Saxon 6/5

692 Saxon Math 6/5

scalene triangle A triangle with three sides of different lengths.

All three sides of this
scalene triangle have
different lengths.

schedule A list of events organized by the times at which
they are planned to occur.

Sarah’s Class Schedule
8:15 a.m. Homeroom
9:00 a.m. Science
10:15 a.m. Reading
11:30 a.m. Lunch and Recess
12:15 p.m. Math
1:30 p.m. English
2:45 p.m. Art and Music
3:30 p.m. End of School

sector A region bordered by part of a circle and two radii.

This circle is divided into 3 sectors.

segment See line segment.
sequence A list of numbers arranged according to a
certain rule.

The numbers 2, 4, 6, 8, … form a sequence. The rule is “count
up by twos.”

side A line segment that is part of a polygon.

This pentagon has 5 sides.

similar Having the same shape but not necessarily the same
size. Similar figures are proportional.

A
D

C BE F

∆ABC and ∆DEF are similar. They have the same shape, but
not the same size.

Glossary 693

solid See geometric solid.

sphere A round geometric solid having every point on its
surface at an equal distance from its center.

sphere

spread A value that describes how the data in a set are
distributed. See also range.

5, 12, 3, 20, 15 The range of this set is 17. Range,
which is the difference between the
greatest and least numbers, is one
measure of the spread of data.

square (1) A rectangle with all four sides of equal length.

2 in.

2 in. 2 in. All four sides of this square
are 2 inches long.

2 in.

(2) The product of a number and itself.

The square of 4 is 16.

square root One of two equal factors of a number. The symbol
for the principal, or positive, square root of a number is .

A square root of 49 is 7 because 7 ¥ 7 = 49.

49 = 7

statistics A branch of mathematics that deals with the
collection, analysis, organization, and display of numerical data.

Some activities performed in statistics are taking surveys and
organizing data.

stem-and-leaf plot A method of graphing a collection of
numbers by placing the “stem” digits (or initial digits) in
one column and the “leaf” digits (or remaining digits) out to
the right.

Stem Leaf

2 135668 In this stem-and-leaf
3 0022456689 plot, 3 2 represents 32.
4 001112335778

5 0112358

694 Saxon Math 6/5

straight angle An angle that measures 180° and thus forms a
straight line.

C D Angle ABD is a straight angle.
AB Angles ABC and CBD are
not straight angles.

sum The result of addition.

7 + 6 = 13 The sum of 7 and 6 is 13.

tally mark A small mark used to help keep track of a count.

I used tally marks to count the goals
scored. I counted seven goals.

term (1) A number that serves as a numerator or
denominator of a fraction.

5 terms
6

(2) A number in a sequence.

1, 3, 5, 7, 9, 11, ...

Each number in this sequence is a term.

tessellation The repeated use of shapes to fill a flat surface
without gaps or overlaps.

tessellations

transformation The changing of a figure’s position through
rotation, reflection, or translation.

Transformations

Movement Name
flip reflection
slide translation
turn rotation

translation Sliding a figure from one position to another
without turning or flipping the figure.

translation

Glossary 695
trapezium A quadrilateral with no parallel sides.

trapezium not trapeziums

trapezoid A quadrilateral with exactly one pair of parallel
sides.

trapezoids not trapezoids

triangle A polygon with three sides and three angles.

triangles

triangular numbers Numbers that can be represented by
objects arranged in a triangular pattern.

36 10

Triangular numbers include all the numbers in this sequence:

+2 +3 +4 +5 +6

1, 3, 6, 10, 15, 21, …

U.S. Customary System A system of measurement commonly
used in the United States.

Pounds, quarts, and feet are units in the U.S. Customary System.

Venn diagram A diagram made of overlapping circles used
to display data.

3 This Venn diagram shows data on the
students’ pets. Three students do not
7 56 have a cat or a dog. Seven students
have a dog, but not a cat. Six students
dogs cats have a cat, but not a dog. And five
students have both a dog and a cat.

696 Saxon Math 6/5

vertex (Plural: vertices) A point of an angle, polygon, or
solid where two or more lines or line segments meet.

One vertex of this cube is
colored. A cube has eight
vertices.

vertical Upright; perpendicular to horizontal.

horizontal line oblique line

vertical line not vertical lines

volume The amount of space a geometric solid occupies.
Volume is measured in cubic units.

This rectangular prism is
3 units wide, 3 units high,
and 4 units deep. Its volume
is 3 · 3 · 4 = 36 cubic units.

whole numbers All the numbers in this sequence: 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, ….

The number 35 is a whole number, but 35A and 4.2 are not.
Whole numbers are the counting numbers and zero.

x-axis The horizontal number line of a coordinate plane.

y

3
2
1

–3 – 2 ––11 123 x x-axis
–2
–3

y-axis The vertical number line of a coordinate plane.

y

y-axis

3

2

1

–3 – 2 – 1 123 x
–1
–2
–3

INDEX

Note: Asterisks (*) indicate that the cited topic is covered in a lesson Warm-up.
Page locators followed by the letter “n” are references to footnotes on the indicated pages.

A Activities (cont.)
meters, 329–330
Abbreviations money, 8–10
Celsius (C), 128 multiplication table, 69
centimeters (cm), 217 parallel segments, 152
Fahrenheit (F), 128 percents, 366–367
feet (ft), 382 perpendicular segments, 152
fluid ounces (oz), 444 place value, 8–10
gallons (gal), 444 probability experiment, 303–305
grams (g), 397 seconds, fractions of, 350
inches (in.), 218 tessellations, 622–625
kilograms (kg), 397 See also Investigations; Word problems
kilometers (km), 382
liters (L), 444 Acute angles, 156, 175, 198
meters (m), 382 Acute triangles, 175
metric tons (t), 397 Addends, 20
miles (mi), 382
milligrams (mg), 397 missing, 39–40
milliliters (mL), 444 Addition, 20–22
millimeters (mm), 217
ounces (oz), 397 addends, 20
pints (pt), 444 algorithm, 21–22
pounds (lb), 397 associative property of, 116
quarts (qt), 444 commutative property of, 20
tons (tn), 397 of decimals, 377–378, 512–513, 566, 614
yards (yd), 382 estimation of sums, 524*, 528*
See also Symbols and signs fact families, 31–32, 62
of fractions
Activities
angles with common denominators, 202–204,
drawing, 200–201 598–600
measuring, 198–200
circles, measuring, 270 manipulatives to illustrate, 202–204
decimals identity property of, 21
comparing, 340 missing numbers in, 39–40
meters, parts of, 329 of mixed numbers, 214
relationship to fractions and of money amounts, 21–22, 59–60
percents, 366–367 multiplication as repeated, 58–59
fractions of one-digit numbers, 20–21
halves, 6 order of operations and, 115
manipulatives to illustrate, 98–100, place value and, 22
148–150 missing-digit problems, 58*, 62*, 72*,
relationship to decimals and
percents, 366–367 82*, 91*, 123*, 184*
of seconds, 350 subtraction as inverse of, 31–32
graphing on coordinate grid, 523 sums, 20
measuring word problems
angles, 198–200
circles, 270 combining, 43, 46–49
height, 235 “some and some more” pattern,
with meters, 329–330
46–49, 247
Algorithms, 21

addition, 21–22
division, 123–125, 166, 207
multiplication, 59
subtraction, 34–36
Alignment of digits. See Decimal points

697

698 Saxon Math 6/5 Celsius (C), 128
Center of circle, 269
Altitude (height) and volume, 533 Centigrade scale, 128
Angles, 155–156 Centimeters (cm)

activities, 198–201 cubic (cm3), 532–533
acute, 156, 175, 198 as decimal part of meter, 328–330
congruence of, 328* square (cm2), 372
formation of, 155–156 as unit of length, 217–218, 382
measuring, 198–201 Central tendency, 441
mean (average), 246–247, 439–441, 617*
with protractor, 199–201 median, 439, 441
naming, 308–309 mode, 440–441
obtuse, 156, 175, 198 See also Data
quadrilaterals, classifying by, 223–227 Cents, ¢, 17, 333
regular polygons and, 269 See also Money
right, 155, 175–176, 198 Centuries, 133
straight, 156, 198 Certain, probability of event, 284–285
symbol for, ¿, 309 Chance, 285
triangles, classifying by, 175–176 Charts. See Tables and charts
Approximation. See Estimation Circle graphs, 422
Area, 371 See also Graphs
arrays, 448*, 589* Circles, 269
calculating, 371–373, 448*, 589* activities, 270
estimating, 525, 538 center of, 269
formula for, 373 circumference of, 269
irregular polygons, 594 degrees in, 199
mental math, 594*, 598*, 613* diameter of, 269
perimeter and, 371 graphs (See Circle graphs)
of square, 372–373 measurement of, 269–270
units of, 371–372 radius (radii) of, 269
Arithmetic sequences, 1–2, 359 sectors in, 286
Arrays, 413–414, 448*, 589* Circumference, 269
Associative property of addition and Classification, 175
of quadrilaterals, 223–227
multiplication, 116 of triangles, 175–176
Average, 246–247, 439, 617* Clocks, 133–134
Axis, 472, 521–523 See also Time
Clockwise, 459
B Clusters in line plots, 253
Coins
Bar graphs, 417 flips, possible permutations of, 142*,
comparative, 486–487
creating, 417–418, 420–421 155*, 166*, 554*
data analysis and, 256, 417–421, 486–487 multiplication, 77*, 548*
histograms, 419 multiplication, rolls of, 77*, 548*, 576*
horizontal, 420–421 See also Money
interpreting, 417 Combining, word problems about, 43, 46–49
See also Data; Graphs Commas, in place value, 25–26, 263
Common denominators, 202–204, 598–600
Base and exponents, 401–403 Common fractions, 338–340
Base 5 number system, 632–633 Common years, 132
Base 10 number system, 632–633 Commutative property
Billions, in place value, 263 of addition, 20
Boiling point, 128 of multiplication, 68, 82–83, 88, 449
Comparing, word problems, 43, 45, 170–172
C

Calendars, 132–133
See also Time

Capacity, 444–445
See also Volume

Comparisons Index 699
of bar graphs, 486–487
of decimals, 340, 350–351, 549–550 Counting (cont.)
of fractions by tens, 4*
with common denominators, 598–599 by twelves, 128*, 132*, 142*, 151*,
pictures to illustrate, 189–190 155*, 162*, 180*, 184*, 258*
of lengths, 435* by twenties, 39*
numbers through hundred thousands, by twenty-fives, 39*, 46*, 52*, 58*, 62*,
25–27 101*, 242*
place value and, 26 by fifties, 30*, 34*, 52*, 62*, 67*, 77*,
symbols for, >, <, =, 12 106*
using number lines, 186 by sixties, 263*, 268*
of whole numbers, 12–13 by hundreds, 4*
in word problems, 43, 45, 170–172 by two hundred fifties, 46*, 101*
by five hundreds, 30*, 34*, 106*
Composite numbers, 412–414
See also Prime numbers Counting numbers, 1
through hundred thousands, 25–27
Computation, mental. See Mental math whole numbers and, 4
Cones, 435 writing, with words, 25–27
Congruence, 158
Cubes, 435–436, 532–533
angles, 328* volume of, 349*, 382*, 401*, 458*,
of figures, 158 508*, 532*, 532–533, 559*, 584*,
of rectangles, 298*, 307*, 397* 617*
transformations and, 458–460
triangles, 277*, 344*, 377*, 425* Cubic numbers, 401–403, 537*, 617*
Conversion Cubic units, 532–533
of decimals to fractions, 338–340 Cups, 445
of fractions Cylinders, 435

to decimals, 338–340 D
to percents, 143
of improper fractions Data, 251
to mixed numbers, 386–387 analysis, 251–257, 417–424, 472–475,
to whole numbers, 386–387 486– 487
within metric system central tendency (See Central tendency)
units of capacity, 444–445 clusters, 253
units of length, 217–218, 328–330, collecting
experiments, 285–286, 302–305
382–383 surveys, 421
units of mass, 397–398 displaying
of mixed numbers to improper fractions, using bar graphs, 256, 417–421,
486– 487
584–586 using circle graph (See Circle graphs)
of percents to fractions, 143 using frequency tables, 251–253,
of units of time, 132–133 303–306, 417–421
within U.S. Customary System using histograms, 419
using line graphs, 256–257, 472–475
units of capacity, 444–445 using line plots, 251, 253–255
units of length, 218–219, 382–383 using pictographs, 421–422
units of weight, 397–398 using pie graphs (See Circle graphs)
Coordinate planes, 521–523 using scale drawings, 573–575
Coordinates, 521 using schedules, 559–560
Counterclockwise, 459 using stem-and-leaf plots, 419–420
Counting intervals, in frequency tables, 252–253
by halves, 6 mutual exclusivity, 422
by threes, 111*, 115*, 207*, 246* outliers, 254
by fives, 77*, 82*, 87*, 91*, 111*, 115*, range, 441
spread, 441
119*, 123*, 132*, 151*, 155*
by sixes, 162*, 189*, 207*, 263*, 268*
by sevens, 119*, 123*, 189*
by eights, 189*

700 Saxon Math 6/5 Degrees, °
in angle measurement, 198–199
Days, 132 protractors, 199–201
See also Time in turn (rotation) measurement, 459
of temperature, 128–129
Decades, 133
Decagons, 157 Denominators, 96, 365–366
Decimal places, 323 common, 203
Decimal points in adding and subtracting fractions,
202–204, 598–600
adding decimals and, 377–378, 513, comparing fractions with or without,
566, 614 599
renaming fractions to have, 598–600
alignment in addition and subtraction, in common fractions, 338–340
377–378, 513, 528–529, 566, 614 equivalent fractions and, 408
fractions equal to 1, 293–294, 386–387
comparing decimals, 350–351, 549–550 fractions equal to A, 111–112
dividing decimals and, 274, 613–614 in ratios, 505
money and, 17, 60, 274, 377 reducing fractions, 426, 468
multiplying decimals, 565–566, 569–570,
Depth, 435
614 Diagrams
place value and, 322–324, 344–345
subtracting decimals and, 377–378, 513, graphs (See Graphs)
for ordinal numbers, 27
526, 566, 614 for place value, 25, 263
Decimals probability, 284
for probability experiments, 303–305
activities, 366–367 Diameter, 269
adding, 377–378, 512–513, 566, 614 Dice. See Dot cubes (dice)
comparing, 340, 350–351, 549–550 Differences, 31
dividing word problems

by decimal numbers, 613–614 about comparing, 45, 170–172
by 10, 100, and 1000, 609–610 elapsed-time, 172
by whole numbers, 603–604, 613 larger-smaller-difference, 171–172
equivalent, 354 later-earlier-difference, 172
fractions See also Subtraction
relationship to, 338–340, 365–367 Digits, 2
of seconds, 349–350 alignment of (See Decimal points)
as money amounts, 17, 59–60, 274, in even numbers, 4
expanded notation, 238, 264
322–324, 377 in odd numbers, 4
multiplying, 564–566, 614 Distance on a number line, 53–54
See also Length
by 10, 100, and 1000, 576–577 Distributive property of multiplication,
three-digit numbers, 281 259–260, 431*, 435*, 439*, 444*,
with zeros as placeholders, 528–529, 448*, 453*, 458*, 463*, 467*
Dividends, 91–92
569–570, 608–609 Divisibility, 107–108, 208–209, 354*
naming, 344–345 Division
on number lines, 334 algorithm, 123–125, 166–167, 207–208
ordering, 350–351, 548–550 answers
percents and, 365–367 checking, 124–125, 167
place value in, 322–324, 344–345 two-digit, 273–274
of decimals
using money to illustrate, 17, 59–60, by decimal numbers, 613–614
274, 322–324, 377 by 10, 100, and 1000, 609–610
by whole numbers, 603–604, 608–609,
reading, 548–550
rounding, 537–538 613
simplifying, 517–518
subtracting, 377–378, 512–513, 528–529,

566, 614
with zeros, 528–529
trailing zeros, 354, 517–518
Decimeters, 328–329

Index 701

Division (cont.) English system. See U.S. Customary
dividends, 91–92 System, units of
divisors, 91–92
“equal groups” word problems and, 103 “Equal groups” word problems
estimating and, 482, 490–491, 537, 576 average and, 246–247
factors and, 87 dividing and, 102–103
facts and fact families, 87–88 fractions and, 96–98, 230–231
of fractions, 453–455, 499–500 multiplying and, 43–45, 101–103
as inverse of multiplication, 88, 106
long division, 124–125, 166–167, 207 Equal sign, =, 12
missing-digit problems, 202*, 223* Equations, 39
of money amounts, 274, 603–604
by multiples of ten, 273–274, 609–610 addition (See Addition)
in order of operations, 115 with decimals (See Decimals)
quotients, 91–92, 166–167 division (See Division)
reading, 92 formulas, 373
remainders, 107 multiplication (See Multiplication)
one-digit division with, 106–107 one-step (See Missing numbers)
writing quotients as mixed numbers, with percents (See Percents)
194–195, 212–213, 289–290 solving, 242–243, 373, 589–590
short division, 207–208 subtraction (See Subtraction)
symbols for, ÷, —, , 87, 91–92 two-step, 242–243
by two-digit numbers, 273–274, 481–482, in word problems, 43–45, 242–243,
490–491
of whole numbers, 106–107 589–590
writing, 91–92 Equilateral triangles, 176
Estimation, 313
Division algorithm chart, 123
Division bar, —, 91–93 of area, 525, 538
Division box, , 87, 91–92 of quotients, 482, 490–491
Division sign, ÷, 91–92 of products, 313, 525, 538
Divisors, 91–92 of sums, 314
Dodecagons, 157 of weight, 439*
Dollars, $ See also Rounding
Even numbers, 4–5
fractions of, 97, 143 Exact numbers, 162
percents of, 143 Expanded form, 9, 16–17
quarter of, 97 Expanded notation, 238–239, 264
as related to percents, 143 Experiments, probability, 285–286, 302–306
See also Money Exponents, 401–403
Dot cubes (dice), 246*, 285, 302–304, 486*,
F
528*
Double-line graphs, 474–475 Faces of geometric solids, 436
Drawing Fact families

angles, 200–201 addition and subtraction, 31–32, 62
fractions, pictures of, 180–181, 189–190 multiplication and division, 88
lines and line segments, 52–53, 151–152 Factors, 68, 82, 119–120
rectangles, 181, 190 composite numbers, 412–414
with rulers (See Rulers) in division, 87, 119
scale drawings, 573–575 exponents, 401–403
triangles, 176, 377* greatest common factor (GCF), 431–432,
See also Graphs
468
E missing, 119
in multiplication, 68, 82–3
Edges of geometric solids, 436 in multiplication tables, 68
Eighths, investigation of, 147–150 prime numbers, 412–414
Elapsed-time word problems, 134, 172 Fahrenheit (F), 128–129
Endpoints, 52, 308 Feet (ft)
square, 371–372
as unit of length, 217–218, 382
Fibonacci sequence, 363, 412*

702 Saxon Math 6/5

Fifths, 147–150 Fractions (cont.)
Fifties, counting by, 30*, 34*, 52*, 62*, 67*, of money amounts, 486*, 554*, 584*,
603*
77*, 106* multiplying, 391–393
Figures. See Geometric figures to find equivalent, 407–408, 425–427
Fives using manipulatives to illustrate,
391–392
base 5 number system, 632–633 by whole numbers, 448–449
counting by, 77*, 82*, 87*, 91*, 111*, on number lines, 184–186
numerators (See Numerators)
115*, 119*, 123*, 132*, 151*, 155* percents and, 365–367
divisibility by, 107–108, 208 pictures of, interpreting, 142–143
tally marks, 54 probabilities as, 302–305
Flipping (reflecting) geometric figures, ratios as, 504–505
reading, 96
459– 460 reciprocals, 494–496, 499*, 499–500,
Fluid ounces (fl oz), 445 504*, 508*, 512*, 517*
Formulas, 373 reducing, 425–427, 431*, 435*, 439*,
Fours, divisibility by, 354* 444*, 448*, 453*, 458*, 463*,
Fourths, 96–100 467*, 467–468, 486*, 490*,
Fractions, 96 494*, 499*
renaming, 598–600
adding, 214 representing with pictures, 111–112,
with common denominators, 202–204, 180–181
598–600 rounding, 284*, 289*
using manipulatives to illustrate, of seconds, 349–350
202–204 subtracting, 214
with common denominators, 202–204,
of circles, 431*, 444* 598–599
common denominators, 202–204, using manipulatives to illustrate,
202–204
598–600 from whole numbers, 294–295,
comparing, 111–112, 189–190 317–318
to complete a whole, finding, 298–299 terms of, 425–427, 467–468
converting of time, 134
of a whole, 298–299
to decimals (and vice versa), 338–340 word problems
to percents (and vice versa), 143 “equal groups,” 96–98, 103
decimals and, 344–345, 365–367 fraction of a group, 230–231
denominators (See Denominators) writing
dividing, 453–455, 499–500 decimals and, 338–340
drawing pictures to represent, 180–181, quotients as mixed numbers, 194–195,
212–213, 289–290
189–190 with words, 96
“equal groups” word problems, 96–98,
Freezing point of water, 128
103 Frequency, 252
equal to 1, 293–294, 298* Frequency tables
equal to A, 111, 307*, 313*, 317*, 322*,
in data display, 251–253, 304–306,
338*, 365* 417– 421
equivalent, 407–408, 425–427
of a group, 230–231 relative, 304–306
half (See Half) Full turn, 360°, 459
improper (See Improper fractions)
investigations, 96–100, 147–150 G
lowest terms, 467–468
manipulatives Gallons (gal), 444–445
GCF (greatest common factor), 431–432, 468
activities, 98–100, 148–150
adding, 202–204
dividing, 453–455
multiplying, 391–392
relationships to fractions, decimals,

and percents, 365–367
subtracting, 202–204
mixed numbers (See Mixed numbers)

Geometric figures Index 703
circles (See Circles)
classifying, 175–176, 223–227 Hundred billions, in place value, 263–264
congruence of, 458–460 Hundred millions, in place value, 263–264
cubes, 435–436, 532–533 Hundreds
naming, with letters, 307–309
polygons, 156–158 counting by, 1*, 4*, 8*, 12*, 16*, 20*,
quadrilaterals (See Quadrilaterals) 25*, 82*
rectangles (See Rectangles)
solids, 435–436, 532–533 dividing decimals by, 609–610
squares (See Squares) multiplying
transformations of, 458–460
triangles (See Triangles) decimals by, 576–577
by multiples of, 137–139
Geometric sequences, 359–364 naming whole numbers and, 16–17
Geometric solids. See Solids in place value, 16–17, 25, 263–264
Geometric transformations Hundred thousands, in place value, 25,
263–264
reflections (flips), 459–460 Hundredths
rotations (turns), 458–459 as common fractions, 339
translations (slides), 458–460 as decimals, 338–340
Geometry, defined, 52 in place value, 323–324, 548
Grams (g), 397–398 writing, as decimal number, 338–340
Graphing, 521–523 Hyphens, writing numbers and, 17
Graphs
axis, 472, 521–523 I
bar (See Bar graphs)
circle (See Circle graphs) Identity property of addition, 21
to display data, 256–257, 417–424, Identity property of multiplication, 68, 407
Improper fractions, 386
472–475, 486–487
line graphs (See Line graphs) converting to mixed or whole numbers,
number lines (See Number lines) 386–387
origin, 521–523
pictographs, 421 simplifying, 476–477
pie (See Circle graphs) Inches (in.), 12–13
See also Data; Diagrams
Greater than, >, 12–13 cubic (in.3), 532–533
Greatest common factor (GCF), 431–432, square (in.2), 372–373
Inequalities, 12–13
468 in word problems, 43, 45, 170–172, 444*
Grid, coordinate, 521–523 See also Comparisons
Integers, 53
H Intersecting lines, 151, 155
See also Angles
Half Inverse operations
fraction manipulatives, 98–100 addition and subtraction, 31–32
fractions equal to, 96–100, 111–112, multiplication and division, 88, 106
307*, 313*, 317*, 322*, 338*, Investigations
365* data analysis, 251–257, 417–424, 472–475,
of a number, 4–6
warm-up problems, 162*, 166*, 175*, 486–487
268* displaying data, 417–424
fractions, 96–100, 147–150
Half lines (rays), 52 graphing, 521–523
Half turn, 180°, 459 graphs, 417–424, 472–475
Height and volume, 533 measuring angles, 198–201
Heptagons, 157 organizing and analyzing data, 251–257,
Hexagons, 157, 269, 543–544
Histograms, 419 417–424, 472–475, 486–487
Hours, 132–134 pattern recognition, 359–364
probability, 302–306
scale drawings, 573–575
solving word problems, 43–45
tessellations, 621–625
Isosceles triangles, 176

704 Saxon Math 6/5 Lines of symmetry, 542–545
warm-up problems, 467*, 494*, 517*,
K 542*, 569*, 594*, 608*, 613*

Kilometers (km), 382 Liquid measure, 444–445
metric system and, 444–445, 467*
L U.S. Customary System and, 444–445,
453*, 458*, 463*, 467*, 490*,
Larger-smaller-difference word problems, 512*, 554*
171–172
Liters (L), 444–445
Later-earlier-difference word problems, 172 Logical-reasoning problems, 193*, 217*,
LCM (least common multiple), 580–581,
238*, 263*
598–600 Long division, 123, 166, 207–208
Leap years, 132 Lowest terms, 467–468
Least common multiple (LCM), 580–581,
M
598–600
Legends, 421 Manipulatives
Length dot cubes (dice), 246*, 285, 302–303,
486*, 528*
in area formula, 373 for fractions, 98–100, 148–150, 202–204,
converting units of 365–366, 391–392
marbles, 286
within metric system, 218, 333–334, for measuring capacity, 444–445
382–383, 391*, 397*, 407*, paper, 194, 463, 307*
569* protractors, 199–201
rulers, 217–219, 329–330, 333–334
within U.S. Customary System, 218, spinners, 286, 304
246*, 258*, 277*, 382–383,
386*, 425*, 435*, 532*, 589* Marbles, 286
Mass, 397–380
measuring, with ruler, 217–219
number lines and, 53–54, 334 See also Weight
perimeter and, 268–269 Mean, 246–247, 439, 441
units of
See also Central tendency
metric system, 217–219, 382–383 Measurement
U.S. Customary System, 218, 382–383
in volume formula, 533 activities
See also Area angles, 200
Lesson reference numbers, 6n circles, 270
Less than, <, 12–13
Linear measurement. See Length of angles, 198–201
Line graphs, 256–257, 472–475 of area (See Area)
Line plots, 251, 253–255 of capacity, 444–445
Lines, 52–53 of central tendency (See Central tendency)
drawing, 54 of circles, 199, 269–270
horizontal, 52–53 of length (See Length)
intersecting, 151 linear (See Length)
naming, 308 of liquid capacity (See Liquid measure)
in number lines (See Number lines) of mass, 397–398
oblique, 52–53, 152 of temperature, 128–129
parallel, 151 of time, 132–134
perpendicular, 152 of turns, 459
segments of (See Segments) of volume, 532–533
symbol for, ù, 308 using protractors, 199–201
vertical, 52–53 of weight, 397–398
Line segments. See Segments See also Metric system; U.S. Customary

System
Median, 439–441

See also Central tendency

Index 705

Mental math Mental math (cont.)
money, 58*, 62*, 77*, 162*, 548*, 554*,
adding, estimating sum, 524*, 528* 584*, 603*
cost per unit, 542*
area, 594*, 598*, 613*, 698* fractions and, 554*, 584*, 603*
multiplying
average (mean), 617* estimating product, 532*, 569*,
580*, 589*
counting by multiples ten and one-hundred,
72*
by threes, 111*, 115*, 207*, 246* percents, 277*, 617*
perimeter, 594*, 598*, 613*
by fives, 77*, 82*, 87*, 91*, 111*, 115*, quarters and quarts, 448*, 453*
119*, 123*, 132*, 151*, 155* reciprocals, 499*, 504*, 508*, 512*, 517*
reducing, 431*, 435*, 439*, 444*, 448*,
by sixes, 162*, 207*, 263*, 268* 453*, 458*, 463*, 467*, 486*,
490*, 494*, 499*
by sevens, 119*, 123*, 189* Roman numerals
for numbers 39 and below, 476*,
by tens, 1*, 4*, 8*, 12*, 16* 481*, 486*, 490*, 494*, 499*,
504*, 508*, 512*, 517*, 524*,
by twelves, 128*, 132*, 142*, 151*, 528*, 532*, 537*, 542*
155*, 162*, 175*, 180*, 184*, for numbers 40 and above, 548*,
202*, 258* 554*, 559*, 564*, 569*, 576*,
580*, 584*, 589*, 594*, 598*,
by twenties, 20*, 25* 603*, 613*, 617*
rounding
by twenty-fives, 39*, 46*, 52*, 58*, lengths, 280*, 284*, 289*, 293*,
62*, 101*, 242* 386*, 391*
to nearest ten, 166*, 175*, 223*,
by fifties, 30*, 34*, 52*, 62*, 67*, 230*, 234*
77*, 106* to nearest hundred, 170*, 184*,
202*, 242*, 246*
by sixties, 263*, 268* score, 234*
simplifying, 504*, 508*, 517*, 524*,
by one hundreds, 1*, 4*, 8*, 12*, 16* 528*, 532*, 537*
thirds, 328*
by two hundreds, 20*, 25*, 82* time
centuries, 142*, 155*, 166*, 559*
by five hundreds, 30*, 34*, 62*, 67*, days in common years, 128*, 151*
106* days in leap years, 128*, 151*
days in weeks, 189*, 293*
distributive property, 431*, 435*, 439*, decades, 142*, 155*, 166*
444*, 448*, 453*, 458*, 463*, 467* hours in days, 155*, 277*
minutes in hours, 268*, 603*
divisibility by 4, 354* months in years, 137*, 162*, 170*,
180*
division, estimating quotient, 537*, 576* seconds in minutes, 263*, 598*
weeks in years, 137*
dozens, 175*, 184*, 202* weight
conversions, 401*, 444*, 458*, 528*,
estimating 580*, 594*

cost per unit of weight, 548* Meters (m), 328–330, 382
Metersticks, 329–330
miles per gallon, 564*

products, multiplying fractions,
532*, 569*, 580*, 589*

quotients, 537*, 576*

sums, 524*, 528*

finger or hand activities, 333*, 386*,
391*, 407*, 435*

fractions, 284*, 289*, 298*, 307*, 313*,
317*, 322*, 338*, 365*, 439*, 613*

halving, 162*, 166*, 175*, 268*, 307*,
313*, 317*, 322*, 338*, 365*

length conversions, 246*, 258*, 277*,
386*, 391*, 397*, 407*, 412*,
425*, 435*, 532*, 569*, 589*

liquid measures, 448*, 453*, 458*,
463*, 467*, 554*

logical reasoning (family problems),
184*, 189*, 202*, 207*, 212*,
223*, 234*, 242*

miles per gallon, 564*

mixed numbers, 494*, 499*

706 Saxon Math 6/5 Money
activity, 8–10
Metric system adding amounts of, 21–22, 59–60
decimal number lines and, 334 base 5 number system and, 632–633
units of cents (See Cents)
capacity, 444–445 coin problems, 77*, 142*, 155*, 166*,
length, 217–219, 382–383 548*, 554*, 576*
liquid measure, 444–445 counting by units of, 58*, 62*, 77*, 162*
weight, 397–398 decimal points and place value, 17,
59–60, 322–324, 548
Metric tons (t), 397–398 dividing amounts of, 124, 274, 603–604
Midnight, 134 dollars (See Dollars)
Miles (mi), 382 estimating, 314, 548*
Miles per gallon (mpg), 564* mills, 548
Mill, 548 multiplying amounts of, 77*, 78, 139,
Millennia, 133 281, 548*, 576*
Milligrams (mg), 397–398 notation, 17
Milliliters (mL), 444–445 percents of a dollar, 143
Millimeters (mm), 217–218, 328–330, place value and, 8–10, 22, 34–36, 59–60,
322–324, 548
333–334, 382 subtracting amounts of, 34–36, 59–60,
Millions, in place value, 263–264 263*
Minus sign, – symbols for, $, ¢, 17, 355
writing amounts of, 17, 355
for negative numbers, 53–54, 508
for subtraction, 30–31 Months in year, 132, 137*, 142*, 162*,
Minutes, 132–133, 263*, 598* 170*, 180*
Mirror images, 542
Missing-digit problems Multiples, 67
addition, 58*, 62*, 72*, 82*, 91*, 123*, dividing by multiples of 10, 273–274
least common multiple (LCM), 580–581,
184* 598–600
division, 202*, 223* in multiplication tables, 67–68
multiplication, 137*, 151*, 162*, 234*, multiplying by multiples of 10 and 100,
72*, 137–139
280*, 317*, 333*, 354*, 391*
subtraction, 106*, 115*, 128* Multiplication, 58–59
Missing numbers arrays as models of, 413–414
in division, 87–88 associative property of, 116
in “equal groups” problems, 44–45, checking answers, 124
commutative property of, 68, 82–83, 449
101–103 of decimals, 564–566
missing factors, 119 by multiples of 100, 576–577
in multiplication, 83–84, 119 three-digit numbers, 281
in subtraction, 62–64 with zeros as placeholders, 528,
in word problems 569–570, 608–610
distributive property of, 259–260
about combining, 47–49 in “equal groups” word problems, 44–45,
about separating, 44, 72–74 101–103, 247
See also Sequences estimating answers, 532*, 569*, 580*, 589*
Mixed measures, simplifying, 234–235 factors, 82–83
Mixed numbers of fractions, 391–393, 448–449
adding, 214 equivalent, 407–408
converting to improper fractions, reciprocals, 494–496
by whole numbers, 448–449
584–586 identity property of, 68, 407–408
multiplying, 617–618 as inverse of division, 88, 106
on number lines, 184–186
picturing, 193
as quotients, 194–195, 212–213, 289–290
rounding, 524–525
simplifying, 476–477
subtracting, 214
See also Fractions
Mode, 440–441
See also Central tendency

Multiplication (cont.) Index 707
missing-number problems, 83–84, 137*,
151*, 162*, 234*, 280*, 317*, Numbers (cont.)
333*, 354*, 391* fractions (See Fractions)
of mixed numbers, 617–618 improper fractions, 386–387, 476–477
of money, 77*, 548*, 576* integers, 53
by multiples (See Multiples) missing (See Missing numbers)
by one-digit numbers, 77–79 mixed (See Mixed numbers)
in order of operations, 115 negative, 53–54, 508–509
partial products, 259 odd, 4–5
as related to addition, 58–59 ordinal, 27
of rounded numbers, 538 percents of (See Percents)
symbol for, ¥, 59 positive, 608
of three-digit numbers, 277–278, 280–281 prime, 412–414
of two-digit numbers, 258–260 Roman numerals (See Roman numerals)
of whole numbers, 448–449 rounding (See Rounding)
zero property of, 68 whole (See Whole numbers)

Multiplication sign, ¥, 59 Numerators, 96
Multiplication tables, 67–69, 107–108 adding, subtracting, and comparing
fractions with common
missing-number problems and, 84 denominators, 203–204, 598–600
perfect squares, 464 in equivalent fractions, 407–408, 425–427
prime numbers, 413 in fractions equal to 1, 293–294
in fractions equal to A, 111–112
N in ratios, 504–505
reducing fractions and, 425–427,
Naming 467– 468
angles, 308–309
decimals, 344–345, 549 O
lines, 308
percents, 554–556 Oblique lines, 52–53, 151–152
points on a number line, 53–54 Obtuse angles, 156, 175, 198
polygons, 307–309 Obtuse triangles, 175–176
renaming fractions, 598–600 Octagons, 157–158, 269
triangles, 175–176 Odd numbers, 4–5
whole numbers, 16–17, 25–27, 263–264 One

Negative numbers, 53–54, 508–509 equivalent fractions and, 407–408,
N-gons, 157 425–426, 598–600
Nines, divisibility by, 208–209
Noon, 134 fractions equal to, 293–294, 598–600
Number cubes. See Dot cubes (dice) multiplication and equivalent fractions,
Number lines, 53–54
407– 408
decimals on, 334, 537–538 as multiplicative identity, 68, 407–408
fractions on, 184–186 with power of ten, 403
mixed numbers on, 184–186, 524–525 reciprocals, as related to, 494–496
negative numbers on, 53–54, 508–509 reducing fractions and, 407–408, 425–427,
rounding and, 162–163, 537–538,
467–468
524–525 subtracting fractions from, 294–295, 317
as scales, 128–129 One-digit numbers
Numbers adding, 20–21
comparing (See Comparisons) division with remainders, 106–107
composite, 412–414 multiplying by, 77–79
counting, 1, 4, 25–27 Ones, in place value, 25
decimal (See Decimals) Operations
even, 4–5, 119, 189 of arithmetic (See Addition; Division;
exact, 162
expanded form, 9 Multiplication; Subtraction)
inverse (See Inverse operations)
order of, 115

708 Saxon Math 6/5 Permutations (cont.)
tic-tac-toe, 212*
Order of operations, 115 “walk” and “wait,” 175*
See also Addition; Division;
Multiplication; Subtraction Perpendicular lines, 151–152, 521–523
Pictographs, 421
Ordinal numbers, 27 Pie charts/pie graphs, 422
Origin on coordinate planes, 521–523
Ounces (oz), 234–235, 397–398, 444–445 See also Circle graphs
Outcomes, experimental, 285–286 Pints (pt), 444–445
Outliers, 254 Placeholder, zero as, 528, 569–570, 608–609
Place value, 8–10, 322
P
in addition, 22
Parallel lines, 151–152, 223–227 base 5, 632–633
Parallelograms, 157, 223–227 chart, 25, 263, 323
Parentheses, ( ), 115 commas and, 25–26, 264
in decimals through ten-thousandths,
in coordinates, 521
order of operations and, 115–116 322–324, 338–340, 344–345,
Partial products, 259 548–550
Patterns expanded notation and, 238–239, 264
addition (“some and some more”), 46–49, money amounts and, 8–10, 34–36, 59–60,
322–324
247 powers of ten and, 403
multiplication (See “Equal groups” reading, 25–27
in subtraction, 34–36
word problems) template for, 9–10
subtraction, in whole numbers through hundred
billions, 25–27, 263
larger-smaller-difference, 171–172 Place Value Template, 9–10
later-earlier-difference, 172 Plane figures, 156–158, 435, 621–625
recognizing, 359–364 See also Angles; Circles; Polygons
tessellations, 621–625 Points, 52, 521
See also Sequences Polygons, 156–158
Pentagons area of, 372–373, 594
as polygon, 157 congruence of, 158
regular, 269 irregular, 594
symmetry in, 542–543 naming
Percents, 143, 554 letters as representations of, 307–309
activities involving, 366–367 by sides, 157–158
converting, to fractions, 143 regular, 269
decimals and, 365–367 sides of, 156–157
fractions and, 365–367 symmetry in, 542–544
of a group, 554–556 tessellations and, 621–625
interpreting pictures of, 143 vertices of, 156
mental math, 277*, 617* Pounds (lb), 397–398
symbol, %, 143, 555 Powers. See Exponents
writing, 143 Prime numbers, 412–414
Perfect squares, 464 Prisms, rectangular, 435–436, 532–533
Perimeter, 268–269 Probability, 284–286
mental math, 594*, 598*, 613* experiments, 285–286, 302–306
of rectangles, 268–269 spinners and, 286, 304–305
of squares, 269 Problem solving. See Solving equations;
of triangle, 269, 378 Warm-up problems; Word problems
Permutations, 481 Products, 68
dot cube, 246*, 486*, 528* division and, 87–88
letters, 34*, 39*, 46*, 170* estimating, 538
of socks, 504* in multiplication tables, 68
of telephone numbers, 207* partial, 259
with three elements, 34*, 39*, 46*, 52*,

67*, 87*, 111*, 142*, 170*, 175*,
180*, 371*, 453*, 481*

Products (cont.) Index 709
reciprocals of fractions and, 494–496
See also Multiplication Reading (cont.)
scales, 128–129, 333–334
Proper fractions, 386–387 tick marks, 53–54
Properties time, 133
whole numbers through hundred
associative, of addition, 116 billions, 16–17, 25–27, 263–264
associative, of multiplication, 116
commutative, of addition, 20 Reciprocals, 494–496, 499–500
commutative, of multiplication, 68, Rectangles, 226

82–83, 449 area of, 372–373, 448*, 589*
distributive, of multiplication, 259–260 congruence of, 158, 298*, 307*, 397*
identity, of addition, 21 perimeter of, 268–269
identity, of multiplication, 68, 407–408 as quadrilaterals, 157, 223–227
zero, of multiplication, 68 representing equivalent fractions with,
Protractors, 199–201
Pyramids, 435 181, 190
similarity of, 313*
Q Rectangular solids, 435–436
volume of, 532–533
Quadrilaterals, 157 Reducing, 425–427, 467–468
classifying, 223–227 mental math, 431*, 435*, 439*, 444*,
as polygons, 157
as rectangles (See Rectangles) 448*, 453*, 458*, 463*, 467*,
regular, 269 486*, 490*, 494*, 499*
as squares (See Squares) using manipulatives to illustrate, 426–427
tessellations and, 622–624 Reflections of geometric figures, 459–460
as trapeziums, 225–226 Reflective symmetry, 542–545
as trapezoids, 157, 224–227 Regrouping, 36
Regular polygons, 269
Quarters (coins), 97 Relative frequency, 304–305
See also Money Remainders, 107
in one-digit division, 106–107
Quarter turn, 90°, 459 writing quotients as mixed numbers,
Quarts (qt), 444–445 194–195, 208, 212–214, 289–290
Quotients, 91–93 Renaming fractions, 598–600
Rhombuses, 226–227
in division, two-digit, 273–274 Right angles (90°), 155–156
writing, as mixed numbers, 194–195, measurement of, 198
as quarter turns, 459
212–214, 289–290 in triangle classification, 175–176
zeros in, 166–167 Roman numerals, 629–631
See also Division See also Warm-up section in
Lessons 91–120
R Rotational symmetry, 544–545
Rotations of geometric figures, 458–459
Radius (radii), 269 Rounding, 162–163
decimals, 537–538, 549
Range, 441 lengths, 280*, 284*, 289*, 293*
to nearest
Ratios, 504–505 ten, 166*, 175*, 223*, 230*, 234*
hundred, 170*, 184*, 202*, 242*,
Rays, õ, 52–53, 308
Reading 246*
mixed numbers, 524–525
angles, 155–156 money amounts, 324
whole numbers using a number line,
decimals through ten-thousandths,
162–163
338–340, 344–345, 548–550 See also Estimation

degrees measurements of angles, 198

division problems, 91–93

expanded notation, 238–239, 264

fractions, 96, 184–186

multiplication problems, 59, 391

numbers through hundred billions,

16–17, 25–27, 263–264

710 Saxon Math 6/5 Simplifying
decimals, 517–518
Rulers improper fractions, 476–477
centimeter (cm), 217–218, 333–334 mixed measures, 234–235
inch (in.), 218–219
metersticks, 329–330 Sixties, counting by, 263*, 268*
millimeter (mm), 217–218 Sliding (translating) geometric figures,

S 458– 459
Solids, 435–436
Scale drawings, 573–575
Scale models, 575 volume of, 532–533
Scalene triangles, 176 Solving equations
Scales
one-step process (See Missing numbers)
on protractors, 199–201 two-step process, 242–243
on rulers, 217–218, 333–334 “Some and some more” word problems, 43,
on thermometers, 128–129
Schedules, 559–560 46–49, 247
Seconds, 132 “Some went away” word problems, 44, 72–74
fractions of, 349–350 Space, three dimensional, 435
warm-up problems, 263*, 564*, 598* Spatial relationships and transformations,
Sectors, 286, 304
Segments 458– 460
drawing, 54 Spheres, 435–436
horizontal, 52–53 Spinners, 286, 304
intersecting, 151 Spread, 441
naming, 308 Square centimeters (cm2), 372
oblique, 52–53, 152 Square corners, as related to right angles, 155
parallel, 151 Square feet (ft2), 371–372
perpendicular, 152 Square inches (in.2), 372–373
of polygons, 156 Square numbers, 268*, 273*, 293*, 401–402
svyemrtibcoall,fo5r2,–5à à 3à à, 308 Square roots, 322*, 463–464
Sequences, 1–2 Squares, 227
arithmetic, 359–360
of counting numbers, 1*, 1 area of, 373
cubed numbers, 537* perimeter of, 269
even numbers, 4 as quadrilaterals, 157, 223, 226–227
Fibonacci, 363, 412* symmetry in, 543–544
geometric, 359–360 Squares, perfect, 268*, 273*, 401–402
in multiplication table, 67 Square units, 371–373
number lines and, 53 Standard form, 239
odd numbers, 5 Statistics, 251
periods in, 360 Stem-and-leaf plots, 419–420
triangular numbers, 258*, 268* Story problems. See Word problems
Short division, 207–208 Straight angles, 156, 198
Sides Straight edges. See Rulers
of angles, 155–156 Strategies for estimating answers. See
area and, 373
of polygons names and, 156–157 Estimation
quadrilateral classification and, 223–227 Subtraction, 31–32, 34–36
triangle classification and, 175–176
Similar figures, 158, 313*, 338*, 407* of decimals, 377–378, 512–513
Simple probability, 284–286 alignment of digits, 377–378, 512–513,
566
with zeros, 528–529

difference, 31
exchange in, 34–36
fact families for, 31–32, 62

Subtraction (cont.) Index 711
of fractions, 202–204, 214
with common denominators, 202–204 T
with different denominators, 598–600
from 1, 294–295, 317 Tables
from whole numbers greater than 1, calendars, 133
317–318 of decimal operations, 566, 603
using manipulatives, 202–204 division algorithm chart, 123
as inverse of addition, 31 frequency, 251–253, 303–305, 417–420
in larger-smaller-difference problems, multiplication, 67–69
170–172 of ordinal numbers, 27
in later-earlier-difference problems, 172 place-value diagram, 263, 323
in long division, 123, 166, 207–208 warm-up problems, 246*, 476*, 486*,
missing-addend problems and, 39–40 580*
with missing digits, 106*, 115*, 128* See also Data
with missing numbers, 39–40, 62–64
of mixed numbers with common Tally marks, 54–55, 304
denominators, 204, 214 Temperature, 128–129
of money amounts, 34–36, 59–60 Tens
in order of operations, 115
place value and, 34–36 base 10 number system, 632
in problems about comparing, 45, counting by, 1*, 4*, 8*, 12*, 16*
170–172 dividing decimals by, 609–610
in problems about separating, 44, 72–74 divisibility by, 107–108
in “some went away” problems, 72–74 multiplying by multiples of, 72*,
symbol for, –, 30
of whole numbers, 30–31, 34–36 137–139, 576–577
across zero, 36 naming whole numbers, 16–17
in place value, 25, 263
Subtract step in long division, 123, 166, powers of, 402–403
207–208 Ten thousands, in place value, 25
Ten-thousandths, in decimal place value, 548
Sums, 20 Tenths
See also Addition as common fraction, 338–339
as decimal, 338–340
Surveys, 423–424 in decimal place value, 323–324, 548
Symbols and signs as fractions, 96–100
on number line, 334
angle, ¿, 309 writing, 338–340
bar notation, — Terms
lowest, 467–468
for division, 91–92 of sequences, 1
for fractions, 96 Tessellations, 621–625
cents, ¢, 355 Thermometers, 128–129
of comparison, >, <, =, 12 Thirds, 147–150
division bar, —, 91–92 Thousands
division box, , 87, 91–92 dividing decimals by, 609–610
division sign, ÷, 91–92 multiplying decimals by, 576–577
dollar, $, 17 in place value, 25, 263
equal sign, =, 12 Thousandths, in decimal place value,
fraction bar, —, 96
greater than inequality, >, 12 344–345, 548
less than inequality, <, 12 Three-digit numbers, multiplying by,
minus sign, –, 30
multiplication symbol, ¥, 59 277–278, 280–281
parentheses, ( ), 115 Threes
percent, %, 555
square root, Õ á, 322* counting by, 111*, 115*, 207*, 246*
times sign, ¥, 59 divisibility by, 208–209
See also Abbreviations Tick marks, 53
Symmetry, 542–545 on number lines, 53–54
on rulers, 218
Tilings (tessellations), 621–625

712 Saxon Math 6/5 Two-digit numbers
dividing, 273–274, 481–482, 490–491
Time, 133–134 multiplying, 258–260
calendars, 133
clocks, 133–134 Twos, divisibility by, 107–108
elapsed, 172 Two-step problems, 242–243
line graphs and, 472–474
mental math finding an average, 246–247
century, 142*, 155*, 166*, 559* about fractions of a group, 230–231
days in common years, 128*, 151*
days in leap years, 128*, 151* U
days in weeks, 189*, 293*
decades, 142*, 155*, 166* Units of measurement. See Measurement
hours in days, 155*, 277* U.S. Customary System, units of, 235
minutes in hours, 268*, 603*
months in years, 137*, 142*, 162*, capacity, 444–445
170*, 180* length, 218, 382
seconds in minutes, 263*, 598* liquid measure, 444–445
years, 137*, 476* weight, 397–398
units of, 132–133
V
Tons (tn), 397–398, 439*
Tools. See Manipulatives Venn diagrams, 422–424
Totals, and average, 246–247, 439 Vertex (vertices)
Trailing zeros, 354, 517–518
Transformations, 458–460 of geometric solids, 436
letters to represent, 307–309
reflections (flips), 459 lines of symmetry and, 543–544
rotations (turns), 458–459 of polygons, 156
translations (slides), 458–469 protractor use and, 199–200
Translation of geometric figures, 458–469 Volume, 532–533
Trapeziums, 225–226 of geometric solids, 532–533
Trapezoids, 157, 223–227 units of, 444–445, 532
Triangles
acute, 175–176 W
classifying by angles and sides, 175–176
congruence of, 277*, 344*, 377*, 425* Warm-up problems
drawing, 344*, 377*, 425* addition, missing digits in, 58*, 62*,
equilateral, 176 72*, 82*, 91*, 123*, 184*
isosceles, 176 angles, congruence of, 328*
naming, 175–176 area of rectangle, 448*
obtuse, 175–176 coins
perimeter of, 269, 378 multiplication, 77*, 548*, 576*
as polygon, 157 possible permutations of flips, 142*,
regular, 269 155*, 166*, 554*
rotational symmetry and, 544 congruence
scalene, 176 angles, 328*
similarity of, 338*, 407* rectangles, 298*, 307*, 397*
symmetry in, 542–543, 544 triangles, 277*, 344*, 377*, 425*
tessellations involving, 621–624 counting numbers
transformations of, 344*, 377*, 425* sequences, 1*, 189*
Triangular numbers, 242*, 258*, 268* sums of specified three-digit
Turning (rotating) geometric figures, 458–459 numbers, 25*, 30*
Turns, measuring, 459 three-digit, number of, 8*
Twelves, counting by, 128*, 132*, 142*, three-digit numbers specified digits,
12*, 16*, 20*
151*, 155*, 162*, 180*, 184*, 258* two-digit, number of, 4*
Twenties, counting by, 20*, 25* cubic units, 349*, 382*, 401*, 458*,
Twenty-fives, counting by, 39*, 46*, 52*, 508*, 532*, 559*, 584*, 617*
division, missing digits in, 202*, 223*
58*, 62*, 101*, 242*

Warm-up problems (cont.) Index 713
dot patterns, 242*, 258*
folding congruent rectangles, 307* Warm-up problems (cont.)
fractions triangular numbers, 242*, 258*, 268*
of circles, 431*, 444* years, 476*
inequalities and, 444*
inequalities, 444* Weight
lengths, 386*, 435* units of, 397–398
line of symmetry, 467*, 494*, 517*, versus mass, 397–398
542*, 569*, 594*, 608*, 613* warm-up problems, 401*, 439*, 444*,
liquid measurements, 463*, 490*, 512* 458*, 580*, 594*
missing digits
addition, 58*, 62*, 72*, 82*, 91*, Whole numbers, 4
123*, 184* adding, 20–22
division, 202*, 223* comparing, 12–13
multiplication, 137*, 151*, 162*, 234*, in decimal numbers, 344–345
280*, 317*, 333*, 354*, 391* dividing, 106–107
subtraction, 106*, 115*, 128* division by, 603–604
multiplication even and odd, 4–5
coins, 77*, 548*, 576* in expanded notation, 238–239, 264
missing digits in, 137*, 151*, 162*, factors of, 119–120
234*, 280*, 317*, 333*, 354*, multiplying, by fractions, 448–449
391* place value in, 25–27
multistep problems, 132* reciprocals of, 494–495
patterns rounding to nearest, 524–525
coin flips, 142*, 155*, 166*, 554* square roots, 463–464
combinations, 230*, 371* subtracting, 30–31, 34–36
dice combinations, 246*, 486*, 528* fractions from, 294–295, 317–318
letters, 34*, 39*, 46*, 170* writing
logical reasoning (family problems), with digits, 2
193*, 217*, 238*, 263* with words, 16–17
three-element, 34*, 39*, 46*, 52*,
67*, 87*, 111*, 142*, 170*, Width
175*, 180*, 371*, 453*, 481* in area formula, 373
percents, 170* in perimeter formula, 268
perfect squares, 617* in volume formula, 533
perimeter, 284* See also Area; Perimeter
rectangles
congruence of, 298*, 307*, 397* Word problems, 43–45
perimeter and lengths of sides, 284* addition
similarity of, 313* combining, 43, 46–49
sequences “some and some more” pattern,
counting, 1*, 189* 46–49, 247
of cubed numbers*, 537* average, 246–247
dot patterns, 258* chance and probability, 285–286
similarity about combining, 43, 46–49
of rectangles, 313* about comparing, 45, 170–172
of triangles, 338*, 407* division, 96–98, 101–103
square roots, 322* elapsed-time, 172
squares, perimeter and lengths of sides, equal groups
284* average (mean), 246–247
time, seconds in day, 564* division, 96–98, 101–103
triangles missing-number problems, 44–45,
congruence of, 277*, 344*, 377*, 425* 101–103
translations of, 377*, 425* finding information to solve, 43–45
similarity of, 338*, 407* fractions, 96–98
equal groups, 96–98, 101–103
of a group, 230–231
larger-smaller-difference pattern, 170–172

714 Saxon Math 6/5

Word problems (cont.) Zero (cont.)
later-earlier-difference pattern, 172 in multiplication
with many or no solutions, 589–590 with decimals, 576–577
missing-number by multiples of 10 and 100, 137–139
combining, 46–49 by three-digit numbers that include,
“equal groups,” 44–45, 101–103 280–281
separating, 44, 72–74 as placeholder, 528, 569–570, 608–609
multiplication, equal groups, 44–45, property of, for multiplication, 68
101–103 in quotients, 166–167
probability, 285–286 subtracting across, 36
remainders, 106–107 as whole number, 4
schedules, 559–560
separating, 44, 72–74
spinners and probability, 286
subtraction
comparing, 45, 170–172
larger-smaller-difference pattern,
170–172
later-earlier-difference pattern, 172
separating, 44, 72–74
“some went away,” 72–74
two-step, 242–243

Writing
decimals, 338–340, 354
division problems, 91–93
expanded notation, 238–239, 264
fractions, 96
money amounts, 17, 355
numbers, through hundred thousands,
25–27
percents, 143, 555
place value, 25–27
quotients as mixed numbers, 194–195,
212–213, 289–290
time, 133–134
whole numbers, 2, 16–17

X

X-axis, 521

Y

Yard (yd), 218, 382
square yards (yd2), 371

Y-axis, 521
Years, 132

Z

Zero
as additive identity, 21
in decimal addition and subtraction, 378
in money amounts, 60, 529

SStudent EditionAXON MATH™ 6/5 Hake
Saxon