Brigid Houlihan March 24, 2015

Subject/Skills: Mathematics/Geometry Grade Level: 9, 10, & 11 Number of Learner(s): 6

Time of Lesson (Period): Period 4 Length of Lesson: 50 minutes (11:04-11:54) Lesson # in Unit of Study: #9 in the Advanced Triangles Unit, second lesson on congruence/proofs specifically

Curriculum Frameworks

Grade Level: 9-12 Subject: Mathematics Strand: Geometry- Congruence Standard G-CO 7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. (Massachusetts Curriculum Framework for Mathematics, March 2011, page 95).

Grade Level: 9-12 Subject: Mathematics Strand: Geometry- Congruence Standard G-CO 8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. (Massachusetts Curriculum Framework for Mathematics, March 2011, page 95).

Grade Level: 9-12 Subject: English Language Arts and Literacy Strand: Speaking & Listening Standard SL 1: Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 912 topics, texts, and issues, building on others ideas and expressing their own clearly and persuasively. (Massachusetts Curriculum Framework for English Language Arts and Literacy, March 2011, page 63).

Purpose As a result of this lesson, students will be able to describe the 6 triangle congruence postulates (SSS, SAS, ASA, AAS, HL, CPCTC) identify which congruence postulate proves two triangles are congruent (SSS, SAS, ASA,

AAS, HL, CPCTC)

Objectives &

Function

CURRENT: Students will build on their knowledge of the properties of similarity and congruence specific to triangles.

FUTURE: Students will work towards demonstrating their ability to use known information about triangles to construct and solve geometric proofs.

Pre-requisite Skills &

Knowledge

Students have the knowledge that triangles are 4 sided figures triangles have an interior angle sum of 180 triangles can be similar figures triangles can be classified by their sides (isosceles, scalene, equilateral) and their angles

(right, acute, obtuse, equiangular)

Schedule/Pacing Description of Lesson Materials

Warm-up/Activator

6 minutes - 11:10

Students will complete card sort warm up activity: matching diagrams of triangles to the appropriate congruence postulate

Triangle Congruence Card Sort

Review of Agenda 2 minutes - 11:12

Teacher reviews/explains the daily agenda. N/A

Homework Review

8 minutes - 11:20

Teacher will project the Are they Congruent? worksheet on the board and review with students.

iPad & iPad Stand Are they Congruent? WS

Content Activity

15 minutes - 11:35

Students will create a set of flashcards for the 5 congruence postulates.

Teacher will demo on the projector as needed.

iPad & iPad Stand flashcards, glue, & scissors Congruence Postulates

reference sheet

Content Practice

8 minutes - 11:43

Students will work in pairs to label triangle diagrams and identify the appropriate congruence postulate.

Teacher will demo on the projector as needed.

Congruence Postulates reference sheet/flashcards

Congruence Postulates worksheet

Content Practice 2

8 minutes - 11:51

Teacher will guide students through completion of a basic triangle congruence proof, using the projector. This will serve as an example for the homework.

Teacher will encourage students to use color to mark up the original diagram.

Triangles Proofs Reference Sheet

Homework 1 minute - 11:52

Teacher will assign students page 1 of the Triangles Proofs Packet

Triangles Proofs Packet

Lesson Closure

2 minutes - 11:54

The class will complete a What Stuck exit activity, writing something that stuck with them from the days lesson on a post-it note and putting it on the What Stuck Wall.

Post-it notes

IEP Goals Objectives/Benchmarks

VERBATIM RE-WRITE INSTRUCTIONAL IMPACT

Student 1

Student 1 will appropriately use mathematical vocabulary orally during class and within written work with at most 1 prompt from the instructor on 4 out of 5 measured occasions.

When engaging in class discussion and within written work, Student 1 will appropriately use mathematical vocabulary with no more than 1 teacher prompt, on 4 out of 5 measured occasions over the fall semester.

Teacher models the appropriate use of thematic vocabulary.

Teacher provides frequent opportunities for review and integration of thematic vocabulary.

Student 1 With increasing independence Student 1 will use his own notes as reference material to complete class assignments with increasing independence.

When questions arise during the completion of class assignments, Student 1 will refer to his own notes as a resource before asking for teacher assistance on 4 out of 5 measured occasions over the fall semester.

Teacher will encourage student to go to his reference section and use resource materials before answering a question from the student.

Modifications/Specially Designed Instruction Student 1 VERBATIM

CONTENT: The content of the general curriculum will be modified through the provision of key concepts and the

accompanying elimination of extraneous detail.

METHODOLOGY/DELIVERY OF INSTRUCTION: 1:1 and small group instruction thematic approach provide graphic organizers/templates provide cueing strategies for language and attention hands-on activities visual models, charts, or diagrams highly structured approach provide kinesthetic techniques multisensory approach teacher modeling extra processing time additional wait time for processing and responding

PERFORMANCE CRITERIA: daily homework & classwork performance

Accommodations & Adaptations Student 1 VERBATIM

Student 1 will be provided with extra time to complete tasks Student 1 will be provided organizational strategies, such as charts, timelines, compensatory strategies provide frequent practice and review of skills provide predictable class routines give clear and concise directions provide nonverbal cues to help maintain focus ask to have student reverbalize directions prior to attempting tasks provide clear expectations for performance convey immediate feedback on performance introduce material in small steps with frequent review use a slow deliberate rate of speech when presenting material orally

Possible Problems Possible Solutions

Student(s) do not remember information about the 6 congruence postulates.

Teacher will provide more prompting and/or review of information during the warm-up/lesson activator.

Student(s) have a difficult time cutting, pasting, and glueing to create flashcards.

Teacher works with individual student/small group while others are working independently - OR - Teacher pairs struggling student up with confident student.

Student(s) have a difficult time setting up identifying which congruence postulate justifies congruence in a particular diagram.

Teacher provides a structured example for students to follow. Teacher will direct students to reference their flashcards.

Students need more time to complete a particular activity during the lesson.

Teacher adapts lesson as necessary.

Assessment Teacher will record data as students complete card-sort warm-up activity. Students will complete a worksheet having to identify the appropriate congruence

postulate. Teacher will check and record data. Students will complete one page of the Triangle Congruence Proofs Packet for

homework. This packet mirrors the activities done in class and will provide a clear indication of student understanding. Students homework will be checked the following day for accuracy. This will ensure students met the following lesson purpose statements.

Extension of the Lesson Tomorrow: Students will complete similar in-class activities for additional skill practice as a continuation of the lesson.

Next Week: Students will have a quiz on triangle congruence. Unit of Study: In this unit, students will apply their knowledge of the properties of

triangles to complete geometric proofs.