Let’s Bring LONG + LIVE + MATH to SUSD · MSMS and HSMS Reviewer’s Guide 1 Let’s Bring LONG + LIVE + MATH to SUSD! Your Reviewer’s Guide for Carnegie Learning’s Middle School

MSMS and HSMS Reviewer’s Guide 1

Let’s Bring LONG + LIVE + MATH to SUSD!Your Reviewer’s Guide for Carnegie Learning’s Middle School and High School Math Solutions

It’s time to scale your magic. The experience your students have with math now will make everything else possible — learning how to think, solve problems, persevere, and passionately pursue careers that challenge and reward them.

Carnegie Learning combines the market’s best math resources with a powerful “all in” passion for service. Our goal? To deliver a deeper level of blended learning. One where students are given opportunities to learn together (using printed resources or interactive eBook) and learn individually (using MATHia® Software).

So let’s get started. This Guide will walk you through the materials you received and the MSPS Review Site will let you see digital resources and MATHia (see box to the right for login info).

STEP 1

Check out your box.

Each box will contain:

¨ Teacher Implementation Guide (except Algebra II - coming soon!)

¨ Student Edition

Access to digital versions of teacher and student coursematerials, plus MATHia Software, through our SampleCenter

Explore the SUSD Review Site: www.carnegielearning.com/scottsdale

To access our Sample Center, MATHia, and eBook, use:

Usernames: [email protected]@[email protected]@cl.com

Password: longlivemath

STEP 1

Check out your box.

Each box will contain:

¨

¨

Did You Know? Carnegie Learning’s Middle School Math Solution was just ranked the #1 Blended Middle School Solution by EdReports?

Learn more at www.carnegielearning.com/scottsdale

¨


STEP 2

Grab the Teacher Implementation Guide. Read the frontmatter and the teacher facilitation notes.

FRONTMATTERWe invite you to familiarize yourself with our program design by reading the frontmatter of our Middle School and High School Math Solution books. This section will:

• Take you through Carnegie Learning’s philosophy and introduce you to the program.

• Take you through the progression of content through the grade-specific course. You’ll also be able to see the standards progression by grade level. To see the Arizona correlations, go towww.carnegielearning.com/scottsdale.

• Discuss how Carnegie Learning supports students as they encounter topics and the various lesson characteristics that foster student creativity and critical thinking.

FACILITATION NOTESEvery topic in the Teacher Implementation Guide contains facilitation notes. These serve to guide teachers and support them with pacing, differentiation techniques, essential questions, what to look for in student work, ELL supports, common misconceptions, and other tips.

M2-57D • TOPIC 1: Ratios

Questions to ask• What is the ratio 60 : 10 reduced? • Is your weight less on the Moon or on Earth? • One pound on the Moon is equivalent to how many pounds on Earth? • Two pounds on the Moon is equivalent to how many pounds on Earth?

Misconceptions• For Question 1, students may write the the ratios in fractional form,

resulting in the statement 60 ___ 10 1 30 ___ 5 5 90 ___ 15 . Then, they look at those “fractions” and decide to divide them, resulting in the incorrect statement 6 1 6 5 6. Remind students that part-to-part ratios are notfractions, so they cannot be divided to yield a quotient. You may wantto discourage students from displaying their part-to-part ratio work in fractional form (unless they are using proportions).

• To help clarify Ralph’s misconception, you may want to refer to Vicki and Benjamin’s age problem in Activity 1.1.

Have students work with a partner or in groups to complete Questions 3 through 5. Share the responses as a class.

Questions to ask• How is an equivalent ratio determined using division?• How is an equivalent ratio determined using multiplication?• How is an equivalent ratio determined using addition?• What is an example of an equivalent ratio that is not in the table? How

did you determine the ratio?• What is an incorrect way to use addition to determine an

equivalent ratio?

Summary A ratio table is a useful tool to represent equivalent ratios. The ratio between the cells of a column is the same for all columns. To determine equivalent ratios, you can add, subtract, multiply, or divide any column.

Activity 4.2Using Equivalent Ratio Tables

Facilitation NotesIn this activity, students use a given ratio to complete an equivalent ratio table. Then the table of values is used to answer questions in the same scenario.

Ask a student to read the introduction aloud. Have students work with a partner or in groups to complete Questions 1 through 3. Share responses as a class.

C01_TIG_M02_T01_L04_57A-57f.indd 57D 31/03/17 12:39 PM

LESSON 4: A Trip to the Moon • M2-57C

Getting Started: I’m Your Density

Facilitation NotesIn this activity, students consider the pictorial representations of population density and decide which state has the greatest and least population density.

In preparation for this activity, research the population density of your state and/or city. Students will need this data for Question 2.

• US: 76 people per square mile. How does that compare?• Possible site to research density of your state: https://en.wikipedia.org/

wiki/List_of_U.S._states_by_population_density• Research distances between local landmarks or roads to help students

visualize a square mile.

Ask students to work with a partner or in groups to complete Questions 1 and 2. Post the information needed to answer Question 2 in the classroom. Share responses as a class.

SummaryPictorial representations are used to describe ratios in real-world scenarios.

Activity 4.1Introduction to Ratio Tables

Facilitation NotesIn this activity, students use the ratio of weight on Earth to weight on the Moon to solve problems. They analyze strategies used to determine equivalent ratios of weight on Earth : weight on the Moon.

Ask a student to read the introduction scenario aloud. Discuss the information as a class. Have the students review the worked example individually.

Questions to ask• Why are the values in the table considered ratios rather than rates?• Does the ratio represent a part-to-part or part-to-whole relationship?• Why does adding two ratios create a third equivalent ratio?

Have students complete Questions 1 and 2 with a partner. Then share the responses as a class.

Engage

Develop

C01_TIG_M02_T01_L04_57A-57f.indd 57C 31/03/17 12:39 PMFacilitation Notes from Course 1 of the Middle School Math Solution

Facilitation Notes from Algebra I

M2-1J • TOPIC 1: Linear Functions

© C

arne

gie

Lear

ning

, Inc

.

• Does it matter what order you subtract the values to determine the slope from a table of values? Explain.

• What units are used for the first differences?• What units are used for slope?• How did you create a table to represent a linear function? Is there

another way to do this?

Summary The expression an 5 a1 1 d(n 2 1) can be rewritten as an 5 a0 1 dn, where a0 represents the y-intercept. First differences is a strategy to determine whether a table of values represents a linear function.

Activity 1.3Connecting Constant Difference, Slope, and Average Rate of Change

Facilitation NotesIn this activity, students generalize the concepts of constant difference and slope by using variable expressions for the consecutive terms. They use a table, a graph, and algebraic reasoning to demonstrate that the slope of a linear function is always equal to the constant difference of the corresponding arithmetic sequence. The average rate of change formula using function notation is introduced as another form of the slope formula.

Have a students read the introduction. Discuss as a class.As students work, look for

• Confusion related to variable expressions being used as term numbers and why they are being used instead of constants.

• Sense-making that an expression with more than one term can be substituted for x in f(x)

• Incorrect use of the Distributive Property and subtraction leading to errors in determining the constant difference.

Questions to ask• What is different about the table of values in this activity? • What does the n-value represent?• How do you know term values, or input values, are consecutive?• Explain the meaning of the labels on the x-axis and y-axis.

Have students work with a partner or in a group to complete Questions 1 through 3. Share responses as a class.

A1_TIG_M02_T01_L01_01A-01N.indd 1J 12/22/17 6:35 PM

LESSON 1: Connecting the Dots • M2-1I

© C

arne

gie

Lear

ning

, Inc

.

First Differences Strategy1. Check that input values have an interval of 1.2. Subtract consecutive output values.

3. If the differences are constant, the relationship is linear.

• Have them use arrows for direction and write the subtraction for common differences.

n an

1 34

2 42

3 50

4 58

42 2 34 5 8

50 2 42 5 8

58 2 50 5 8

• To assist all students, clarify the use of the terms first differences, constant differences, and common differences. First differences is a strategy to determine whether a table of values represents a linear relationship. Because constant differences and common differences have the same meaning, and common differences is primarily used for sequences, moving forward the term constant differences will be used.

MisconceptionStudents are sometimes confused as to whether the order of subtraction of table values matters. Clarify that if the x-values are in ascending order, subtracting y2 2 y1 consistently gives you first differences for comparison purposes and tells you the correct slope. Remember, slope describes both the steepness and direction of a line. If the x-values are in ascending order, subtracting y1 2 y2 consistently gives you first differences for comparison purposes, but it will not give you the correct slope. In terms of slope, the steepness value will be correct, but the direction (increasing or decreasing) will be wrong.Questions to ask

• Why does one table have an input of 0 and the other table does not?• Why is the second column titled y 5 f(x)?• Does it matter what order you subtract the values to determine if a

table represents a linear relationship? Explain.

A1_TIG_M02_T01_L01_01A-01N.indd 1I 12/22/17 6:35 PM


LESSON 4: A Trip to the Moon • M2-59

Introduction to Ratio Tables

Gravity is a natural force that attracts objects to each other. Gravity is the pull toward the center of an object like the Earth, a planet, or the Moon. Your weight on the Earth is the measure of the amount of gravitational attraction exerted on you by the Earth. The Moon has a weaker gravitational force than the Earth.

The ratio of weight on Earth : weight on the Moon is approximately 60 lb : 10 lb.

You can use ratio tables to show how two quantities are related. Ratio tables are another way to organize information.

ACTIVIT Y

4.1

The table represents three equivalent ratios of weight on Earth (lb) : weight on the Moon (lb).

The ratio of 60 lb on Earth : 10 lb on the Moon is given.add

42

Weight on Earth (lb) 60 30 90

Weight on the Moon (lb) 10 5 15

WORKED EXAMPLE

Think about how the numbers in the table relate to each other.

42

add

C01_SE_M02_T01_L04.indd 59 07/04/17 4:54 AM

STEP 3

Grab the Student Consumable Textbook and log-in to MATHia through our Sample Center. Experience our Engage, Develop, Demonstrate instructional model. Work the problems. Have fun!

In our Sample Center, you can explore student materials, teacher materials, and MATHia through the Middle School and Hight School drop-downs. Once there, you’ll learn more about our Engage, Develop, Demonstrate instructional model:

Get to know MATHia, the world’s best math learning platform!For students to really learn the math, they have to master the skills. To do that, MATHia is designed by cognitive scientists and master math practitioners to mirror a human math coach better than any other platform. As part of the blended experience, MATHia adapts alongside the texts and printed teacher materials to deliver powerful personalized learning.

LESSON 1: Connecting the Dots • M2-3

© C

arne

gie

Lear

ning

, Inc

.

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

• an 5 2 2 4(n 2 1)• an 5 24 1 2(n 2 1)

• an 5 2 1 4(n 2 1)• an 5 4 1 2(n 2 1)

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 12/22/17 2:05 PM

Carnegie Learning

System Help Glossary Maria HernandezHome

https://www.carnegielearning.com/…

© 2017 Carnegie LearningClient Version: 2.2.58 Server Version: 2.2.58

Go to ProblemStep-by-Step ExampleUnit Overview Step-by-Step Sample Problem

You are writing a book of jokes. Whenever you come up with an idea for a joke, you like to write it down. The trouble is, you might get the idea in your sleep, or while playing ping pong, or during your favorite TV show, and then when you go to write it down, you totally forget what it is. The table shows the ideas you got and the ideas you forgot.

1. Oh, �ddlesticks. You forgot 8 ideas. How many total ideas did you get?

2. Phooey. You had 25 cool ideas, but of course you forgot some. How many did you forget?

1. Oh �ddlesticks. You forgot 8 ideas. How many total ideas did you get?

ideas you got

I want to do these optional tasks.


ideas you forgot


Ideas You Got Ideas You Forgot

5 1

15 3

25

35

5

7

Problem Solving with Equivalent Ratios and Rates using Tables

you got and the ideas you forgot.

1. Oh, �ddlesticks. You forgot 8 ideas. How many total ideas




ideas you forgot ideas you forgot


Ideas You Forgot

1

3

5

7

Workspace Introduction

Get started with Problem Solving with Equivalent Ratios and Rates using Tables by studying the sample problem, then do the Step-by-Step example.

Begin Step-by-Step Example

Example:Bettina works in the aquarium section of a pet store. Every week, she has to add water conditioner to each �sh tank in the store. Water conditioner removes chlorine and keeps the water safe for �sh.

The table represents a set of equivalent ratios of the number of drops of water conditioner needed to the size in gallons for various �sh tanks.

Skip and go to problem

Number of Drops of Conditioner Size of Fish Tank in Gallons

10 4

20 8

Carnegie Learning

Progress I’m DoneUnit Overview Step-by-Step Hints

System Help Glossary Maria Hernandez

© 2017 Carnegie LearningProblem: errsdn002 Client Version: 2.0.448 Server Version: 2.0.448

Actions per minute are used to measure the number of actions (such as chords strummed or swords slashed) completed per minute of video game play. Your favorite video game is Rockin’ Warrior Robots. To complete the �rst stage, you must defeat Metalhead Max, a stealthy guitar-playing robot whose hobbies include rocking in his band and slaying dragons. Metalhead Max’s action per minute rate during battle is represented on the double number line.

Use the double number line to calculate the unknown values.

Minor Tick Marks

0 120 240 360 480 600 720 840 960

Number of Actions

Time (minutes)

1. Metalhead Max completed 520 actions. How many minutes did he battle?

minutes

I want to do the optional double number line tasks.

2. How many actions did Metalhead Max complete if he battled for 12 minutes?

actions


0 6 12 18 24 30 36 42 48

Sample Problem


Problem Solving with Equivalent Ratios and Rates using Double Number Lines Home

Middle School Textbook and MATHia Software

Algebra I Textbook and MATHia Software

EngageActivate student thinking by

tapping into prior knowledge and real-world experiences

DevelopBuild deep mathematical understanding through

collaboration and questioning

DemonstrateStudents refl ect on and

evaluate what was learned


For teachers, MATHia transforms data into insight and action better than any other platform. MATHia’s reports leverage predictive analytics through the APLSE Report, while Leadership Reports provide a constant stream of performance and usage data to monitor district-wide, school-wide, classroom, and district progress toward learning goals.

APLSE Report Standards ReportSession Report Student Detail Report

APLSE Report: All Students Export Print

DATE RANGE

AVERAGE APLSEAPLSE OVER TIME

AVERAGE WORKSPACES COMPLETED

AVERAGE IMPROVEMENT AVERAGE HINTS AND ERRORS

AVERAGE PACE

From To09/08/16 05/08/17KEY Proficient

On-Track On-Track On-Track

Current

09/0810/08

11/0812/08

01/0802/08

03/0804/08

05/08

as of 05/08/17991

800

600

400

200

0

50% 12.5% 37.5%

SCORE DISTRIBUTION

Approaching Proficiency

Projected

Needs Remediation

4 STUDENTS ON TRACK STUDENT APPROACHING STUDENTS OFF-TRACK1 3

38%

41% 75%

Carnegie Learning


REPORTSHello, Jane Doe

©2017 Carnegie Learning Inc

STEP 4

See what LONG + LIVE + MATH looks like up close. Watch three videos at www.carnegielearning.com/scottsdale.

Video 1: “Carnegie Learning Overview”

Video 2: “The Carnegie Learning Way: A Story About Math Transformation.”

Video 3: “Transforming the Math Classroom”

Leadership Report

Carnegie Learning


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%

APLSE Report

Leadership Report


STEP 5

Explore MATHia from a student’s perspective: To do this, go to our Sample Center, where all of Carnegie Learning’s print resources, eBook, and MATHia demos are found.www.carnegielearning.com/sample-center/

Usernames:

[email protected]@[email protected]@cl.com

Password: longlivemath

https://www.carnegielearning.com/sample-center/

Carnegie Learning

You can explore the problems in MATHia by selecting Middle School and clicking on Try MATHia Software.

Once on the MATHia Software page, click on the button that says Launch Middle School (or High School) Student Experience. This will take you into the student launch page.

https://www.carnegielearning.com/vsk-login…

Carnegie Learning

Carnegie Learning


1 of 75 Workspaces Complete

1%Your Progress

Session Total0:00 00:04

0 7

0 1

Time*

Problems*

Workspaces

Relating Quantities5 Units14 Workspaces


Let’s Go!

Review

3

Composing and Decomposing5 Units20 Workspaces


Let’s Go!

21

Determining Unknown Quantities7 Units22 Workspaces


4



1 of 1 Workspace Complete

Pre-Launch Protocol1 Unit1 Workspace


If you’d like to experience various problems, click into the various workspaces located under the Launch Middle School or High School Student Experience.

You can then explore sample modules for each course. These modules will take you into unit overviews and problems for you to try.

https://www.carnegielearning.com/vsk-login…

Carnegie Learning

Carnegie Learning

Progress I’m DoneUnit Overview Step-by-Step Hints


© 2017 Carnegie LearningProblem: errsdn002 Client Version: 2.0.448 Server Version: 2.0.448

Actions per minute are used to measure the number of actions (such as chords strummed or swords slashed) completed per minute of video game play. Your favorite video game is Rockin’ Warrior Robots. To complete the �rst stage, you must defeat Metalhead Max, a stealthy guitar-playing robot whose hobbies include rocking in his band and slaying dragons. Metalhead Max’s action per minute rate during battle is represented on the double number line.

Use the double number line to calculate the unknown values.

Minor Tick Marks

0 120 240 360 480 600 720 840 960

Number of Actions

Time (minutes)

1. Metalhead Max completed 520 actions. How many minutes did he battle?

minutes


2. How many actions did Metalhead Max complete if he battled for 12 minutes?

actions


0 6 12 18 24 30 36 42 48

Sample Problem

26

26

240

ü

ü

Skills

Calculate value on double number line other than halfway between major tick marks.

Calculate value on double number line halfway between major tick marks.

Enter calculated denominator value.

Enter calculated numerator value.

Enter value visible on double number line.

Plot equivalent ratio on double number line.

Identify minor tick marks interval.

Progress to Mastery

ü


Problem Solving with Equivalent Ratios and Rates using Double Number Lines Home

Carnegie Learning

System Help Glossary Maria HernandezHome


Problem Solving with Equivalent Ratios and Rates using Tables

Go to WorkspaceCurrent Workspace 2 of 3: Problem Solving with Equivalent Ratios and Rates using Double Number LinesBack to Module

Relating Quantities > Unit Overview

Workspaces

WHY THIS MATTERS:

WHAT YOU’LL LEARN: 1Problem Solving with Equivalent Ratios and Rates using Double Number Lines2Problem Solving with Equivalent Ratios and Rates using Graphs3

Review

Let’s Go!

• Use a table to solve problems involving equivalent ratios

and rates.

• Use a double number line to solve problems involving

equivalent ratios and rates.

• Use a graph to solve problems involving equivalent ratios

and rates.

You will use what you know about ratios to solve problems using ratio tables, double number lines, and graphs.

• Unit: Ratio and Rate Reasoning

WHAT THIS CONNECTS TO:

Key Terms

ratio

rate

equivalent ratiosdouble number line

33%FINISHED

Problem Solving using Ratio and Rate Reasoning



STEP 6

And while you’re in our Sample Center, check out our assessments.

You and your review team have immediate access to all grade-level print resources (student consumable textbook, Spanish textbook, Family Guide, Skills Practice Book) online through our Sample Center. You’ll also find our assessments — Pre- and Post-Tests, End of Topic Tests, and Standardized Test Practice.

Ratios: Pre-Test • 1

Pre-TestName Date

1. the table shows the ages of Lily and Joe.

Lily’s age 1 2 3 4 5Joe’s age 5 6 7 8 9

is the relationship additive or multiplicative?

2. there are 43 girls and 25 boys in the Valley View Middle school chorus.

a. Write the ratio of girls to boys and the ratio of boys to girls in the chorus.

b. are the ratios you wrote part-to-part or part-to-whole ratios?

c. Write the ratio of girls in the chorus to the total number of chorus members and the ratio of boys in the chorus to the total number of chorus members.

d. are the ratios you wrote part-to-part or part-to-whole ratios?

e. Which is greater: the ratio of girls to the total number of chorus members, or the ratio of boys to the total number of chorus members? Explain your reasoning.

RATIOS

C01_AS_Pre_M02_T01.indd 1 7/22/17 1:25 PM

RATIOS

Standardized TestName Date

1. Which table shows an additive relationship?

a.

Muffins sold 1 2 3 4 5

Amount earned (dollars) 4 8 12 16 20

b.

Rectangle width (inches)

1 2 3 4 5

Rectangle length (inches)

5 10 15 20 25

c.

Cups of water 1 2 3 4 5

Tablespoons of drink mix

3 6 9 12 15

d.

Jack’s age 1 3 5 7 9

Pat’s age 4 6 6 10 12

2. Essam buys 3 apples, 5 bananas, and 7 carrots from a market. What is the ratio of bananas to carrots?

a. 7 to 5b. 5 to 7c. 3 to 7d. 7 to 3

RATIOSRATIOSRATIOSRATIOSRATIOSRATIOSRATIOSRATIOS

36 • ModulE 2: Relating Quantities

C01_AS_MC_M02_T01.indd 36 7/22/17 1:24 PMRatios: End of Topic Test Form A • 9

End of Topic Test Form AName Date

1. the table shows the relationship between red and blue marbles.

Red marbles (r) 4 10 11 18 29Blue marbles (b) 1 7 8 15 26

a. Write the relationship between red and blue marbles as an equation.

b. is this an additive or multiplicative relationship? Explain your reasoning.

2. in a group of rectangles, the length of each rectangle is twice the width. is this an additiveor multiplicative relationship? Explain your reasoning.

3. the Lakeland Middle school boys’ golf team is made up of seventh and eighth graders. there are 12 seventh graders and 17 eighth graders on the team.

a. Write the ratio of seventh graders to eighth graders and the ratio of eighth graders to seventh graders on the team.

b. are the ratios you wrote part-to-part or part-to-whole ratios?

RATIOS

C01_AS_EoTA_M02_T01.indd 9 7/22/17 1:24 PM

STEP 7 Reach out if you have any questions! Ray Gosha is your contact and can be reached at [email protected].

Thanks for exploring what we have to off er. We’re excited to bring LONG + LIVE + MATH to life throughout SUSD. Together, we can transform math learning

Documents

Let’s Bring LONG + LIVE + MATH to SUSD · MSMS and HSMS Reviewer’s Guide 1 Let’s Bring LONG + LIVE + MATH to SUSD! Your Reviewer’s Guide for Carnegie Learning’s Middle School