Angela CooperKirk Webber

Theresa AllisonEDCI 591

Transitioning from Algebra to Geometry_____________________________________________________________________________________ Unit Title – Transitioning from Algebra to Geometry Lesson Title – Find Distances Course Title – Algebra/Geometry Time Frame – 1 day lesson (normal scheduling: 50 minute class period) Topic/Concept – Finding Distances (Section 3.3) Prerequisite/Prior Knowledge – A working knowledge of the Pythagorean

Theorem. Purpose and/or Goal(s) – To use the Pythagorean Theorem to find the distance

between two points on a grid and to relate areas of squares to the lengths of the sides.

Standards – Geometry Core Standard 3: Triangles

o Prove the Pythagorean Theorem and its converse and use them to solve problems. Develop simple geometric proofs involving triangles. Define trigonometric functions in terms of angles of right triangles and use them to solve problems.

[Standard Indicators: G.2.16, G.2.17, G.2.14, G.2.19, G.2.21] Geometry Core Standard 7: Coordinate Geometry

o Find slopes, lengths and midpoints of line segments using coordinate geometry. Use these measures to show whether shapes are similar or congruent, and whether line segments are parallel or perpendicular. Find the equation of a circle in the coordinate plane.

[Standard Indicators: G.1.1, G.1.4, G.1.6, G.3.5] NCTM Process Standards:

o Problem Solving, Reasoning &Proof, Communication, Connections, and Representation.

NCTM Reasoning with Algebraic Symbolso Connecting algebra with geometry.

Materials Needed – Transparency 3.3 (“Looking For Pythagoras” by Connected Mathematics

2). See Appendix E. Labsheet 3.3 (“Looking For Pythagoras” by Connected Mathematics 2) Handouts pgs. 35 (“Looking For Pythagoras” by Connected Mathematics

2) Homework pgs. 38-45 (Students will bring back to class.)

Launch – See Appendix B Explore – See Appendix B Summary – See Appendix B

After the summary, we would extend the lesson by looking at the relationship between the coordinates and their lengths. We would begin doing this on the overhead.

o Student volunteers wouldo draw the coordinate system.o name each point using (x,y) notation.

Have groups discuss and find the relationship between the coordinates and the side lengths that they found for their triangles. After sufficient time for discussion, summarize as a class.

Assessment – The teacher will informally assess the students’ understanding during the class period. The teacher will use the students’ answers to determine if more details or examples are needed, or if the students have a general understanding of the material. The teacher will be assessing the students while they are working by walking around and checking on the progress the students are making. This assessment will be informally done by listening to the students’ responses and the feedback that the students are giving. The teacher will use the homework as a formal assessment to assess each individual student’s understanding.

Homework questions: Extensions 27-35 pgs. 43, 44

Homework answers: Homework answers can be found in Appendix D.

References/Resources – “Looking for Pythagoras” from Connected Mathematics 2(2009 by Michigan State University)

Prentice Hall and Pearson Prentice Hall.Indiana Academic Standards: Mathematics Teacher Edition. (2006, August 21). Retrieved

February 4, 2009, from Indiana Department of Education: http://dc.doe.in.gov/Standards/AcademicStandards/PrintLibrary/docs-math/

2006-math-geometry.pdf.

National Council of Teachers of Mathematics (2000). Principles and Standards for School

Mathematics. Retrieved February 5, 2009, from http://my.nctm.org/standards/

document/index.htm. Appendices –

Appendix A – Student Textbook Questions Appendix B - Launch/Explore/Summary & Student Page Answers Appendix C - Homework QuestionsAppendix D - Homework answer key Appendix E - Transparencies

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Appendix A

Appendix BLaunch/Explore/Summary & Student Page Answers

Appendix CHomework 24, 27-35

Appendix D Homework Answers

Appendix ETransparencies