Overview

Module 4: Polynomial and Quadratic Expressions, Equations, and Functions

Students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions using polynomial functions―more specifically quadratic functions as well as square root and cube root functions.

Topic B: Using Different Forms for Quadratic Functions

Topic C: Function Transformations and Modeling

Module 5: A Synthesis of Modeling with Equations and Functions

Students synthesize what they have learned during the year by selecting the correct function type in a series of modeling problems without the benefit of a module or lesson title that includes function type to guide them in their choices. This supports the CCLS requirement that student’s use the modeling cycle, in the beginning of which they must formulate a strategy.

Topic B: Completing the Modeling Cycle

High School Math Schedule of Assessed Standards (SAS)

Week 1: April 16

Standards Addressed in Week's Lessons

Topic B

N.RN.B.3

A.SSE.A.1

A.SSE.A.2

A.SSE.B.3

A.APR.B.3

A.CED.A.1

A.CED.A.2

A.REI.B.4

F.IF.B.4

F.IF.B.6

F.IF.C.7

F.IF.C.8

Notes:

Lesson 13 (P)

Be sure to ask students for two answers to questions as they may be inclined to not recognize the +,-

Lesson 14 (P)

Encourage students to test some answers by using three methods to solve: factoring, quadratic formula, and completing the square.

An extra day this week is provided for pacing. Consider using this time to differentiate by organizing small group instruction using Problem Set questions.

Week 2: April 23

Standards Addressed in Week's Lessons

Topic B

N.RN.B.3

A.SSE.A.1

A.SSE.A.2

A.SSE.B.3

A.APR.B.3

A.CED.A.1

A.CED.A.2

A.REI.B.4

F.IF.B.4

F.IF.B.6

F.IF.C.7

F.IF.C.8

Notes:

Lesson 15 (P)

Students return to the concept of using the 𝑥-intercepts of the graph of a quadratic to write a formula for the corresponding quadratic function which was explored in Lesson 9 of Topic A.

Lesson 16 (E)

Students will need a graphing calculator and graph paper for this lesson.

Lesson 17 (P)

In opening exercise, consider starting by substituting values and creating a graph together as a class before students work independently. Students can then use that graph as a visual reference during the discussion.

An extra day this week is provided for pacing. Consider using this time to differentiate by organizing small group instruction using Problem Set questions.

Week 3: April 30

Standards Addressed in Week's Lessons

Topic C

A.CED.A.2

F.IF.B.6

F.IF.C.7

F.IF.C.8

F.IF.C.9

F.BF.B.3

Notes:

Lesson 18 (E)

Two days are provided for this lesson. Exploratory Challenge questions 1 & 2 should be included in day one. On day two do Exploratory Challenge #3.

Lesson 19 (P)

Concepts in this lesson relate directly to those in Module 3, Lessons 17 and 18. In this lesson, the functions will expand to include quadratic, square root, cube root, and absolute value.

Lesson 20 (E)

In this lesson, we will review some of Module 3’s work with quadratic functions but will focus on cubic, square root, and cube root functions.

Week 4: May 7

Standards Addressed in Week's Lessons

Topic C

A.CED.A.2

F.IF.B.6

F.IF.C.7

F.IF.C.8

F.IF.C.9

F.BF.B.3

Notes:

Lesson 21 (P)

For students who struggle with this process, it may be helpful to guide them through the steps. At first, give a simpler function, such as 𝑓(𝑥) = 𝑥2 + 6𝑥, and help them complete the square.

Lesson 22 (E)

Provide students with the discussion questions ahead of time so that they have time to brainstorm responses prior to the class discussion.

Lesson 23 (M)

Consider modeling gravities effect to start class by modeling objects falling to the ground.

An extra day this week is provided for pacing. Consider using this time to differentiate by organizing small group instruction using Problem Set questions.

Week 5: May 14

Notes:

Lesson 24 (P)

Provide time and space for students to share their graphing ideas either on board or strategically to various partners.

Two days are provided this week to give End of Module assessment, return assessment, and remediate Module 4 material as needed.

Lesson 1 (P)

As the modeling cycle is used throughout the Module 5, consider making an anchor chart of the models steps for students to reference. As lesson reinforces learning from the entire year, consider grouping strategically to allow circulation to be more purposeful during group work time.

Standards Addressed in Week's Lessons

Topic C

A.CED.A.2

F.IF.B.6

F.IF.C.7

F.IF.C.8

F.IF.C.9

F.BF.B.3

Topic A

N.QA.A.2

A.CED.A.2

F.IF.B.4

F.IF.B.5

F.BF.A.1

F.LE.A.1

F.LE.A.2

Standards Addressed in Assessment

End of Module

N-RN.B.3

A-SSE.A.1

A-SSE.A.2

A-SSE.B.3a

A-SSE.B.3b

A-APR.B.3

A-CED.A.1

A-CED.A.2

A-REI.B.4

F-IF.B.4

F-IF.B.6

F-IF.C.7a

F-IF.C.7b

F-IF.C.8a

F-IF.C.9

F-BF.B.3

Week 6: May 21

Module

Notes:

Lesson 2 (P)

Writing in a math journal or notebook is suggested for this lesson and all of Module 5. Encourage students to keep and use their journal as a reference throughout the module.

Lesson 3 (P)

Consider having students reference their math journals during discussion and questions throughout lesson.

Lesson 4 (E)

Consider cutting out graphs at end of section to save time and distribute individually or in strategic groups.

Standards Addressed in Week's Lessons

Topic A

N.QA.A.2

A.CED.A.2

F.IF.B.4

F.IF.B.5

F.BF.A.1

F.LE.A.1

F.LE.A.2

Topic B

N.QA.2

N.QA.3

A.CED.1

A.CED.2

F.IF.B.4

F.IF.B.5

F.IF.B.6

F.BF.A.1

F.LE.A.1

F.LE.A.2

Week 7: May 28

Module

Topic

Notes:

Lesson 5 (P)

Remind students that in Module 3 Lessons 1, 2, and 3, they learned about the linear relationship in arithmetic sequences and the exponential relationship in geometric sequences. The classwork review is designed to help students reinforce that prior learning.

Lesson 6 (P)

Consider using scaffolding box in teacher's edition to create a check box graphic organizer for identifying needs of each problem.

Standards Addressed in Week's Lessons

Topic B

N.QA.2

N.QA.3

A.CED.1

A.CED.2

F.IF.B.4

F.IF.B.5

F.IF.B.6

F.BF.A.1

F.LE.A.1

F.LE.A.2

Week 8: June 4

Module

Topic

Lesson 7 (P)

Two days are provided for this lesson. A portion for the first day should be used for technology/calculator review. Consider using data from engage tables in lesson and adjusting column topics to more easily relate your students to data they might see on a regular basis.

Lesson 8 (P)

Consider using Problem Set questions during small group station time this week to differentiate learning form lesson.

Lesson 9 (P)

As this is the culminating lesson of year, consider having students display their work in a gallery walk to demonstrate learning.

Standards Addressed in Week's Lessons

Topic B

N.QA.2

N.QA.3

A.CED.1

A.CED.2

F.IF.B.4

F.IF.B.5

F.IF.B.6

F.BF.A.1

F.LE.A.1

F.LE.A.2

Week 9: June 11

Assessment

End of Module Assessment

Administer after lesson 9

Standards Addressed in Module Assessment

End of Module

N-Q.A.2

N-Q.A.3

A-CED.A.1

A-CED.A.2,

F-IF.B.4

F-IF.B.5,

F-IF.B.6

F-BF.A.1,

F-LE.A.1

F-LE.A.2

Notes:

Four days are provided this week for Module 5 assessment, returning of assessment, and remediation of Module 5 material as needed.