Middle School Math Solution Reviewer’s Guide - Carnegie Learning

Middle School Math Solution Reviewer's Guide

We are honored to provide you with Carnegie Learning's Middle School Math Solution.

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).

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

STEP 1

Check your list.

You should have the essentials:

? This Reviewer's Guide! ? Teacher Implementation Guides, Volume 1 & Volume 2 ? (1) Student Consumable Textbook with MATHia access ? (1) Student Skills Practice Book (if students do not have

regular access to technology) ? Access to Assessments, Student Performance Tasks,

Family Guide, and Spanish textbooks (available online through the Virtual Sample Kit)

STEP 2

Get to know us and spend time with a teacher and her students by going to detroit.

Watch the following three videos: Video 1: "Carnegie Learning Overview" Video 2: "The Carnegie Learning Way: A Story About Math Transformation." Video 3: "Transforming the Math Classroom"

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STEP 3

Grab the Teacher Implementation Guide. Read the front matter and examine teacher facilitation notes.

FRONT MATTER ? FM 9?FM 14 will take you through Carnegie Learning's philosophy and introduce you to the program. Note that

our program supports a Learning Together, Learning Individually classroom model. ? FM 15?FM 23 will 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 Michigan correlations, go to detroit. ? FM 25?FM 30 discusses how Carnegie Learning supports students as they encounter topics and the various lesson characteristics that foster student creativity and critical thinking.

FACILITATION NOTES Every 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 as student work, ELL supports, common misconceptions, and other tips.

Getting Started: I'm Your Density

Facilitation Notes In 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:

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

Activity 4.1

Introduction to Ratio Tables Facilitation Notes In 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

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

_6_0_ 10

1

_3_0_ 5

5

_91_50_.

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 not

fractions, so they cannot be divided to yield a quotient. You may want

to 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 4.2

Using Equivalent Ratio Tables

Facilitation Notes In 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.

M2-57D ? TOPIC 1: Ratios

LESSON 4: A Trip to the Moon ? M2-57C

C01_TIG_M02_T01_L04_57A-57f.indd 57D

31/03/17 12:39 PM

C01_TIG_M02_T01_L04_57A-57f.indd 57C

31/03/17 12:39 PM

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STEP 4

Grab the Student Consumable Textbook and log into MATHia through our Virtual Sample Kit. Experience our Engage, Develop, and Demonstrate instructional model. Work the problems. Have fun!

Carnegie Learning's Middle School Math Solution uniquely integrates our textbook resources with MATHia, our intelligent math learning platform.

Students will receive instruction and work through interactive lessons within the textbook. Each lesson delivers our Engage, Develop, and Demonstrate instructional model. ? 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 -- in an environment where collaboration, conversations and questioning are routine practices. ? Demonstrate: We provide opportunities for students to reflect on and evaluate what was learned. Ongoing formative assessment underlies the entire experience, driving real-time adjustments, next steps, insights, and measurements.

And MATHia punctuates student learning by seamlessly aligning with textbook topics and providing problems for further exploration. 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 on-grade level skill mastery.

AC TIVIT Y

4.1 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.

WORKED EXAMPLE

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

42

add

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

Carnegie Learning

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Problem Solving with Equivalent Ratios and Rates using Tables Home System Help Glossary

Unit Overview Step-by-Step Sample Problem

Step-by-Step Example

Maria Hernandez Go to 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?

ideas you got

I want to do these optional tasks.

Workspace Introduction

2. Phooey. You had 25 cool ideas, but of course you forgot

1.

Oh, ddlesticks. did you get?

You

forgot 8 ideas. Get started with

How many total ideas Problem Solving with Equivalent

RatiossoanmdeR.aHteoswusminganTaybdleids byyosutufdoyrignegtt?he

sample problem, then do the Step-by-Step example.

ideas you forgot

2.

Psohmooee. yH. oYwoumhaandy2d5idcoyooEBul eixdtfatoienmraagpwseol,ter?bk:suint

of

the

course you forgot

aquarium section of a pet

store.

Every

week,

she

I want to do

has to add water

these optional

conditioner to each

tasks.

sh

tank in the store. Water conditioner removes chlorine and keeps the water safe for sh.

Ideas You Got

5 15

The table represents a set of equivalent ratios of the number of drops of water conditioner needed to the size in

Idgealalonss YforovuarioFuos rsghotatnks.

Number of Drops of Conditioner Size of Fish Tank in Gallons

1

10

4

3

20

8

25

5 Skip and go to problem

35

7

Begin Step-by-Step Example

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LESSON 4: A Trip to the Moon ? M2-59

07/04/17 4:54 AM

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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 provide administrators and instructional leaders with interactive data so they can view student performance across the district, buildings, and even at the class level.

Note: If your students have limited access to technology, please see the Student Skills Practice Book.

Carnegie Learning

...

REPORTS

Hello, Jane Doe

Leadership Report 12 Schools selected

87 Classes selected

2 Class Categories selected

2 Class Profiles selected Period: 08/21/16 to 03/05/17

Carnegie Learning

...

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

44% 440 out of 1000

AVERAGE USAGE On Track 90 minutes Approaching On Track: 60-89 minutes

90 minutes per week

AVERAGE USAGE PER STUDENT

Minutes spent in MATHia per student per week

Minutes

350 300 250 200 150 100

50 0

08/21/16

09/18/16

10/16/16

11/13/16 Weeks

12/11/16

AVERAGE SYLLABUS COMPLETION

23%

APLSE PERFORMANCE

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

REPORTS

59%

APLSE Report

Session Report

PRINT

Student Detail Report: All Students EXPORT

1 2 3 4 Next

Kelvin Middle School

01/15/17

On Track

Average Usage 134

01/08/17

02/26/17

03/05/17

i

Acre Middle School Byte Middle School Carat Middle School Celsius Middle School Fahrenheit Middle School Hertz Middle School Joule Middle School Kelvin Middle School Ounce Middle School Pascal Middle School Tonne Middle School Torr Middle School Average (12 Schools)

Student Name

Adams, Janet Baker, Lindsey Bartlett, Michael Franklin, Sam Harrison, Sara Jacobs, Beth Ming, Jo Peterson, Phillip Ruiz, Marco Trazzoli, Kim Tresport, Jacob Williams,Shania Zeller, Trevor

% Syllabus Complete

76 44 53 45 49 35 32 0 36 49 4 5 1

Average Performance Score (out of 100)

100 88 77 78 61 92 90 0 87 100 100 100 99

Hello, Jane Doe

Standards Report

Student Detail Report

Export

Print

Current Module

One-Step Equations ... Numeric and Algebraic ... Numeric and Algebraic ... Numeric and Algebraic ... Numeric and Algebraic ... Ratios, Rates, and Percents ... Ratios, Rates, and Percents ... Not Started Ratios, Rates, and Percents ... Numeric and Algebraic ... One-Step Equations and ... Fraction and Decimal ... Pre-Launch Protocol

Time on Task (in minutes)

637 90 707 422 566 551 300 0 101 96 8 27 1

Student Usage Totals

Modules Completed

Units Completed

Workspaces Completed

4

10

56

3

6

37

3

8

39

3

6

33

3

6

36

2

5

26

2

5

24

0

0

0

2

5

27

3

7

36

1

1

3

0

0

4

0

0

1

?2017 Carnegie Learning Inc

?2017 Carnegie Learning Inc

Carnegie Learning



To experience MATHia from a student's perspective, go to our Virtual Sample Kit, where all of Carnegie Learning's print resources and MATHia demos are found: vsk-login.

Reference your printed Reviewer's Guide for your username and password.

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

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Carnegie Learning

...

Carnegie Learning

...

Once on the MATHia Software page, click on the button that says Launch Middle School Student

Experience. This will take you into the student launch page with a rocketship!

Carnegie Learning

...

Your Progress

Time*

Session 0:00

Problems*

0

Workspaces

0

Total 00:04 7 1

System Help Glossary

Maria Hernandez

1%

1 of 75 Workspaces Complete

Pre-Launch Protocol

1 Unit 1 Workspace

1 of 1 Workspace Complete

1

Review

Composing and Decomposing

2

5 Units 20 Workspaces

Let's Go!

0 of 20 Workspaces Complete

Relating Quantities 5 Units 14 Workspaces

0 of 14 Workspaces Complete

Client Version: 2.0.448 Server Version: 2.0.448

3

Let's Go!

Determining Unknown

4

Quantities

7 Units 22 Workspaces

0 of 22 Workspaces Complete

? 2017 Carnegie Learning

If you'd like to experience various problems, click into the various workspaces located under the

Launch the Middle School Experience button.

Carnegie Learning

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Home System Help Glossary

Maria Hernandez

Back to Module

Current Workspace 2 of 3: Problem Solving with Equivalent Ratios and Rates using Double Number Lines

Relating Quantities > Unit Overview

Problem Solving using Ratio and Rate Reasoning

Workspaces

Go to Workspace

WHAT YOU'LL LEARN:

? 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.

Key Terms ratio rate equivalent ratios double number line

1 Problem Solving with Equivalent Ratios and Rates using Tables

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

3 Problem Solving with Equivalent Ratios and Rates using Graphs

Review Let's Go!

WHY THIS MATTERS:

WHAT THIS CONNECTS TO: You will use what you know about ratios to solve problems using ratio tables, double number lines, and graphs. ? Unit: Ratio and Rate Reasoning

Client Version: 2.2.58 Server Version: 2.2.58

33%

FINISHED

? 2017 Carnegie Learning

Carnegie Learning

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Problem Solving with Equivalent Ratios and Rates using Double Number Lines Unit Overview Step-by-Step Sample Problem Hints

Home System Help Glossary Progress

Maria Hernandez

I'm Done

Actions per minute are used to measure the number of actions

1. Metalhead Max completed 5S2k0ilalsctionPs.roHgorwesmsantoy mMinaustteesry

(such as chords strummed or swords slashed) completed per

did he battle?

minute of video game play. Your favorite video game is Rockin'Calculate value on double number line other

Warrior Robots. To complete the rst stage, you must defeat

than ha2lf6way bmeitnwueteens major tick marks.

Metalhead Max, a stealthy guitar-playing robot whose hobbies include rocking in his band and slaying dragons. Metalhead

? I want to do the optional double number line tasks. Calculate value on double number line

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.

2. Hhaolwfwmayabneytawceteionnms adjiodrMticektamlhaerakds.Max complete if he battled

for 12 minutes? Enter calculated denominator value.

?

240 actions

?EntIewr caanltctuoladteodthneumopetriaotnoar lvdaoluueb. le number line tasks.

Enter value visible on double number line.

Minor Tick Marks

Plot equivalent ratio on double number line.

0 Number of Actions

Identify minor tick marks interval.

120

240

360

480

600

720

840

960

Time (minutes) 0

6

12

18

24

30

36

42

48

26

Problem: errsdn002 Client Version: 2.0.448 Server Version: 2.0.448

? 2017 Carnegie Learning

You can then explore sample modules from Middle School Courses 1, 2, and 3. These modules will take you into unit overviews and problems for you to try.

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