Overview

Module 3: Linear and Exponential Functions

Students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.

Topic B: Functions and Their Graphs

Topic C: Transformations of Functions

Topic D: Using Functions and Graphs to Solve Problems

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 A: Quadratic Expressions, Equations, Functions, and Their Connection to Rectangles

Topic B: Using Different Forms for Quadratic Functions

Week 1: February 5

Module

Topic

Standards Addressed in Module Assessment

Mid Module

F-IF.A.1

F-IF.A.2

F-IF.A.3

F-IF.B.4

F-IF.B.5

F-IF.B.6

Assessment

Mid Module

Administer after lesson 14

Standards Addressed in Week's Lessons

Topic B

F.IF.A.1

F.IF.A.2

F.IF.B.4

F.IF.B.5

F.IF.C.7

F-IF.C.7a

F-BF.A.1a

F-LE.A.1

F-LE.A.2

F-LE.A.3

Notes:

Lesson 13 (M)

Consider showing video of Mars landing to hook in students.

Lesson 14 (P)

Encourage students to use graphing calculators to determine the linear and exponential regression functions. The steps for finding the exponential regression are listed below.

Two days are provided this week for Mid Module assessment, returning assessment, and remediation of Module 3 material as needed.

Week 2: February 12

Notes:

Lesson 15 (E)

Consider adding relevant vocabulary to a word wall, anchor chart, or student definition notebook to keep track of new words.

Lesson 16 (P)

This lesson ties work from Module 1 on solving systems of two-variable equations to work with functions and leads students to the understanding of what the solution set to a one-variable equation can be.

Lesson 17 (E)

Two days are provided for this lesson. Some students with engageAUSL experience have been exposed to transformations in Grade 8, Module 2& 3. Spend day one recalling what a transformation is and how it is an adjustment to a function as well as Exploratory Challenge 1. Day two begin with Exploratory Challenge 2.

Week 3: February 19

Notes:

Lesson 18 (P)

Use careful transformation language during lesson as student will build upon transformation information during much of geometry the following year.

Lesson 19 (E)

Spend time prior to lesson reviewing transformations with horizontal scaling. Consider modeling with graphing software on board to save time spent drawing.

Lesson 20 (E)

In Lessons 17–19, students study translations and scalings of functions and their graphs. In this lesson, these transformations are applied in combination with piecewise functions.

Week 4: February 26

Standards Addressed in Week's Lessons

Topic D

A.CED.A.1

A.SSE.B.3

F.IF.B.4

F.IF.B.6

F.IF.C.9

F.BF.A.1

F.LE.A.2

F.LE.B.5

Notes:

Lesson 21 (P)

Consider giving students function for opening exercise for pacing purposes.

Lesson 22 (M)

Prepare technology ahead of time to show video from opening section. Create groups ahead of time with varying ability levels so that they can assist students who may struggle with the reading comprehension aspect of this exercise.

Lesson 23 (M)

Prepare technology ahead of time to display Newton's law of cooling

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: March 5

Notes:

Lesson 24 (M)

Two days have been provided for this lesson. Break the class into four large groups (which may be split into smaller groups that work on the same task) on day one. On day two have students reveal results from their group and work through question 2-4 of Problem Set if time allows.

Two days are provided this week for End of Module assessment, returning of assessment, and remediation of Module 3 material as needed.

Lesson 1 (P)

Lengths of time suggested for the examples and exercises in this lesson assume that students remember some of what is presented in the examples from work in earlier modules and earlier grades. Students may need more or less time with this lesson than is suggested. The teacher should make decisions about how much time is needed for these concepts based on students’ needs.

Standards Addressed in Week's Lessons

Topic D

A.CED.A.1

A.SSE.B.3

F.IF.B.4

F.IF.B.6

F.IF.C.9

F.BF.A.1

F.LE.A.2

F.LE.B.5

Topic A

A.SSE.A.1

A.SSE.A.2

A.SSE.B.3

A.APR.A.1

A.CED.A.1

A.CED.A.2

A.REI.B.4

A.REI.D.11

F.IF.B.4

F.IF.B.5

F.IF.B.6

F.IF.C.7

Standards Addressed in Module Assessment

End of Module

A-CED.A.1

A-REI.D.11

A-SSE.B.3c

F-IF.A.1,

F-IF.A.2

F-IF.A.3

F-IF.B.4

F-IF.B.6,

F-IF.C.7a

F-IF.C.9,

F-BF.A.1a

F-BF.B.3

F-LE.A.1

F-LE.A.2

F-LE.A.3

F-LE.B.5

Week 6: March 12

Module

Topic

Notes:

Lesson 2 (P)

Consider using small group station work time this week to helping students reinforce multiplication of binomials and factoring quadratic polynomials from Problem Set questions (this a recommended fluency of Algebra 1).

Lesson 3 (P)

In opening exercise, using graphic diagrams benefits visual learners, and the task lends itself to using algebra manipulatives. The Problem Set can be used for fluency practice in small groups later this week (this is a recommended fluency of Algebra 1).

Lesson 4 (P)

While the lesson emphasizes splitting the linear term, continue to allow students to work with more than one factoring method.

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

Standards Addressed in Week's Lessons

Topic A

A.SSE.A.1

A.SSE.A.2

A.SSE.B.3

A.APR.A.1

A.CED.A.1

A.CED.A.2

A.REI.B.4

A.REI.D.11

F.IF.B.4

F.IF.B.5

F.IF.B.6

F.IF.C.7

Week 7: March 19

Module

Topic

Notes:

Lesson 5 (E)

Problem set problems can be used for small group stations at end of week.

Lesson 6 (P)

Example 1 works best when two different methods are projected for students side by side.

Lesson 7 (P)

Reminding students of their success writing linear or exponential equations from problem situation in module 1 & 3 will be helpful leading into this lesson where they do the same with quadratic .

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

Standards Addressed in Week's Lessons

Topic A

A.SSE.A.1

A.SSE.A.2

A.SSE.B.3

A.APR.A.1

A.CED.A.1

A.CED.A.2

A.REI.B.4

A.REI.D.11

F.IF.B.4

F.IF.B.5

F.IF.B.6

F.IF.C.7

Week 8: April 2

Module

Topic

Notes:

Lesson 8 (E)

Consider adding vocabulary to student journal, word wall, and/or anchor chart. Prepare to project photographs of real world quadratics so all students can easily see.

Lesson 9 (P)

If students do not have time in class to complete Exercise 4, consider adding it to the Problem Set.

Lesson 10 (P)

Prepare technology to show video during Opening Exercise.

One day is provided this week to give Mid Module assessment.

Assessment

Mid Module Assessment

Administer after lesson 10

Standards Addressed in Week's Lessons

Topic A

A.SSE.A.1

A.SSE.A.2

A.SSE.B.3

A.APR.A.1

A.CED.A.1

A.CED.A.2

A.REI.B.4

A.REI.D.11

F.IF.B.4

F.IF.B.5

F.IF.B.6

F.IF.C.7

Standards Addressed in Module Assessment

End of Module

A-CED.A.1

A-REI.D.11

A-SSE.B.3c

F-IF.A.1,

F-IF.A.2

F-IF.A.3

F-IF.B.4

F-IF.B.6,

F-IF.C.7a

F-IF.C.9,

F-BF.A.1a

F-BF.B.3

F-LE.A.1

F-LE.A.2

F-LE.A.3

F-LE.B.5

Week 9: April 9

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:

One day is provided this week to return assessment and remediate Module 4 material as needed.

Lesson 11 (E)

Note that all quadratic expressions in this lesson have a leading coefficient of 𝑎 = 1; other leading coefficients are addressed in Lesson 12. It may be helpful to hint to students that in later lessons we use this method of rewriting expressions to solve quadratic equations that are not factorable.

Lesson 12 (P)

Problem set problems can be used for small group stations later this week