California Mathematics Grade 6 Noteables (California Mathematics Grade 6)

302 Pages·2008·10.36 MB·English

by  Glencoe / McGraw-Hill

Contributing Author
Dinah Zike
Consultant
Douglas Fisher, Ph.D.
Director of Professional Development
San Diego, CA
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Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the
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no part of this book may be reproduced in any form, electronic or mechanical, including
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Send all inquiries to:
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ISBN: 978-0-07-879263-2 California Mathematics Grade 6 (Student Edition)
MHID: 0-07-879263-0 Noteables™: Interactive Study Notebook with Foldables™
1 2 3 4 5 6 7 8 9 10 009 16 15 14 13 12 11 10 09 08 07
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Contents
4-3 Problem-Solving Investigation:
Make an Organized List . . . . . . . . . . . .84
Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 4-4 Simplifying Fractions . . . . . . . . . . . . . .85
Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . .2 4-5 Fractions and Decimals . . . . . . . . . . . . .87
1-1 A Plan for Problem Solving . . . . . . . . . .4 4-6 Fractions and Percents . . . . . . . . . . . . .90
1-2 Powers and Exponents . . . . . . . . . . . . . .6 4-7 Percents and Decimals . . . . . . . . . . . . .92
1-3 Squares and Square Roots . . . . . . . . . . .8 4-8 Least Common Multiple . . . . . . . . . . . .94
1-4 Order of Operations . . . . . . . . . . . . . . .10 4-9 Comparing and Ordering Rational
1-5 Problem-Solving Investigation: Numbers . . . . . . . . . . . . . . . . . . . . . . . .96
Guess and Check . . . . . . . . . . . . . . . . . .12 Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . .98
1-6 Algebra: Variables and Expressions . . .13
1-7 Algebra: Equations . . . . . . . . . . . . . . . .15
1-8 Algebra: Properties . . . . . . . . . . . . . . . .18
1-9 Algebra: Arithmetic Sequences . . . . . .20 Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102
1-10 Algebra: Equations and Functions . . . .23 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . .103
Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . .26 5-1 Estimating with Fractions . . . . . . . . . .104
5-2 Adding and Subtracting Fractions . . .106
5-3 Adding and Subtracting Mixed

Numbers . . . . . . . . . . . . . . . . . . . . . . .108
Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
5-4 Problem-Solving Investigation:
Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . .32
Estimate Possibilities . . . . . . . . . . . . . 110
2-1 Integers and Absolute Value . . . . . . . .34
5-5 Multiplying Fractions and Mixed
2-2 Comparing and Ordering Integers . . .36
Numbers . . . . . . . . . . . . . . . . . . . . . . .111
2-3 The Coordinate Plane . . . . . . . . . . . . . .38
5-6 Algebra: Solving Equations . . . . . . . .113
2-4 Adding Integers . . . . . . . . . . . . . . . . . .41
5-7 Dividing Fractions and Mixed
2-5 Subtracting Integers . . . . . . . . . . . . . . .44
Numbers . . . . . . . . . . . . . . . . . . . . . . .115
2-6 Multiplying Integers . . . . . . . . . . . . . . .46
Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . .117
2-7 Problem-Solving Investigation:
c.
n Look for a Pattern . . . . . . . . . . . . . . . .48
nies, I 2-8 Dividing Integers . . . . . . . . . . . . . . . . .49
mpa Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . .50 Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120
o
C Vocabulary Builder . . . . . . . . . . . . . . . . . . . . .121
Hill 6-1 Ratios . . . . . . . . . . . . . . . . . . . . . . . . . .123
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a 6-2 Rates . . . . . . . . . . . . . . . . . . . . . . . . . .125
Gr Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
c 6-3 Measurement: Changing Customary
M Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . .55
The 3-1 Writing Expressions and Equations . . .57 Units . . . . . . . . . . . . . . . . . . . . . . . . . .128
of 6-4 Measurement: Changing Metric
n 3-2 Solving Addition and Subtraction
o Units . . . . . . . . . . . . . . . . . . . . . . . . . .131
si Equations . . . . . . . . . . . . . . . . . . . . . . .59
Hill, a divi 33--34 SPorolvbinlegm M-Suolltviipnlgic aIntivoens tEigqautaiotino:ns . . . . .61 66--56 APDrlrogabewble rama D:- SSiaoogllvvriiannmgg I.Pn .r vo.e p.s o.t i.rg t.ia o.t .ni o.s n .. :.. .. .. .. .. ..113346
w- Work Backward . . . . . . . . . . . . . . . . . . .63
Gra 3-5 Solving Two-Step Equations . . . . . . . . .64 6-7 Scale Drawings . . . . . . . . . . . . . . . . . .137
Mc 6-8 Fractions, Decimals, and Percents . . .140
oe/ 3-6 Geometry: Perimeter and Area . . . . . .67 6-9 Percents Greater Than 100% and
nc 3-7 Functions and Graphs . . . . . . . . . . . . . .69
e Percents Less than 1% . . . . . . . . . . . .142
Gl Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . .72
© Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . .144
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Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76
Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . .77
4-1 Prime Factorization . . . . . . . . . . . . . . .79
4-2 Greatest Common Factor . . . . . . . . . . .81
California Mathematics Grade 6 iii
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Contents
10-2 Complementary and Supplementary
Angles . . . . . . . . . . . . . . . . . . . . . . . . .230
Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . .148 10-3 Statistics: Display Data in a Circle
Vocabulary Builder . . . . . . . . . . . . . . . . . . . . .149 Graph . . . . . . . . . . . . . . . . . . . . . . . . . .232
7-1 Percent of a Number . . . . . . . . . . . . .151 10-4 Triangles . . . . . . . . . . . . . . . . . . . . . . .236
7-2 The Percent Proportion . . . . . . . . . . .153 10-5 Problem-Solving Investigation:
7-3 Percent and Estimation . . . . . . . . . . .155 Use Logical Reasoning . . . . . . . . . . . .238
7-4 Algebra: The Percent Equation . . . . .157 10-6 Quadrilaterals . . . . . . . . . . . . . . . . . . .239
7-5 Problem-Solving Investigation: 10-7 Similar Figures . . . . . . . . . . . . . . . . . . .241
Determine Reasonable Answers . . . .159 10-8 Polygons and Tessellations . . . . . . . . .243
7-6 Percent of Change . . . . . . . . . . . . . . .160 10-9 Translations . . . . . . . . . . . . . . . . . . . . .245
7-7 Sales Tax and Discount . . . . . . . . . . . .162 10-10 Reflections . . . . . . . . . . . . . . . . . . . . . .247
7-8 Simple Interest . . . . . . . . . . . . . . . . . .165 Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . .250
Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . .167

Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . .254
Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . .172
Vocabulary Builder . . . . . . . . . . . . . . . . . . . . .255
Vocabulary Builder . . . . . . . . . . . . . . . . . . . . .173
11-1 Area of Parallelograms . . . . . . . . . . . .257
8-1 Line Plots . . . . . . . . . . . . . . . . . . . . . . .175
11-2 Area of Triangles and Trapezoids . . .258
8-2 Measures of Central Tendency and
11-3 Circles and Circumference . . . . . . . . .260
Range . . . . . . . . . . . . . . . . . . . . . . . . .177
11-4 Area of Circles . . . . . . . . . . . . . . . . . . .262
8-3 Stem-and-Leaf Plots . . . . . . . . . . . . . .180
11-5 Problem-Solving Investigation:
8-4 Bar Graphs and Histograms . . . . . . . .184
Solve a Simpler Problem . . . . . . . . . . .263
8-5 Problem-Solving Investigation:
11-6 Area of Complex Figures . . . . . . . . . .264
Use a Graph . . . . . . . . . . . . . . . . . . . . .188
11-7 Three-Dimensional Figures . . . . . . . .266
8-6 Using Graphs to Predict . . . . . . . . . . .189
11-8 Drawing Three-Dimensional
8-7 Using Data to Predict . . . . . . . . . . . . .191
Figures . . . . . . . . . . . . . . . . . . . . . . . . .268
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8-8 Using Sampling to Predict . . . . . . . . .193 o
11-9 Volume of Prisms . . . . . . . . . . . . . . . .270 p
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8-9 Misleading Statistics . . . . . . . . . . . . . .195 11-10 Volume of Cylinders . . . . . . . . . . . . . .271 rig
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Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . .197 Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . .273 t ©
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Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . .201 cG
Vocabulary Builder . . . . . . . . . . . . . . . . . . . . .202 Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . .278 raw
Vocabulary Builder . . . . . . . . . . . . . . . . . . . . .279 -H
999---123 SSTiahmmep pFluele nE Sdvpaeamncteessn ..t a.. l.. C.. ..o ..u ..n ..t ..i n.. g.. .. .. .. .. .. .. .. ..220046 1122--21 ETshteim Payttihnagg Soqreuaanre T Rhoeootrsem . . .. .. .. .. .. .. .. ..228802 ill, a divis
12-3 Problem-Solving Investigation: io
Principle . . . . . . . . . . . . . . . . . . . . . . . .209 n
9-4 Permutations . . . . . . . . . . . . . . . . . . . .210 Make a Model . . . . . . . . . . . . . . . . . . .285 T of
12-4 Surface Area of Rectangular Prisms .286 he
9-5 Combinations . . . . . . . . . . . . . . . . . . .212 M
12-5 Surface Area of Cylinders . . . . . . . . . .289 c
9-6 Problem-Solving Investigation: G
Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . .291 ra
Act It Out . . . . . . . . . . . . . . . . . . . . . . .214 w
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9-7 Thoretical and Experimental ill C
Probability . . . . . . . . . . . . . . . . . . . . . .215 o
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9-8 Compound Events . . . . . . . . . . . . . . . .217 pa
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Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . .219 ies
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Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . .224
Vocabulary Builder . . . . . . . . . . . . . . . . . . . . .225
10-1 Angle Relationships . . . . . . . . . . . . . .227
iv California Mathematics Grade 6
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Organizing Your Foldables
Have students make this Foldable to help them
organize and store their chapter Foldables.
Begin with one sheet of 11" × 17" paper.
Fold
Fold the paper in half lengthwise. Then unfold.

Fold and Glue
Fold the paper in half widthwise and glue all of the edges.

Glue and Label
Glue the left, right, and bottom edges of the Foldable
to the inside back cover of your Noteables notebook.
c.
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California Mathematics Grade 6 v
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This note-taking guide is designed to help you succeed in
California Mathematics Grade 6. Each chapter includes:
CHAPTER
3
Algebra: Linear Equations and Functions
Use the instructions below to make a Foldable to help you
organize your notes as you study the chapter. You will see
Foldable reminders in the margin of this Interactive Study
Notebook to help you in taking notes.
The Chapter Opener
Begin with a sheet of 11" × 17" paper.
contains instructions and
Fold the short sides illustrations on how to make a
toward the middle.
Foldable that will help you to
Fold the top to the organize your notes.
bottom.
Open . Cut along the
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California Mathematics Grade 6 55
vi California Mathematics Grade 6
vvii__887799226633 vvii 1122//2266//0066 33::4422::3300 PPMM
Lessons cover the content of the
3–2 Solving Addition and Subtraction Equations lessons in your textbook. As your
Standard 6AF1.1 Write and solve one-step linear equations in one variable.
6MR2.4 Use a variety of methods, such as words, numbers, symbols, charts, teacher discusses each example,
graphs, tables, diagrams, and models, to explain mathematical reasoning.
BUILD YOUR VOCABULARY (pages 55–56) have students follow along and
Each MlAeIN sIDsEAon is complete the fill-in boxes. Take
(cid:129) Solve addition and Inverse operations, such as 2 from the
corrsuebtralctaiont eqeuatdions .to notes as appropriate.
equation x + 2 = 6, each other.
the California
Standards. EXAMPLES Solve an Addition Equation
Solve 14 +y= 20. Check your solution.
14 + y = 20 Write the equation.
KEY CONCEPTS ̲̲̲̲̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲̲̲̲̲ 14 from Examples parallel the
Subtraction Property of each side. Simplify.
Equality. If you subtract = examples in the textbook.
the same number from
ethaech t wsiod es iodfe sa nre emqauiant ion, Check
equal. 14 + y= 20 Write the original equation.
Addition Property of
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in Mississippi plus 4,000 is 76,000
= 6 Simplify. The solution is
reminds you to take
. 4,000 = 76,000
notes in your Foldable. California Mathematics Grade 6 59
+ 4,000 = 76,000 Write the equation.
̲ ̲̲̲̲̲ ̲̲ =̲̲ ̲̲ ̲̲̲̲̲ Subtract from
each side.
= Simplify.
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72 California Mathematics Grade 6
California Mathematics Grade 6 vii
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NOTE-TAKING TIPS
Notes are a reminder to the students as to what they learned in class. Taking
good notes can help students succeed in mathematics. The following tips will
help students take better classroom notes.
(cid:129) Before class, ask what your teacher will be discussing in class. Review
mentally what you already know about the concept.
(cid:129) Be an active listener. Focus on what your teacher is saying. Listen for
important concepts. Pay attention to words, examples, and/or diagrams
your teacher emphasizes.
(cid:129) Write your notes as clear and concise as possible. The following symbols
and abbreviations may be helpful in your note-taking.
Symbol or Symbol or
Word or Phrase Word or Phrase
Abbreviation Abbreviation
for example e.g. not equal ≠
such as i.e. approximately ≈
with w/ therefore ∴
without w/o versus vs
and + angle ∠

(cid:129) Use a symbol such as a star (★) or an asterisk (*) to emphasize important
concepts. Place a question mark (?) next to anything that you do not C
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understand. py
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(cid:129) Ask questions and participate in class discussion. t ©
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(cid:129) Draw and label pictures or diagrams to help clarify a concept. n
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(cid:129) When working out an example, write what you are doing to solve the /M
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problem next to each step. Be sure to use your own words. ra
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(cid:129) Review your notes as soon as possible after class. During this time, organize ill, a
and summarize new concepts and clarify misunderstandings. d
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Note-Taking Don’ts Tf
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(cid:129) Don’t write every word. Concentrate on the main ideas and concepts. G
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(cid:129) Don’t use someone else’s notes as they may not make sense. -H
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(cid:129) Don’t doodle. It distracts you from listening actively. m
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viii California Mathematics Grade 6
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C H A PTE
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1
1
Introduction to Algebra and Functions

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Use the instructions below to make a Foldable to help you
organize your notes as you study the chapter. You will see
Foldable reminders in the margin this Interactive Study
Notebook to help you in taking notes.
Begin with eleven sheets of notebook paper.
Staple the eleven sheets
together to form a
booklet.
Make each one 2 lines
longer than the one
before it.
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Hill C Write the chapter title
w- on the cover and label
a (cid:18)(cid:14)(cid:18)
Gr each tab with the lesson (cid:18)(cid:14)(cid:19)
The Mcon of number. (cid:42)(cid:78)(cid:84)(cid:39)(cid:79)(cid:84)(cid:85)(cid:82)(cid:1)(cid:34)(cid:79)(cid:78)(cid:65)(cid:68)(cid:49)(cid:67)(cid:76)(cid:78)(cid:71)(cid:52)(cid:84)(cid:85)(cid:82)(cid:68)(cid:34)(cid:73)(cid:69)(cid:79)(cid:67)(cid:79)(cid:79)(cid:66)(cid:1)(cid:78)(cid:84)(cid:70)(cid:66)(cid:76)(cid:49)(cid:82)(cid:73)(cid:86)(cid:79)(cid:83)(cid:79)(cid:65)(cid:76)(cid:73)(cid:69)(cid:76)(cid:78)(cid:82)(cid:78)(cid:65)(cid:77)(cid:71)(cid:78)(cid:14) (cid:18)(cid:18)(cid:14)(cid:14)(cid:21)(cid:20)
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e/ NOTE-TAKING TIP: When taking notes, it is often
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California Mathematics Grade 6 1
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C H A PTE
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1
BUILD YOUR VOCABULARY
This is an alphabetical list of new vocabulary terms you will learn in Chapter 1.
As you complete the study notes for the chapter, you will see Build Your
Vocabulary reminders to complete each term’s defi nition or description on
these pages. Remember to add the textbook page number in the second
column for reference when you study.
Found Description or
Vocabulary Term Defi nition
on Page Example
algebra
algebraic expression
[al-juh-BRAY-ihk]
arithmetic sequence
[air-ith-MEH-tik]
base
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coeffi cient righ
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defi ning the variable e/M
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domain ill, a
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equation Tf
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[ih-KWAY-zhuhn] M
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equivalent expression -H
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evaluate ies
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exponent
2 California Mathematics Grade 6
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