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 E: Proving Properties of Geometric Figures

Module 2: Similarity, Proof, and Trigonometry

Just as rigid motions are used to define congruence in Module 1, so dilations are added to define similarity in Module 2.

Topic C: Similarity and Dilations

Topic D: Applying Similarity to Right Triangles

High School Math Schedule of Assessed Standards (SAS)

Please contact Katie Lyons with any questions.

Week 1: November 7

Week 2: November 14

Assessment

End of Module Assessment

Administer after lesson 34

Standards Addressed in Week's Lessons

Topic E

G.CO.C.9

G.CO.C.10

G.CO.C.11

Topic G

G.CO.A.1

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.B.8

G.CO.C.9

G.CO.C.10

G.CO.C.11

G.CO.D.12

G.CO.D.13

Notes:

Lesson 30 (P)

Lesson extends the learning of midsegments from lesson 29.

Unit F Lesson 31 & 32 Omit

For pacing considerations these lessons have been omitted. They work both supporting content of the major works of the grade.

Lesson 33 (E)

Students should work in strategic small groups to complete question #8 of the Classwork section.

Lesson 34 (E)

Students should work in strategic small groups to complete Classwork section.

One day built in this week for assessment.

Standards Addressed in Module Assessment

End of Module

G-CO.A.2,

G-CO.A.3,

G-CO.B.7,

G-CO.B.8,

G-CO.C.10,

G-CO.C.11,

G-CO.D.13

Week 3: November 21

Notes:

One day built in this week for returning assessment and remediation of module 1.

Week 4: November 28

Notes:

Lesson 1 (P)

Note that students first studied scale drawings in Grade 7 (Module 1 Lessons 16–22). Teachers may need to modify the exercises to include the use of graph paper, patty paper, and geometry software (e.g., freely available GeoGebra) to make the ideas accessible. Construction tools will be needed for this lesson.

Lesson 2 (P)

Note that students need rulers, protractors, and calculators for this lesson. Note that students last studied dilations in Grade 8 Module 3. . If time is short, consider moving from Example 1 to Example 2.

Lesson 3 (P)

Students will need compass, straightedge, and set squarers; setsquares reduce the time needed for the construction (setsquares can be made in class; refer to Grade 7 Module 6 Lesson 7). Modeling images should be made larger for teachers to demonstrate for all students more easily.

Lesson 4 (S)

While revealing the proofs for the parallel and ratio method provide opportunities for students to discuss with students and for teachers to check for understanding.

Week 5: December 5

Standards Addressed in Week's Lessons

Topic A

G.SRT.A.1

G.SRT.B.4

G.MG.A.3

Topic B

G.SRT.A.1

G.SRT.B.4

Notes:

Lesson 5 (S)

Some students may recall Fundamental Theorem of Similarity (FTS) from Grade 8. Have students work strategically in elbow partners to solve Dilation Proof.

Lesson 6 (S)

Module 1 Lesson 17. Exercises 1–5 can be used to provide students with good visuals to review the learned transformations and the conclusion that they are distance-preserving.

Lesson 7 (P)

Extend the lesson to two days so that all examples and exercises can be given the time required to develop student understanding of the dilation of segments.

Week 6: December 12

Notes:

Lesson 8 (S)

Doing Problem Set from lesson 7 will help support the work of lesson 8.

Lesson 9 (E)

Two days is provided to extend lesson. On the first day students complete all parts of the Exploratory Challenge, and on the second day students work to prove their conjectures about how dilations map angles. The last Discussion of the lesson (dilating a square inscribed in a triangle) is optional and can be completed if class time permits.

Lesson 10 (E)

Materials needed for lesson: Chart paper, yard stick, compass, straightedge, and set square

Week 7: December 19

Standards Addressed in Week's Lessons

Topic B

G.SRT.A.1

G.SRT.B.4

Topic C

G.SRT.A.2

G.SRT.A.3

G. SRT.B.5

G.MG.A.1

Notes:

Lesson 11 (E)

Students can take responsibility for their own learning by hand-drawing the houses; however, if time is an issue, teachers can provide the drawings of the houses located at the beginning of Exploratory Challenge 1. Use patty paper or geometry software to help students focus on the concepts.

Lesson 12 (P)

Before moving to curvilinear examples, teachers may chose to scaffold by using more linear figures. i.e. start with a letter like F or T and move to letters like J or C.

Lesson 13 (P)

This is the only lesson where students actually construct what happens to a figure that undergoes a similarity transformation. Teachers may chose to photocopy and enlarge specific examples to make student construction easier. Exit ticket may take more than 5 minutes to complete.

Week 8: January 9

Module

Topic

Notes:

Lesson 14 (P)

Lessons 12–13 were intentionally not focused on triangles to emphasize that instructors need to move away from equating similarity with triangles or strictly rectilinear figures and rather to think of and teach similarity as a broader concept.

Lesson 15 (S)

Consider using small group time this week to provide students opportunities for reinforcing how to write a proof.

Lesson 16 (P)

This lesson's work foreshadows ratios related to trigonometry and sets kids up for Topic E from this module.

Lesson 17 (E)

In this lesson, students learn the other conditions that can be used to deem two triangles similar, specifically the SAS and SSS criteria.

Standards Addressed in Week's Lessons

Topic C

G.SRT.A.2

G.SRT.A.3

G. SRT.B.5

G.MG.A.1

Week 9: January 16

Module

Topic

Notes:

Lesson 18 (P)

Students may find it useful to use Problem Set problems during small group time this week to practice angle bisector theorem.

Lesson 19 (S)

Two days are given for this lesson. Cover 1st half of lesson on day one, up to the second discussion section on Eratosthenes theory. Give question one from exit ticket on day one. On day two, do Eratosthenes theory onward and give exit ticket question two.

Lesson 20 Omit

Include as much story narrative as you see fit. Discuss how people might find the distance to any planet, moon, or sun.

One extra day this week built in for assessment.

Assessment

Mid Module Assessment

Administer after lesson 20

Standards Addressed in Week's Lessons

Topic C

G.SRT.A.2

G.SRT.A.3

G.SRT.B.5

G.MG.A.1

Standards Addressed in Module Assessment

Mid-Module

G-SRT.A.1

G-SRT.A.2

G-SRT.A.3

G-SRT.B.4

G-SRT.B.5

G-MG.A.1

G-MG.A.3

Week 10: January 23

Module

Topic

Notes:

One extra day this week built in for returning assessment and remediation work of the first half of module 2.

Lesson 21 (P)

This lesson serves as a foundational piece for understanding trigonometric ratios related to right triangles. Extra time during small groups this week should be used to provide students with additional opportunities from Problem Set. Teachers may want to have 3x5 cards available for students to work with during example 1.

Lesson 22 (P)

Two days are provided for this lesson to split up into multiplying radicals on day one and dividing radicals on day two. The concept is building on knowledge from 8th grade and Algebra 1 math and students should be asked to recall what knowledge they have to start class.

Standards Addressed in Week's Lessons

Topic D

G.SRT.B.4

Week 11: January 30

Standards Addressed in Week's Lessons

Topic D

G.SRT.B.4

Topic E

G.SRT.C.6

G.SRT.C.7

G.SRT.C.8

Notes:

Lesson 23 (P)

Students should practice adding and subtracting radicals during small group time this week.

Lesson 24 (E)

Whiteboards are recommended of Opening Exercise. The Exploratory Challenge requires jigsaw learning and the class will need to be divided into two strategically.

Lesson 25 (E)

Consider asking students to create a poster of Discussion Problem diagram to display on the classroom wall.