Sandia High School Geometry Team

Lesson: Triangle Tessellation

Team Planning•Our team: Heidi Draper, Andy Diewald, Jessica Esquibel, Ann Goswick, Brenda Lyons, and Noralyn Parsons.

•Our team met at lunch and before school to work on this lesson. We built off of the strengths and weaknesses from previous experiences.

Our Students• Student Population:

– 68% Anglos, 23% Hispanics, 3.9% Asians, 2.6% Native Americans, and 2% African-Americans .

– Class observed was an inclusion class with about 1/3 of the class being part of the special ed. program. (Class has two teachers.)

•Students are fairly motivated and are accustomed to working in groups and individually.

Overarching Goals

•Students will be able to concisely explain what they have learned in geometry.•Students will be self-confident and willing to take risks.

Lesson Objectives

• Students will understand that when given two parallel lines and a transversal there are two groups of congruent angles, big angles and small angles.

•Students will understand that any big angle is supplementary to any small angle. B S

Previously Learned Concepts

• Students have covered the following topics prior to this lesson:– Angles– Triangle types (isosceles, equilateral,

scalene)– Triangle Angle Sum– Parallel Lines– Congruency– Linear Pair– Straight Angles– Vertical Angles– Angle Addition

Concepts to be Learned•Students will use a tessellation to:

become familiar with the terms of the lesson.understand the properties associated with the following types of angles: (alternate interior, alternate exterior, corresponding, and same-side interior).

Concepts to be Used in Future Lessons

•Students will be able to apply the knowledge gained from this lesson to: Solve geometric proofs

Solve problems associated with polygon angle sum.Solve problems associated with exterior angle theorem.

Misconceptions•Two lines are parallel just because we don’t see them intersect.•Students may think that special angles will always be congruent. They forget that the lines cut by the transversal must be parallel.

•Students may confuse the special angle types. Students seem to struggle the most with corresponding angles.

Materials

• Tag board triangles (for the students)

• White sheets of paper• 3 colored pencils for each

student• 3 colors of overhead pens• Overhead triangle• Overhead transparency of

completed tessellation

Lesson Time Schedule

• 10 minutes to introduce topic• 30 minutes for students to begin

tessellation• 10 minutes for discussion• Following Day: Lesson expands

to specific angle types.

*Note: We did this lesson on a flex day so we had 75 minutes for the lesson.

Visual Tool•The key instructional tool in this lesson is the tessellation and the making of the tessellation.

Possible Student Problems/Concerns

• Students will want to know if they have to fill the whole page with triangles.

•Students may struggle with tracing and rotating the triangle and with coloring the angles. •Students’ lines may not come out parallel if their tracing is off.

Engaged Student Learning• Students will be tracing triangles and coloring

angles. • Students will be looking at their tessellation and

exploring angle relationships.• Students will be writing down their observations

as they work on the tessellation.• Students will take notes throughout the class

discussion.

The teacher will be walking around the room answering questions and observing throughout the lesson.

Mathematical understanding

• The effectiveness of the lesson will be based on how well the students grasp the topics that follow this lesson.– If students are using the tessellation as a visual

tool and get in the habit of coloring congruent angles, then the lesson will be a success.

Changes• Students should write down their

observations as they work on their tessellation.

•Make sure triangles are not too small.•When discussing big angles and small angles, color the two angles that make up the big angle one color on the overhead transparency.

•Should students be allowed to use a ruler to expedite the process?

Summary• Based on observation, the lesson was a

success.–Students used the tessellation as a visual tool.–Students used colored pencils to mark congruent triangles.–Students were able to “fall back on” the ideas of big angles and small angles when they were struggling with the specific angle types. –The class was able to use the tessellation in lessons that followed to discuss different topics.

Assessment

*Immediate assessment based on observation.*Unit test results were better than in previous years without using the lesson.

Students acquired a deeper understanding of the concepts because of the techniques used in this lesson.

What The Teachers Learned•Teaching with a visual tool helps all levels of students.

• Need to use the visual tool as often as possible and add more visuals whenever possible.

• Using smaller terms (big and small angles) that the students can fall back on helps ease some students’ stress. This allows the students to simplify what often seems overwhelming.

Thank you!