Overview

Module 4: Connecting Algebra and Geometry Through Coordinates

In this module, students explore and experience the utility of analyzing algebra and geometry challenges through the framework of coordinates.

Topic B: Perpendicular and Parallel Lines in the Cartesian Plane

Topic C: Perimeters and Areas of Polygonal Regions in the Cartesian Plane

Topic D: Partitioning and Extending Segments and Parameterization of Lines

Module 5: Circles With and Without Coordinates

This module focus on circles and brings together the ideas of similarity and congruence studied in Modules 1 and 2, the properties of length and area studied in Modules 3 and 4, and the work of geometric construction studied throughout the entire year. It also includes the specific properties of triangles, special quadrilaterals, parallel lines and transversals, and rigid motions established and built upon throughout this mathematical story.

Topic A: Central and Inscribed Angles

Topic D: Equations for Circles and Their Tangents

High School Math Schedule of Assessed Standards (SAS)

Week 1: April 16

Assessment

Mid Module

Administer after lesson 8

Standards Addressed in Week's Lessons

Topic B

G.GPE.B.4

G.GPE.B.5

Standards Addressed in Module Assessment

Mid Module

G-GPE.B.4

G-GPE.B.5

G-GPE.B.7

Notes:

Lesson 7 (S)

Consider providing visuals to reinforce slope verses standard form.

Lesson 8 (P)

Lesson 5 & 6 are referenced continuously through this lesson. Consider demonstrating Opening Classwork with geometry software in front of class.

One extra day this week given for Mid Module assessment.

Week 2: April 23

Notes:

One extra day this week given for returning assessment and remediating Module 4 material.

Lesson 9 (P)

Consider referencing Grade 6, Module 5, Lesson 5-8 to see students understanding of decomposing.

Lesson 10 (S)

To save time, consider giving students questions with shapes already pre-graphed.

Lesson 11 (P)

Consider giving extra practice at graphing inequalities to start lesson. Teacher can circulate and support students that need reinforcement of concepts.

Week 3: April 30

Assessment

End of Module

Administer after lesson 15

Standards Addressed in Week's Lessons

Topic D

G.GPE.B.4

G.GPE.B.6

Notes:

Lesson 12 (P)

Students will need graph paper for opening exercise. Consider allowing students to use graph paper to answer exit ticket questions.

Lesson 13 (P)

Consider pacing this lesson over two days to give students addition practice of proofs.

Lesson 14 Omit

Lesson 14 is omitted for pacing considerations. It explores parametric equations while will be revisited in higher math courses like calculus.

Lesson 15 (S)

Teachers should provide students patty paper or geometry software for Opening Exercise.

An extra day is given this week for End of Module assessment.

Standards Addressed in Module Assessment

End of Module

G-GPE.B.4

G-GPE.B.5

G-GPE.B.6

G-GPE.B.7

Week 4: May 7

Notes:

An extra day is given this week for returning assessment and remediation of Module 4 material.

Lesson 1 (E)

For Opening Classwork, provide each student a sheet of plain white paper, a sheet of colored card stock, and a colored pen. Consider creating an anchor chart with relevant circle vocabulary.

Lesson 2 (P)

As you continue to add to the relevant circle vocabulary anchor chart/word wall, you may want to add visuals for reference.

Lesson 3 (E)

Compass and straightedge needed for lesson.

Week 5: May 14

Standards Addressed in Week's Lessons

Topic A

G.C.A.2

G.C.A.3

Topic B

G.C.A.1

G.C.A.2

G.C.B.5

Notes:

Lesson 4 (E)

Have available for each student (or group) a straightedge, white paper, and trapezoidal paper cutouts, created by slicing standard colored 8.5 × 11 inch sheets of paper or card stock from edge to edge using a paper cutter. There should be a variety of trapezoids with different acute angles available.

Lesson 5 (E)

For Opening Exercise, include a diagram in which point 𝐵 and angle ABC are already drawn.

Lesson 6 (E)

Continue to build student made anchor charts/word wall with relevant vocabulary and visuals. Consider using Problem Set during small group stations this week.

Lesson 7 (S)

Consider having students make a t-chart to show characteristics of a minor verses a major arc.

Week 6: May 21

Module

Topic

Notes:

Lesson 8 (E)

For Exploratory Challenge, put students in heterogeneous groups of three, and present the task. Set up a 5-minute check to be sure that groups are on the right path and to give ideas to groups who are struggling. Have groups show their work on large paper or poster board and display work, then have a whole class discussion showing the various ways to achieve the proof.

Lesson 9 (P)

Two days are given for this lesson. Spend extra time reviewing relevant vocabulary for circles and systematically doing small group work to give student repeated practice with arc length and area.

Lesson 10 (P)

The lesson is intended to be 45 minutes of problem solving with a partner. Differentiate by first modeling a problem or two, giving Problem Set in class for those that move through problems quickly, and allow those that need more support to finish lesson problems at home if needed. Do regular checks for understanding as students work.

Standards Addressed in Week's Lessons

Topic B

G.C.A.1

G.C.A.2

G.C.B.5

Week 7: May 28

Module

Topic

Notes:

Lesson 11 (E)

Several constructions will be needed for lesson. Post steps for each construction on the board for easy reference. Where needed, provide some or all students with partially completed constructions for pacing considerations.

Lesson 12 (P)

Exercise problems can be done in groups that are assigned specific problems. Groups can come back together to share out as a class.

Lesson 13 (E)

Add theorems to class list.

Standards Addressed in Week's Lessons

Topic C

G.C.A.2

G.C.A.3

Week 8: June 4

Module

Notes:

Lesson 14 (S)

The study of secant lines actually began in Lessons 4–6 with inscribed angles, but we did not call the lines secant then.

Lesson 15 (E)

Students need a protractor for opening exercise.

Lesson 16 (E)

Consider omitting Exploratory Challenge 1 or 2 for pacing considerations.

Lesson 17 (P)

Consider allowing students to write the equation of a drawn circle during small group stations this week.

Standards Addressed in Week's Lessons

Topic C

G.C.A.2

G.C.A.3

Topic D

G.GPE.A.1

G.GPE.A.4

Week 9: June 11

Assessment

Mid/End of Module Assessment

All of Mid Mod and Question 2 & 3 in End of Mod

Administer after lesson 17

Standards Addressed in Module Assessment

Mid/End of Module Assessment

G-C.A.1

G-C.A.2,

G-C.A.3

G-C.B.5

Notes:

Four days are provided this week to do Mid/End of Module, return assessment, and remediation of Module 5 material.