Holt McDougal Florida Larson Geometry

449 Pages·2009·5.71 MB·English

Holt McDougal
Florida
Larson Geometry

Best Practices Toolkit

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All rights reserved.

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ISBN 13: 978-0-547-24223-1
ISBN 10: 0-547-24223-9

1 2 3 4 5 6 7 8 9 XXX 15 14 13 12 11 10 09

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Best Practices Toolkit

GEOMETRY BEST PRACTICES TOOLKIT
Contents

Letter from Authors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Geometry Best Practices Toolkit at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Geometry Best Practices Toolkit Quick Start Guide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

Strategies for Effective Teaching

The Big Picture of Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–2

Research-Based Solutions for the Classroom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–4

Reading, Writing, Notetaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–32

Differentiated Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33–86

English Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87–118

Inclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119–148

Strategies for Success with Sample Worksheets . . . . . . . . . . . . . . . . . . . . . . . . . . . 149–172

Using Technology in the Classroom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173–178

Tips for New Teachers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179–202

Math Background Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203–244

Alternate Openers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245–327

Alternative Assessment and Scoring Rubrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328–337

Teacher Survival Activities

Start-of-School Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338–349

Before-Vacation Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350–357

Substitute Teachers’ Activities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358–381

Quick Change-of-Pace Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382–405

Bulletin Board Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406–417

Answers

Answer Key. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A1–A9

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A letter from
the authors

Dear Colleagues,

We wanted to create a program that would help your students succeed in
mathematics and make your teaching job easier. To achieve these objectives, we
reviewed and addressed the curriculum and assessment guidelines of many states
and of the National Council of Teachers of Mathematics. We also developed an
extensive collection of teacher resources to assist you in the classroom. Our overall
goal was to prepare your students both for important assessments and for future
mathematics courses.

Our commitment has always been to writing books that contain accurate
mathematics, sound pedagogy, and student-friendly presentations. We believe that a
balance of teaching approaches is generally most effective. Therefore, we combine
clear, straightforward instruction in concepts and skills with thought-provoking
student activities, relevant real-life applications, and powerful strategies for problem
solving and communication. We have also incorporated feedback from many teachers
and students nationwide who have used earlier editions or pilot materials in the
classroom.

During more than 18 years of working together as an author team, we have remained
dedicated to helping students at all levels achieve high mathematics standards. Our
textbooks provide differentiated instruction for struggling students, carefully
constructed examples and practice for the majority of students, and demanding
challenge exercises for more advanced students.

We wish you success as you strive to give every student in your classroom a quality
mathematics education.

Ron Larson
Laurie Boswell

Tim Kanold
Lee Stiff

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Geometry Best Practices Toolkit
at a Glance

What is the Geometry Best Practices Toolkit?

The Geometry Best Practices Toolkit is a collection of essays, lesson notes, activities, and other
tools that have broad use across the Geometry curriculum. When you need to repair a piece of furni-
ture, assemble a toy, hang a picture, or fi x a leaky faucet, you look into your toolkit to fi nd the right
tool for the job. Similarly, you can look into the Geometry Best Practices Toolkit to fi nd the right
tool to address a need, such as English Learner instruction or activities for substitute teachers.

How do I use the Geometry Best Practices Toolkit?

• Essays provide useful information and strategies for diversifi ed and varied classroom
instruction.

• Lesson Notes provide specifi c suggestions for customizing the lessons in the Geometry
textbook to accommodate different types of students and learning styles.

• Copymasters provide additional lessons and practice for students.

• Activities provide tools for individual student practice or group activities to accommodate
a variety of situations.

• The Quick Start Guide on the following pages identifi es toolkit resources that you can use
for a wide range of specifi c instructional needs.

What kinds of resources does the Geometry Best
Practices Toolkit include?

• Classroom and lesson strategies and tools can be found under the Strategies for Effective
Teaching section.

• Activity tools can be found under the Teacher Survival Activities section.

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Geometry Best Practices Toolkit
Quick Start Guide

When you need to . . .

You can use . . .

Review key chapter vocabulary and
provide notetaking strategies
Reading, Writing, and Notetaking
• Strategies for Reading Mathematics
(pp. 9–32)

Provide instruction for different learning
styles and adapt lessons for advanced
and below level learners

Differentiated Instruction
• Essay (pp. 33–38)
• Lesson Notes (pp. 39–86)

Provide instruction and adapt lessons
for English learners
English Learners
• Essay (pp. 87–90)
• English Learner Strategies for Math (pp. 91–94)
• Lesson Notes (pp. 95–118)

Provide instruction and adapt lessons
for students with special needs
Inclusion
• Essays (pp. 119–124)
• Lesson Notes (pp. 125–148)

Provide a variety of strategies for
learning mathematics
Strategies for Success with Sample Worksheets
• Vocabulary (pp. 149–154)
• Reading (pp. 155–160)
• Critical Thinking (pp. 161–164)
• Problem Solving (pp. 165–168)
• Manipulatives (pp. 169–172)

Learn about technologies to aid in and
enhance classroom instruction
Using Technology in the Classroom (pp. 173–178)

Learn tips for teaching and understand
common errors, especially if you are a
new teacher

Tips for New Teachers (pp. 179–202)

Better understand the mathematics in a
lesson
Math Background Notes (pp. 203–244)

Ideas for starting a lesson
Alternate Openers (pp. 245–327)

Learn how to assess students’ solutions
and provide rubrics
Alternative Assessment and Scoring Rubrics
(pp. 328–337)

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When you need to . . .

You can use . . .

Give students alternative practice and
activities
Start-of-School Activities (pp. 338–349)
Before-Vacation Activities (pp. 350–357)
Quick Change-of-Pace Activities (pp. 382–405)

Provide activities for a substitute
teacher
Substitute Teachers’ Activities (pp. 358–381)

Create a bulletin board with classroom
activities to reinforce the concepts
learned in a chapter

Bulletin Board Ideas (pp. 406–417)

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The Big Picture of Mathematics

by Dr. Ron Larson, Lead Author of the Larson Mathematics Series
What is Mathematics? You would think that this is an easy question to answer. But, it isn’t.
Was mathematics discovered or was it invented? Is mathematics a logical system that exists
devoid of applications or is mathematics a problem solving language whose very essence
is solving real-life problems? Is correct calculation an important part of mathematics or is
it only important to be able to “set the problem up” correctly? Is mathematics a system of
rules or is mathematics a way of thinking?
As mathematics teachers, it is important for us to realize that mathematics is all of these
things. We need to be careful to pass this understanding on to our students so that they will
not have a narrow answer to the question “What is Mathematics?” We need to show them the
bigger picture of mathematics.

Mathematics As Calculation

Most people equate mathematics with calculation. While this view of mathematics is too
limited, it is still true that calculation plays a critical role in mathematics.
I worry when I hear educators dismissing calculation as “something best left to calcula-
tors” or even worse, as “drill and kill.” I prefer to think about other phrases that describe
the importance of calculation, such as “practice makes perfect.”
When I drive across a bridge, I am thankful that the teacher of the civil engineer who
designed the bridge believed in the importance of correct calculation.
The point is that part of our job as mathematics teachers is to help prepare skilled profes-
sionals who can fl y planes, prescribe medicines, and do any of thousands of other techni-
cally diffi cult jobs.
But, there may be a stronger reason for teaching students to calculate correctly. It is simply
the way that students learn best. They learn specifi c examples fi rst. Generalization comes
later.
After a career in mathematics, it is clear to me that we derive important insights into a
mathematical theory when we see how it relates to actual calculations.

Mathematics As A Field of Study

Mathematics, of course, is not simply a collection of techniques for calculating sums,
products, slopes, and so on. Mathematics has content. It has a vocabulary of defi ned and
undefi ned terms. It has a collection of axioms and theorems.
The vocabulary and rules of mathematics comprise much of the curriculum we teach
from grade school through high school.
Like it or not, the vocabulary of mathematics is formal. It has to be in order to provide for
clear communication. It is important that students know the difference between an expres-
sion and an equation. We evaluate an expression. We solve an equation.
The rules of mathematics are also formal—they are rigid and unforgiving. We don’t do stu-
dents favors when we allow them to approach mathematics in a sloppy manner. Mathematics
must be approached carefully, with the confi dence that comes from knowing its rules.

Mathematics As a Modeling Language

It is diffi cult to know which of the many faces of mathematics was the fi rst to show itself on
our planet. Surely, one of the fi rst was the use of symbols and calculations to model and solve
real-life problems.

The Big Picture of
Mathematics

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Performing calculations
Using midpoint and distance formulas (1.3), finding angle measures (1.4, 1.5, 8.1),
finding area (1.7, 11.1–11.3, 11.5–11.6), using ratios and proportions (6.1, 6.2),
using the Pythagorean Theorem (7.1–7.4), using trigonometry (7.5–7.7), finding
surface area (12.2, 12.3, 12.6, 12.7), finding volume (12.4, 12.5, 12.7)

Mathematics as Calculation

Mathematics as a Field of Study

Using mathematical
vocabulary
Points, lines, planes, rays, and angles (1.1–1.5), polygons (1.6, 4.1, 8.6), inductive
and deductive reasoning (2.1, 2.3), space figures (12.1), transformations (4.7, 4.8,
6.7, 9.1, 9.3–9.7)

Knowing mathematical
principles
Using postulates (2.4), using properties of equality and congruence (2.5, 2.6),
writing proofs (2.6, 3.3, 5.1, 5.6)

Mathematics as a Modeling Language

Using mathematical models
Notation for translation (4.8), coordinate proof (5.1), composition of
transformations (9.5), indirect measurement (6.4, 7.5), vectors (9.1), matrices as
models for transformations (9.2), geometric probability (11.7), algebraic models
(throughout; see also Algebra Reviews and Skills Review Handbook)

Translating real-life
situations to mathematical
models, obtaining solutions,
then translating solutions
back into real-life contexts

Skating rink (1.7), shopping mall (2.6), roller coaster (3.4), sculpture (4.1),
sightseeing (5.5), city travel (6.6), swimming pool (7.3), carpentry (8.4), softball
(9.2), gardening (10.3), commuter trains (10.7), track (11.4), transportation (11.7),
compact discs (12.2), consumer economics (12.7)

Thinking logically
Inductive and deductive reasoning (2.1, 2.3), counterexamples (2.1), conditional
statements (2.2), using properties (2.5, 2.6), writing proofs (2.6, 3.3, 5.1, 5.6),
analysis and reasoning exercises (throughout)

Mathematics as Logical Thought

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To me, the perennial debate about the virtues of applied versus pure mathematics isn’t
productive. From a historical point of view, it seems clear that both must be taught—
hand-in-hand—from grade school through high school.
To be good at mathematics, students must understand the various types of models we use:
linear, quadratic, cubic, radical, rational, exponential, logarithmic, and trigonometric. They
must learn to translate real-life situations to mathematical models, obtain mathematical solu-
tions, and then translate those solutions back into the context of the real-life application.

Mathematics As Logical Thought

Perhaps the most diffi cult task we face as mathematics teachers is to teach our students to
think logically.
The real world is fi lled with logical fallacy—such as some advertisements and political
slogans that contain illogical arguments. As mathematics teachers, we can improve our
nation and our world by teaching careful logical thought to our students.
In light of all these things, I hope that this text helps your students get a view of the
bigger picture of mathematics.

The Big Picture of
Mathematics

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Research-Based Solutions for the Classroom

The Holt McDougal program refl ects current research in education. The Student
Edition (SE), Teacher’s Edition (TE), Best Practices Toolkit (BPT), Chapter Resource
Books (CRB), and other ancillaries provide opportunities for teachers and students to
experience a number of different learning strategies both in school and at home.

One group of instructional strategies used in this program are the instructional strategies
presented in Classroom Instruction that Works*, a publication from the Association for
Supervision and Curriculum Development. The nine strategies discussed in that publi-
cation are summarized below, along with some specifi c instances in the Holt McDougal
program.

1. Identifying Similarities and Differences

This strategy includes comparing and classifying and suggests representing
comparisons in graphic or symbolic form.

Geometry examples include exercises throughout the chapters, showing
relationships between types of fi gures, classifying geometric objects, and
utilizing concept maps.

See, for example, SE25, SE554, SE570, TE4, TE43, TE153, TE554.

2. Summarizing and Notetaking

This strategy includes deciding when to delete, substitute, or keep information
in writing a summary and using a variety of notetaking formats —e.g., outlines,
webbing, or a combination technique—and suggests encouraging students to use
notes as a study guide for tests.

Geometry examples include Key Concept and Concept Summary boxes and
Chapter Summary (SE); Strategies in Reading Mathematics, Vocabulary Strategies,
and Reading Mathematics (BPT); Notetaking Guide workbooks

See, for example, SE16, SE115, SE294, BPT9–32, BPT149–160.
3. Reinforcing Effort and Providing Recognition

This strategy includes making the connection between effort and achievement
clear to students and providing recognition for attainment of specifi c goals to
stimulate motivation.

Geometry examples include Guided Practice (SE); Essential Question, Motivating
the Lesson, Closing the Lesson, Daily Homework Quiz (TE)

See, for example, SE153, TE235–238, TE241, BPT259, BPT267.
4. Homework and Practice

This strategy includes making the purpose of homework assignments clear to stu-
dents and focusing practice assignments on specifi c elements of a complex skill.

Geometry examples include Practice Workbook; Skill Practice and Problem
Solving, Chapter Review, Extra Practice (SE); Warm-Up Exercises, Extra
Examples, Extra Practice, Homework Check, Diagnosis/Remediation (TE)

See, for example, SE101–104, SE435–438, TE177–181, TE184, TE250–253,
TE256.

* Marzano, Robert J., Debra J. Pickering, and Jane E. Pollock, Classroom Instruction that Works: Research-Based
Strategies for Increasing Student Achievement and its accompanying handbook. Alexandria, Virginia: Association
for Supervision and Curriculum Development, 2001.

Research-Based
Solutions

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5. Nonlinguistic Representations

This strategy includes creating nonlinguistic representations—including creating
graphic organizers, making physical models, generating mental pictures, draw-
ing pictures and diagrams, and engaging in kinesthetic activity—to help students
understand content in a whole new way.

Geometry examples include Technology Activities and Multiple Representations
exercises (SE); Differentiated Instruction notes (TE); Differentiating Instruction
Lesson Notes and Teaching with Manipulatives (BPT)

See, for example, SE150, SE659, TE4, TE50, TE99, TE159, TE198, BPT43, BPT169–172.

6. Cooperative Learning

This strategy includes a description of the fi ve defi ning elements of coopera-
tive learning—positive interdependence, face-to-face interaction, individual and
group accountability, interpersonal and group skills, and group processing—and
gives suggestions for grouping techniques.

Geometry examples include Grouping (TE) and Projects (CRB); Bulletin Board
Ideas (BPT)

See, for example, TE123, TE124, TE332, TE414, BPT408.

7. Setting Objectives and Providing Feedback

This strategy includes using instructional goals to narrow what students focus on
and suggests providing feedback that is specifi c to a criterion and encouraging stu-
dents to personalize their teacher’s goals and to provide some of their own feedback.

Geometry examples include Prerequisite Skills vocabulary and skills check, Before/
Now/Why in student lessons, and Activity Questions (SE); Essential Question, Key
Discovery (TE); questions, goals, and objectives given on Investigating Geom-
etry Activity, Technology Activity pages, Assessment Strategies and Rubrics with
Samples (BPT)

See, for example, SE148, SE309, SE387, TE250, TE342, TE387, TE466,
BPT328-337.

8. Generating and Testing Hypotheses

This strategy includes using a variety of structured tasks to guide students
through generating and testing hypotheses, using induction or deduction, and
suggests asking students to clearly explain their hypotheses and their conclusions
to help deepen their understanding.

Geometry examples include Exploring Geometry Activities, Open-Ended,
Extended Response, and Writing exercises throughout book (SE); Activity/Key
Discovery, Mathematical Reasoning (TE)

See, for example, SE150, SE336, SE347, SE462, TE17, TE40, TE123, TE127, TE332.

9. Cues, Questions, and Advance Organizers

This strategy includes asking questions or giving explicit cues before a learning
experience to provide students with a preview of what they are about to experience;
using verbal and graphic advance organizers, or having students skim information
before reading as an advance organizer.

Geometry examples include Animated Geometry, Before/Now/Why at start of
lessons, pre-reading lesson elements such as Key Vocabulary lists and Example
heads throughout book (SE); Essential Question (TE); Teaching Problem Solving
Strategies (BPT)

See, for example, SE73, SE406, SE600, TE196, TE259, TE399, TE542, BPT165–168.

Research-Based
Solutions

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Reading, Writing, Notetaking

Vital Skills for Today and the Future

Vital Skills Today more than ever, students need strong skills in reading, writing,
and notetaking in mathematics in order to understand course content, be successful on
important state and national assessments, and develop the ability to become indepen-
dent learners. Acquiring these skills in a Geometry course will build an important
foundation for more advanced courses and for adult life. The Holt McDougal program
provides many opportunities in the textbook and in the teacher’s materials to help
students develop their reading, writing, and notetaking skills.

Recent Research Recent brain research and classroom research in reading and
writing have provided new insights into learning and also confi rmed the value of well-
known practices of successful teachers. Although the focus of this research is often
on reading in language arts and social studies, many of the strategies also help those
reading mathematical material. Two important aspects of reading addressed by research
are vocabulary development and reading comprehension. Geometry offers substantial
learning support in these core areas.

Vocabulary Development

The textbook provides strong support to students in learning, practicing, and review-
ing vocabulary. In the Prerequisite Skills box on the opening page of each chapter, key
review words are practiced in the Vocabulary exercises. In the Big Ideas box on the
facing page, the key vocabulary words for the chapter are listed. Then, at the beginning
of each lesson, the key vocabulary for the lesson appears under the Vocabulary list, and
new vocabulary in the lesson is emphasized by boldface type with yellow highlight-
ing. Reading notes in the margin serve as a built-in vocabulary, reading, and problem
solving tutor. In the Teacher’s Edition, Reading Strategy, Vocabulary, and other notes
suggest ways teachers can help students read and learn new vocabulary words. See
SE pp. 72, 149, 225, 310, 319; TE pp. 277, 326, 505, 536.

In the Exercises, the Skill Practice exercises include vocabulary as well as writing
exercises. The Chapter Reviews provide a list of key vocabulary and include vocabu-
lary exercises. See SE pp. 19, 84, 359.

Various sections throughout the Best Practices Toolkit give specifi c suggestions for
helping students understand and remember vocabulary. The Strategies for Reading
Mathematics which follows this article on pp. 9–32 contains visual glossaries for some
of the key vocabulary in each chapter. Also see, Teaching Mathematical Vocabulary
and Reading in Math, pp. 149–160.

Reading Comprehension

Establishing a Context A useful comprehension strategy supported by both
brain and classroom research is connecting new learning to prior knowledge. This
strategy is incorporated throughout Geometry in the Before/Now/Why sections at
the beginning of chapters and Before/Now/Why lists at the beginnings of lessons.
In the Teacher’s Edition, a Motivating the Lesson note in each lesson helps teachers
give students a real-life context to help them anticipate the math facts covered in the
lesson. See SE pp. 306, 307, 370, 371, 491; TE pp. 3, 245, 416, 563, 688.

Reading, Writing,
Notetaking

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Facilitating Understanding In order to create a student-friendly book, the
authors kept these principles in mind as they wrote: Students can learn new concepts
more easily when they are presented in short sentences that use simple syntax and are
accompanied by appropriate tables, charts, and diagrams. Clear defi nitions that enable
students to determine easily whether a particular mathematical object fi ts the defi nition
or not are essential for comprehension. Students need special help in understanding
the symbols of mathematics and knowing how to use them in writing mathematical
expressions. See SE pp. 11, 43, 225.

Refl ecting on Learning An effective strategy for increasing both reading com-
prehension and thinking skills is refl ection on what has been read or learned and how
it was learned (metacognition). The Chapter Review pages in each chapter review what
students learned in the chapter. Throughout the book, students explain their reasoning
in Short Response, Extended Response, and Reasoning exercises. In the Teacher’s Edi-
tion, Essential Questions, Questioning Strategies, and Activity Assessments all suggest
questions to ask to test understanding and promote classroom discussions. See
SE pp. 295–298, 393, 405; TE pp. 165, 244, 389, 493, 534, 614.

Using Graphic Organizers Graphic organizers such as charts, Venn diagrams,
or concept maps can be especially helpful for classifying mathematical objects such
as types of numbers or types of equations. These organizers are used throughout the
textbook. See SE pp. 554, 570.

Writing Opportunities

In order to become good writers, students need frequent opportunities to practice their
writing skills. These opportunities occur throughout the textbook in the Short Response,
Extended Response, Reasoning, and Writing exercises, as well as in the Investigating
Geometry Activities. See SE pp. 40, 47, 254, 383, 716.

Effective Notetaking

Taking effective notes is an important reading, learning, and review strategy, and yet
math teachers throughout the country report that many students enter a Geometry course
with limited notetaking skills. Thus, the authors identifi ed the goal of helping students
develop their notetaking skills as an important objective of the program, and they have
incorporated many notetaking aids into the program. See, especially, the Key Concept
and Concept Summary boxes in many lessons in the textbook which carry the subhead
For Your Notebook. All of the theorems and postulates are boxed throughout the textbook
also with the subhead For Your Notebook. See also the Notetaking Guide workbooks and
overhead visuals in the teacher’s materials. See SE pp. 16, 115, 399, 415.

Reading, Writing,
Notetaking

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Copyright © Holt McDougal. All rights reserved.

7
Geometry
Best Practices Toolkit

CRISS: CReating Independence through
Student-owned Strategies

Project CRISS was founded to help develop thoughtful, independent readers and
learners through instructions based on strategies arising from scientifi cally-based
cognitive and social learning research of the past 25 years. The chart below lists the key
CRISS principles, together with examples from the Holt McDougal Student Edition
that support them.

Background Knowledge Background
knowledge is a powerful determinant of
reading comprehension. Look for intro-
ductory materials that both activate prior
knowledge and provide background knowl-
edge.

Animated Geometry, pp. 73, 149, 371;
Chapter Prerequisite Skills, pp. 148, 222,
448;
Before/Now/Why, pp. 9, 98, 250;
Skills Review Handbook, pp. 905 –931

Active Involvement Good readers are en-
gaged with the text and with their learning.
Look for methods and activities that involve
higher level thinking and motivate students
to learn.

Exploring Geometry Activities, pp. 88, 283,
526;
Chapter Review, pp. 60– 64, 513 –516;
Worked-out Examples, pp. 36, 373, 784;
Skills Review Handbook, pp. 905 –931

Discussion Students need many opportu-
nities to talk with one another about their
reading and about what they are learning.
Look for activities that open doors for
discussion, in pairs, in groups, and with the
whole class.

Exploring Geometry Activities, pp. 48, 414;
Technology Activities, pp. 185, 257, 659;
Spreadsheet Activities, pp. 799, 871;
Focus On ..., 96 –97, 204 –205, 642– 644

Metacognition Good readers are meta-
cognitive. They are goal-directed, and they
know how to interact with print to construct
meaning. Look for opportunities to help
teach students to become more aware of
their own learning through discussion and
writing as they refl ect on the how and why
of their understanding.

Throughout the text, students refl ect on
their learning and explain their reasoning.
Examples include:
Writing exercises, pp. 12, 161, 383;
Error Analysis exercises, pp. 39, 230, 419;
Challenge exercises, pp. 47, 192, 488

Writing Students need multiple opportuni-
ties to write about what they are learning.
Look for activities that occur naturally
throughout the textbook and activities in
teacher’s materials that are correlated to the
textbook.

Short Response exercises, pp. 20, 200, 395;
Extended Response exercises, pp. 22, 193,
464;
Writing exercises, pp. 109, 229, 352

Reading, Writing,
Notetaking

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