Overview

Module 1: Congruence, Proof, and Constructions

The heart of the module is the study of transformations and the role transformations play in defining congruence.

Topic C: Transformations/Rigid Motions

High School Math Schedule of Assessed Standards (SAS)

Please contact Katie Lyons with any questions.

Week 1: September 6

Notes:

Lesson 1 (Modeling Cycle Lesson)

Need compass & straightedge. Ensure students understand that, even though the vocabulary terms may be familiar, they should pay careful attention to the precision of each definition. A vocabulary journal, word wall, or vocabulary anchor chart may be good to start today to build on during the year. Students will need to do at least question 1 in the problem set to prepare them for the Opening Exercise of Lesson 2.

Lesson 2 (Exploration)

Need compass & straightedge. Remind students to focus on the vocabulary they are using in the directions because it becomes the basis of writing proofs as the year progresses.

Week 2: September 12

Notes:

Lesson 3 (M)

Need compass & straightedge. Students watch a brief video clip to set the stage for the construction problem. Students need to complete Problem Set questions 1-5 to be prepared for Opening Exercise of lesson 5.

Lesson 4 (M)

Need compass & straightedge. Students need to complete Problem Set question 2 for Opening Exercise in lesson 5.

Lesson 5 (E)

Will need a makeshift compass (i.e., a string and pencil).

Week 3: September 19

Notes:

Lesson 6 (Problem Set Lesson)

Consider making poster of Key Facts and posting in room. In discussion section, consider drawing pictures as you discuss to help students visualize.

Lesson 7 (P)

Check to see whether facts from Lesson 6 are fluent. Differentiate by spending small group station time to reinforce facts from lesson 6 &7.

Lesson 8 (P)

Teachers should continue to build add vocabulary in a systematic way: word wall, student vocabulary journal, etc.

Lesson 9 (P)

Teachers will need to prepare technology to view whole class video clip. Students begin diving into proofs. Blow up Basic Property Reference Chart and post in room so students can use for proofs.

Week 4: September 26

Standards Addressed in Week's Lessons

Topic B

G.CO.C.9

Topic C

G.CO.A.2

G.CO.A.3

G.CO.A.4

G.CO.A.5

G.CO.B.6

G.CO.B.7

G.CO.D.12

Notes:

Lesson 10 (P)

Encourage students to mark up diagrams until the necessary relationships for the proof become more obvious. Have students complete Problem Set to set them up for success in lesson 11.

Lesson 11 (P)

Teachers will need to prepare technology to view whole class video clip. To begin Classwork for lesson 11, students will do best if they have completed the Problem Set from lesson 10.

Lesson 12 (M)

Two days are given for this lesson to help students recall transformation vocabulary and intuitively how transformations effect motion. Photocopying of Pair Cards will be needed prior to lesson.

Week 5: October 3

Standards Addressed in Week's Lessons

Topic C

G.CO.A.2

G.CO.A.3

G.CO.A.4

G.CO.A.5

G.CO.B.6

G.CO.B.7

G.CO.D.12

Notes:

Lesson 13 (E)

Students will need to use compass, scissors, and straightedge for constructions. However, if students are struggling, it may be necessary to modify the exercises to include the use of graph paper, patty paper, or geometry software (such as the freely available Geogebra).

Lesson 14 (E)

Students will need a compass and straightedge.

Lesson 15 (E)

Opportunity to talk to students about symmetry outside of math before starting lesson.

Lesson 16 (E)

This may be the first time many students have seen vectors, so some additional explanation may be needed (a vector is a directed line segment that has both length and direction). Refer to Grade 8 Module 2 Lesson 2 for supplementary materials on use of vectors, as well as on translations in general.

Week 6: October 11

Module

Topic

Notes:

Lesson 17 (Socratic Lesson)

Students will need construction tools. Students will need to complete Problem Set to set them up for success on lesson 18.

Lesson 18 (S)

To do the Opening Exercise, students will need to have completed the Problem Set from lesson 17.

Lesson 19 (S)

Consider being strategic in selecting elbow partners for example 2.

Standards Addressed in Week's Lessons

Topic C

G.CO.A.2

G.CO.A.3

G.CO.A.4

G.CO.A.5

G.CO.B.6

G.CO.B.7

G.CO.D.12

Week 7: October 17

Module

Topic

Notes:

Lesson 20 (S)

This lesson focuses on language and how to discuss and write about congruence.

Lesson 21 (P)

Teachers can use this lesson to provide practice for Mid Module assessment.

Two days build in this week for assessment, return assessment, and remediation

Assessment

Mid Module Assessment

Administer after lesson 21

Standards Addressed in Week's Lessons

Topic C

G.CO.A.2

G.CO.A.3

G.CO.A.4

G.CO.A.5

G.CO.B.6

G.CO.B.7

G.CO.D.12

Standards Addressed in Module Assessment

G-CO.A.1

G-CO.A.2

G-CO.A.4

G-CO.A.5

G-CO.B.6

G-CO.C.9

G-CO.D.12

Week 8: October 24

Module

Topic

Notes:

Lesson 22 (P)

Consult 8th Grade Module 2 Lesson 10 to see scaffolding needing for SAS, ASS, and SSS work in this lesson.

Lesson 23 (E)

The goal of this lesson is to compare two different proof techniques by investigating a familiar theorem.

Lesson 24 (P)

Ask students to refer to their notes on SAS to recall these steps before proceeding with the rest of the proof. Exercises require using all three triangle congruence criteria.

Standards Addressed in Week's Lessons

Topic D

G.CO.B.7

G.CO.B.8

Week 9: October 31

Notes:

Lesson 25 (E)

Introduce vocabulary: Hypotenuse-Leg Triangle Congruence Criteria (HL)

Lesson 26 (P)

Consider using a T-Chart for all proofs.

Lesson 27 (P)

Students complete proofs requiring a synthesis of the skills learned in the last four lessons.