Destination Math Training Manual

Transcription

Part of the Destination SuccessTM Solution
for Learning Management System version 3
Training
Manual
www.riverdeep.net
Part of the Destination SuccessTM Solution
for Learning Management System version 3
Training
Manual
For more information about Riverdeep products
visit www.riverdeep.net
© 2005 Riverdeep Interactive Learning Limited. All rights reserved. This manual may not be reproduced in any form or by any means
without the prior written permission of Riverdeep, Inc. LLC, 100 Pine Street, Suite 1900, San Francisco, CA 94111.
Destination Math for Learning Managment System version 3
Training Manual
Table of Contents
1.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2.
Training Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Destination Math Checklist for Initial Training . . . . . . . . . . . . . . . . . . . . . .3
3.
Overview of Launching Destination Math . . . . . . . . . . . . . . . . . . . . . . . . 4
4.
Navigation of Destination Math: Mastering Skills
and Concepts: Courses I and II for Grades K-3
11
Navigation of Destination Math: Mastering Skills
and Concepts: Courses III and up for Grades 4-12
17
5.
6.
Scope and Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7.
Introduction to Print Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
8.
Hands-on Exploration and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 47
9.
Classroom Management of Technology . . . . . . . . . . . . . . . . . . . . . . . . . 49
10. Meeting the Challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Introduction
1
Destination Math
The Destination Math series is a carefully sequenced, comprehensive curriculum that
demonstrates how mathematical issues arise from real-life situations. These courses focus on
the importance of mastering the underlying skills and concepts of the topics presented and the
ability to apply the learned skills and concepts to solve meaningful problems. The Destination
Math program is designed around performance objectives that reflect national and state
mathematical standards. Each course supports individualized instruction, collaborative learning,
and whole-class presentation.
Key product features that will be addressed in the training include the following:
• guided practice activities that use the program tools
• investigation through computerized simulations and models to show mathematical concepts
• use of data collection and analysis
• interpretation of graphical representations
• a focus on problem solving and development of analytical skills
In addition, you’ll learn how to correlate Destination Math to state and national standards by
visiting www.riverdeep.net.
1
Training Objectives
2
Throughout the training, the following objectives will be addressed:
• Emphasize how the use of Destination Math can increase students’ academic achievement through
concept-based instruction
• Show how state and national standards can be targeted as the focus of the Destination Math lesson
• Demonstrate the flexibility of Destination Math by showing how the program can be used
successfully in a variety of classroom settings, including:
•
lab instruction
•
one computer in a classroom
•
small computer centers within the classroom
• Acquaint teachers with integration ideas and implementation strategies that target their specific
classroom needs
• Help teachers design lesson plans that include Destination Math as a key component of the lesson
All the objectives will be addressed through instructor-led demonstrations, guided practice,
participant exploration, and review sessions for sharing. This training’s goal is to provide you
with enough information to start incorporating Destination Math as part of your classroom
instruction.
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Destination Math
Checklist for Initial Training
Initial each item as it is completed:
Destination Math Key Features
__________
Launch Destination Math.
__________
Review main menu features—be able to find a specific session.
__________
Launch a tutorial and explore buttons, navigation button, and tools.
__________
Explore all three levels of workouts and the Show Me feature.
__________
Access the print materials.
__________
Explore various tutorials and workouts while thinking of ways to
incorporate them into the classroom.
Lesson Planning and Classroom Management
__________
Be familiar with the three main implementation strategies.
__________
Create a Destination Math lesson plan using the implementation strategy
that applies to your classroom situation.
__________
Incorporate all print materials that are appropriate.
I have successfully completed all of the above.
_______________________________________________________________
Signature
_______________________________________________________________
Date
3
Overview
of Launching
3
Destination Math
• Activity 1: Launching Destination Success
• Activity 2: Launching a Destination Math course with a Teacher User Name and Password
• Activity 3: Launching a Destination Math course with a Student User Name and Password
This section shows you how to launch Destination Math through your Destination Success
Portal.
For this program to work properly, you must log in to the network as a student or as a teacher
when you first turn on the computer. The program has different permissions for teachers and
students, so it’s important to always log in either as a student or as a teacher.
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Activity 1:
Launching Destination Success
1. On the desktop, access Destination Success by clicking
Internet Explorer and typing the following
URL: __________________________________________
2. Click the user name box and type your user name.
Click the password box and type your password.
3. Click the green Log In arrow.
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Activity 2:
Launching a Destination Math Course with a
Teacher User Name and Password
If you use a teacher user name and password, follow these steps to launch a Destination Math
course. This will give you access to the teacher functions for Destination Success LMS v3.0.
1. From the Home screen, click Explore Content.
2. Select the Math tab at the top if it is not already selected.
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3. Click the green Launch button next to Destination Math
Course I to begin exploration.
Activity 3:
Launching a Course with a Student User
Name and Password
If you use a student user name and password, follow these steps to launch a Destination Math
course. Students who are capable of entering text can type their user name and password.
Students who cannot yet read and write can select Simple Log In (see section below for
nonreaders/nonwriters). If you do not have a specific user name and password, you can use
“rdstudent” for the user name and “student” for the password. This will give you access to the
student functions for Destination Success LMS v3.0.
1. Click Exploration from the Home screen.
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2. Select the Destination Math Course you want by clicking
the green Launch button.
For Nonreaders/Nonwriters
1. Click Simple Log In.
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2. Select the class name and the student’s name.
Then click OK.
3. Select Exploration, then launch a course as you did in
the previous activity.
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Destination Math: Mastering Skills and Concepts: Course I and Course II navigate differently
than Mastering Skills and Concepts: Course III and up. Each navigation will be discussed at
length in different sections. For navigation of Courses I and II, grades K-3, see section 4. For
navigation of Courses III and up, see section 5.
10
Navigation of
Destination Math:
Mastering Skills and
Concepts: Courses I
and II for Grades K-3
4
• Activity 1: Lesson and Workout Navigation
• Activity 2: Navigation Tool and Practice Navigation
In this section, you’ll learn to navigate through Courses I and II. The look and feel is different
from Courses III through Algebra; however, the progression is the same—there are still
modules, units, and sessions.
Courses I and II introduce fun, interactive characters called Noodles for students to enjoy.
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Training Manual
Activity 1:
Lesson and Workout Navigation
1. Click the green Launch button for Course I from the
math content page.
2. Click a module (mode of transportation). Each module
holds different units. For this example, click Module 1.
3. Click a unit (travel bag) at the bottom of the screen. For
this example, click Unit 1: Numbers from 1 to 5.
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Each unit has several sessions (travel brochure) which contain a lesson, practice, workout, and
Aims page. The Aims page is accessed by clicking the letter A in the middle of the travel
brochure. This screen provides the user with learning objectives and key words for the lesson.
The lesson is accessed by clicking the character on the left side of the brochure. This is the
section that teaches the learner the material. The practice area is accessed by clicking the white
notepad. This section is a series of questions covering one learning objective at a time. The
workout is accessed by clicking the brown pouch. This section is one application-based question
covering all the learning objectives for that lesson. Every unit has a practice area that can be
accessed by clicking the notepad with the pencil in the lower right corner of the screen.
Practice Area
Aims
Lesson
Return to
Modules
Workout
Unit
Practice
Exit
4. Click the lesson One Fewer Than and Zero. This will allow
you to view the whole lesson and follow with the
practice and workout questions.
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5. The image below describes the function of each button
when in a lesson or workout.
Help
Tools –
Glossary
Base-10 blocks
Number cubes
Navigation –
Allows users to
move easily
from lesson to
practice to
workout
Exit – Takes the
user back to the
unit page
14
Back to start –
Takes the user
back to the
first page in
the lesson
Back – Takes
the user
back one
page at a
time
Pause
Repeat Page –
Repeats the
information
for the current
page
Continue – When this
button glows and
spins, click it to
proceed to the next
page of the screen
Training Manual
Activity 2:
Navigation Tool and Practice Navigation
1. While in the lesson One Fewer Than and Zero, click the
Navigation Tool.
The orange and yellow rectangles tell you where you are
in the lesson. The Practice button moves you to the
practice for that session, and the Workout button moves
you to the workout for that session.
2. Click Practice.
3. The image below describes the functions of new buttons
when in a practice area.
Back to the
last page in
the lesson
Previous
question
Next
Question
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Practice:
Lessons/Practice Areas/Workouts
Continue through various lessons, practice areas, and workouts in Course I and Course II that
apply to what you are teaching.
16
Navigation of
Destination Math:
Mastering Skills and
Concepts:
Courses III and up
for Grades 4-12
5
• Activity 1: Tutorial Navigation
• Activity 2: Navigation Tool
• Activity 3: Tools
• Activity 4: Workout Activities and the Pace Method
In this section, you’ll learn to navigate through Courses III and up. The look and feel is very
different from Courses I and II; however, the progression is the same—there are still modules,
units, and sessions.
Courses III, IV, and V introduce a fun, interactive character called Dijit for students to enjoy.
Algebra Courses I and II introduce a male and a female mathematician for the student to
interact with.
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Training Manual
Activity 1:
Tutorial Navigation
In this section, you’ll learn how to access the tutorials. A tutorial teaches the student the
concepts step by step. Every tutorial within Destination Math is correlated to state and national
standards. The objectives that are taught within each lesson are listed on the first page of each
tutorial. The tutorials within Destination Math are easy to navigate, interactive, and engaging.
1. Click the green Launch button for Course IV from the
math content page.
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Below is an image of the main menu screen. The progression to access a Destination Math
tutorial or workout is module, unit, session.
Module
Tutorial
Workouts
color coded
by difficulty
level
Green – easy
Blue – medium
difficulty
Purple - hard
Exit
Unit
Session
2. The tabs along the top are called modules. Click the
modules to see what happens.
3. On the right edge of the screen, as you click the different
modules, you’ll see the units for each module listed. As
you click the different units, what do you see changing?
(Note: Units are independent of each other, meaning that
you can go into any unit at any time; they do not build
upon each other.)
4. As you click the units, the sessions appear in the middle
box. Sessions, unlike units, are dependent upon each
other. If you go into the second session, for example, the
program assumes that you have completed the first
session. Some information is presented in consecutive
order, session by session, so you might miss something if
you skip ahead. But nothing in the program prevents you
from going into a session out of order.
5. Click a session. Within each session, you can choose a
tutorial or workout.
6. Click the module Fractions, unit Equivalent Fractions, and
session Identifying the Factors of a Number. Click
Tutorial. This will allow you to view the entire tutorial
and follow with the workouts when finished.
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Training Manual
7. Once the tutorial loads, the first screen is the Aims page.
This screen provides the learning objectives and key
words for the session.
8. Click the yellow arrow to begin the lesson.
9. Click the Pause button to pause the lesson.
10. The image below describes the function of each button
when in a tutorial or workout.
Navigation Tool –
Allows the
user to move
from tutorial
to workouts
easily
Tools –
Glossary
Calculator
Exit –Takes
the user
back to the
unit page
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Training Manual
Back – Takes
the user back
one page at a
time
Pause
Repeat Page –
Repeats the
information for
the current page
Continue – When this
glows yellow or when
the screen stops, click
it to continue to the
next page
Practice:
Name That Session!
Elementary Teachers
• Within Course III, find the fifth module, first unit, and third session. What is the name of the
session?*
Middle School Teachers
• Within Course V, find the fourth module, third unit, and first session. What is the name of the
session?†
High School Teachers
• Within Algebra Course I, find the second module, second unit, and first session. What is the name
of the session?‡
Answers:
* Triangles
† Exploring and Solving Direct Variation Problems
‡ Exploring the Slope-Intercept Equation of a Line
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Training Manual
Activity 2:
Navigation Tool
1. While in the tutorial Identifying the Factors of a Number,
click the Navigation tool on the right side of the screen.
2. The image below is what appears at the bottom of the
screen after clicking the navigation tool.
3. The triangle pointer tells you which section you are in
within the session. The numbers in the orange sections
(between the A and S) represent the objectives being
taught—these are the objectives we saw on the Aims
page. The A is for the Aims page. The S stands for
Summary. The numbers in colors at the end of the bar are
the workouts. Workouts will be discussed in the next
activity of this section.
4. To view the objectives, move your mouse so the cursor is
over one of the numbers in the orange section. Notice
that the triangle has not moved.
5. To move to a different objective or place within the
tutorial, click the Triangle pointer and drag it to where
you want to go. Then click OK. You now have the
flexibility to move about the program, so you are not
limited to completing the entire tutorial in one sitting.
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Training Manual
Activity 3:
Tools
1. Now click Tools. Here you’ll find a glossary and
calculator.
Glossary
Calculator
2. Click Glossary. The glossary will appear. Click any letter
in the alphabet to see a list of words and their
definitions.
3. To exit, click the X at the top of the screen.
4. Click Calculator. The calculator will appear. To enter
numbers, use the mouse and click the number pad or use
the numbers on your keyboard. This is both a scientific
calculator and a statistics calculator. The purple buttons
are for statistics. Enter a number and click load; continue
to do so until you have three or four numbers. Then click
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Training Manual
avg to find the average. The average of the numbers
entered will appear on the left.
5. To exit, click the X at the top of the calculator as you did
for the glossary.
Activity 4:
Workout Activities and the PACE Method
In this section, you will explore a series of workouts that provide students with an opportunity
to apply one or more of the skills and concepts learned in the tutorial you encountered in the
previous session. Like the tutorials, each workout is presented within the context of a real-life
problem. One unique aspect of the workout section is the Show Me feature, which provides
students with a step-by-step explanation of how to solve each workout. Students may elect to
view all or part of the solution, returning to the workout at any point during the explanation
process. The Show Me explanations guide the learner through an approach to problem solving
called PACE, which is an acronym for Problem, Analysis, Computation, and Evaluation. Students
become familiar with a systematic approach to solving a problem that includes the following
steps:
P Identify and restate the problem to be solved.
A Analyze and collect pertinent information given in the problem.
C Calculate and communicate the process used to solve the problem.
E Evaluate, check, and verify your answer within the context of the problem.
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Each workout question is color coded by difficulty level—green, blue, or purple. The answer
button’s background color and the colored numbers in the navigation bar’s numbers reflect the
difficulty level of the problem on the screen.
The difficulty level colors
will be shown here.
Green (level 1) workouts are knowledge-based questions that address exactly one learning
objective from the preceding session. They generally measure baseline learning and include the
phrasing “in other words” to assist students with identifying the math content being
investigated in the workout.
Blue (level 2) workouts are application-based questions that address one or two learning
objectives with two or more steps involved in the solution process. They do not include the
transitional phrase “in other words” to clue the students in on the content.
Purple (level 3) workouts focus on higher-order thinking skills that will address at least two
learning objectives. They are more narrative in design and may include extraneous information.
These questions may also draw on previous knowledge from earlier tutorials. The “purple”
questions usually require students to be working on a higher level that requires thinking skills,
such as compare and contrast, and analyze.
The type of workout that is available at the end of a tutorial depends on the complexity of the
tutorial. In general, the tutorial in Session 1 will be followed by either green (level 1) or blue
(level 2) workouts. The tutorials in Sessions 2 and 3 can be followed by workouts containing all
three types of problems.
Remember: This program was not designed as a “drill-and-kill” program; there are a maximum
of eight workouts per session and workouts are of varying levels. There is one question per
workout.
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Training Manual
Launching a Workout
Workouts directly follow a tutorial. You can access workouts in one of three ways.
1. Click the Workout button of your choice from the main
menu screen.
2. During a tutorial, click the navigation tool and click the
Workout question of your choice.
3. At the end of the tutorial, click Continue when
prompted.
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Training Manual
Practice
The workouts described below will give you one workout of each level (green, blue, and purple)
to try.
1. Depending on your grade level, launch one of the
following:
I
Elementary Teachers
1. From the main menu, go to Course III.
2. Click the Fractions module.
3. Click the first unit: Proper and Improper
Fractions.
4. Click the third session: Equivalent Fractions; then
click the first Workout button.
II
Middle School Teachers
1. From the main menu, go to Course IV.
2. Click the Integers and Order of Operations
module.
3. Click the second unit: Multiplying and Dividing
Signed Numbers.
4. Click the third session: Finding Quotients Using
Reciprocals; then click the first Workout button.
III High School Teachers
1. From the main menu, go to Algebra Course I.
2. Click the Language of Algebra module.
3. Click the first unit: Variables, Expressions, and
Equations.
4. Click the third session: Evaluating and
Simplifying Expressions; then click the first
Workout button.
2. During a workout, when prompted to answer the
question, click Show Me to explore this specific feature.
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Training Manual
3. You can return to the workout any time to enter your
own answer by clicking the blue Workout button at the
bottom of the screen. At the end of each workout
question, click Continue to move to the next workout.
4. At the end of each workout, click Continue to move to
the next workout.
5. When you have finished all the workouts, the prompt
shown here will appear. You can click Continue to go
directly to the next tutorial or Menu to go back to the
main menu screen, where you can choose another unit
or session.
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6
Scope and
Sequences
Destination Math
Mastering Skills and Concepts: Course I
Scope and Sequence: Grades K–1
Module 1: Number Sense
Unit 1 Numbers from 1 to 5
• Counting from 1 to 5
• Creating Sets of 1 to 5
• Creating Representations of the Numbers
from 1 to 5
Unit 2 Numbers from 1 to 10
• Counting from 5 to 10
• Creating Sets of 5 to 10
• Creating Representations of the Numbers
from 5 to 10
• One More Than
• One Fewer Than and Zero
Unit 3 Numbers to 100
•
•
•
•
•
Counting from 10 to 20
Skip-Counting by Tens and Fives
Skip-Counting by Twos
Unit 4 Comparing and Ordering
• More Than, Less Than, or the Same
• Comparing Numbers within 100
Module 2: Addition and Subtraction
Unit 1 Addition
•
•
•
•
Combining and Joining within 10
Comparing within 10
Sums within 20, with 10 as One Addend
Sums within 20
Unit 2 Subtraction
• Differences within 10
• Differences within 20
Module 3: Geometry and Measurement
Unit 1 Measurement
•
•
•
•
Length
Weight
Clock and Calendar Time
Money
Unit 2 Geometry
• Triangles and Rectangles
• Three-Dimensional Shapes
Module 4: Algebraic Thinking
Unit 1 Patterns and Displays
• Shapes
• Number Patterns
• Tables and Graphs
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Training Manual
Destination Math
Mastering Skills and Concepts: Course II
Scope and Sequence: Grades 2–3
Module 1: Number Sense
Unit 1 Numbers to 999
•
•
•
•
Counting by Grouping
Place Value: Tens and Ones
Place Value: Hundreds, Tens, and Ones
Expanded Forms and Equivalent
Representations of a Number
• Comparing and Ordering
Unit 2 Numbers to 9,999
• Place Value: Thousands, Hundreds, Tens,
and Ones
• Comparing and Ordering
Module 2: Operations with Numbers
Unit 1 Addition and Subtraction
•
•
•
•
•
Sums Less Than 100
Sums Less Than 1,000
Differences within 100
Differences within 1,000
Estimates and Differences within 9,999
Unit 2 Multiplication
• Repeated Addition and Arrays
• Skip Counting to Show Multiplication
• Finding Products Less Than 100
Unit 3 Division
• Meaning of Division
• Dividing by a 1-digit Number
• Fractional Parts
30
Module 3: Geometry and Measurement
Unit 1 Geometry
• Area
• Volume
Unit 2 Measurement
• Time
• Money
• Temperature
Module 4: Algebraic Thinking
Unit 1 Properties and Relationships
• Number Patterns and Properties
Training Manual
Destination Math
Mastering Skills and Concepts: Course III
Scope and Sequence: Grades 4-6
Module 1: Numbers and Number Sense
Unit 1: Large and Small Numbers
• Whole Numbers to One Million
• Ordering and Rounding Whole Numbers
• Negative Whole Numbers
Unit 2: Numbers as Factors
• Finding Factors
• Prime and Composite Numbers
• Identifying Common Factors
Module 2: Operations with Numbers
Unit 1: Addition and Subtraction of
Whole Numbers
• Whole Number Sums
• Differences between Large Numbers
Unit 2: The Integers
• Integer Sums
• Differences between Integers
Unit 3: Multiplication and Division of
Whole Numbers
• Two-Digit Multipliers
• Introduction to Long Division
• Two-Digit Divisors
Module 3: Fractions
Unit 1: Proper and Improper Fractions
•
•
•
•
Proper Fractions
Improper Fractions
Equivalent Fractions
Ordering and Rounding Fractions
Unit 3: Multiplication and Division
• Finding Products
• Quotients and Remainders
Module 4: Decimals
Unit 1: Introduction
• Tenths, Hundredths, and Thousandths
• Ordering and Rounding
• Ratios, Decimals and Percents
Unit 2: Addition and Subtraction
• Adding Decimals
• Subtracting Decimals
Unit 3: Multiplication and Division
• Multiplying Decimals
• Dividing Decimals by Whole Numbers
Module 5: Geometry
Unit 1: Measurement
•
•
•
•
Lines, Angles, and Circles
Rectangles and Squares
Triangles
Parallelograms and Trapezoids
Unit 2: Coordinate Geometry and Algebra
• The Coordinate Plane
• Symmetry and Transformations
Module 6: Data Analysis and Probability
Unit 1: Modeling and Displaying Data
• Displaying and Analyzing Data
• Looking at Chance
Unit 2: Addition and Subtraction
• Sums Involving Like Denominators
• Differences Involving Like Denominators
• Working with Unlike Denominators
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Destination Math
Mastering Skills and Concepts: Course IV
Module 1: Fractions
Unit 1: Essentials of Fractions
• Recognizing a Fraction
• Exploring Proper and Improper Fractions
• Working with Mixed Numbers
Unit 2: Equivalent Fractions
• Identifying the Factors of a Number
• Expressing Fractions in Lowest Terms
• Writing and Comparing Equivalent Fractions
Unit 3: Multiplying Fractions
• Finding Products of Fractions, Whole
Numbers, and Mixed Numbers
• Using GCF in Finding Products
• Representing Multiplication
Unit 4: Dividing Fractions
• Estimating Quotients of Fractions
• Using Multiplicative Inverses
• Solving Missing Value Problems When
Dividing Fractions
Unit 5: Adding Fractions
• Adding with Like Denominators
• Adding with Unlike Denominators
Adding Fractions
Unit 6: Subtracting Fractions
• Subtracting with Like Denominators
• Subtracting with Unlike Denominators
Subtracting Fractions
Module 2: Decimals
Unit 1: Essentials of Decimals
• Investigating Decimal Place Values
• Rounding Decimals
• Exploring Repeating and Terminating
Decimals
Unit 2: Adding and Subtracting Decimals
• Using Place Value Grids
• Regrouping with Whole Numbers
• Regrouping with Hundredths
32
Unit 3: Multiplying Decimals
• Multiplying Decimals by Powers of 10
• Calculating Products
• Finding the Volume of a Prism
Unit 4: Dividing Decimals
• Dividing Decimals by Whole Numbers
• Estimating and Finding Quotients
• Dividing by Powers of 10
Module 3: Percents
Unit 1: Essentials of Percents
• Investigating the Meaning of Percent
• Expressing Percents as Proper Fractions
• Expressing Percents Greater that 100% as
Improper Fractions
Unit 2: Finding Percents of Quantities
• Finding Percents of a Whole
• Expressing Ratios as Percents
• Calculating the Whole from a Part and a
Percent
Unit 3: Increasing and Decreasing Percents
• Calculating Percent Increases
• Calculating Percent Decreases
• Calculating Simple Interest
Module 4: Integers and Order of Operations
Unit 1: Adding and Subtracting Signed
Numbers
• Exploring the Number Line and Absolute
Value
• Adding with Absolute Value
• Subtracting with Absolute Value
Unit 2: Multiplying and Dividing Signed
Numbers
• Finding Products of Signed Numbers
• Representing the Multiplication of Signed
Numbers
• Finding Quotients Using Reciprocals
Unit 3: Order of Operations
• Simplifying Expressions
• Introducing the Distributive Property
• Using Grouping Symbols
Training Manual
Destination Math
Mastering Skills and Concepts: Course V
Module 1: Essentials of Algebra
Unit 1: Algebra Fundamentals
• Introducing Variables
• Identifying Components of Algebraic
Expressions
• Replacing Variables in a Formula
Unit 2: Evaluating an Algebraic Expression
• Representing the Dimensions and Area of a
Rectangle
• Combining Like Terms
• Evaluating Expressions Using Substitution
Unit 3: Simple Equations
• Using Variables to Express Relationships
• Simplifying Algebraic Expressions
• Solving Simple Equations
Unit 4: Variables on Both Sides of the Equation
• Writing Equations
• Simplifying Both Sides of an Equation
• Checking the Solution to an Equation
Unit 5: Solving Literal Equations
• Identifying the Variables in a Given Formula
• Rewriting a Formula in Terms of a Different
Variable
• Substituting Values and Solving an Equation
Module 2: Fundamentals of Geometry
Unit 1: Geometry Fundamentals
• Naming and Measuring Angles
• Defining Complementary and
Supplementary Angles
• Recognizing Congruent Angles
Unit 2: Triangles
• Classifying Triangles by Sides
• Exploring the Area of a Triangle
• Classifying Triangles by Angles
Unit 3:Volume and Surface Area
• Calculating the Volume of a Right Triangular
Prism
• Calculating the Surface Area of a Right
Triangle
• Calculating the Volume and Surface Area of
a Right Cylinder
Module 3: Radicals and Exponents
Unit 1: Introduction to Radicals and the
Pythagorean Theorem
• Exploring the Pythagorean Theorem
• Investigating Squares and Square Roots
• Defining Irrational Numbers
Unit 2: Introduction to Scientific Notation
• Writing Numbers Using Scientific Notation
• Comparing Numbers Using Scientific
Notation
• Writing Numbers between 0 and 1 in
Scientific Notation
Module 4: Ratio and Proportion
Unit 1: Ratio
• Defining Ratio
• Expressing Ratio as Equivalent Fractions and
Decimals
• Forming Ratios Between Unlike Quantities
Unit 2: Proportion
• Defining Proportion
• Solving for a Variable in a Proportion
• Applying the Means/Extremes Property
Unit 3: Direct and Inverse Variation
• Exploring and Solving Direct Variation
Problems
• Exploring Inverse Variation
• Solving Inverse Variation Problems
Unit 4: Similar Polygons
• Defining Similarity
• Identifying Equivalent Ratios
• Setting Up and Solving Proportions in Similar
Polygons
Module 5: Fundamentals of Statistics
Unit 1: Interpreting and Constructing Graphs
• Exploring Line Graphs
• Exploring Bar Graphs
• Interpreting Pie Charts
33
Training Manual
Destination Math
Mastering Skills and Concepts: Course V
Unit 2: The Mean, Median, and Mode
• Defining Mean and Median
• Defining Mode
• Calculating the Mean, Median, and Mode
Unit 3: Frequency Distribution and Histograms
• Creating and Interpreting a Frequency Chart
• Defining a Histogram
• Exploring Cumulative Frequency Charts
Module 6: Fundamentals of Probability
Unit 1: Simple Probability
• Defining and Expressing Probability
• Calculating Probabilities on a Color Wheel
• Determining Probability of Complementary
Events
Unit 2: Probability of Combined Events
• Calculating the Probability of Independent
Events
• Determining the Sample Space of an
Experiment
• Calculating the Probability of Dependent
Events
Destination Math
Mastering Algebra: Course I
Module 1: The Language of Algebra
Module 3: Systems of Linear Equations
Unit 1: Variables, Expressions, & Equations
Unit 1: Graphic Solutions of Linear Systems
• Translating Words into Expressions
• Applying Properties of Real Numbers
• Evaluating & Simplifying Expressions
• Finding the Point of Intersection
• Graphing Parallel & Perpendicular Lines
Unit 2: Linear Equations in One Variable
• Applying Inverse Operations
• Transforming Equations Using Multiple
Operations
• Solving Absolute Value Equations
Module 2: Linear Functions & Equations
Unit 1: The Rectangular Coordinate Plane
• Graphing Ordered Pairs
• Defining Slope
• Finding x- & y- Intercepts
Unit 2: Introduction to Functions
• Exploring the Slope-intercept Equation of a
Line
• Exploring the Point-slope Equation of a Line
• Relations & Functions
34
Unit 2: Algebraic Solutions of Linear Systems
• Using Substitution to Eliminate a Variable
• Using Addition and Subtraction to Eliminate
a Variable
Module 4: Linear Inequalities
Unit 1: Inequalities in One Variable
• Applying Inverse Operations
• Graphing Solutions on a Number Line
• Solving Absolute Value Inequalities
Unit 2: Inequalities in Two Variables
• Graphing Solutions on a Rectangular
Coordinate Plane
• Solving Systems by Graphing
Training Manual
Destination Math
Mastering Algebra: Course II
Module 1: The Real Number System
Unit 1: Rational & Irrational Numbers
• Defining the Real Numbers
• Working with Radicals
• The Square Root Function
Module 2: Powers and Polynomials
Unit 1: Polynomial Arithmetic
• Working with Powers
• Adding & Subtracting Polynomial
Expressions
• Multiplying Polynomials
Unit 2: Factoring Polynomials
Module 4: Algebraic Equations & Functions
Unit 1: Radical Functions & Equations
• Solving Radical Equations
• The Inverse of the Square Root Function
Unit 2: Rational Functions & Equations
• Rational Operations
• Rational Functions
• Rational Equations
Module 5: Describing Data
Unit 1: Statistical Displays
• Scatter Plots & Best-fit Curves
• Stem-and-leaf Plots & Box Plots
• Finding Common Factors
• Factoring Quadratic Trinomials
• Special Cases
Module 3: Quadratic Functions & Equations
Unit 1: Graphic Quadratic Functions & Equations
• Graphing Parabolas
• Analyzing Properties of Parabolas
• Solving Quadratic Equations by Graphing
Unit 2: Solving Quadratic Equations Using
Algebra
• Factoring & the Zero Product Theorem
• The Square Root Method & Completing the
Square
• The Quadratic Formula
35
Introduction to
Print Materials
7
In this section, you will become familiar with the Destination Success Math print materials.
These materials provide for student accountability and classroom integration. For classroom
implementation flexibility, at the top of each page is space for students to record their names
and the date.
For Destination Math: Mastering Skills and Concepts: Courses I and II, the print materials
include classroom extension activities for each session.
36
Training Manual
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Training Manual
For Destination Math: Mastering Skills and Concepts: Courses III through IV, the following print
materials are included:
Student Logbook—to be used during the tutorial
• The layout contains the course, module, unit, and session headings at the top of the page.
• The right margin of the page contains the learning objectives and keywords for the session.
• The questions and statements on the page follow the sequence of the content in the tutorial.
• The problems include fill-in-the-blank and brief constructed responses.
• The question contents include definitions, rules, and other related key math concepts.
Your Turn—to be used as a follow-up to workouts, as a homework page or for in-class work
• The layout contains the course, module, unit, and session headings at the top of the page.
• The problems focus on the content presented in the tutorial.
• The problems have been constructed to correlate to the session's learning objectives.
• The problems include fill-in-the-blank, multiple choice, and brief constructed responses.
• The problems include skill-building and application-based examples.
Unit Review
• The questions are arranged by session, with appropriate session titles identified on the page.
• The last section, titled “Putting It All Together,” integrates objectives of individual sessions for a
cumulative unit problem.
• The problems include fill-in-the-blank, multiple choice, and brief constructed responses.
Unit Assessment
• These sheets are two-sided pages.
• The questions have been designed to correlate to the learning objectives of the unit.
• The problems include fill-in-the-blank, multiple choice, brief constructed responses, and extended
responses.
For Destination Math: Mastering Algebra: Courses I and II, the print materials include the
student logbook, your turn, unit assessment and a unit investigation.
Unit Investigation
• These sheets are two-sided pages.
• The questions have been designed to correlate to the learning objectives of the unit.
• The problems are alternative assessment based, designed to explore an algebraic concept that
serves as the theme for the unit.
The print materials also include a table of contents and an annotated answer key. The print
materials can be found on our Web site at www.riverdeep.net or on the main login page of
your Destination Success LMS v3.0 Portal.
41
Training Manual
Activity 1:
Using the Print Materials
1. Access the session from the sample logbook sheet that
applies most closely to your grade level.
2. Complete the tutorial as a student by filling out the
logbook.
3. Keep track of the time to see how long it would take
your students to go through the tutorial while filling out
the logbook. Remember that completion time will vary
depending on the length of the tutorial and the work
habits of the student who completes the tutorial.
4. Complete at least one workout and then fill out the Your
Turn page.
5. For MSC Courses III–V and MA Courses I and II, complete
at least one student logbook workout, and then
complete the Your Turn page. MSC Course I and II print
materials engage students in hands-on learning activities
as well as written assignments.
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Training Manual
SAMPLE DESTINATION ACTIVITIES
Course: MSC III; Module 2: Unit 1: Addition and Subtraction of Whole Numbers; Whole
Number Sums
Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 2: Operations with Numbers
UNIT 1: Addition and Subtraction
of Whole Numbers
Whole Number Sums
As you work through the tutorial, complete the following.
1. What is your mission for this lesson? ________________________
_________________________________________________________
Key Words:
Sum
Estimate
2. The lengths of four of the Great Lakes are given in this chart.
Great Lake
Length
(miles)
Superior
350
Huron
206
Erie
241
Ontario
193
Rounded Values
(miles)
a. Round each length to the nearest hundred, and write the values
in the chart.
Plus sign (+)
Commutative
Property of Addition
Learning
Objectives:
• Estimate the sum
of two or more
3-, 4-, and 5-digit
numbers.
• Find the sum of
two or more
3-, 4-, and 5-digit
numbers.
• Check an addition
by using the
Commutative
Property of
Addition.
b. What is the estimated length in miles of the journey from Lake
Superior to Lake Ontario? _________
3. When you add the actual lengths of the lakes, the sum of the
numbers in the ones place before regrouping is _____ .
4. You can represent ten ones with the digit _____ in the ones place and
the digit _____ in the tens place.
5. The sum of the numbers in the tens place before regrouping is _____ .
6. You can regroup 19 tens by writing the digit _____ in the tens place
and the digit _____ in the hundreds place.
7. The sum of the numbers in the ____________________ place is 9.
Destination
Math
43
Training Manual
Course: MSC IV; Module 1: Fractions; Unit 1: Essentials of Fractions: Recognizing a Fraction
Name ___________________________________
Date ________________________
COURSE: MSC IV
MODULE 1: Fractions
UNIT 1: Essentials of Fractions
Recognizing a Fraction
As you work through the tutorial, complete the following
statements and questions.
1. “Fraction” comes from the Latin word meaning __________ .
2. When describing gases that make up Earth’s atmosphere:
a. how many of the 5 equal parts of the circle represent nitrogen?
__________
b. how many of the 5 equal parts represent oxygen and other
gases? __________
c. does the air we breathe have more nitrogen or more oxygen
and other gases? _______________________________________
d. explain how you decided on your answer to part c. _________
______________________________________________________
Key Words:
Fraction
Numerator
Denominator
Learning
Objectives:
• Learning that a
fraction is a part
of a whole through
the use of area
models
• Identifying the
numerator and
denominator of a
fraction
• Identifying
fractional parts of
a whole number
based on a
diagram
3. What symbol is used to describe an approximate value? _________
4. When describing the Earth’s surface:
a. how many of the 10 equal parts of the circle represent water?
__________
b. how many of the 10 equal parts of the circle represent land?
__________
5. Create an example of how fractions can describe the people present
in your classroom today. Be sure to include a diagram, a fraction,
and a description for each diagram.
Destination
Math
44
Training Manual
Course: MSC V; Module 2: Fundamentals of Geometry; Unit 2.1 Geometry Fundamentals;
Naming and Measuring Angles
Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 1: Geometry Fundamentals
Naming & Measuring Angles
In the figure below, PO ⊥ TM and RO is parallel to SM. Use the letters to
name as many examples of each of the following as you can.
1. a right angle __________
S
P
R
2. an obtuse angle __________
3. a straight angle __________
M
O
4. a pair of parallel line segments
T
__________
5. a pair of perpendicular line segments __________
Defining Complementary & Supplementary Angles
In the diagram below, ⬔BOD is a right angle. Use the diagram to complete
the questions.
C
D
B
40°
A
50°
40°
E
O
6. Name two acute angles that make up ⬔AOC.
______________________
7. Name an angle complementary to ⬔BOC. __________________________
8. Name an angle supplementary to ⬔COE.
__________________________
destination
MATH
45
Training Manual
Mastering Algebra Course I; Module 1: The Language of Algebra; Unit 2: Linear Equations in
One Variable; Session 1 Applying Inverse Operations
Name _______________________________________
Date ___________________________
MASTERING ALGEBRA I: Course 1
MODULE 1: The Language of Algebra
UNIT 2: Linear Equations in One Variable
Applying Inverse Operations
Your
Turn
1. If ⫺6 is added to the right side of the equation x ⫹ 6 ⫽ 9, what is the
expression on the left side of the equation?
____________________________________
2. For which equations is x ⫽ 18? ____________
a. 3x ⫽ 54
b. x ⫺ 8 ⫽ 10
c. 4 ⫹ x ⫽ 14
3. For each of the following equations, identify an inverse operation that
can be used to find the solution.
a. x ⫹ 5 ⫽ 10 ____________ ______
b. y ⫺ 24 ⫽ 7 ____________ ______
c. ( 61ᎏ )t ⫽ 9 ____________ ______
d. 4n ⫽ 12 ____________ ______
4. Rewrite the formula C = dy solved for the variable d in terms of C and y.
________________________
5. A music teacher purchased 3 compact discs for a music class. The total
cost of the CDs including tax was $51.84.
a. If x represents the cost of one CD, what equation represents the total
cost of all of the CDs? ____________
b. Solve for x to find the cost of each CD. ____________
destination
MATH
46
Hands-on
Exploration
and Discussion
8
You, as a teacher, will want to be familiar with the lessons before the students experience them.
Destination Success Math is a flexible program, and there are many different ways to use it.
Here are just a few.
• You may want all your students to go through the tutorial individually.
• You may want to use the tutorial as an introduction or conclusion to a lesson; if so, you can present
this lesson to the whole class by using a projection device, stopping it at any time to do
independent work or board work.
• You may want to use part of the tutorial as a quick review before starting a new topic—for
example, as a refresher on prerequisite skills for a new topic.
• You may want to use the workouts as daily math problems, using a projection device for the whole
class to work on and using Show Me as the last teachable moment.
• You may want to use the tutorial for the whole class and the workouts individually.
47
Training Manual
Activity:
Exploration
Some concepts may be presented entirely differently from the way you normally present them.
This strategy accommodates the fact that students have different learning styles and may need
to see different ways of solving problems. As an exploration exercise, follow these steps:
1. Take 20 minutes and go into various tutorials and
workouts based on topics you will be covering in the next
few weeks and months.
2. Take a look at the content, how it is taught, and think
about the different ways in which you could incorporate
this into your classroom.
Mark down the ones you like or dislike.
48
Classroom
Management
of Technology
9
Implementation Models—Best Practices
To facilitate your experience as a teacher in getting the greatest student benefits using
programs from Riverdeep, we suggest the following best practices, which have proven to be
successful in classrooms.
Presentation or Demo Model
Presenting lessons that introduce, reinforce, enrich, or extend concepts—using a projection
device connected to a computer for whole- or small-group instruction— can include these
techniques:
1. Begin with what students already know.
Select a lesson that shows a concept students already know. Move to what they do not
know while integrating new concepts in small increments.
2. Establish learners’ intrinsic need for the learning.
Link concepts to what students relate to and want to learn about. Students tend to learn
best when they make connections between what they are learning and what they relate
to—tie concepts to applications and topics that interest them.
3. Provide real-life applications.
Transfer what is learned in the presentation lesson to practical situations. Allow students
to see how the new skills apply to their own specific needs. Foster discussions of ways to
actively incorporate the new skills and allow time for students to practice these new
skills.
4. Create and maintain learners’ interest.
Be excited yourself! Encourage students to take an active part in the learning process.
Capitalize on the interactive and engaging Riverdeep lessons by involving students at
every opportunity.
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Training Manual
5. Foster discussion and active participation.
Use group discussions, demonstrations, projects, and real-life applications to tap the
students’ experiences and willing participation. Allow students to lead the presentations
while “teaching” each other.
6. Give students choices about their learning.
Allow them to be involved in determining which lessons or parts of lessons they want to
have presented. Some lessons lend themselves best to individual exploration, while
others are appropriate when experienced in presentation mode. After lessons are
introduced in the classroom in presentation mode, students can work individually on
them when lab or classroom computers are available.
7. Use flexible pacing and provide direction, integration, and extension at every
opportunity. Elicit students’ expectations and understanding as the lesson is being
presented. Rethink and readjust goals, outcomes, and pacing if necessary.
8. Give informational materials to students.
Reinforce and enhance the information presented in the lessons by expecting students to
take notes, and by giving them logbooks that accompany each lesson as well as
handouts of key points and reference material guides.
9. Provide recognition, encouragement, and approval.
Encourage students to share personal experiences. Maintain good eye contact. Be an
active listener when they are sharing and respond to them positively.
Lab Model
Maximizing instruction during computer lab time can be accomplished with these best
practices:
• Provide one computer per student to accommodate the whole class. This is optimal for
individualized instruction.
• Have two or more sessions per week on the curricular area of focus.
Note: If schedules don’t allow for optimal lab time for all students, provide for
focused groups of students.
Empowerment and participation of teachers can contribute greatly to the success of the
implementation. Experience has shown the following teacher actions to be key:
• Remain in the lab with students.
• Actively engage in instruction and the learning process during lab time.
• Integrate and extend the lab instruction with classroom instruction.
• Regularly review and discuss program reports and progress with students by using lab time to
conduct one-on-one conferences with them.
• On occasion have all students work on the same lesson as a group.
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Training Manual
Computers-in-the-Classroom Model
Best practices for providing for students to use computers on a rotation basis include:
• Post a schedule of times/students/assigned computers to assure equity of access and maximum use
of computers.
• Schedule additional access to computers for students who need focused enrichment or
remediation.
• Schedule computer time before and after school and at the end of lunch period as well as during
center time. A worthy goal to strive for can be to have all computers in use every minute of the day.
• Use the presentation or demo model to introduce concepts to whole or small groups of students
and provide individual access to classroom or lab computers as a follow-up.
• Have volunteers help students who are working on the computers. Consider student assistants,
classmates, and parent or community volunteers.
Set clear expectations about attentiveness to lessons and care of computers. If misuse occurs,
loss of privilege is often an effective consequence.
51
Meeting
the Challenge
10
Technology isn’t a discrete content area—it’s a dynamic knowledge-building tool that can play
an important role in all levels and subjects of instruction. Building on the knowledge base and
techniques you’ve gained, you can incorporate technology successfully into a variety of lessons
for a variety of purposes.
Note: Using technology in your curriculum effectively means developing ideas—a
process that can’t end today. It’s important to review what you’ve learned in this
training, discuss your ideas with each other, and use your creativity to build on
technology in your unit and lesson plans.
Let’s not teach technology for technology’s sake—let’s refrain from isolating computer skills or
relying on mere skill and practicing repetitive programs. A computer in the hands of an inspired
student is much more than a glorified typewriter, video game, or passive electronic textbook.
Let’s lead students to use the computer as a tool for learning— creating, analyzing,
communicating, and researching.
Students learn by exploring, experimenting, discovering, organizing, making decisions, and
expressing their growing knowledge. We must give them a context that encourages and
facilitates higher levels of learning. Just memorizing facts and mastering isolated sets of skills
won’t prepare them for today’s workplace or meaningful citizenship.
Let’s meet the challenge of preparing students for their futures rather than teaching them
based on our past. A curriculum offers instruction, but technology makes the ride more
interesting.
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www.riverdeep.net
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