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High School Math Solution Reviewer’s GuideWelcome to your review of Carnegie Learning’s brand new High School Math Solution, which is still being developed as we speak. As part of that work, we are in the process of building our new Integrated Math Solution. This new 2018 copyright builds on extensive teacher feedback and experience with our previous Integrated Math series. This will be a groundbreaking new set of materials, complementing and leveraging similar strategies used in our highly rated (forthcoming from Ed Reports) Middle School Math Solution. These include robust supports for teachers, highly individualized learning through adaptive software (MATHia), and a distinct focus on building a coherent, rigorous program that integrates the mathematical practices into EVERY lesson.

Other providers think of blended learning as a simple mix of print resources for instruction and software for practice. Carnegie Learning delivers a deeper level of blended learning, where students are given opportunities to learn together (using printed resources) and learn individually (using MATHia® Software or printed Skills Practice materials). This blend ensures students develop both the conceptual understanding and procedural fluency necessary to succeed in mathematics.

We invite you to follow this Step-by-Step Reviewer’s Guide to learn more about us and our program, as you embark upon a new math journey. Let’s begin your review.

STEP 1

Organize your materials.

Since final print versions are in production, we only provided a “table” copy of the Integrated I Student Text, copyright 2018. Please review and know that additional resources are available on the Murrieta microsite mentioned below. In addition, each reviewer has been given a hard copy of the following in their “teacher kit”:

¨ This Reviewer’s Guide!

¨ (1) High School Sampler

¨ (1) MATHia Brochure

Digital resources available on the custom microsite (www.carnegielearning.com/Murrieta):

• Introduction videos from the Solution’s author Sandy Bartle Finocchi, Senior Academic Officer at Carnegie Learning

• Draft files from the new Integrated Math I, copyright 2018

• Draft files from the new Integrated Math II, copyright 2018

• Tables of contents for Integrated Math I, Integrated Math II, and Integrated Math III, including MATHia

• Access to MATHia through the Teacher’s Toolkit which gives you full view of all MATHia (learning software that is designed to support learning with intelligent tutoring, conceptual understanding reinforcement, skill mastery and practice).

• Additional materials will be added as they are completed.

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STEP 2

Find out more about our Carnegie Learning Way, including our instructional approach, at the Murrieta microsite: www.carnegielearning.com/Murrieta.

• Video 1: Carnegie Learning Overview• Video 2: Transforming the Math Classroom• Video 3: Integrated Math Introduction• Video 4: Integrated Math I Overview• Video 5: Integrated Math II Overview• Video 6: Integrated Math III Overview• Video 7: Integrated Math Final Thoughts

STEP 3

Grab the High School Math Solution Sampler. Read the front matter and examine the sample teacher notes.

To get the full view of the teaching and learning experience, please read the High School Math Solution Sampler.

SAMPLER• Pages 2–4 tells you about Carnegie Learning and our overall approach to

supporting you in the classroom.

• Pages 5–7 shows a sample progression of the structure through a lesson including our engage, develop, and demonstrate approach.

• Pages 8–13 takes you through how we support blended learning, the research findings on the impact of our approach and curriculum, and the features of the Solution.

• Pages 14–15 has the Table of Contents for Integrated Math I. To see the table of contents for all three Integrated Math texts, go to www.carnegielearning.com/Murrieta.

• Page 17 lists and explains each of the components of the Carnegie Learning High School Math Solution.

• Pages 19–60 gives a sample of the Teacher Implementation Guide and the support for each Module, Topic, and Lesson that teachers receive including pacing guidance, questions to ask, mathematical practices, differentiation strategies, and ELL Tips. Every chapter in the Teacher Implementation Guide provides an overview of content and pacing suggestions. Each lesson in the guide supports teachers with tips for differentiation, guiding questions, grouping suggestions, common misconceptions, and ELL support.

• Pages 61–69 demonstrates additional program features, including Skills Practice, Performance Tasks, Assessments, and Family Guides.

• Pages 70–75 provides insight into MATHia, our intelligent tutoring and mastery-based software that differentiates and fully supports each student.

Visit the Murrieta microsite to view the High School Math Sampler as well as other great resources, including product timeline, ELL support document, new product comparison, and MATHia Software brochure.

TP-HSMS-2017 7m 10/17

ARE YOU READY FOR SOMETHING BETTER?Carnegie Learning is challenging the status quo in math learning. Rejecting traditional “sage on the stage” instruction, Carnegie Learning embraces a research-proven “guide on the side” instructional approach that improves math results and promotes deeper conceptual understanding, critical thinking and collaboration.

High School Math Solution Sampler

www.carnegielearning.com/samples

Sign up for our Virtual Sample Kit to review additional print materials and try the MATHia® Software Platform!

www.carnegielearning.com/samples

HSMS-Sampler-Cover-Saddle.indd 1 10/13/17 11:12 AM

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STEP 4

Review the Integrated Math I and Integrated Math II Student Text Lessons.

Students will receive instruction and work through interactive lessons within the textbook. Each lesson in the series delivers our Engage, Develop, and Demonstrate instructional model. It is through this model that students will be motivated, develop their conceptual understanding of mathematics, and demonstrate their learning.

• Engage: We activate student thinking by tapping into prior knowledge and real-world experiences. Our lessons provide an introduction that generates curiosity and plants seeds for deeper learning.

• Develop: We build a deep understanding of mathematics through a variety of activities, real-world problems, sorting activities, worked examples, and peer analysis, all in an environment where collaboration, conversations and questioning are routine practices.

• Demonstrate: We provide opportunities for students to refl ect on and evaluate what was learned. Ongoing formative assessment underlies the entire experience, driving real-time adjustments, next steps, insights, and measurements.

With the instructional approach in mind, review the lessons in Integrated Math I and II. For a clear overview of Integrated Math and what makes it special, be sure to watch the videos from Sandy Bartle Finocchi.

STEP 5

See how the textbook connects with the software. Login to the MATHia Teacher’s Toolkit and review the Integrated Math and RtI content available in MATHia. Work the problems. Have fun!

Carnegie Learning’s High School Math Solution uniquely integrates our textbook resources with MATHia, our intelligent math tutoring and learning platform. MATHia punctuates student learning by working with the textbook topics and providing students the opportunity to deepen conceptual understanding and build procedural fl uency. This component of the program mimics a human tutor and carefully assesses how individual students approach problem solving. MATHia adjusts and provides the necessary help each student needs in order to achieve — and move beyond — on-grade level skill mastery.

LESSON 1: Connecting the Dots • M2-3

Consider the four explicit formulas, each representing a different arithmetic sequence.

• an 5 2 2 4(n21)• an 5 24 1 2(n21)

• an 5 2 1 4(n21) • an 5 4 1 2(n21)

1. Match each explicit formula with its graph. Describe the strategies you used.

Connecting FormsAC TIVIT Y

1.1

Askyourself:

How do you know by the form of the explicit formula that it represents an arithmetic sequence?

4

210

y

x43 5

2

–2–4–6

86

101214

Graph A

4

02

–2–4–6–8–10–12–14–16

21

y

x43 5

Graph B

4

02

–2–4

86

1012

1614

21

y

x43 5

Graph C

4

02

–2–4

86

1012

1614

21

y

x43 5

Graph D

2. Consider the set of graphs and identify the function family represented. Based on these formulas and graphs, do you think that all arithmetic sequences belong to this function family? Explain your conjecture.

A conjecture is a mathematical statement that appears to be true, but has not been formally proven.

A1_SE_M02_T01_L01.indd 3 9/26/17 1:54 PM

Evaluating Linear Functions

© 2017 Carnegie LearningProblem: gof001 Client Version: 2.4.27 Server Version: 2.4.27

Go to ProblemUnit Overview Sample Problem

Carnegie Learning

System Help Glossary Maria Hernandez

https://www.carnegielearning.com/…

Step-by-Step Example

Given:

h(z) = –8.1z – 6

Answer each question using the worksheet.

1. If h(z) = –8.1(7) – 6, what is z?

2. Evaluate h(z) for z = 3.

3. Evaluate h(z) for z = 8.

Evaluating Linear Functions

© 2017 Carnegie LearningProblem: gof001 Client Version: 2.4.27 Server Version: 2.4.27

Go to ProblemUnit Overview Step-by-Step Sample Problem

System Help Glossary Maria Hernandez

Step-by-Step Example

Given:

h(z(z( ) = –8.1z) = –8.1z z – 6z – 6z

Answer each question using the worksheet.

1. If h(z(z( ) = –8.1(7) – 6, what is z) = –8.1(7) – 6, what is z z?

2. Evaluate h(z(z( ) for z) for z z = 3.z = 3.z

3. Evaluate h(z(z( ) for z) for z z = 8.z = 8.z

h(z)z

Question 1

Question 2

Question 3

–8.1(7) – 6 –62.7

3

8

Substituted h(z) Result

Workspace Introduction

Get started with Evaluating Linear Functions by studying the sample problem, then do the Step-by-Step example.

Begin Step-by-Step ExampleSkip and go to problem

Example:

To evaluate a function in one variable means to determine the value of the function by replacing the variable with a given value, and simplifying the result. For instance, suppose that you want to evaluate the function f(x) for the value x = 1. You could represent this as f(1). Substitute the value of 1 for x into the function and simplify.

a. If f(x) = 4x – 7, what is f(5)?

b. Evaluate h(x) = –0.5x + 3 for x = –2.

a. From the expression f(5), you know that x = 5. So, substitue 5 for x in the

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Through MATHia, you will have access to reports that predict the trajectory of student learning, performance on standardized assessments, the amount of time spent on the platform, as well as content mastery. MATHia’s leadership reports give administrators and instructional leaders interactive data so they can view student performance across the district, buildings, and even at the class level.

For students who have limited access to technology, please see the Student Skills Practice Book.

To experience MATHia, log into the Teacher’s Toolkit: www.carnegielearning.com/login.

As a teacher, login with the teacher credentials. You can explore each workspace and any of the problems in MATHia by loging into the teachers toolkit and selecting the Content Browser in the upper right hand corner. Click between courses to see all the individual workspaces and to launch them.

As a student, login with the student credentials. You will see three courses in MATHia, one for each of the Integrated courses. Click on each one to view the student experience.

Leadership Report

Carnegie Learning

https://www.carnegielearning.com/…

REPORTSHello, Jane Doe

©2017 Carnegie Learning Inc

EXPORTPRINTAVERAGE USAGE PER STUDENTMinutes spent in MATHia per student per week

1 2 Next3 4 i

Acre Middle SchoolByte Middle SchoolCarat Middle SchoolCelsius Middle SchoolFahrenheit Middle SchoolHertz Middle SchoolJoule Middle SchoolKelvin Middle SchoolOunce Middle SchoolPascal Middle SchoolTonne Middle SchoolTorr Middle School

Average (12 Schools)08/21/1

6

09/18/1

6

10/16/1

6

11/13/1

6

12/11/1

6

01/08/1

7

02/26/1

7

03/05/1

7

300

350

250

200

150Min

utes

Weeks

100

50

0

1 2 3

On Track

Average Usage 134

01/15/17

Kelvin Middle School

12 Schools selected 87 Classes selected 2 Class Categories selected 2 Class Profiles selected Period: 08/21/16 to 03/05/17

AVERAGE USAGE

90

On Track 90 minutesApproaching On Track: 60-89 minutes

minutesper week 23%

AVERAGE SYLLABUS COMPLETION

ACTIVE STUDENTS

44% 440 out of 1000

On Track 90%Approaching On Track: 70-89%

59%

APLSE PERFORMANCEOn Track 70-100%Approaching On Track 50%-69%

Carnegie Learning

https://www.carnegielearning.com/…

REPORTSHello, Jane Doe

©2017 Carnegie Learning Inc

APLSE Report Standards ReportSession Report Student Detail Report

Student Detail Report: All Students Export Print

Student Name % SyllabusComplete

Average PerformanceScore (out of 100)

Current ModuleTime on Task(in minutes)

ModulesCompleted

UnitsCompleted

Adams, Janet 76 100 One-Step Equations … 637 4 10Baker, Lindsey 44 88 Numeric and Algebraic … 90 3 6

Bartlett, Michael 53 77 Numeric and Algebraic … 707 3 8

Franklin, Sam 45 78 Numeric and Algebraic … 422 3 6

Harrison, Sara 49 61 Numeric and Algebraic … 566 3 6Jacobs, Beth 35 92 Ratios, Rates, and Percents … 551 2 5

Ming, Jo 32 90 Ratios, Rates, and Percents … 300 2 5Peterson, Phillip 0 0 Not Started 0 0

Ruiz, Marco 36 87 Ratios, Rates, and Percents … 101 2 5

7Trazzoli, Kim 49 100 Numeric and Algebraic … 96 3

0

Tresport, Jacob 4 100 One-Step Equations and … 8 1 1Williams,Shania 5 100 Fraction and Decimal … 27 0

Zeller, Trevor 1 99 Pre-Launch Protocol 1 0

0

0

WorkspacesCompleted

56

37

39

33

36

26

24

27

36

0

3

4

1

Student Usage Totals

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First you will see the whole table of contents for the course. This is full of modules, which break down into units and then workspaces. Workspaces are where you will do some work!

At the unit level, you will see some introductory material including learning goals, a short video and connections to prior learning.

Then at the workspace level you will begin to do some math. Notice how the Progress Bar within each workspace adjusts as you work and approach mastery! It will not move you on to a new topic until all of your skills are mastered. If you don’t know how to proceed, try a hint, which adjusts through research-driven adaptivity for each student to provide relevant help.

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STEP 6

Be ready for what is coming soon!

We know that this does not give you the full High School Math Solution. It is being written and produced as we speak. The Solution will be the freshest learning experience for both your teachers and students. We will keep you updated as each piece is released, including student lessons, Teacher’s Implementation Guides, assessments, performance tasks, and Skills Practice.

As you conduct your review, please contact David Ware with any questions.

Phone: 949.632.4503Email: dware@carnegielearning.com

We’re here to help!LINEAR FUNCTIONS: Pre-Test • 1

Pre-Test Name  Date

3. Rewrite the explicit formula of this sequence an 5 5 1 3(n 2 1) in function form f(x) 5 ax 1 b.

4. The sequence generated by an 5 22 1 4(n 2 1) can be represented by the linear function f(n) 5 4n 2 6. How is the fi rst term of the sequence related to the y-intercept of the function?

5. Does this table of values represent a linear function? If so, write the function. If not, explain why it does not represent a linear function.

x f(x)

5 24

6 27

7 211

8 214

6. This table represents a linear function. Complete the table for consecutive values of the input. Use the table to demonstrate that the diff erence is constant between consecutive output values of any linear function.

x f(x) 5 ax 1 b

k a(k) 1 b

k 1 1 a(k 1 1) 1 b

k 1 2

k 1 3

LINEAR FUNCTIONS

A1_AS_Pre_M02_T01.indd 1 01/09/17 2:11 PM

LINEAR FUNCTIONS: Post-Test • 1

Post-TestName  Date

3. Rewrite the explicit formula of this sequence an 5 2 1 6(n 2 1) in function form f(x) 5 ax 1 b.

4. The sequence generated by an 5 23 1 2(n 2 1) can be represented by the linear function f(n) 5 2n 2 5. How is the fi rst term of the sequence related to the y-intercept of the function?

5. Does this table of values represent a linear function? If so, write the function. If not, explain why it does not represent a linear function.

x f(x)

11 22

12 24

13 28

14 210

6. This table represents a linear function. Complete the table for consecutive values of the input. Use the table to demonstrate that the diff erence is constant between consecutive output values of any linear function.

x f(x) 5 ax 1 b

s a(s) 1 b

s 1 1 a(s 1 1) 1 b

s 1 2

s 1 3

LINEAR FUNCTIONS

A1_AS_Post_M02_T01.indd 1 01/09/17 2:11 PM