5th Grade Math student-ebook-course-11

Reciprocals Renderings, 580
calculating, 156–160 Representation
defined, 157, 260, 350
in division of fractions, 281, 359 Formulate an equation, 61, 66, 70, 71, 76, 79, 80,
product of, 349 85, 114, 134, 135, 143, 148, 159, 219, 229, 237,
242, 247, 252, 270, 283, 296, 312, 382, 387,
Rectangles 388, 396, 415, 416, 623
area of, 164–168, 364–365, 474
formula for, 200 Manipulatives/Hands-On, 8, 13–15, 32, 33, 37,
characteristics of, 333 38, 45, 48–50, 72, 76, 78, 82, 88–91, 94, 98,
drawing, 319 104, 107, 109–111, 115, 121, 125–129, 136–138,
lines of symmetry, 574 140, 142, 143, 148, 149, 151, 162, 163, 221,
as parallelograms, 334, 371 230, 231, 245, 248, 251, 257, 265, 282, 286,
perimeter of, 364–365, 474 289, 291, 301, 302, 305, 315, 352, 364–366,
similar, 568–569 369–371, 379, 394, 398, 405, 408, 415, 425,
as squares, 334 427, 429, 435, 459, 469, 483, 492, 500, 501,
vertices of, 365 504, 505, 509, 516, 518, 523, 530, 543, 544,
558, 560, 562, 563, 575, 577, 584–585, 596,
Rectangular prisms 600, 605, 608, 614, 616, 618, 625–626
attributes of, 314
bases of, 426 Model, 38, 42, 45, 94, 97, 98, 100, 104, 109, 110,
cubes as, 497 115, 119, 120, 121, 125, 126, 129, 135–138,
drawing, 314, 315 140, 143, 148, 149, 151, 159, 217, 223, 224,
faces of, 315 230, 237, 245, 247, 252, 256, 260, 274, 275,
surface area of, 497 279, 284, 288, 294, 305, 312, 324, 334, 355,
volume of, 426–430 367, 369, 370, 379, 394, 398, 401, 402, 406,
408, 414, 416, 425, 430, 440, 458–459, 462,
Reducing fractions 467, 469, 476, 478, 485, 492, 501–502, 510,
by canceling, 358–362, 376 516, 521, 528, 530, 537, 550, 558, 560, 565,
common factors in, 150–155, 175 576, 577, 603, 613, 615, 622, 629
by grouping factors equal to one, 280–285
manipulatives for, 136–140 Represent, 10, 11, 14, 16, 17, 31, 34, 35, 44, 45,
before multiplying, 493–496 48, 49, 53, 54, 55, 57, 62, 76, 80–81, 86, 90,
prime factorization for, 346–348 91, 103, 106, 110, 115, 116, 121, 127, 131, 135,
rules for, 307 142, 147, 155, 162, 163, 222, 224, 257, 271,
and units of measure, 423 279, 284, 296, 304, 315, 318, 319, 323, 325,
339, 344, 348, 356, 357, 365–367, 370, 373,
Reflections (flips) of geometric figures, 562–564 388, 396, 415, 416, 435, 486, 487, 530, 560,
Regrouping in subtraction of mixed numbers, 188, 570, 610, 615, 624, 635

250–253, 329–332 Representative samples, 214
Regular polygons, 44, 311 Rhombus, 333–334, 596
Relationships Right angles, naming, 146–147
Right triangles, 410, 485
of corresponding sides, 569 Roosevelt, Franklin D., 81
inverse operations. See Inverse operations Roots. See Square roots
ratios and proportions, 431–432, 442–443, 529 Rotational symmetry, 575
remainders-divisors, 15 Rotations (turns) of geometric figures, 562–563
sides to angles in triangles, 484 Rounding. See also Estimation
sides to vertices in polygons, 311
spatial, in cube faces, 315 decimals, 268–271
Relative frequency, 470 estimating by, 83
Remainder halfway rule, 83
in decimal division, 236 money, 268–270
divisors and, 15 with number lines, 82
as mixed numbers, 132–135 whole numbers, 82–86
writing, 582 Rounding up, 83
of zero, 99 Rule of three, 452
Reminders. See Memory aids Rules. See also Order of Operations
Renaming. See also Naming for decimal division, 276–277
fractions of functions, 498–499
for reducing fractions, 307
multiplying by one, 221–224, 290 of sequences, 50
purpose of, 307
SOS memory aid, 295–298 S
without common denominators, 285–294
mixed measures, 593 Sample, 55
mixed numbers, 306–309 Samples, representative, 214

680 Saxon Math Course 1

Sample space, 300 Solids (cont.) INDEX
Scale faces of, 314–319
geometric, 314–319
in drawings and models, 52, 578–581 investigations of, 314–319
drawing to, 578–581 vertices of, 315, 319, 631
models, 578–581 volume of, 630–636
on rulers, 38
temperature, 51, 52 Solving equations. See Equations
Scale factor, 432, 578–581 SOS method
Scalene triangles, 484, 485
Scales, 50–57 adding mixed numbers, 306–309
Segments. See also Lines for fraction problems, 295–298, 342, 349
bisecting, 417–418 fractions chart from, 375
in creating complex shapes, 484 Spatial relationships, 315
defined, 37 Spheres, 314
length of, 37, 353–357 Spinners, 300–301, 380
on line graphs, 95 “Splitting the difference,” 52
lines and rays, 36–41 Square (sq.), 165
measuring, 38, 39 Square angles, 146
naming, 353–354 Square centimeters (cm2), 164, 197, 409, 422
properties of, 37 Squared numbers
symbol for, 37, 353 exponents of, 195–199, 380–381
Separating, word problems about, 58–62, 187, 188, 250 inverse of, 197
Sequences perfect squares of, 460–464
addition, 50 Square feet (ft2), 164
even number, 51 Square inches (in.2), 164
multiplication, 50 Square meters (m2), 164
odd number, 51 Square miles (mi2), 164
types of, 50–57 Square roots
Shapes, complex. See Complex shapes calculators for finding, 462
Short-division method, 15 defined, 262
SI (International System of Units), 37 estimating, 460–464
Sides exponents and, 195–199
corresponding, 567–569 inverse of, 197
of parallelograms, 369 of perfect squares, 460–464
and perimeter, 107 symbol for (∙∙), 197
of polygons, 311 Squares
of quadrilaterals, 311 area of, 165, 196–197, 474
of regular octagons, 311 as bases of pyramids, 315
of regular polygons, 44, 311 characteristics of, 333
of squares, 43, 107 as faces of Platonic solids, 315
of triangles, 484 as parallelograms, 334
Signs. See Symbols and signs perimeter of, 43, 72, 474
Signed numbers as rectangles, 334
adding, 543–547 as rhombuses, 334
defined, 543 sides of, 43, 107
electrical-charge model, 543–547 Square units, 164, 196–197, 365
product of, 587–589 Squaring a number, 196–197, 380
quotient of, 588 Stack, 338
Sign Game, 543–545 Standard notation, 170, 593–594
Similar figures, 566–572 Standard number cubes, 18
Simple interest, 606 Statistical operations. See also Data
Simplifying mean, 95, 266
calculators for, 231–232 median, 266
decimals, 231–234 mode, 266
fractions, 276–279 range, 266
order of operations for, 29, 436–440, 480 Stem-and-leaf plots, 267
for problem-solving, 20, 23, 63, 295–298, 306–309, Substitution, 475
Subtraction. See also Difference
342, 349, 375–379 addition as inverse of, 9, 10
SOS memory aid, 295–298 checking answers, 9, 20, 61, 251
Solids commutative property in, 8, 10
area of, 316–317, 630–636 of decimals, 9, 191–194, 276–277
edges of, 315, 497
from whole numbers, 195–199
681
Index

Subtraction (cont.) Symbols and signs (cont.)
for division (cont.)
elapsed-time, 68–72, 170–171 bar (—), 14, 133, 385
dollar sign ($), 8, 13
fact families, 7–11 dots
for multiplication (•), 12–13, 422
of fractions on number cubes, 18, 68
as period in abbreviations (.), 38
with common denominators, 127–131, 342 equal to (=), 47, 110, 381, 453
fraction bar (—), 14, 133, 385
with different denominators, 285–294 greater than (>), 47, 110, 381
of inequality
SOS memory aid, 295–298 greater than (>), 47, 110, 381
less than (<), 47, 110, 381
three-step process, 295–298 less than (<), 47, 110, 381
lines (↔), 37, 353
from whole numbers, 187–190 in multiplication
dot (•), 12, 13, 422
of integers, 517–523 parentheses (), 13, 31
×, 12, 441
later-earlier-difference, 170 negative numbers (-), 73, 543
opposite numbers (-), 544
“less than” in, 75 parentheses ( ) for multiplication, 12, 13, 422
percent (%), 174, 390
minuends role, 8, 19 points, 353
positive numbers (+), 543, 587
of mixed measures, 592–596 ratios (:), 122
rays (→), 37, 353
of mixed numbers segments (—), 37, 353
square root (∙∙), 197, 262
process for, 136–140
Symmetry, 573–578
with regrouping, 188, 250–253, 329–332
T
using common denominators, 329–332
Temperature, 51. See also Thermometers
from whole numbers, 187–190 Tens

of money, 7–11, 379 base ten number system, 64, 179
in decimals, 182
of negative numbers, 74 dividing using mental math, 272–276
factors of, 100
order of operations, 9, 29 multiplying by, 13

place value in, 9 with mental math, 239–243
multiplying decimals by, mentally, 255–256
subtrahends role, 8, 19 Tenths, 179
Terms
of units of measure, 421–425 of fractions, 157, 343
of sequences, 50
unknown numbers in, 18–22, 60–61 Theoretical probability, 470
Thermometers, 51, 52, 517
of whole numbers, 7–11 Thinking skills, 3, 4, 8, 9, 13, 14, 15, 20, 24, 29, 37, 51,
52, 59, 64, 69, 82, 90, 94, 102, 106, 112, 117, 128,
and decimals, 195–199 136, 141, 142, 146, 151, 161, 171, 175, 179, 188,
192, 201, 214, 218, 232, 236, 240, 246, 250, 251,
word problems 255, 269, 272, 290, 307, 326, 330, 332, 336, 337,
346, 349, 354, 358, 359, 363, 364, 381, 382, 391,
about comparing, 68–72 396, 409, 418, 427, 428, 448, 452, 457, 471, 472,
484, 485, 488, 504, 508, 517, 519, 525, 528, 528,
about separating, 58–62, 188 534, 543, 551, 553, 557, 558, 562, 574, 593, 612,
618, 622, 623, 626, 627
elapsed-time, 68–72 Thousands, 64, 183, 533
Thousandths, 533
words that indicate, 75 Three-step method, 295–298
Tick marks on number lines, 46, 74, 88
Subtraction patterns, 60, 68–70, 171

Subtrahends, 8, 19

Sum-of-digits divisibility tests, 113

Sums, 8, 83. See also Addition

Sunbeam as metaphor, 37

Supplementary angles, 353–357, 369, 504, 508

Surface area. See Area

Surfaces, 145

Surveys. See also Qualitative data; Quantitative date

analyzing data from, 5–57, 211, 215

bias in, 214

closed-option, 57

conducting (collecting data), 55, 57, 211–215

displaying data from, 56–57, 212–215

open-option, 57

in probability experiments, 470–471

samples, 55–56, 213–214

Symbols and signs. See also Abbreviations

approximately equal to (≈), 246, 462
calculator memory keys, 608

of comparison

approximately equal to (≈), 246, 462
equal to (=), 47, 381

greater than (>), 47, 110, 381

less than (<), 47, 110, 381

degrees (°), 161

for division

(÷), 14 box ( ∙_____), 14
division

682 Saxon Math Course 1

Time, 170. See also Elapsed-time Unknown numbers (cont.) INDEX
Timekeeping systems, 170 missing products, 123
Totals, ratio problems involving, 528–532 in proportions, 432, 442–443
Trailing zeros, 14 in rate problems, 123
Transformations of figures in sequences, 50
in subtraction, 18–22, 60–61
reflections (flips), 562–564 in word problems, 59, 60
rotations (turns), 562–563
translations (slides), 562–563 Unknowns, 20
Translations (slides) of geometric figures, 562–563 U.S. Customary System, 37, 404–405, 534. See also
Transversals, 503–507
Trapeziums, characteristics of, 333 Units of measure
Trapezoids, characteristics of, 333 U.S. military system of timekeeping, 170
Tree diagrams, 524 Use logical reasoning. See Problem-solving
Triangles
activity, 408–409 strategies
acute, 485
angles, sum of measures, 508–512 V
area of, 408–412, 474
classifying, 311, 484–487 Variables, isolating, 19
congruent, 562, 566–567 Vertex (vertices)
equilateral, 484, 485
as face of Platonic solid, 315 of angles, 146, 147
isosceles, 484, 485 of polygons, 311
lines of symmetry, 574 of rectangles, 365
obtuse, 485 of solids, 315, 319, 631
perimeter of, 474 Vertical axis, 95, 363
as polygons, 484 Vocabulary. See Math language; Reading math
right, 410, 485 Volume
scalene, 484, 485 bases of solids and, 318
sides of of cones, 631–633
of cubes, 318, 428
for classification, 484 of cylinders, 626–629, 631–633
relationship to angles, 484 defined, 426
similar, 567–568 of prisms, 630–631
Triangular prisms, 314, 316 of pyramids, 630–631
Trillions, 63–67 of rectangular prisms, 426–430
Turns, measuring, 465–469, 508–509 units of measure, 426, 627
Two-step equations, 13, 553–556
W
U
Water, freezing and boiling points of, 51
Unit multipliers, 597–601. See also Conversion Weight versus mass, 533–537
Units of measure. See also Measurement; Mixed Whole numbers

measures adding, 7–11
for area, 164, 197, 365, 422, 618 to decimals, 195–199
arithmetic with, 421–425
capacity, 404–405 counting numbers and, 46
converting, 598 defined, 46
of length, 37–38, 43, 164, 422 dividing, 12–18
mass and weight, 533–535
metric system, 37, 38, 404–405 decimals by, 235–238
reducing, 423 doubling, 51
speed, 423 even and odd, 51
uniform, 43 in expanded notation, 169–173
U.S. Customary System, 37, 404–405, 534 factors and, 102, 105
for volume, 426, 627 finding the
Unknown numbers. See also Missing numbers
in addition, 18–22 when fraction is known, 612–616
checking answers, 19, 20, 25–26 when percentage is known, 621–625
defined, 20 fractional parts of, 32–35, 117–121
in division and multiplication, 23–27 multiplying, 12–18, 588
in equal groups, 78–81 on number lines, 46
in fractions and decimals, 225–230 place value in, 64
rounding, 82–86
subtracting, 7–11
decimals, 195–199
fractions from, 187–190
mixed numbers from, 187–190

Index 683

Whole numbers (cont.) X
writing
with decimal points, 195–199 x-axis, 363
as fractions, 151, 342 x symbol for multiplication, 12, 441

Width, abbreviation for, 475 Y
Win-loss ratio, 123
Work backwards. See Problem-solving strategies y-axis, 363
Write a number sentence or equation. See Problem- Years. See Age, calculating; Elapsed-time

solving strategies Z
Writing. Also see Communication
Zero
decimals. See Decimals in division, 14
equations, 19, 543 in expanded notation, 169
exponents, 196, 380–381 exponents and, 381
fractions. See Fractions in multiplication, 14
large numbers, 64–65 opposite of, 74
money, 79, 195 as placeholder, 205–215, 277
numbers. See Expanded notation; Proportions; as power, 381
properties of, 51, 73, 74, 101
Standard notation remainders of, 99
percents. See Percents in rounding, 82
proportions, 432 sign of, 73, 74
ratios, 385–389 trailing, 14
remainders, 582 in whole numbers, 46
whole numbers
Zero property of multiplication, 14
with decimal points, 195–199
as fractions, 151, 342

684 Saxon Math Course 1

Structured for Results.

Like an elegant tapestry, a complicated, structured
beauty exists inside mathematics. To fully grasp its
beauty, you must peel back its layers to reveal its
essence—its core. Saxon Math Course 1 contains a
distinct look and approach that reveal and develop
the core of mathematics. More importantly, our core
positions students for success.

ISBN 1-5914-1783-X

90000
9 781591 417835