the structured scaffolding provided and because of the importance of 100% understanding before moving forward in the lesson.

            Objective A2b uses the information learned in A2a in practice problems.  This was also given a goal of 100% accuracy because if students truly understand the objective learned in A2a, the problems are extremely easy with little to no room for error because of calculation.

            Objective A2c involves recognizing pairs of congruent angles based on the rules learned while working towards the previous objectives.  The identification of congruent angles is key in future lessons and future math classes.

            This goal is an important lesson before students enter geometry where they must complete proofs regarding congruent angles formed by a transversal crossing parallel lines.  These ideas all also take place on the plane which is the unit. 

Learning Goal 3

            Another goal of the unit is to understand transformations on the coordinate plane.  Transformations are manipulations of two-dimensional (planar) shapes.  These shapes exist on the plane and are created by line segments, angles, vertices and other figures learned in the early lessons of the unit.  It is important for students to understand that all of these figures can be represented on the coordinate plane and that shapes can look different and still be congruent.

            In objective A3a, students graph transformations of line segments and triangles.  They are representing that the shapes are the same size and the same shape, but look different.  They use their previous knowledge of the coordinate plane and of simple shapes.

            Students must also identify transformations when they see them.  This is an important step in having students recognize congruent and similar shapes when they are facing in different directions.

            Students further demonstrate understanding in objective A3c by sketching transformations with or without graph paper.  This shows that they are not just blindly copying a formula for finding and plotting points, but that they understand the key components of different transformations.

            This learning goal fits into the unit of plane geometry because it involves figures that are in the plane.  This is a necessary step that leads to the understanding of congruent and similar shapes in geometry.

References

Wyoming Department of Education. (2012). Common Core State Standards for Mathematics. Retrieved, March 18, 2014 from http://edu.wyoming.gov/sf-docs/standards/final-2012-math-standards.pdf