5th Grade Math student-ebook-course-11

INVESTIGATION 12

Focus on
Volume of Prisms, Pyramids, Cylinders,
and Cones

Surface Area of Prisms and Cylinders

volume of As we learned in Investigation 6, a prism is a polyhedron with two
prisms and congruent, parallel bases. A pyramid is a three-dimensional object with a
polygon as its base and triangular faces that meet at a vertex.
pyramids
The height of a prism is the perpendicular distance from the prism’s base to
its opposite face. The height of a pyramid is the perpendicular distance from
the pyramid’s base to its vertex.

L1 = L2

W1 = W2

H1 H1 = H2 H2

L1 L2

W1 W2

In the figure above, the base of the pyramid is congruent to the bases of the
prism, so L1 = L2 and W1 = W2. Also, the height of the two solids is the same
so H1 = H2.

Thus, the fundamental difference between the two solids is that the pyramid
has a vertex rather than a second base. As a result, its volume is smaller. We
can see this clearly when we compare the Relational GeoSolids of the two
figures.

We know from Lesson 82 that the formula for finding the volume of a
prism is:

V = lwh

Since lw gives us the area of the base, we can also write the formula as:
V = area of B × h

We can use this formula to derive (develop) the formula for the volume of a
pyramid. To find the volume of a pyramid, we first find the volume of a similar
prism (cube).

By drawing segments from one vertex of a cube to four other vertices, we
can see how a cube can be divided into pyramids. The base of the cube is
the base of one pyramid. Its right face is the base of a second pyramid and
its back face is the base of the third pyramid.

630 Saxon Math Course 1

4�4�2 4�4�2

1

41V�of41 a�p12yramid � 6 pBy�raVm2ohifdas p�yr6ampByid�ram�2hid6spB�y�raBm2�3hidhs �
3
1 � 1 1
4 4 � 2

1 1 22
3 3 17
B � 2h
V of a pyramid � 6 B � 2h � 6 pyramids � B � h �
pyramids 3
3 B � 2h
� 6 pyramid
V of a pyramid

We vsoeleumtheatotfheeaccuhbpeyirsamdivididiesd31SitnAhteo�vtho2rlue�mea2ce72oobnfg�trh7ue2ecn�ut bp2eyS�.raAam27�2idb2s��i7nad�2i7c42abti�n7g27322t21�hat2 � a272b
the

To find the volume of one pyramid, we find the volume of 1 of a prism with
3
the same base and height.

Generalize V of a dpyerraivmedidfo=rSm31Aual�raeta2oo�ffinaBd272×thbeh�ev7iog2lhu�tm=2e�31oaf( B × h) 3 1
Use the 2e72abch� 7of�t4he 2

following pyramids. SA � 2 � a272b � 72 � 2 � a27

1. 2.

8 ft 1 1
6 ft 3 12 ft 3

5 ft

5 1 ft
3

6 ft

3.

2.8 m

2.7 m

3.1 m

volume of A cylinder is a solid with two circular bases that are opposite and parallel to
cylinders each other. Its face is curved. A cone is a solid with one circular base and
and cones a single vertex. Its face is curved. In the figure below, the base of the cone
is congruent to the bases of the cylinder, and the height of the two solids is
the same. Thus, the fundamental difference between the two solids is that
the cone has a vertex rather than a second base. As a result, its volume is
smaller.

Investigation 12 631

r1 r1

H1 H1 H2 H2
r2 r2

Using your Relational GeoSolids of a cone and a cylinder, demonstrate the
difference in volume. First fill the cone with rice or salt. Then empty the cone
into the cylinder. Repeat two more times to show that the volume of the
cylinder is three times the volume of the cone.

In Lesson 120, we learned that the volume of a cylinder can be found by

hmeuiglthiptlyoifntghethceyalinredaeor.fWtheeccairnc41ue�xlapr14ree�nssd21 and multiplying1 a�thfeo41 rr�mesu12ulalt:by the
this process as4

V of a cylinder = π ∙ r2 × h, or π ∙ r2h

Look at the figures below. Apply what we l41ea�rn41e�d 1 the volumes of a

a2 bout

prism and a pyramid to make a reasonable statement about the volum1 es of a 1
V of a py41ra�m41id��12 6 pBy�raVm2ohifdas p�yr6ampByid�ram�2hid6spB�y�raBm2�3hidhs � 631(pBBy��ram2hh
cylinder and a cone.

1 V of13Vao14Vpf�oyarfa14pam�ypriday21mr13a�imd6id�pB�y6�rapB63m2ypB�hriday�msr2ah�imd2hsi26d732�spB�y63�rapB6m2y1pB�hriday�msr21ah�i2md2712hsiBd3�s�3�BhB�3��3h
3

Recall that the volume of a pyrSaAm�id 2is�13at2h72ebv�ol7u2m�e 2ofS�aAar27e�2cbt2a�n�7gau�27l42abr p� r7is32m12� 2 3 a227722b � 7 � 4

�

with the same base and height. The same relationship is true for cones and
iSsA13 22
cylinders. That is, the volume of the cone �the2v�oalu27m2be of a �cy2lin�dae2r72wbit�h7 7
the same height and base area. � 72 4 3 1
� 2

V of a cone = 1 Ba,rethaeoafSrBeAa×�ohf2ethi�geahb2t72a=sbe31� o(7Bf2t�×heh2c)y� lain27d2ebr,�w7e�g4et: 1
insert the 3 2
3
When we formula for
a272b a272b
V of a cone = 1 (SπAr 2�h) 2 � � 72 � 2 � � 7 � 4 3 1
3 2

Generalize Use the appropriate formul1as to find the volume of each of the
following: 3

4. Leave π as π. 1 10 cm
3

5 cm

632 Saxon Math Course 1

3

1 5. Use 22 for π. Estimate to find the answer. 1 14 ft
3 7 2

9.9 ft

SA � 2 � a272b � 72 � 2 � a272b � 7 � 4 3 1 3 1
2 2

6. Leave π as π. 10 in.
1
3

surface The surface area of a prism is equal to the sum 1.2 in.
area of a of the areas of its surfaces. In Investigation 6, 10
we found that we could use a net to help us find
prism surface area.

6
8

If we compare the rectangular prism in the Relational GeoSolids to the
figures on the previous page, we see that we can find the surface area by
adding the area of the six sides.

Area of two faces (top and bottom) = (6 × 8) + (6 × 8)

Area of two faces (sides) = (6 × 10) + (6 × 10)

Area of two faces (front and back) = (8 × 10) + (8 × 10)
Thus the total surface area of the prism is 376 in.2

From this, we can develop a formula for the h
surface area of a prism:

SA = 2lw + 2lh + 2wh

w
l

Generalize Find the surface area of the following rectangular prisms.

7. 8. 11

2
2

13 cm

Investigation 12 633

surface We can think of the surface area of a cylinder as having three parts—the area
area of a of the two bases and the area of its face, its lateral surface area. A net of
cylinder the cylinder makes this easy to see.

7 mm

4 mm 7 mm

4 mm 44 mm

1 � 1 � 1
4 4 2

1 � 1 � 12Tcoircclea,41lcA�ul=a14tπe�rt2h21. eSainrceea of the circular bases, use the formula for the area of a
4 � 4 �
1 1 there are two bases, multiply the formuBla�b2y1 h2. �
4 4 1 1 1 1 V B � 2h � 6 pyramids B 3 h 31(B
2 4 � 4 � 2 of a pyArraema i=d 2�π r62 pyramids � � � h)

3

To calculate the lateral surface area, which is a rectangle, use the formula for

the area of a rectangle lw. In thi1s case, the len1gth (l) is the circumference of
ppyyWtrrhaaeemmcciiddiaVVrcn��oolecff,a66aaolcrppppBBu2yyyyl��arrπrraaaatremmmm.22Tthhiiiihddddhesse��s��wui66r66d3f13atppBBppBBhcyyyye��rr(��rrwaaaaamm22mm)22r1ehhiiihhsiiddaddsshssoe��f��igth66h3BBetppBB��o33cyyfy��rraahhltihnmm221��edhhiiddec3311ssry((laBB��inbd��oBBevrehh��33. ))Wahhse��f’oll lu3311los((wBBes2��7:2
V of a fho)r π.
V of a h)

SA3 = 2πr2 + 2π3rh

11 SA ≈ 2∙( 22 ) 2∙∙7277b22 +2 ∙ ( 22 ) ∙∙a77272∙∙b44� 1 1 1
33 SAS≈A 2�∙2( 7 +� 722 7 )� 2 2 2
11 2�72a) �∙ ( 222 7 � 4 3 1 1
33 2 2
7

SA ≈ 308 + 176

SA ≈ 484 mm2
��TAaahp22ep7722lsibbcSSua��rAAft77aio��22cne��s22a22��reaa��a22aa7722o2277bbf22tbb��h77e��2277c��31y��li44n22d��eaar2277i33s221122bbab�� o77u��t 1 1
SA � 2 4484 m3m21 2. 3 21 3 21
SA � 2 4 1 3 2 3 2
3 2

1 9. M1 artin is installing a 10-feet-tall cylindrical 2 ft
31 thr331aaondwkiumtsouoccfohtlhlewecattaternarkitnhiwsea2ttaefenr.ekHtc,eawnwhaahtnoitlsds.tthoIfetkhneow
3 10 ft

approximate volume of the tank? To wrap

the entire tank with insulation, Martin needs

to find the total surface area. Draw a net of

the cylinder and estimate the surface area.

Leave π as π.

634 Saxon Math Course 1

1
pBy1�r0am.2hidEssti�maBte�3 Lhyd�ia31i(sBm�akhin) g
V of a pyramid � 6 B � 2h � 6
pyramids
3 coffee for dinner guests and wants to know

how much ground coffee her new filter will hold. Estimate the volume of

a cone-shaped filter with a diameter of 14 cm and a height of 9 cm. Use
1 22 1
3 7 for π. 2

11. A cone is inscribed in a right cylinder as 10 in.
15 in.
shown. What is the volume of the cone?
h ft
What is the surface area of the cylinder?

SA � 2 � a272b � 72 � 2 � a272b � 7 � 4 L3e21ave π as π. 3 1
2

1
B � 2h
pyramids � B � h � 31(B � h)
3
12. Jenna’s piano teacher gave her a
1
3 pyramid-shaped metronome to count time.

22 The metronome’s base measures 4 inches
7 1
by 3 2 inches. Calculate the metronome’s

volume if its height is 9 in.

3 1 ft
2

�4 3 1 3 1 4 ft
2 2

13. Estimate Geoff and Sasha drew a sketch of a skateboard ramp they
plan to build using scrap wood. To determine how much wood they
need to build the ramp, which is shaped like a right triangular prism,
estimate the total surface area.

5.2 ft 14 ft
13 ft
7 ft

extensions a. Represent Draw a rectangular prism with the same base and height
as the pyramid shown. Calculate the volume of the prism. Units are in
meters.

4 1
3

4

6 3
4

b. Represent Sketch a cone inside the 12
pyramid shown with the same height.
The diameter of the cone’s base equals 6
the width of the pyramid’s base. Find the 6
volume of the cone. Leave π as π. Discuss Investigation 12 635
which is greater, the volume of the cone or
the volume of the pyramid.

c. Find the surface area of a cube that has a volume of 27 in.3
d. Find the surface area of a cube with an edge of 4 cm.
e. The heights of a rectangular prism with a square base and a cylinder

are equal, and the diameter of the cylinder is equal to one edge of the
prism’s square base. Develop a mathematical argument to prove that
surface areas of the two figures are not equal. (Hint: Use what you
know about the areas of circles and squares to prove your answer.)

636 Saxon Math Course 1

MATH GLOSSARY WITH SPANISH VOCABULARY

A

acute angle An angle whose measure is more than 0° and less than 90°. GLOSSARY

ángulo agudo

(28)

right angle obtuse angle

acute angle not acute angles

An acute angle is smaller than both a right angle and an obtuse
angle.

acute triangle A triangle whose largest angle measures less than 90°. obtuse
triangle
triángulo acutángulo right
triangle
(93)

acute triangle not acute triangles

addend One of two or more numbers that are added to find a sum.
7 + 3 = 10 The addends in this problem are 7 and 3.
sumando
The combining of positive and negative numbers to form a sum.
(1) We use algebraic addition to find the sum of −3, +2, and −11:
(−3) + (+2) + (−11) = −12
algebraic
addition

suma algebraica

(100)

alternate A special pair of angles formed when a transversal intersects two lines.
exterior angles Alternate exterior angles lie on opposite sides of the transversal and are
outside the two intersected lines.
ángulos alternos
externos

(97)

1

2

∠1 and ∠2 are alternate exterior angles. When a transversal
intersects parallel lines, as in this figure, alternate exterior

angles have the same measure.

alternate interior A special pair of angles formed when a transversal intersects two lines.
angles Alternate interior angles lie on opposite sides of the transversal and are
inside the two intersected lines.
ángulos alternos
internos

(97)

1
2

∠1 and ∠2 are alternate interior angles. When a transversal
intersects parallel lines, as in this figure, alternate interior
angles have the same measure.

Glossary 637

4� 20 3 �4

a.m. The period of time from midnight to just before noon.
a.m4. I get up at 7 a.m. I get up at 7 o’clock in the morning.
3� 1(322)
angle(s) The opening that is formed when two lines, rays, or segments intersect.

ángulo(s) These rays form an angle.

(28)

6R2
angle bise3c�t2o0r A line, ray, or segment that divides an angle into two congruent parts.
bisectriz

(Inv. 8) R

VST ¡V���T� isisaannaanngglelebbisiseeccttoorr..
T It divides �∠RRVVSS iinn hhaallff..

VS

area The number of square units needed to cover a surface.

área 5 in.

(31)

2 in. The area of this rectangle
is 10 square inches.

Associative The grouping of addends does not affect their sum. In symbolic form,
Property of a + (b + c) = (a + b) + c. Unlike addition, subtraction is not associative.

Addition (8 + 4) + 2 = 8 + (4 + 2) (8 − 4) − 2 ≠ 8 − (4 − 2)

propiedad asociativa Addition is associative. Subtraction is not associative.
de la suma

(5)

Associative The grouping of factors does not affect their product. In symbolic form,
Property of a × (b × c) = (a × b) × c. Unlike multiplication, division is not associative.
Multiplication
(8 × 4) × 2 = 8 × (4 × 2) (8 ÷ 4) ÷ 2 ≠ 8 ÷ (4 ÷ 2)
propiedad asociativa Multiplication is associative. Division is not associative.
de la multiplicación

(5)

average The number found when the sum of two or more numbers is divided by the
number of addends in the sum; also called mean.
promedio
To find the average of the numbers 5, 6, and 10, first add.
(18) 5 + 6 + 10 = 21

Then, since there were three addends, divide the sum by 3.
21 ÷ 3 = 7

The average of 5, 6, and 10 is 7.

638 Saxon Math Course 1

B

bar graph(s) Displays numerical information with shaded rectangles or bars.
gráfica(s) de barras
50 Average Battery Life in a CD Player
(Inv. 1)

40 This bar graph GLOSSARY
shows data for
Hours 30 three different
brands of
20 batteries.

10

0A B C

Battery Brand

base 1. A designated side or face of a geometric figure.

base

(71)

base base base

2. The lower number in an exponential expression.

base 53 exponent

53 means 5 × 5 × 5, and its value is 125.

bimodal Having two modes. 5, 1, 44, 5, 7, 13, 9, 7

bimodal The numbers 5 and 7 are the
modes of the data at right.
(Inv. 5) This set of data is bimodal.

bisect To divide a segment or angle into two equal halves.

bisecar l

(Inv. 8) A

XY B

MC

Line l bisects X��Y��. Ray MB bisects �AMC.

C

capacity The amount of liquid a container can hold.
Cups, gallons, and liters are units of capacity.
capacidad
A scale used on some thermometers to measure temperature.
(78) On the Celsius scale, water freezes at 0°C and boils at 100°C.

Celsius scale

escala Celsius

(10)

Glossary 639

chance A way of expressing the likelihood of an event; the probability of an event
expressed as a percentage.
posibilidad
The chance of snow is 10%. It is not likely to snow.
(58) There is an 80% chance of rain. It is likely to rain.

circle A closed, curved shape in which all points on the shape are the same
círculo distance from its center.

(27)

circle

circle graph A method of displaying data, often used to show information about
percentages or parts of a whole. A circle graph is made of a circle divided
gráfica circular into sectors.

(40) Class Test Grades

D A This circle graph shows data
5 students 9 students for a class’s test grades.

C
6 students

B
10 students

circumference The perimeter of a circle.
circunferencia
A If the distance from point A
(27) around to point A is 3 inches,
then the circumference of the
circle is 3 inches.

closed-option A survey in which the possible responses are limited.
survey
What is your
encuesta de opción favorite pet?
cerrada
dog
(Inv. 1) cat
bird
fish closed-option survey

common A number that is the denominator of two or more fractions.
denominator
The 52fractions 2 and 3 have com53 mon79 denomin97 ators.
denominador común 5 5

(55)

Commutative Changing the order of addends does not affect their sum. In symbolic form,
Property of a + b = b + a. Unlike addition, subtraction is not commutative.
Addition
8 + 25= 2 + 8 5 8−2≠2−8
propiedad Addition4i�s2c0omm4u�t2a0tiv13e2.� 4 S1u32b�tra4ction is not commutative.
conmutativa de la

suma

(1)

4 4
3� 12 3� 12
640 Saxon Math Course 1

Commutative Changing the order of factors does not affect their product. In symbolic
Property of form, a × b = b × a. Unlike multiplication, division is not commutative.

Multiplication 8×2=2×8 8÷2≠2÷8 GLOSSARY
Multiplication is commutative. Division is not commutative.
propiedad
conmutativa de la

multiplicación

(3)

compass A tool used to draw circles and arcs.

compás

(27)

2 radius gauge
3
1

cm 1 2 3 4 5 6 7 8 9 10

in. 1 2 3 4

pivot point
marking point
two types of compasses

complementary Two angles whose sum is 90°. �A and �B are
angles complementary angles.
A
ángulos
complementarios 60°

(69) 30°
CB

complement of The opposite of an event. The complement of event B is “not B.” The
an event probability of an event and the probability of its complement add up to 1.

complemento de un
evento

(58)

composite A counting number greater than 1 that is divisible by a number other than
number itself and 1. Every composite number has three or more factors.

número compuesto 9 is divisible by 1, 3, and 9. It is composite.
11 is divisible by 1 and 11. It is not composite.
(65)

compound Experiments that contain more than one part performed in order.
experiments

experimentos
compuestos

(Inv. 10)

compound Interest that pays on previously earned interest.
interest
Compound Interest $100.00 Simple Interest
interés compuesto $6.00
$100.00 principal principal
(116) � $6.00 first-year interest (6% of $100) � $6.00 first-year interest (6% of $100)
$112.00 second-year interest (6% of $100)
$106.00 total after one year total after two years
� $6.36 second-year interest (6% of $106)

$112.36 total after two years

compound The outcomes to a compound experiment.
outcomes

resultados
compuestos

(Inv. 10)

Glossary 641

concentric Two or more circles with a common center.
circles
common
círculos concéntricos center
of four
(27) concentric
circles

cone A three-dimensional solid with a circular base and a single vertex.

cono cone

(Inv. 6)

congruent Having the same size and shape.

congruente These polygons are congruent. They
have the same size and shape.
(60)

coordinate(s) 1. A number used to locate a point on a number line.

coordenada(s) A

(Inv. 7) �3 �2 �1 0 1 2 3

The coordinate of point A is −2.
2. An ordered pair of numbers used to locate a point in a coordinate plane.

y

3 B The coordinates of
2 point B are (2, 3). The
x-coordinate is listed first,
1 the y-coordinate second.

�3�2��11 123 x
�2
�3

coordinate plane A grid on which any point can be identified by an ordered pair of numbers.
plano coordenado
y
(Inv. 7)

3 Point A is located at
2 (�2, 2) on this
coordinate plane.
A1

�3�2�–11 123 x
–2
–3

642 Saxon Math Course 1

corresponding A special pair of angles formed when a transversal intersects two lines.
angles Corresponding angles lie on the same side of the transversal and are in the
same position relative to the two intersected lines.
ángulos
correspondientes 1

(97)

2 GLOSSARY

∠1 and ∠2 are corresponding angles. When a transversal
intersects parallel lines, as in this figure, corresponding angles

have the same measure.

corresponding Sides or angles that occupy the same relative positions in similar polygons.
parts
Z
partes
correspondientes C A

(109) B���C� corresponds to Y��Z��.

�A corresponds to �X.

B

XY

counting The numbers used to count; the members of the set {1, 2, 3, 4, 5, …}. Also
numbers called natural numbers.

números de conteo 1, 24, and 108 are counting numbers.
−253, 3.14, 0, and 279 are not counting numbers.
(9)
2
5

cross products The product of the numerator of one fraction and the denominator of

productos cruzados another.

(85) 5 � 16 � 80 20 � 4 � 80

5 12 � 4 16 � 4
4� 20 3 20 5

The cross products of these two fractions are equal.

cube A three-dimensional solid with six square faces. Adjacent faces are
cubo4
(3In�v.16)2 perpendicular and opposite faces are parallel.

cube

cylinder6 RA2three-dimensional solid with two circular bases that are opposite and
cilin3d� r2o0 parallel to each other.

(Inv. 6)

cylinder

VST ¡V T

Glossary 643

D

data Information that is gathered and organized in a way that conclusions can be
datos drawn from it.

(Inv. 4)

data points Individual measurements or numbers in a set of data.

puntos de datos A numeral that contains a decimal point.
23.94 is a decimal number because it contains a decimal point.
(Inv. 5)
Places to the right of a decimal point.
decimal number 5.47 has two decimal places.
6.3 has one decimal place.
número decimal 8 has no decimal places.

(34)

decimal places

cifras decimales

(34)

decimal point The symbol in a decimal number used as a reference point for place value.
punto decimal
34.15
(34)

decimal point

degree (∙) 1. A unit for measuring angles.

grado

(Inv. 3)

There are 90 degrees 360�
(90�) in a right angle.
There are 360 degrees
2. A unit for measuring temperature. (360�) in a circle.

100°C Water boils. There are 100 degrees between
0°C Water freezes. the freezing and boiling points
of water on the Celsius scale.

denominator The bottom term of a fraction. numerator
denominator
denominador 5
9
(6)

diameter The distance across a circle through its center.

diámetro 3 in.

(27) The diameter of this circle is 3 inches.

644 Saxon Math Course 1

559

237
559

difference The result of subtraction.
diferencia
12 − 8 = 4 52usTedh4e�t2�od0521iwffreitreennu53cme 1bi6n10e32tr�hs�:is1049p5, r1o,b2le,79m3, is 4.
12 � 4 5 12 � 4 4 1(1) An3y� 42 9 4, 5, 6, 7, 8, 9.
3 4� 20 3 3� 12 di2git o12f4the sym5bo1l0s
The 4la�s2t0digit in the13n2u�m4ber 7862 is 2.
dígito GLOSSARY

(2)

dividend A number t2hat is divided. 3 7
dividendo
11 5 52 5 4 1122 3 9 The div79idend is 12 in
1 99 (92)9 4�612035 � 12 33 each of these problems.
4 4 100 12272 ÷ 3 = 4 �54
100 4

3� 12
divisible Able to be divided by a whole number without a remainder.
divisible
5 The number 20 is divisible by 4,
(19) 12 i2nche4s� 20 1R1902523�11024034�4321�3205621�RTs4ih2necen53u2m016b÷1032e�r�42h1409a5sisnnoo97tredmivaisinibdleer.by
12 � 487 18 2 � 4 14foot �6 3,
3 73 51
62

3� 20 since 20 ÷ 3 has a remainder.

divisor 1. A number 1b=V24Sy280T4whi43c�h16522a0563nR�o1tV2h42SeTr number is divided.
divisor 3� The divisor is 3 in each¡V T
412a2 99 1122 of these pr¡oVbTlems.
100%14 100 1 21(9a20)9202 2122723÷ 3 33 �� 44
E8
2. A factor of a number.
7
7 5 A li1n2e1is2nfeocagohnmte3dse� 52n�06tafr1Roer2md3iev�1di1s0V24Sow03Tr�34hs2e06orefR1tw02.o faces of a polyhedron intersect. ¡V T
8 2a2 6 edge

arista VST 6 R V2ST One edge of this cube is ¡1V2T ¡V T
3�5220 colored blue. A cube has
(Inv. 6) 8
100% 23 20 edges.
1 2a22

endpoint A point at which a segment ends.

extremo AB

(7) Points A and B aVSreT the endpoints of segment AB.

¡V T

equation A statement that uses the symbol “=” to show that two quantities are equal.

ecuación x � 3 3 � 7 � 10 4�1 x�7

(3)

equations not equations

equilateral A triangle in which all sides are the same length.
triangle
This is an equilateral triangle.
triángulo equilátero All of its sides are the same length.

(93)

equivalent Different fractions that name the same amount.
fractions
1 � 2
fracciones 2 4
equivalentes

(42)

1 and 2 are equivalent fractions.
2 4

Glossary 645

estimate 33 44 33 �� 44 �� 1122 �� 11 99 11 iinn.. ��
33 44 33 1122 1122 22 fftt
estimar To determine an approximate value4.4

(16) We estimate that the sum of 199 and 205 is about 400.

evaluate To find the value of an expression.

evaluar To evaluate a + b for a = 7 and b = 13, we replace a with
7 and b with 13:
(73)
7 + 13 = 20

even numbers Numbers that can be divided by 2 without a remainder; the members of the

números pares set {..., −4, −2, 0, 2, 4, ...}. 44 on33e�s�11p4242lace. 55 44
Even numbers have 363�,�11o22r 44��2200 33��1122
(10) 0, 2, 4, 8 in the

event Outcome(s) resulting from an experiment or situation.

evento • Events that are certain to occur have a probability of 1.

(58) • bEEevveetwnnttessettnhhzaaett raaorreeanucdenrcoteanrienta.ninoht33at��ov22e60o60cpRRcrou22br ahbaivlietieasp2t2rh�o�a1111bt75147514afabRRlilli11atynyowf zheerroe.
•
expanded
notation A way of writing a number as the sum of the products of the digits and the

notación expandida place values of the digits. 121i21s006060w��)r+it5454te(5n 55 1122 1122 11
99 33 33 22
(32) In expanded notation 6753 10) �� 44 �� 44
(6 × 1000) + (7 ×
× + (3 × 1).

experimental The probability of an event occurring as determined by experimentation.
probability
If we roll a number cube 100 times and get 22 threes, the 11 9999
probabilidad of2121getting t4242hree 2222 15151010. 11 44 110000 1
experimental experimental probability is 110000 , or 44

(Inv. 9)

exponent The upper number in an exponential expression; it shows how many times

exponente the base is to be used as a factor.

(38) 511232 155337e72x5p. on22e1n12255t 55
v112a2lue 66
53 means 5 × 5 base its is 1155 77 88
× 5, and 88 88 77

exponential An expression that indicates that the base is to be used as a factor the 22aa22 1122
expression number of times shown by the exponent.

expresión The exponential expr4e3s=sio4n$×$41131410i0s×00e.$.$04v0110a00=0lu0�0�a060t.$4.$e0011d0000b00y00..u00s00in��g 14100a00s%%a
exponencial factor 3 times. Its value is 64.

(73)

expression A combination of numbers and/or variables by operations, but not including

expresión an equal or inequality sign.

equation inequality

3x + 2y (x − 1)2 y = 3x − 1 x < 4
expressions
not expressions

exterior angle In a polygon, the supplementary angle of an interior angle.
ángulo externo
exterior angle
(98)

646 Saxon Math Course 1

F

face A flat surface of a geometric solid.

cara One face of the cube is shaded.
A cube has six faces.
(Inv. 6)

fact family A group of three numbers related by addition and subtraction or by GLOSSARY
multiplication and division.
familia de
operaciones The numbers 3, 4, and 7 are a fact family. They make these four
facts:
(1)
3+4=7 4+3=7 7−3=4 7−4=3

factor 1. Noun: One of two or more numbers that are multiplied.
3 × 5 = 15 The factors in this problem are 3 and 5.
factor
2. Noun: A whole number that divides another whole number without a
(2) remainder.
The numbers 3 and 5 are factors of 15.

3. Verb: To write as a product of factors.
We can factor the number 15 by writing it as 3 × 5.

factor tree A method of finding all the prime factors of a number.

árbol de factores 210 The numbers on each branch of this
factor tree are factors of the number
(65) 21 10 210. Each number at the end of a
3 72 5 branch is a prime factor of 210.

The prime factors of 210 are 2, 3, 5 and 7.

Fahrenheit scale A scale used on some thermometers to measure temperature.

escala Fahrenheit On the Fahrenheit scale, water freezes at 32°F and boils at
212°F.
(10)

fraction(s) A number that names part of a whole.

fracción 1 of the circle is shaded.
4
(6)

1 is a fraction.
4

frequency table Displays the number of times a value occurs in data.
Daily Temperature Highs in October
tabla de frecuencias

(Inv. 1)

Temperature (∙F) Tally Frequency
81–85 16
76–80 9 This frequency
71–75 5 table shows data
for temperatures in
October.

65–70 1

Glossary 647

function A rule for using one number (an input) to calculate another number (an
output). Each input produces only one output.
función
y = 3x
(96)

xy There is exactly one resulting

39 number for every number we
5 15 multiply by 3. Thus, y = 3x
7 21 is a function.
10 30

G

geometric solid A three-dimensional geometric figure.
sólido geométrico
geometric solids not geometric solids
(Inv. 6)

cube cylinder circle rectangle hexagon

graph 1. Noun: A diagram, such as a bar graph, a circle graph (pie chart), or a line
graph, that displays quantitative information.
gráfica
Hair Colors of Students
(Inv. 7)

Rainy Days Red
8
Days 6 Brown 2
4
2 4

Jan. Feb. Mar. Apr. Blond Black
6
4

bar graph circle graph

2. Noun: A point, line, or curve on a coordinate plane.

y

3 The graph of the
2 equation y � x
1

�3�2 123 x

�2
�3

3. Verb: To draw a point, line, or curve on a coordinate plane.

greatest The largest whole number that is a factor of two or more given numbers.
common factor
The factors of 12 are 1, 2, 3, 4, 6, and 12.
(GCF) The factors of 18 are 1, 2, 3, 6, 9, and 18.
The greatest common factor of 12 and 18 is 6.
máximo común
divisor (MCD)

(20)

648 Saxon Math Course 1

H

height The perpendicular distance from the base to the opposite side of a
parallelogram or trapezoid; from the base to the opposite face of a prism or
altura cylinder; or from the base to the opposite vertex of a triangle, pyramid, or
cone.
(71)

height height height GLOSSARY

XXYY XY 22 2 33 3 BBCC BC YYZZ YZ227997 2 7 223113 2 1 11 1
55 5 55 5 9 3 22 2

histogram A method of displaying a range of data. A histogram is a special type 1
2
histograma of bar graph that displays data in intervals of equal size with no space

(Inv. 1) between bars.

33 3 XY 44 4 2 33 S��co343434re�35s�o11n34112222T�e��st111221 �BC1119922 9 Y11Ziinn.. ��12inf2221t1.4479� 22214 22 1
3 5 44 12 3
44 4 33 22 fftt

10

Frequency 8

3 6 3 4 12 h9istogra1 min.
4 4 3 12
4 4 � � � 1 12 2 ft � 1 2
3 24

2

0 21–28 29–36 37–44 45–52 53–60

horizontal Parall4e4l to4the horizon44; per4pendicSuclaorre55to ve5rtical. 44 4 44 4
33��11223� 12
horizontal 33��11223� 12 33��11223� 12 44��22004� 20 33��11223� 12

(18)

oblique line vertical line

33��2260603RR�322�2601h4R2or2izonta22l��li11n1175e475432RR�� 1111412754 R 1 5 not horizontal lin4es 4
11 1 4� 20 3� 12 3� 12
I
The sum of any number and 0 is equal to the initial number. In symbolic
Identity Property
of Addition fo21r21m0606,��aT2154+06h543e��02Id60=54eRna9595t.2itTyh95ePrnoupmebr2te�y1r111133o27035142f�Ri+�sA13d1r4204edf=�eitrir1o4e3nd itso1133s22ahs�o�1wt3h424ne�bayd4dthitiisv2121estiadtee21nmtietyn.t: 22 2 99 9
44 4 1100 10
propiedad de
identidad de la suma The product of any number and 1 is equal to the initial number. In symbolic 11 9
66 1
(1) form, aT21 ×h21e0614242Id�=e54na42t.itT1y12h200220eP0 rn95o1u20p2m0e1515b10r10teyr o15110fisM1414rue13lf2tei41pr�rleicd4atto4141ioans i41tsh1se311h2990m0o99�00wul1n4t9i0p9b0lyic1199t0a09h900tiisve192109i0dent2i277t22y. 222
statement: 74
Identity Property 11
of Multiplication 22

propiedad de 94 × 1 = 94
identidad de la

multiplicación

(2, 3)

improper A fraction with a numerator equal to or greater than the denominator.
fraction 1 55 959 19110902211iinfnfo1occo2ohh1teteinfssoc�o2�h72te1s1 � 1110000
1122 12 21, 553377, an537d4222112255 a2r1e251210i182m8505 pr1o85p1510er8787frac8741tion7878s. 8 e4qu6a6l to1610.0
fracción impropia 1122 12 improper fractions are greater than 7
All
(Inv. 2) or

integers The set of counting numbers, their opposites, and zero; the members of the
set {…, −2, −1, 0, 1, 2, …}.
números positivos,
negativos y el cero $$111100−$001.$511.$010221710000a00�0�n.$000d1.$0.$0014150�03070a000r.$0e001.0.0i0n00t20e��1.g205e101r00s�00.%%11850a0n%d −087.9282aaar22e2n78ao2t inte11g22e56aras2122.22 a22 22331221i3nfoc228o80h0tes28�052521

(14)

$1100.00 � $1000.00 Glossary 649 8
$1000.00 1 2a22 20
� 100% 2a2 23

3 � 4 � 12 � 1 9 1 in. � 1 2
4 3 12 12 2 ft 24

interest An amount added to a loan, account, or fund, usually based on a percentage
interés of the principal.
(116)
If we borrow $500.00 from the bank and repay the bank $575.00

44 5 for the loa4n, the interest o4n the loan is $575.00 − $500.00
20 4 = $753.0�01.2 4 3� 12
24 3� 12 5 4� 3A�n12angle that op3e� n1s2 inside
� 12 i4n�te20rior angle
to the of a polygon.
ángul interno

602R� 1275 2502� 7 R 1 (98) 4 interior This hexagon has six
15 3� 12 angle interior angles.
R 14� 14 4
3� 12

14 1
1
�R541 International See metric system.
inteSrny1a3sc21ti3oe2�nm(a�74)l
5 1321� 4 1 2 9 16�0 21� 9 6 � 9
913S2is�tem4a 2 22 94 �21 10 15 10 15
4 4 10

intersect To share a point or points.
intersecar

134221�1 4 22 1121 � 4 (28) 1 1 299 99 9 27�21 21 TThheeysesht1w6a0161ro3e2�litn�h1e9e5s4pionitnetrMs1e3.2ct�. 4
1001 530 1 992 4 1400 M272 10010
22 1 100 99 6
4 100

00 50 4 4

11 57 1 o2p1e25ra7cioonp411e8e5sirnianvvtei8eorr1sns9a0es9s087 Ope5619r09a0t78aaio+−nsbbth−+a2t7bb256“1==u21niaadnfooco”hteosne�a1611n2o1tihnAifnoec1dvorh0.dete0irtss43ioe�no1a13p2ned�ras14uti0bo0tnr43asc. tion are
1550 3 15 4
2
8 8 7 (1)

a × b ÷ b = a (b ∙ 0) Multiplication and division are

0105.00 � $71000.00 8 5 a2÷a21b=21×ianfobcoh=(teas1a≥2�0a(1)b22∙ 0) inverse operations.
008.$0100�001.00800% 100% 6 1 2a22 = a 2(a 3≥ 0) 2810 00234Sro52q3outsarainreg280iannvderf52isnedionpgesrqautiaornes.
7�
2a2

� 100% irrational Numbers that cannot be expressed as a ratio of two integers. Their decimal
numbers expansions are nonending and nonrepeating.
números 2irraac2iona(l8e9s) 1 2a22π and 23 are ir28r0ation52al numbers.

isosceles A triangle with at least two sides of equal length.
triangle
Two of the sides of
triángulo isósceles this isosceles triangle
have equal lengths.
(93)

L

least common The smallest whole number that is a multiple of two or more given numbers.
multiple (LCM)
Multiples of 6 are 6, 12, 18, 24, 30, 36, ....
mínimo común Multiples of 8 are 8, 16, 24, 32, 40, 48, ....
múltiplo (mcm) The least common multiple of 6 and 8 is 24.

(30)

650 Saxon Math Course 1

legend A notation on a map, graph, or diagram that describes the meaning of the
symbols and/or the scale used.
rótulo

(Inv. 11)

kitchen The legend of this scale
bath 1
living/dining 1 inch � 5 feet drawing shows that 4 inch GLOSSARY
4
represents 5 feet.

line A straight collection of points extending in opposite directions without end.
línea
AB
(7)

line AB or line BA

line graph A method of displaying numerical information as points connected by line
gráfica lineal segments.

(18)

100Income
(in thousands)
This line graph has a
80 horizontal axis that shows
60 the number of completed
40 years of education and a

vertical axis that shows the
20 average yearly income.

4 8 12 16 20
Years of Education

line of symmetry A line that divides a figure into two halves that are mirror images of each
línea de simetría other.

(110)

lines of symmetry not lines of symmetry

line plot A method of plotting a set of numbers by placing a mark above a number on
a number line each time it occurs in the set.
diagrama de puntos
X This is a line plot of the
(Inv. 4) X numbers 5, 8, 8, 10, 10,
X X XX X 11, 12, 12, 12, 12, 13, 13,
M X X XXXXX XXXX 14, 16, 17, 17, 18, and 19.
0 5 10 15 20

mass The amount of matter in an object.
Grams and kilograms are units of mass.
masa
See average.
(102)

mean

media

(18)

median The middle number (or the average of the two central numbers) of a list of

mediana data when the numbers are arranged in order from the least to the greatest.

(Inv. 5) In the data at right,
7 is the median.
1, 1, 2, 5, 6, 7, 9, 15, 24, 36, 44

Glossary 651

metric system An international system of measurement based on multiples of ten. Also
called International System.
sistema métrico
Centimeters and kilograms are units in the metric system.
(7)

minuend A number from which another number is subtracted.
minuendo
12 − 8 = 4 The minuend in this problem is 12.
(1)

mixed number(s) A whole number and a fraction together.
número(s3) mixto(s)
2 BC TheYmZ ixed2n79umber 2 1 means21 “two and one thAiCrd.” 3
5 5 (17) 3 6

mode The number or numbers that appear most often in a list of data.
moda
In the data at right, 5, 12, 32, 5, 16, 5, 7, 12
(Inv. 5) 5 is the mode.

4 mu34lt�ipl34e(�s) 1122A�pr1oduct19o2 f a co12uinfnt. t�ing214num2ber and another number.
3

múltiplo(s) The multiples of 3 include 3, 6, 9, and 12.

(25)

N

negative Numbers less than zero.
numbers
−15 and −2.86 are negative numbers.
números negativos 19 and 0.74 are not negative numbers.

(9)

net A two-dimensional representation of a three-dimensional figure.
red 5 4 4
4 (Inv.412�) 20 3� 12
3� 12 3� 12 top

7R1 side
2� 15 side
R2 back front
14 bottom
4 1
5
5 nonex13a2m�pl4e A non13e2x�am4ple is 1 2 an 9 Non-e�x21amples 6 b�e 9 to
2 9 the2 opposite o4f exam1p0le. ca1n0 1u5sed
4 contraejemplo
prove that a fact or a statement in mathematics is incorrect.
57 (Inv. 2)
3 The integer 7 is a non-example of an even number, and a circle
11 1
22 A 1 is a no9n9-examp9l9e of a polygon. point o1n32th�e 4line
100 nu5m0 ber li4ne line4for rep1r0e0senting10a0 nd
22 1
recta numérica
graph7ing numbers.6Each
(9)
corresponds to a number.
n185umerato87r
number line
numerador
�2 �1 0 1 2 3 4 5
(6)
2 15 The t78op term o56f a fraction. 12 inches � 1 100 3
2 1 foot 4

9 numerator

10 denominator

0.00 � $1000.00 � 100% 2a2 1 2a22 23 82
$1000.00 20 5

652 Saxon Math Course 1

O vertical line GLOSSARY

oblique line(s) 1. A line that is neither horizontal nor vertical.

línea(s) oblicua(s)

(28)

horizontal line

oblique line not oblique lines

2. Lines in the same plane that are neither parallel nor perpendicular.

perpendicular

lines parallel lines

oblique lines not oblique lines

obtuse angle An angle whose measure is more than 90° and less than 180°.

ángulo obtuso

(28)

right angle acute angle

obtuse angle not obtuse angles

An obtuse angle is larger than both a right angle and an acute angle.

obtuse triangle A triangle whose largest angle measures more than 90° and less than 180°.

triángulo acute right
obtusángulo triangle triangle

(93)

obtuse triangle not obtuse triangles

odd numbers Numbers that have a remainder of 1 when divided by 2; the members of the
set {..., −3, −1, 1, 3, ...}.
números impares
Odd numbers have 1, 3, 5, 7, or 9 in the ones place.
(10)

open-option A survey that does not limit the possible responses.
survey
What is your favorite sport? open-option survey
encuesta de opinión
abierta

(Inv. 1)

operations of The four basic mathematical operations: addition, subtraction, multiplication,
arithmetic and division.

operaciones 1�9 21 � 8 6 � 22 3�1
aritméticas
the operations of arithmetic
(12)

opposites Two numbers whose sum is 0.

opuestos (−3) + (+3) = 0
The numbers +3 and −3 are opposites.
(14)

Glossary 653

order of 4The4order in wh4ich t4he four fund5ame5ntal operat4ions4occur. 4 4
operation3s� 1213.� S12implify root4s�. 204� 20 3� 123� 12 3� 123� 12
p3o� 1w2e3r�s1a2nd
orden de las
operaciones 2. Multiply or divide in order from left to right.
(5)
260o3W3R.u�itAt2eh260drpmdRaoar2esntnd,tbhseeu2sfbo�et11rrse7a54,2cswRt�ime11i1n754psoilRmirfdy1pienlrigfyfroowumittshlieidnfetthttoheerpipgaharerte.nnththeesseess, .from innermost to
3�

ordered pair A pair of numbers1, wri1tten in a specific order, that are used to designate the 3
par orde2nado po35sition of a pBoCint on aYcZoordin2a97te plane2. 31See also12 coordinate(s).AC 6
XY
5 (Inv. 7)
16 �215406 4 5 5 (0, 113)2 �134(22,�3)4 1(332.4�,13542.7�) 4 1 −21 22 9 9 �21 �21
20 � 5 9 9 a 2 , b 44 10 10

ordered pairs

3 o4rigin 1. T34h�e l34oc�at11io22n�of1the nu9mber 102infot. n�a21n4 um2ber line.
4 410 1 119090 219090 12
o3rigen 1 2 2 22 22 11 12 4 3
2 4 4 100 10050 14�1 193090 99 22 22 11
(Inv1. 7) �31510 14�2 100 77 66
2

origin on a number line

2. The point (0, 0) on a coordinate plane.

12 12 57 57 2 15 2 1515 15 7 2 7 8 cooriog78ridninoante56a 5 121info1co2h1teinfsoc�ohte1s � 1100 43100 3
12 12 3 3 2 28 8 8 8 7 plan6e 4
1

4 �2��11 12 1 2a2122a22 23 23 8 82 2
3� 12 20 205 5
4 5 4 �2 4
P 3� 1$2110$01.$01100000�.$001.$040010�0�02000.$001.000000�.0100�03%1� 0102% 3� 12
2a2 2a2

6 Rpl2ínaeraasllpealrlainle2ela�ss175 LRin1es in the same plane that do not intersect.
20 (28)14
3� parallel lines

parallelogram 1A quadrilateral that has two pairs of parallel sides.
paralelogramo

(64)

16 � 4 5 12 � 4 12 � 4 1 2 9 �21 6 � 9
20 5 9 3 3 2 4 10 10 15
parallelograms not a

parallelogram

percent A fraction whose denominator of 100 is expressed as a percent sign (%).
2 por ci2e2nto 11
1 100(33) 50 1 1 99 = 9919%090 = 99 pe27r2cent 1 12 � 4
4 100 6 3
2 4 4

perfect square The product when a whole number is multiplied by itself.
cuadrado perfecto
The number 9 is a perfect square because 3 × 3 = 9.
(38)

12 57 pepreirmí2me1e2t5teror T15he distan7ce aroun8d a closAe56d, flat shape.121infocohtes � 1 100 3
12 3 4
8 8 7

(8) 6 in.

The perimeter of this rectangle

4 in. 4 in. (from point A around to point A) is

$1100.00 � $1000.00 � 100% 6 in.2a2 1 2a22 20 inches. 8 2
$1000.00 23 20 5

654 Saxon Math Course 1

perpendicular A line, ray, or segment that intersects a segment at its midpoint at a right
bisector angle, thereby dividing the segment into two congruent parts.

mediatriz

(Inv. 8)

4 4 54 This v4ertical line is a GLOSSARY
3� 12 3� 12 A 4� 20 B 3� 12C p3e�rp12endicular bisector of AC.

3� 6 Rpe2rpendicu2la�r175 R1 lines that intersect at right angles.
20 lines14 Two

líneas 1
perpendiculares
(28) perpendicular lines not perpendicular lines

16 � 4 5 12 � 4 12 � 4 1 2 9 �21 6 � 9
20 5 9 3 3 2 4 10 10 15

pi () The number of diameters equal to the circumference of a circle.
p22i (π) 11 Ap41 proximate41 values190o90f pi are190930.14 and 272. 12
1 2 1 3 � 4
2 4 100(47) 50 6

pictograph A method of displaying data that involves using pictures to represent the
pictografía data being counted.
(Inv. 5)

12 57 2 15 15 7Tom 8 5 1T2h1iisnfocioshteasp�ict1ogra1p0h0. 3
12 3 2 8 8Bob 7 6 4
Sue
It shows how many stars
Ming
Juan each person saw.

$1100.$010g0rá0�pf0iic.$ea010gc0irr0cau0pl.ah0r0 �Se1e0c0i%rcle graph. 2a2 1 2a22 23 82
20 5
(40)

place value The value of a digit based on its position within a number.

valor posicional 341 PPlalacceevvaalulueetetellsllsuussththaat t44inin334411isiswwoorrththfofouurrtteennss..In
23 adIndaitdiodnitiaonndasnudbstruabctrioacntipornobplreombslewmes awliegnalidgingitdsigwitisth
(12) thweitshatmhe spalamceepvlaalcuee.value.
�7
371

plane A flat surface that has no boundaries.
The flat surface of a desk is part of a plane.
plano
The period of time from noon to just before midnight.
(28) I go to bed at 9 p.m. I go to bed at 9 o’clock at night.

p.m. An exact position on a line, on a plane, or in space.
A This dot represents point A.
p.m.

(32)

point

punto

(69, Inv. 7)

Glossary 655

polygon A closed, flat shape with straight sides.

polígono

(60)

polygons not polygons
not polyhedrons
polyhedron A geometric solid whose faces are polygons.
poliedro
polyhedrons
(Inv. 6)

cube triangular pyramid sphere cylinder cone
prism

population A certain group of people that a survey is about.

población

(Inv. 4)

XYnpuomsbiteivres N52umbe0r.s25g35raenadte1r5th7aanrBezCeproos. itiveYnZumb2e97rs. 2 1 1 AC 3
−40 and 0 are not positive numbers. 3 2 6
números positivos

(14)

power(s) 1. The value of an exponential expression.

potencia(s) 4 An e1x6piosn43teh�net.f34o�urt11h22p�ow1er of 29 beca1u2isnfte. �2421=4 16.

3 (73) 23. 12 2

4

The expression 24 is read “two to the fourth power.”

prime The expression of a composite number as a product of its prime factors.
factorization The prime factorization of 60 is 2 × 2 × 3 × 5.

factorización prima

(65)

prime number(s) A counting number greater than 1 whose only two factors are the number 1
and itself.
número(s) primo(s)
4 7 is a prime nu5mber. Its only f4actors are 1 and47.
(19) 3� 12 10 is not a 4p�ri2m0e number.3It�s1f2actors are 13, �21, 25, and 10.

4
3� 12

principal The amount of money borrowed in a loan, deposited in an account that
earns interest, or invested in a fund.
capital
2� 1I7f5wRe1borrow $750.00, the principal is $750.00.
(116) A pol1yh4edron with two congruent parallel bases.

6R2 1
3� 20 prism

prisma

(Inv. 6)

16 � 4 5 12 � 4 12 � 4 1 29 �21 6 � 9
20 5 9 3 3 2 4 10 10 15
rectangular prism
triangular prism

probability A way of describing the likelihood of an event; the ratio of favorable

probabilidad outcomes to all possible outcomes.
ro41lling 3190w90ith 12
1 2 (58) 22 Th15e10 proba41bility of a a s19t0a90ndard nu27m2 ber cube is 1 . 3 � 4
24 100 6

product The result of multiplication.
producto
5 × 4 = 20 The product of 5 and 4 is 20.
(2)

12 57 2 15 15 7 8 5 12 inches � 1 100 3
12 3 2 8 8 7 6 1 foot 4

656 Saxon Math Course 1

proportion A statement that shows two ratios are equal.
prop21orci(ó83n)
2�4 12 � 4 2 9 �21 6 � 9
3 4 10 10 15
1
These two ratios are equal, so this is a proportion. GLOSSARY
4 BC
protractor A tool used to measure and draw angles.
190t9r02an79spor1t90(a9I0ndv.o32r)
1 YZ 1 22 AC 132 � 416 6350130 61020 70 80 90 100 110 61020 50130
4 3 71 110 100 90 80 70

2

15300 14040 14040 15300 protractor

20 160
160 20

78 5 12 inches 10 3 170
612inftp. �yra214mid2 1 foot 170 4 10

� 1 100
4 812 7 9 0 180
3 12 12 180 0

� � 1

A three-dimensional solid with a polygon as its base and triangular faces
pirámide that meet at a vertex.
(Inv. 6)

0% 2a2 1 2a22 23 82 pyramid
20 5

Q

2 3 quadrilateral Any four-sided polygon. 3
5 5 cuadrBiláCtero 4YZ 7 1 1 6
5 4 (603) � 12 2 9 2 3 2 AC

4� 20 3� 12

Each of these polygons has 4 sides. They are all quadrilaterals.

4 3 � 34q�ucau11lai22tliat�attiivv1eo Ex19p2 resQseu12dainflti.int�aotir2v14reelda2atitnagatroe categories rather than quantities or numbers.
3 4 categorical: Examples include the month in

(Inv. 4) which someone is born and a person’s favorite flavor of ice cream.

quantitative Expressed in or relating to quantities or numbers.
cuantitativo
�4 12 � 4 2 Quan9titative da�ac21tiaty,atrheennuum1m6e0bri�ecra1lo9:5fEpxaaimrspolef sshinocelsudseomtheeone owns,
3 1 (Inv. 4) 4 popu1la0tion of
2

and the number of hours per week someone watches television.

quotient The result of division.
4� 2c1509o09c0ient(2e)
14 99 44 12
1 3� 142 100 272312� 1÷2 3 = 4 1 3� 12 3 4 The quotient is 4 in each of these
4 6 � problems.

R
7R1
27 28� 15 5 radraidu(2i7so)121(Pinfloucorhatel:s radii ) The distance from the center of a circle to a point on the circle.
�1 100 3
8 7 14 6 4

1 A 2 in. The radius of circle A is 2 inches.

5 12 � 41 2a22 12 �243 8 1 2 2 9 �21 6 � 9
%9 3 3 20 2 5 4 10 10 15
2a2

2 22 11 1 1 99 99 22 1 12 � 4
4 100 7 6 3
4 100 50 4 100 Glossary 657

range The difference between the largest number and smallest number in a list.

intervalo To calculate the range of the
data at right, we subtract the
(Inv. 5) smallest number from the
largest number. The range of
this set of data is 29. 5, 17, 12, 34, 29, 13

rate A ratio of measures.

tasa

(23)

ratio A comparison of two numbers by division.

razón

(23)

There are 3 triangles and 6 stars. The ratio of triangles to stars is
1 BC21 YZ 2A97 C 1 3 1 (o63r
2 3 2 3 6 (or 2 ), which is readAaCs “3 to 6” “1 to 2”).

rational numbers Numbers that can be expressed as a ratio of two integers.

números racionales

(23)

234 � 12 � 1 9 12infrtra.ay�yo 214dAirp2eacrttioonf.a line that begins at a point and continues without end in one
12 12

XY (27) 3 BC A YZ 2 7 XY 2 13XYB 21 23 AC35 BC B63YCZ 2 79Y
55 9 52 55

ray AB

reciprocals Two numbers whose product is 1.
recíprocos
3 � 4 � 12 � 1 T192hus, th12einft.f34r�ac2t1i4ons234 and 4 are reci34p43ro�ca34ls�. 113422��341� 112219�2 1 1 in.9
3 (340) 4 3 12 3 2 ft1
43

rectangle A quadrilateral that has four right angles.
re4ctángulo 4
45 (64)
3� 142� 20 3� 12 3� 12

rectangles not rectangles

rXeYctangular S52ee prism.53 BC YZ 2 7 XY 2 1 21 3 AC BC 3 YZ
prism 9 3 52 5 6

prisma rectangular 5 44 44 4 45 54
3�31�212 3� 12 3� 12 4� 20 4� 20 3� 12
4 (Inv. 6) 4
3� 12 reduce3� 1T2o rewrite a f4ra�c2t0ion in lowes3t �te1r2ms. 3� 12
3 reducir 2F�3411li7p54p1R6in0I142gf�wa1ef9i534greu�dreu34tc1o9�e0pt11hro22ed�furac1c�etia21onm1i9r2r,owr i3em�1g16a220eig60nftt.�eR�34. .12925134 � 3 4 12
� 442 2 4 4 � 3 � 12 �1 9
1332�1�2906044Rre2frleefc�letx21i(1oi21(ó02n86n)) 3 12
1 22 6R
47 20 22� 7 R 1 7R1
15 2� 15
14
14
1 11
reflection
1 199 99 12 4272 1 12
4 6100 100 3 � 3 � 4
6
16 4 5 12 12 16 4 210642�95 4 59 12 ��421 12 143216�0 �4 912
20 � 5 9 3 � 4 3 � 4 20 � 5 5 190 3 3 � 153 �

44 5 4 44 4 5 3� 1
3� 12 3� 12 3� 12 3� 12 4� 20
127inches �78 1 3�110205634 3�1122inches � 14� 20100 3
18 foot 1 foot 4
2 1 99 1121 919
1 22 11 1 4 100 1 99 21 22 222 11 221 1 11 344 � 4 1040
4 2 100 42 7 1040 501060 4 50
2 100 50 4

658 3S�22a60xoRn2Math2Cour2s�e111754 R 1 6R2 7R1
3� 20 2� 15
8 2 8 2
14

regular polygon A polygon in which all sides have equal lengths and all angles have equal
polígono regular measures.

(60)

regular polygons not regular polygons GLOSSARY

rhombus A parallelogram with all four sides of equal length.

rombo

(64)

rhombuses not rhombuses

right angle An angle that forms a square corner and measures 90°. It is often marked
ángulo recto with a small square.

(28)

obtuse angle acute angle

right angle not right angles

right triangle A triangle whose largest angle measures 90°.
triángulo rectángulo
acute obtuse
(93) triangle triangle

right triangle not right triangles

rotation To rotate, or turn a figure about a specified point is called the center of
rotación rotation.

(108)

rotation

rotational A figure has rotational symmetry when it does not require a full rotation for
symmetry the figure to look as if it re-appears in the same position as when it began
the rotation, for example, a square or a triangle.
simetría rotacional

(110)

original 45° turn 90� turn 150° turn 180� turn 210° turn 270� turn
position

round A way of estimating a number by increasing or decreasing it to a certain
redondear place value. Example: 517 rounds to 520

(16)

S

sales tax The tax charged on the sale of an item and based upon the item’s purchase
price.
impuesto sobre la
venta If the sales-tax rate is 7%, the sales tax on a $5.00 item will be
$5.00 × 7% = $0.35.
(41)

Glossary 659

sample A smaller group of a population that a survey focuses on.

muestra

(Inv. 1)

sample space Set of all possible outcomes of a particular event.
espacXioYmuestral 2 3 spacBeCof 6YZnumb2er97 is2{131, 1 AC 3
5 The a 1– cube 2, 3, 5, 6}. 6
(58) sa5mple 42 ,

scale A ratio that shows the relationship between a scale drawing or model and
the actual object.
escala
If afedetr,a43twh�iengs34co�af lte11h22eoff�ltoho1er plan of a house has the legend 1 inch =
(10) 4 2 draw192ing 1 in. 1
3 is 2 ft � 24 . 2
3
4

scale drawing A two-dimensional representation of a larger or smaller object.
Blueprints and maps are examples of scale drawings.
dibujo a escala
The number that relates corresponding sides of similar geometric figures.
(Inv. 11)
25 mm The scale factor from
scale factor

factor de escala

(Inv. 11)

10 mm 10 mm the smaller rectangle
4 mm to the larger rectangle

4 4 5 4 is 2.5.4
sca3l�e1m2 odel A th3r�e1e2-dimensiona4l �re2n0dering of a 3la�r1g2er or smaller3o� b12ject.

modelo a escala Globes and model airplanes are examples of scale models.

(Inv. 11)

scalene triangle A triangle7wRit1h three sides of different lengths.
triángulo 2e6s0caRle(2n93o)
2� 15 All three sides of this
3� 14
1 scalene triangle have
different lengths.

sector A region bordered by part of a circle and two radii.
16 �se54(Icnvt.o5r) 5 12 12 1 2 9 �21 6
20 9 3 � 4 3 � 4 2 4 10 10 � 1

This circle is divided into 3 sectors.

12 22 11 1 1 99 99 22 1 12 � 4
A pa10r0t of a5l0ine with4 two distin4ct end1p0o0ints. 100 7 6 3
2segmen4t
A B
segmento

(7)

segment AB or segment BA

s1e2 quenc5e7 AThlei2st1n25oufmnbuem18r5sb2e,rs4,ar6r87,a8n,g.e..dfoarc78mcoardsienqgutoe56naccee. rTtahien rruull1ee2.1isinf“occohoteusnt�up1 by t1w0o0s34.”

12secuenc3ia

(10)

similar Having the same shape but not necessarily the same size. Corresponding
semejante angles of similar figures are congruent. Corresponding sides of similar
$1100.$(0110090)0�0f.$i0g10u0r0e0s.0a0re�pr1o0p0o%rtional.
2a2 A 1 2a22 23 82
20 5

D

C BE F

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

660 Saxon Math Course 1

simple interest Interest calculated as a percentage of the principal only.

interés simple Simple Interest Compound Interest

(116) $100.00 principal $100.00 principal

$6.00 first-year interest (6% of $100) � $6.00 first-year interest (6% of $100)

� $6.00 second-year interest (6% of $100) $106.00 total after one year GLOSSARY

$112.00 total after two years � $6.36 second-year interest (6% of $106)

$112.36 total after two years

solid See geometric solid.

sólido

(Inv. 6)

sphere A round geometric solid in which every point on the surface is at an equal
esfera distance from its center.

(Inv. 6)

sphere

square 1. A rectangle with all four sides of equal length.
cuadrado
2 in.
(64)

2 in. 2 in. All four sides of this square

XY 2 3 BC YZ2 in. 2 7 2a31re 2 inc1hes long. AC 3
5 5 9 6
2

2. The product of a number and itself.

The square of 4 is 16.

3 square root 3 Op�ons34eit�oivfe11t,w22soq�uea1qruearlofao19c2t toofrsa of a number. The symbol for the principal, or
4 4 n12uinftm. �be21r4is 2 .
raí4z cuadrada
A square root of 49 is 7 because 7 × 7 = 49.
3 (38)

statistics The science of gathering and organizing data in such a way that conclusions
estadística can be made; the study of data.

(Inv. 4)

stem-and-leaf A method of graphing a collection of numbers by placing the “stem” digits
plot (or initial digits) in one column and the “leaf” digits (or remaining digits) out
to the right.
diagrama de tallo y
hojas Stem Leaf 4
4 5 1 3 536� 1642 8 3� 12 In this stem-and-
3� 12 (Inv. 5) 4� 20 2
leaf plot, 3∙5
4 3 0022456689 represents 35.
3� 12

4 001112335778

7R1 5 0112358

6R2 subtr2a�h1e5nd A number that is subtracted.
3� 20 sustra1e4ndo
1 (1) 12 − 8 = 4 The subtrahend in this problem is 8.

sum The result of addition.
suma
16 � 4 5 12 � 4 7 + 6 =13213�T4he sum o1f 7 and 6 is213. 9 �21 6 � 9
20 5 9 (1) 3 2 4 10 10 15

1 2 22 11 1 1 99 99 22 1 12 � 4
4 100 100 7 6 Glossa3ry 661
2 4 100 50 4

supplementary Two angles whose sum is 180°. 3
BC YZ aánngg2ul97eloss 1 1 6
2 3 AC
suplementarios 2B ∠AMB and ∠CMB are
supplementary.
(69)

AMC

� 4 � 12 � 1 su1r92face a12rinfet.a� 2T14he2total area of the surface of a geometric solid.
3 12
área superficial Area of top � 5 cm � 6 cm � 30 cm2
30 cm2
(Inv. 6) Area of bottom � 5 cm � 6 cm �

Area of front � 3 cm � 6 cm � 18 cm2

3 cm Area of back � 3 cm � 6 cm � 18 cm2

Area of side � 3 cm � 5 cm � 15 cm2

6 cm 5 cm � Area of side � 3 cm � 5 cm � 15 cm2

Total surface area � 126 cm2

5 3 � e1sn42ucru(vIenevs.t1ya) A metho4d of collecting data about a particular population.
4� 20 3� 1M2ia conducted a sur vey by asking each of her classmates the
name of his or her favorite television show.
T

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

término(s) 5 terms
6
(10, 30)

2. A number in a sequence.

2�4 12 � 4 1 Ea42ch numbe19r0in this1s,�e3q21, u5e,n7c, e9,is11a16,0t.e.�.rm19.5
3 2
1
4 theoretical The probability that an event will occur, as determined by analysis rather
probability than by experimentation.
7 probabilidad teórica
8 The theoretical probability o1f32ro�llin4g a three with a standard
1 99 (Inv. 9) nu2m72 ber cube is 1
99 6 .
4 100 100

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

transformación Transformations

(108) 12 inches � 1 100 3Movement Name
1 foot 4 flip reflection
85
76

slide translation

turn rotation

0% 2a2trantrsalsalatci1oió2nn a22Sfiglidurineg. 2a f3igure fr8om on2e position to another without turning or flipping the

20 5

(108)

translation

662 Saxon Math Course 1

transversal A line that intersects one or more other lines in a plane.

transversal transversal

(97)

XY 23 BC YZ 2 7 2 1 1 AC 3 GLOSSARY
55 9 3 2 6

trapezium A quadrilateral with no parallel sides.
trapezoide

(64)

3 4 3 � 4 � 12 � 1 9 1 in. � 1 2 not trapeziums
4 3 4 3 12 24
tra1p2 ezium2 ft

trapezoid A quadrilateral with exactly one pair of parallel sides.

trapecio

(64)

trapezoids not trapezoids

4 diatgrrea4emda idaegárrabmol A 5visual represent4ation of a compo4und experiment.
3� 12 3S�p1in2ner 3�C1o2in
3� 12 (Inv. 10) 4� 20 H

1

6R2 7R1 T
3� 20 2� 15
H This tree diagram shows all
14 2 6 possible outcomes for a
1
1 spinner with 3 sectors being
32
T spun and a coin being flipped.

16 � 4 5 12 � 4 12 � 4 2H 9 �21 6 � 9
20 5 9 3 3 4 10 10 15

T

triangular prism See prism.
1 2 p2r2isma tr1ia1ngular 1 1 99 99 12
4 100 100 22 1 3 � 4
2 4 100 50 (Inv. 6) 4 7 6

U

unit multiplier A ratio equal to 1 that is composed of two equivalent measures.
factor de conversión
12 57 15 15 (114) 7 8 5 12 inches 3
12 3 2 2 88 7 6 1 foot � 1 100 4

We can use this unit multiplier to convert feet to inches.

unknown A value that is not given. A letter is frequently used to stand for an unknown

$1100.00 � $1000.00 incógnita number. 1 2a22 23 82
$1000.00 2a2 20 5
� 100(3%)

Glossary 663

U.S. Customary A system of measurement used almost exclusively in the United States.
System
Pounds, quarts, and feet are units in the U.S. Customary
Sistema usual de
2 1 Syst1em. AC 3
BC YZ 2EE79 .UU(7.) 3 6
2
V

vertex (Plural: vertices) A point of an angle, polygon, or polyhedron where two or
vértice
4 12 1 9 1 in. �(28)214 more lines, rays, or segments meet.
3 � 12 � 12 2 ft A dot
2 is placed at one vertex of this

cube. A cube has eight vertices.

vertical Upright; perpendicular to horizontal.

vertical horizontal line

(18)

oblique line

5 4 4 not vertical lines
4� 20 3� 12 3� 12 vertical line

�4 vertices See vertex.

1 vértices
4
(Inv. 6)
7
8 volume The amount of space a solid shape occupies. Volume is measured in cubic
units.
% volumen
This rectangular prism is
(Inv. 6, 82)
12 � 4 2 9 �21 3aisnud3n4i∙ts3u1wn6∙0ii4tds�e=d,1e9335e6upnc. iuIttsbsihcviogulhnu,imtse.
3 1 4 10
2

W

1 19090wepige1hs90o9t0 The me272asure of how16heavy an obj1e32ct�is.4
4 The weight of the car was about 1 ton.

(102) The members of the set {0, 1, 2, 3, 4, …}.
121inf−0oc,o3h2t,e50s,.5a�n6d,1a1n3d41a0r0e34wahreolneont uwmhobleersn.umbers.
whole numbers

números enteros

8 5 (9)
76

X

x-axis The horizontal number line of a coordinate plane.
eje de las x
2a2 23 82 y
1 (2Inv.a7)22 20 5 3

2

1 x x-axis
�3�2�1�1 1 2 3

�2

�3

664 Saxon Math Course 1

Y

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

eje de las y y
y-axis
(Inv. 7)
3
2 GLOSSARY
1

�3�2��11 123 x
�2
�3

Z

Zero Property of Zero times any number is zero. In symbolic form, 0 × a = 0.
Multiplication The Zero Property of Multiplication tells us that 89 × 0 = 0.

propiedad del cero
en la multiplicación

(2)

Glossary 665

INDEX Activities (cont.)
perpendicular bisectors, 417–418
A prime numbers, 102
probability experiment, 471–472
Abbreviations. See also Symbols and signs protractors, using, 162–163
a.m., 170 rulers, inch, 37–38, 88–89
area (A), 475 segments, bisecting, 417–418
base (b), 475 Sign Game, 543–545
calculator memory keys, 608 transformations, 562–563
Celsius (C), 80
centimeter (cm), 37 Acute angles, 146–147, 161, 503–504
cup (c.), 404 Acute triangles, 485
Fahrenheit (F), 80 Addends, 8, 18–22, 59
foot (ft), 37 Addition
gallon (gal), 404
Greatest Common Factor (GCF), 175 addends in, 8, 18–22, 59. See also Sums
height (h), 475 algebraic, 518–520, 543–547
inch (in.), 37, 38 associative property of, 30
kilometer (km), 37 checking answers by, 8
kilowatt hours (kwh), 494 commutative property of, 8, 9, 10
length (l), 475 of decimals, 8–9, 191–194, 276–277
lines, 353
liter (L), 37 and whole number, 195–199
meter (m), 37 even and odd numbers, 51
mile (mi.), 37 fact families, 7–11
millimeter (mm), 37 of fractions
ounce (oz.), 404
perimeter (P), 475 with common denominators, 127–131, 342
pint (pt.), 404 with different denominators, 285–294
p.m., 170 SOS memory aid, 295–298
quart (qt.), 404 three or more, 320–323
rays, 353 three-step process, 295–298
segments, 353 identity property of, 8
square (sq.), 165 of integers, 517–523, 543–547
square centimeters (cm2), 197, 409 of mixed measures, 534, 592–596
width (w), 475 of mixed numbers, 136–140, 306–309
yard (yd), 37 of money amounts, 7–11, 362, 379
of negative numbers, 518, 519
Act it out. See Problem-solving strategies on number lines, 518
Activities order of operations, 29
place value in, 8
algebraic addition of integers, 543–544 of positive numbers, 518
angles in problems about combining, 58–62
of signed numbers, 542–547
bisecting, 418–420 subtraction as inverse of, 9, 10, 19
measurement, 162–163 sums, 8, 83
area of three numbers, 30
of parallelograms, 370–371 of units of measure, 421–425
of triangles, 408–409 unknown numbers in, 18–22
bisectors of whole numbers, 7–11
angle, 418–420 and decimals, 195–199
constructing, 420 word problems, 58–62
perpendicular, 417–418 Addition patterns, 58–62
circles, drawing, 142 Addition sequences (arithmetic sequences), 50
circumference, 244–246 Advanced Learners. See Enrichment
comparing geometric solids, 315 Age, calculating, 69–70. See also Elapsed-time
compasses, 142 Algebra, 123
coordinate planes, 365–367 adding integers, 517–523, 543–547
drawing comparing integers, 47
circles, 142 graphing in the coordinate plane, 364
on the coordinate plane, 365–367 graphing on the coordinate plane, 363–367,
experimental probability, 470–473 499–500, 581
fraction manipulatives, 109 multiplying integers, 587–591
parallelogram area, 370–371 ordering integers, 517–520
perimeter, 42–43

666 Saxon Math Course 1

Algebra (cont.) Area (cont.) INDEX
solving equations for unknown numbers estimating, 447–451, 617–620
in addition, 18–22 of geometric solids, 316, 630–636
in division and multiplication, 23–27, 123 of lateral surface, 634
in equal groups, 78–81 of parallelograms, 369–371, 409, 474
in fractions and decimals, 225–230 perimeter compared to, 164
in proportions, 432, 442–443 of prisms, 633
in rate problems, 123 of rectangles, 164–168, 364–365, 474
in sequences, 50 of rectangular prisms, 497
SOS method, 295–298, 306–309, 342, 349, of right triangles, 410
375–379 of squares, 165, 196–197, 474
in subtraction, 18–22, 60–61 of triangles, 408–412, 474
in word problems, 59, 60 surface area, 316–318, 633–636
subtracting integers, 517–523 units of measure, 164, 197, 365, 422, 618
writing algebraic equations, 543
“are in” as indicator of division, 135
Algebraic addition of integers, 517–521, 543–547 Arithmetic mean. See Mean
Algebraic logic calculators, 437 Arithmetic operations. See also Addition; Division;
Alternate angles, exterior and interior, 504
a.m., 170 Multiplication; Subtraction
“and” in naming mixed numbers, 184 alignment in, 191
Angle bisectors, 418–420 answer terms of, 65
Angle pairs, 504 with money, 7–18, 92, 258, 362, 379, 616
Angles rules for decimals, 276–277
SOS memory aid, 295–298, 306–309
activity with, 162–163 terms for answers of, 65
acute. See Acute angles with units of measure, 421–425
adjacent, in parallelograms, 369 words that indicate, 250
alternate interior, 504 Associative property, 30
bisecting, 418–420 Average, 93–98. See also Mean
classifying, 163 Axis, horizontal and vertical, 95, 363
complementary, 353–357
corresponding, 504, 567–569 B
degree measures of, 145
drawing with protractors, 161–163 Bar graphs, 55, 84, 211, 265
exterior, 504, 508–509 Base(s)
interior, 146, 504, 508–512
measuring with protractors, 161–163 base ten, 64, 179
naming, 145–149 exponents and, 196
obtuse, 146–147, 161–163, 503, 504 Bases of geometric figures
opposite, in parallelograms, 368, 369 abbreviations for, 475
in parallelograms, 368, 369 cylinders, 634
in quadrilaterals, sum of measures, 508–512 parallelograms, 370
right, 146–147 prisms, 630
supplementary, 353–357, 369, 504, 508 pyramids, 315, 630
symbol for, 145 rectangular prism, 426
of transversals, 503–507 Base ten place value system, 64, 179
in triangles Benchmarks to estimate length, 37
Bias, in surveys, 214
classification using, 485 Bimodal distribution, 267
sum of measures of, 508–512 Bisectors
vertex of, 147 angle, 418–420
Apex, 315 geometric construction of, 417–420
Approximately equal to (≈), 246, 462 perpendicular, 417–418
Approximation. See also Estimation Body temperature, 51
Approximation, pi and, 246, 449, 627 Boiling point, 51
Arcs, drawing with compasses, 418
Area C
abbreviation for, 475
activity, 408–409 Calculators. See also Graphing calculator, online
of bases, 427 activity references
of circles, estimating, 447–451 with algebraic logic, 437
of complex shapes, 557–560 for checking answers, 608
of cones, 630–636 for compound interest, 608
of cubes, 497 for converting fractions to decimals, 386
of cylinders, 634–635
Index 667

Calculators (cont.) Common factors. See Factors; Greatest Common
finding square roots with, 462 Factor (GCF)
memory keys on, 608
order of operations and, 74, 437 Common multiples, 156, 157
simplifying with, 231–232 Common polygons, 311
Communication
Canceling
in reducing fractions, 358–362, 376 Discuss, 13, 14, 15, 19, 20, 24, 43, 47, 75, 83, 112,
in the Sign Game, 543 113, 123, 128, 139, 142, 151, 159, 218, 250,
unit multipliers and, 597–598 256, 300, 307, 346, 359, 369, 404, 427, 448, 457,
467, 471, 488, 498, 543, 553, 588, 612, 623
Capacity, 404–407
“Casting out nines,” 533 Formulate a problem 26, 35, 57, 61, 62, 67, 79–80,
Categories, explaining, 400 86, 97, 98, 140, 252, 261, 293, 308, 330, 344,
Celsius (C), 51, 80 345, 361, 378, 459, 464, 550, 556, 585, 623
Centimeter (cm), 37, 422
Centimeter cubed (cm3), 318 Writing about mathematics 11, 16, 17, 21, 22, 24,
Centimeter squared (cm2), 164, 197, 409, 422 27, 30, 31, 33, 34, 41, 44, 45, 49, 52, 67, 69,
Chance, 299–305, 471. See also Probability 71, 72, 79, 85, 91, 92, 97, 104, 107–108, 111,
Checking answers. See also Inverse operations 125, 129, 143, 144, 148, 219, 223, 224, 246,
253, 258, 267, 270, 278, 287, 290, 305, 313,
in addition problems, 8, 9 323, 328, 330, 335, 340, 346, 356, 363, 373,
calculators for, 608 381, 384, 391, 392, 402, 405, 410, 433, 439,
in division problems, 25, 272 444, 458, 459, 467, 481, 487, 515, 522, 530,
estimating for, 617 547, 552, 576, 595, 619, 622, 627
guess-and-check method, 28, 460–464
in mixed number problems, 329–332, 343 Commutative property
in multiplication problems, 15, 43 of addition, 8, 9, 10
pairing technique, 63 of multiplication, 13, 246, 427, 428
in subtraction problems, 9, 20, 61, 251 subtraction and the, 8, 10
in unknown-number problems, 19, 20, 25–26
Cipher to the rule of three, 452 Comparing
Circle graphs, 205–215, 264–265 decimals, 231–234
Circles defined, 173
activity, 142 exponential expressions, 381
area of, 447–451, 626 fractions, 395–398, 441–446
circumference of, 141–142, 244–246 geometric solids, 315
compasses for drawing, 142 integers, 47
diameter of, 141–142, 190, 246 number lines for, 46–49
fractional parts of, 115 ratios and, 494
measures of, 141–144 symbols for
perimeter of. See Perimeter equal to (=), 47, 381
radius of, 141–142, 190 greater than (>), 47, 110, 381
Circular cylinders. See Cylinders less than (<), 47, 381
Circumference, 141–142, 244–246. See also pi word problems about, 68–72
Classification
parallelograms, 334 Compasses
of polygons, 311 activity, 142
of quadrilaterals, 333–337 for bisecting angles, 418–420
of triangles, 311, 484–487 for bisecting segments, 417–418
Clock faces, fractional parts of, 111, 115 drawing with, 142, 418
Clockwise/counterclockwise, 465 investigations, 417–420
Closed curve, 23 types of, 142
Closed-option surveys, 57
Coins, problems using, 7 Complementary angles, 353–357
Coin toss experiments, 302 Complementary probability, 301–303, 400, 524–527
Combining, in word problems, 58–62 Complex shapes
Commas in number systems, 64–65
Common denominators. See also Denominators area of, 557–560
in addition and subtraction of fractions, 127–131 defined, 538, 557
drawing, 484, 538
renaming both fractions, 289–294 perimeter of, 538–542
renaming one fraction, 285–288 Composite numbers, 102, 337
least common, 286, 320–321 Compound interest, 606–611
in multiplication and division of fractions, 342 Compound outcomes, 524–526
for subtraction of mixed numbers, 329–332 Cones, 314, 630–636
Congruence in geometric figures, 311, 408, 426, 561,
668 Saxon Math Course 1 562, 566–567
Consecutive integers, 88
Construction, of bisectors in geometric figures,
417–420

Conversion. See also Equivalent; Mixed measures Cubic centimeters (cm3), 318 INDEX
of area, 618 Cubic units, 318, 426
decimals Cup (c.), 404–405
fraction equivalents, 381–382, 385–389, Cylinders
395–398
by multiplication, 488–492 area of, 634–635
percent equivalents, 216–217, 390–394, attributes of, 314
488–492 bases of, 634
probabilities to, 387 drawing, 314, 316
ratios to, 385–389 height of, 626
defined, 152 volume of, 626–629, 631–633
fractions
decimal equivalents, 381–382 D
decimals equivalents, 385–389, 395–398
by division, 385–389 Data. See also Graphs
percent equivalents, 216–217, 390–394, collecting, 211–215
488–492, 602–605 displaying
improper fractions bar graphs, 211, 213, 265
to mixed numbers, 133, 324–328, 342 circle graphs, 264
mixed numbers to, 324–328, 342 histograms, 55
of length line graphs, 211, 305
centimeters to millimeters, 38, 39 line plots, 211, 213, 266, 279
feet to yards, 598 pictographs, 264
inches to centimeters, 38 qualitative, 211–213, 264–265
meters to centimeters, 38 quantitative, 211–213, 266–267
metric system, 404 stem-and-leaf plots, 264–267, 384, 487
mixed numbers, 534 interpreting, 211–215
to improper fractions, 324–328, 342 mean, 95, 266
by multiplication, 488–492 median, 266
percents mode, 266
decimal equivalents, 216–217, 390–394, organizing, 211–215
488–492 qualitative, 211–213, 264–265
fraction equivalents, 216–217, 390–394, quantitative, 211–213, 266–267
488–492, 602–605 range, 266
by multiplication, 488–492
to probability, 301–302 Data point, 266
prefixes for, 533 Decimal division, 236, 272–273, 385
of ratios to decimals, 385–389 Decimal numbers. See Decimals
unit multipliers for, 597–598 Decimal place values, 8, 9, 178–181, 184, 239
units of measure, 323, 357, 404–405, 412, 534, 572 Decimal points
U.S. Customary System, 404–405
aligning by, 8, 9, 192
Coordinate plane, 363–367, 499–500, 581 “and” in reading or writing, 240
Corresponding angles, 504, 567–569 in decimal division, 236, 272–273, 385
Corresponding parts, 566–572, 579 money and, 8, 13, 15
Counterclockwise/clockwise, 465 in multiplication by tens and hundreds, 240
“Counting by twos,” 51 purpose of, 178, 184, 241
Counting numbers shifting by division or multiplication, 240, 272–273
whole numbers and, 195–199
defined, 46 words that indicate, 240
integers as, 74, 517 Decimals
multiples and, 156 adding, 8–9, 191–194, 276–277
whole numbers and, 46
Cross products and proportions, 441–446 to whole numbers, 195–199
Cubed numbers, exponent indicating, 380 “and” in reading or writing, 184
Cubes (geometric figures) arithmetic operations rule, 276–277
area of, 497 comparing, 231–234
attributes of, 314 converting
drawing, 314
faces of, 315 by multiplication, 488–492
nets, 318, 319 probabilities to, 387
as rectangular prisms, 497 ratios to, 385–389
as regular polyhedrons, 314 dividing
volume of, 318, 428 rules for, 276–277
by ten and by one hundred, 272–276
by whole numbers, 235–238
dividing by, 254–258

Index 669

Decimals (cont.) Divisibility, 112–116
equivalent, 236 Division
expanded notation, 239–243
fraction equivalents, 381–382, 385–389, 395–398, answers as mixed numbers, 132–135
513–516 “are in” as indicator of, 135
mixed, 183 checking answers, 15, 25, 272
multiplying, 200–204, 232, 239–243, 276–277 converting fractions to decimals using, 385–389
on number lines, 259–263 by decimals, 254–258
percent equivalents, 216–217, 390–394, 488–492, of decimals
513–516
reading, 182–186 rules for, 276–277
rounding, 268–271 by ten and by one hundred, 272–276
simplifying, 231–234 by whole numbers, 235–238
subtracting, 191–194, 276–277 dividends. See Dividends
from whole numbers, 195–199 divisors. See Divisors
unknown factors in, 452–455 equivalent, 225–230
unknown numbers in, 225–230 even numbers and, 51
writing fact families, 8–12
alignment in, 8 factors and, 99
in expanded notation, 239–243 “for each” in, 123, 422
fraction equivalents, 182–186, 380–384, by fractions, 33
385–389, 513–516 of fractions, 359
as percents, 390–394, 488–492, 513–516 common denominators and, 152–153, 342
probabilities as, 387 by fractions, 280–285
ratios as, 385–389 of integers, 587–591
and reading, 182–186 long versus short method, 15
mental math, 272–276
Decimals Chart, 276–279 of mixed numbers, 349–352
Degrees, measuring turns by, 465 of money, 12–18, 362, 379
Denominators. See also Common denominators; multiplication as inverse of, 15, 24, 452
odd numbers and, 51
Fractions order of operations, 29, 30, 47
decimals as, 182 by primes, 337–341
least common, 286, 320–321 quotients. See Quotients
mixed numbers to improper fractions, 325 remainders in, 15, 582
multiplying, 150–151 short-division method, 15
as term of a fraction, 32, 127, 343 of signed numbers, 588
Diagrams. See also Draw a picture or diagram symbols for, 14, 133, 385
graphs. See Graphs of units of measure, 421–425
ratio boxes. See Ratio boxes unknown numbers in, 23–27, 123
Diameter of whole numbers, 12–18
defined, 141, 190 by fractions, 259–263
formula for, 246 word problems, 582–591
radius and, 141–142 words that indicate, 123, 135, 423
Dice (dot cubes), 68, 174 Divisors
Difference. See also Subtraction as decimals, 254–255
defined, 8, 11 defined, 14
greater-lesser, 68 function of, 22
later-earlier, 69, 170–171 missing, 25
in operations of arithmetic, 8, 65 zero as, 14
Digits dot-to-dot drawing, 365–367
place value of, 64 Doubling, 51
shown in standard notation, 593 Draw a picture or diagram. See Problem-solving
summing for factors, 113 strategies
Discuss. See Communication Drawing. See also Diagrams; Graphs
Distance. See also Length activity, 142
average, 263, 455 compasses for, 142, 418
estimating, 478 on coordinate planes, 581
measuring, 59, 478 cubes, 314
Distribution, bimodal, 267 cylinders, 314, 316
Dividends geometric solids, 315–316
defined, 14, 103 prisms, 314, 315
function of, 22 protractors for, 161–163
missing, 25 to scale, 52, 578–581

670 Saxon Math Course 1

E Equations (cont.) INDEX
writing for problem-solving, 78–80, 151–153,
Early Finishers. See Enrichment 165–166, 169–171, 174, 175, 183–184, 192,
Edges, 315, 332, 497 196–198, 217–218, 222, 226–228, 260, 268–269,
Elapsed-time, 68–72, 169–173 290–291, 342–343, 349–350, 409–410, 421–423,
Electrical-charge model in Sign Game, 543–545 427–428, 432–433, 474–475, 490, 509–510,
Endpoints, 37 534, 539, 548–550, 553–554, 557–558, 592–594,
Enrichment 596, 607–608, 622–623, 627

Early Finishers Equilateral triangles, 484, 485
Choose a strategy, 284, 352, 403, 523, 629 Equilibrium, 36
Math applications, 323, 435 Equivalent forms
Math and architecture, 323
Math and geography, 483 decimals, 236
Math and science, 394, 451, 532 defined, 137, 225
Real-world applications, 17, 22, 31, 41, 77, 81, division problems, 225–230, 254–256
92, 98, 104, 108, 116, 126, 131, 144, 155, fractions
160, 177, 194, 204, 238, 249, 253, 258,
263, 279, 294, 298, 305, 309, 332, 357, cross products for determining, 441–446
362, 379, 384, 412, 440, 446, 455, 469, defined, 137
478, 487, 496, 516, 572, 591, 601, 605, equal fractions as, 597
611, 616 example of, 152
fraction-decimal-percent, 513–516
Investigation extensions writing, 391
angles, drawing and measuring with numbers, 225
protractors, 163 ratios, 432, 442
bar graphs, 57 Estimation. See also Approximation
bisectors, geometric construction of, 420 of area, 447–448, 617–620
choose a method, 111 benchmarks for, 37
circle graphs, 214 checking answers with, 617
compare fractions, 111 diameters in a circumference, 245–246
compound experiments, 527 factors in, 30
cones, volume, 635 grids for, 447–448, 617–618
coordinate planes, 367 guess-and-check method, 460–464
cubes, surface area of, 636 probability and, 472–473
displaying data, 267 products of factors that are mixed numbers, 343
examples and non-examples, 111 in reading graphs, 84
experimental probability, 472–473 reasonableness and, 83, 268–270, 460, 487, 582
geometric solids, 319 by rounding, 83
histogram intervals, 57 of square roots, 460–464
prisms, volume, 635 of sums, 83
scale factor, 581 words that indicate, 84
surface area, 318, 636 Even numbers
surveys, 57 “counting by twos,” 51
views of geometric figures, 318–319 factors of, 101
volume, 635 identifying, 112
Even number sequences, 51, 52
Equal groups, 78–81, 117–121 Examples and non-examples, 51, 52, 111, 163, 438
Equalities. See Equivalent Forms Expanded notation
Equations. See also Representation with decimals, 239–243
with exponents, 479–484
addition. See Addition place value and, 169
division. See Division of whole numbers, 169–173
exponential. See Exponents zero in, 169
formulas. See Formulas Experimental probability, 470–473
formulate an. See Representation Explain. See Communication
multiplication. See Multiplication Exponents. See also Powers of ten
order of operations. See Order of Operations bases and, 196
with percents. See Percents correct form for, 380
proportion. See Proportions expanded notation with, 479–484
ratios. See Ratios finding values of, 381
rewriting to simplify, 19 fractions and, 479–484
solving by inspection, 554 function of, 380
subtraction. See Subtraction order of operations with, 381, 479–484
two-step, 13, 553–556
using inverse operations, 554 Index 671

Exponents (cont.) Formulas (cont.)
powers of ten and, 381 for area (cont.)
reading and writing, 196, 380–381 of squares, 196, 474
of triangles, 409, 474
Exterior angles, 504, 508–509 for bases, of prisms, 630
common rates, 123
F for length
circumference, 246
Faces diameter, 246
on number cubes, 18 for perimeter
of rectangular prisms, 315 of octagons, 311
of parallelograms, 474
Fact families of rectangles, 474
addition and subtraction, 7–11 of squares, 474
division and multiplication, 8–12 of triangles, 474
for volume
Facts Practice (Power-Up) of cubes, 428
Each lesson Power-Up presents a facts practice of cylinders, 627
that builds fluency in basic math facts. of prisms, 630
of pyramids, 630–631
Factor pairs, 102
Factors. See also Prime factorization Formulate a problem. See Communication
Four-step problem-solving process, 3, 7, 18, 23, 28,
bases and, 196
common factors, 105–106, 152, 175 36, 42, 59, 63, 69, 70, 87, 436
constant, 413–421 Fractional parts of the whole
defined, 12, 99, 105
divisibility tests for, 112 equal groups stories with, 117–121
division and, 99 naming parts of, 32–35
equal to one, 280–285 Fractional-parts statements, 399–403
in estimation, 30 Fraction bar indicating division (—), 14, 133, 385
of even numbers, 101, 112 Fraction-decimal-percent equivalents, 513–516
greatest common. See Greatest Common Factor Fraction-decimal-percent table, 514
Fraction manipulatives, 109–111
(GCF) Fractions. See also Denominators; Mixed numbers
multiplying, 12, 99 adding
of positive integers, 99–100, 105–106, 114, 280–281,
with common denominators, 127–131, 342
441–442 with different denominators, 285–294
of prime numbers, 101, 106 SOS memory aid, 295–298, 342
products and, 12, 99 three or more, 320–323
reducing fractions and, 150–155, 175 three-step process, 295–298
strategy for finding, 100 canceling terms, 358–362, 376
of ten, 100 common, 32
unknown with common denominators. See Common
denominators
in addition and subtraction, 18–22 comparing, 395–398, 441–446
on both sides of an equation, 453 decimal equivalents, 381–382, 385–389, 395–398,
calculating, 24 513–516
decimal numbers, 452–455 denominator. See Denominators
in division and multiplication, 23–27 dividing
method of solving for, 452–453 by fractions, 280–285, 342, 359
mixed numbers, 452–455 whole numbers by, 33, 259–263
in multiplication, 123 equal to one, 221–224, 290, 597–598
whole numbers and, 102, 105 equivalent
Factor trees, 337–341 cross products for determining, 441–446
Fahrenheit (F), 51, 80 defined, 137
Figures. See Geometric figures equal fractions as, 597
Find a pattern. See Problem-solving strategies example of, 152
Fluid ounces, 405 fraction-decimal-percent, 513–516
Foot (ft), 37 writing, 391
“for each” exponents and, 479–484
in division problems, 423 finding the whole using, 612–616
in rate problems, 123 improper, 138, 324–328, 342
Formulas lowest terms, defined, 277
for area
of bases, 427
of circles, 448–449, 626
of parallelograms, 369, 370, 371, 409, 474
of rectangles, 200, 474

672 Saxon Math Course 1

Fractions (cont.) Geometric figures (cont.) INDEX
multiplying symmetry in, 573–578
common denominators for, 342 triangles. See Triangles
cross product, 441–446
process of, 150–155 Geometric formulas, 474–478. See also Formulas
reducing before, 358–362 Graphing calculator, online activity references, 74,
three or more, 375–379
on number lines, 87–92 106, 157, 269, 364, 433, 480, 607
numerators. See Numerators Graphing functions, 497–502
percent equivalents, 216–217, 390–394, 488–492, Graphs
513–516, 602–605
reciprocals. See Reciprocals bar, 55, 84, 265
reducing. See Reducing fractions circle, 205–215, 264–265
renaming on the coordinate plane, 363–367, 499–500, 581
multiplying by one, 221–224, 290 data on
purpose of, 307
without common denominators, 285–294 bar graphs, 211, 213, 265
simplifying, 276–279 histograms, 55
SOS memory aid for solving problems with, line graphs, 211, 305
295–298, 342, 349 line plots, 211, 266, 305
subtracting pictographs, 264
with common denominators, 127–131, 342 stem-and-leaf plots, 264–267, 384, 487
with different denominators, 285–294 histograms, 55–57
three-step process, 295–298 line, 93–98, 211
from whole numbers, 187–190 on number lines. See Number lines
terms of, 157 pictographs, 264
unknown numbers, 225–230 reading, 84
visualizing on clock faces, 111 stem-and-leaf plots, 267
writing Great Britain, 37
decimal equivalents, 182–186, 380–384, Greater-lesser subtraction pattern, 68
385–389, 513–516 Greater than symbol (>), 47, 381
percent equivalents, 174–177, 513–516, Greatest Common Factor (GCF), 106–111, 152–153, 175
602–605 Grids
as percents, 390–394, 488–492 the coordinate plane, 363–367
whole numbers as, 151 estimating using, 447–448, 617–618
Grouping property. See Associative property;
Fractions chart, 375–379 Parentheses
Freedom 7 spacecraft, 581 Guess-and-check. See Problem-solving strategies
Freezing point, 51
Frequency tables, 54–57, 470–473 H
Functions, 497–502, 552
Halfway, 83, 95
G Height

Gallon (gal), 404–405 abbreviation for, 475
Gauss, Karl Friedrich, 63 of cylinders, 626
GCF (Greatest common factor). See Greatest of parallelograms, 370–371, 409
of prisms, 630
Common Factor (GCF) of pyramids, 630
Geometric figures of triangles, 409–410
Hexagons
bases of. See Bases of geometric figures characteristics of, 311
bisectors, 417–420 irregular, 557
circles. See Circles Higher order thinking skills. See Thinking skills
congruence in, 311, 408, 426, 562, 566–567 Histograms, 54–57
corresponding parts, 566–572, 579 Horizontal axis, 95, 363
cubes. See Cubes (geometric figures) Hundreds
cylinders. See Cylinders in decimals, 182
perimeter of. See Perimeter mental math for
polygons. See Polygons
prisms. See Prisms dividing, 272–276
quadrilaterals. See Quadrilaterals multiplying by, 239–243
rectangles. See Rectangles multiplying decimals by, 255–256
similarity in, 566–572 Hundredths, 179, 184
solids. See Solids
squares. See Squares I

Identity property
of addition, 8

Index 673

Identity property (cont.) Investigations (cont.)
of multiplication, 14, 222, 280, 488 probability experiments, 470–473
protractors, 161–163
Improper fractions pyramids, volume of, 630–636
converting mixed numbers to, 324–328, 342 scale drawings and models, 578–581
defined, 138 scale factor, 578–581
surface area, 630–636
Inch (in.), 37, 38, 39 surveys, 54–57
Inches, cubic (in.3), 318 volume
Indirect information, 399–403 of cones, 630–636
“in each” in equal groups, 79 of cylinders, 630–636
Inequality symbols, 47, 110, 381 of prisms, 630–636
Infinity, 74 of pyramids, 630–636
Information, finding unstated, 399–403
Integers Irrational numbers, 461–462
Irregular shapes, measuring, 618–619. See also
adding, 517–523
algebraic addition of, 520, 543–547 Complex shapes
consecutive, 88 Isolation of the variable, 19
counting numbers as, 74, 517 Isosceles triangles, 484, 485
defined, 74, 75, 88, 517
dividing, 587–591 J
multiplying, 587–591
on number lines, 517 Jordan curve, 23
ordering, 517–520
subtracting, 517–523 K
Interest, compound and simple, 606–611
Interior angles Kilometer (km), 37
forming, 146 kilowatt hours (kwh), 494
sum of measures of, 508–512
of transversals, 504 L
International System of Units (SI), 37
Intersecting lines, angle pairs formed by, 145–149 Language, math, See Math language; Reading math;
Inverse operations Vocabulary
addition and subtraction, 9, 10, 19
division and multiplication, 15, 24, 452 Last-digit divisibility test, 112
squaring and square roots, 197 Lateral surface area, 634
two-step equations, 554 Later-earlier subtraction pattern, 69, 170–171
Investigation extensions. See Enrichment Least common denominator, 286, 320–321
Investigations Least common multiple (LCM), 156–163, 290
angle bisectors, 418–420
angles, drawing and measuring with protractors, adding three or more fractions, 320–321
defined, 286
161–163 Legends, 578
bisectors, constructing, 417–420 Length. See also Circumference; Perimeter
compasses, 417–420 abbreviation for, 475
compound probability experiments, 524–527 activity, 37–38
cones, 630–636 benchmarks for, 37
coordinate planes, 363–367 conversion of units of measure, 38, 39, 598
cylinders, 630–636 estimating, 37
data of segments, 37, 353–357
sides of a square, 43, 107
collection, 211–215 units of measure, 37, 43, 164, 422
displaying, 211–215, 264–267 Less than
interpreting, 211–215 in subtraction, 75
organizing, 211–215 Letters
drawing points designated with, 353
to scale, 578–581 used to represent numbers, 21
using protractors, 161–163 Lincoln, Abraham, 70, 452
experimental probability, 470–473 Line graphs, 93–98, 211
fraction manipulatives, 109–111 Line plots, 211, 213, 266
frequency tables, 54–57 Lines. See also Number lines; Segments
geometric solids, 314–319 intersecting, 145–149
histograms, 54–57 naming, 353
models, to scale, 578–581 oblique, 145
perpendicular bisectors, 417–418 parallel, 145, 503–507
prisms, volume of, 630–636 perpendicular, 145, 369–371, 409, 417–418, 630
properties of, 37
674 Saxon Math Course 1

Lines (cont.) Measurement (cont.) INDEX
segments and rays, 36–41 ratios of, 123–124
symbol for (↔), 37, 353 of rectangles. See Rectangles
transversals, 503–507 of surface area. See Area
of temperature, 51, 52
Line segments. See Segments of turns, 465–469
Lines of symmetry, 573–574 of volume. See Volume
Logical reasoning, See Problem-solving strategies
Long division versus short division, 15 Measures of central tendency. See Mean; Median;
Lowest terms of fractions, defined, 277 Mode

M Median, 266–267, 313
Memory aids
Make a model. See Problem-solving strategies
Make an organized list. See Problem-solving calculator keys, 608
decimal number chart, 277
strategies Please Excuse My Dear Aunt Sally, 480
Make it simpler. See Problem-solving strategies SOS, 295–298, 306–309, 342, 349, 375–379
Make or use a table, chart, or graph. See Problem- Mental Math (Power-Up). A variety of mental math
skills and strategies are developed in the lesson
solving strategies Power-Ups.
Manipulatives/Hands-on. See Representation Meter (m), 37
Marbles, 302–303, 400, 471–473, 524–526 Metric system, 37, 38, 404–405. See also Units of
Mass versus weight, 533–537 measure
Math and other subjects Mile (mi), 37
Miles per gallon (mpg), 123
and architecture, 323, 512 Miles per hour (mph), 123, 422
and art, 332, 347, 590 Milliliter (mL), 404
and geography, 57, 75, 77, 84, 130, 131, 148, 233, Millimeter (mm), 37
Minuends, 8, 19
273, 287, 330, 372, 483 Minus sign. See Negative numbers; Signed numbers
history, 52, 63, 69, 70, 81, 85, 91, 103, 114, 119, Mirror images, 574
Missing numbers. See Unknown numbers
148, 154, 229, 270, 283, 296, 334, 360. 452, Mixed measures. See also Units of measure
560, 575, 577 adding and subtracting, 298, 534, 592–596
music, 327, 360, 624 Mixed numbers. See also Improper fractions
other cultures, 37, 433 adding, 136–140, 306–309
science, 36, 52, 53, 62, 66, 71–73, 76, 77, 79, 80, “and” in naming, 184
85, 97, 98, 103, 106, 108, 125, 130, 134, 154, converting
159, 223, 242, 248, 267, 275, 288, 297, 301,
306, 307, 308, 313, 361, 374, 377, 382, 401, to improper fractions, 324–328, 342
402, 403, 414, 444, 453, 491, 492, 505, 506, by multiplication, 488–492
531, 596 defined, 88
sports, 26, 41, 44, 56, 61, 86, 91, 99, 107, 120, 122, dividing, 349–352
126, 134, 135, 154, 155, 216, 229, 236, 243, division answers as, 132–135
252, 280, 283, 298, 323, 351, 395, 401, 415, 444, factor trees, 339
445, 477–479, 507, 545, 563, 599, 601, 624 multiplying, 326, 342–345
Math language, 21, 22, 64, 65, 74, 84, 88, 103, 105, on number lines, 87–92
114, 122, 127, 135, 138, 146, 152, 156, 165, 190, ratios as, 122
211, 216, 222, 225, 260, 262, 277, 286, 302, 308, subtracting
311, 319, 333, 350, 369, 376, 380, 405, 408, 417, with common denominators, 329–332
418, 426, 431, 432, 442, 461, 465, 494, 503, 529, and reducing answers, 136–140
533, 548, 552, 561, 593, 596, 608 with regrouping, 188, 250–253
Mean, 95, 266–267, 313. See also Average unknown factors in, 452–455
Measurement. See also Units of measure Mode, 266–267, 313
abbreviations of. See Abbreviations Model. See Representation
of angles, 161–163 Models. See also Make a model; Representation
of area. See Area of addition situations, 109, 127, 228, 285–287,
benchmarks for, 37, 405, 534, 553 290, 295, 306–307, 320–321
of capacity, 404–407 of subtraction situations, 127–129, 187–188,
of circles. See Circles 250–251, 290–291, 296
common rates, 123 of parallelograms, 369
of height. See Height to scale, 578–581
of length. See Length Money
linear. See Length arithmetic operations with, 7–18, 92, 235, 258,
parallax in, 50 362, 379, 616
of perimeters. See Perimeter
protractors for, 161–163 Index 675

Money (cont.) Naming (cont.)
coin problems, 7 rays, 353
decimal places in, 8, 13, 179 segments, 353–354
interest, compound and simple, 606–611
rate in, 123 Negative numbers. See also Signed numbers
rounding with, 268–270 addition of, 518, 519
subtracting, 7–11 algebraic addition of, 543–547
symbol for, 8, 13 graphing, 363
writing, 79, 195 integers as, 74
on number lines, 73–77
Multiples. See also Least common multiple (LCM) real-world uses of, 46
calculating, 132–135 symbol for, 73, 543, 544
common, 156, 157, 286, 320
Negative signs (–), 73, 543, 544
Multiplication. See also Exponents Nets, 318, 319, 634
associative property of, 30 Non-examples. See Examples and non-examples
checking answers, 15, 25, 43 Nonprime numbers. See Composite numbers
commutative property of, 13, 246, 427, 428 Nonzero, meaning of, 217
of decimals, 200–204, 232, 239–243, 276–277 Notation. See Expanded notation; Standard notation
division as inverse of, 15, 24, 452 Number cubes. See also Cubes
fact families, 8–12
factors and, 12, 24, 99 faces of, 18
of fractions probability with, 302, 387, 473
common denominators and, 342 Number lines. See also Graphs
cross product, 441–446 addition on, 518
process of, 150–155 comparing using, 46–49
three or more, 375–379 counting numbers on, 46, 74
by fractions equal to one, 221–224 decimals on, 259–263
by hundreds, 239–243 fractions on, 87–92
identity property of, 14, 222, 280, 488 graphing on, 363–367
of integers, 587–591 integers on, 74, 517
mental math for, 239–243 mixed numbers on, 87–92
of mixed numbers, 326, 342–345 negative numbers on, 73–77
of money, 12–18 opposite numbers on, 518, 520
“of” as term for, 150 ordering with, 46–49
“of” as term in, 350 origin of, 363
order of operations, 29, 65 positive numbers of, 73
partial products, 13 rounding with, 82
by powers of ten, 592–596 as rulers, 90
reducing rates before, 493–496 tick marks on, 46, 74, 88
of signed numbers, 587–589 whole numbers on, 46
symbols for, 12, 13, 31, 422 Numbers. See also Digits; Integers
by tens, 13, 239–243 comparing. See Comparing
of three numbers, 30 composite, 102, 337
two-digit numbers, 13 counting. See Counting numbers
of units of measure, 421–425 decimal. See Decimals
unknown numbers in, 23–27, 123 equal to one, 221–224, 280–285, 290, 597–598
of whole numbers, 12–18, 588 equivalent, 225
words that indicate, 150, 350 even, 51, 101, 112
zero property of, 14 greater than one, 489
halfway, 95
Multiplication sequences, 50 large, reading and writing, 64–65
Multistep problems, 65–66 letters used to represent, 19, 21
missing. See Unknown numbers
N mixed. See Mixed numbers
negative. See Negative numbers
Naming. See also Renaming nonprime. See Composite numbers
“and” in mixed numbers, 184 odd, 51, 52
angles, 145–149 percents of. See Percents
complex shapes, 557 positive. See Positive numbers
fractional parts, 32 prime. See Prime numbers
lines, 353 signed. See Signed numbers
polygons, 311 whole. See Whole numbers
powers of ten, 594 writing. See Expanded notation; Proportions;

676 Saxon Math Course 1 Standard notation

Number sentences. See Equations Pairs (cont.) INDEX
Number systems corresponding angles, 504, 567–569
ordered, 363, 500
base ten, 64, 179
commas in, 64, 65 Parallax, 50
place value in, 169 Parallel lines, 145, 503–507
Numerators. See also Fractions Parallelograms
adding, 128
mixed numbers to improper fractions, 326 angles of, 368, 369
multiplying, 150–151 area of, 369–371, 409, 474
subtracting, 128 characteristics of, 333
as term of a fraction, 343 height of, 370–371
as term of fractions, 32 model of, 369
perimeter of, 369, 474
O properties of, 334, 368–374
as quadrilateral, 334
Oblique lines, 145 rectangles as, 334, 371
Obtuse angles rhombus as, 596
sides of, 369
measuring, 161–163 Parentheses
naming, 146–147 clarifying with, 481, 519
of transversals, 503, 504 in order of operations, 29, 47, 381
Obtuse triangles, 485 symbol for multiplication, 12–13, 31
Octagons, 311, 364 Partial products, 13
Odd numbers, 51, 52 Patterns
Odd number sequences, 51 equal groups, 117
Odometers, 59 for problem-solving, 7, 51, 59–61, 63, 68–70, 117,
“Of” as term for multiplication, 150, 350 138, 428
One real world applications using, 319
as multiplicative identity, 13 in subtraction, 60, 68–70, 170–171
numbers equal to, 221–224, 280–285, 290, 597–598 Pentagons, 311
numbers greater than, 489 Per, defined, 123, 423
in numerator, 33 Percents
Open-option surveys, 57 converting
Operations
of arithmetic. See Arithmetic operations by multiplication, 488–492
inverse. See Inverse operations to probability, 301–302
order of. See Order of Operations decimal equivalents, 216–217, 390–394, 488–492,
Opposite numbers 513–516
defined, 518 defined, 216, 548, 602
on number lines, 74, 520 finding the whole using, 621–625
symbol for (-), 544 fraction equivalents, 216–217, 390–394, 488–492,
of zero, 74 513–516, 602–605
Ordered pairs, 363, 500 greater than one hundred, 489
Ordering integers, 46–47 properties of, 216, 390
Order of Operations. See also Commutative property word problems, solving using proportions, 548–552
calculators for, 30, 74 writing
division, 47 decimals as, 390–394, 488–492, 513–516
with exponents, 381, 479–484 fractional equivalents, 174–177, 602–605
memory aid. See Memory aids fractions as, 390–394, 488–492, 513–516
parentheses in, 29, 30, 47, 381 symbol for, 174, 390
Please Excuse My Dear Aunt Sally, 480 Perfect squares, 197, 460–464
process, 28–31 Perimeter
rules for, 29, 47, 480 abbreviation for, 475
for simplification, 29, 436–440, 480 activity about, 42–43
subtraction, 9 area vs., 164
using calculators, 437 of circles. See Circumference
Organized lists for problem-solving, 42 of complex shapes, 538–542
Origin, 363 of octagons, 311
Ounce (oz.), 404–405 of parallelograms, 369, 474
of polygons, 44
P of rectangles, 43, 364–365, 474
of squares, 43, 72, 474
Pairing technique, 63 of triangles, 474
Pairs units of measure, 43

Index 677

Permutations, 42 Powers of ten (cont.)
Perpendicular bisectors, 417–418 place value and, 64
Perpendicular lines whole number place values, 479

angles formed by, 145 Power-Up. See Facts practice (Power-Up); Mental
in area of parallelograms, 369–371 Math (Power-Up); Problem Solving problems
bisectors, 417–418 (Power-Up)
for finding area, 409, 630
pi, 244–249, 448–449, 627 Prime factorization, 101, 337–341, 346–348, 381.
Pictographs, 264 See also Factors
Pie charts. See Circle graphs
Pie graphs. See Circle graphs Prime numbers
Pint (pt.), 404–405 activity with, 102
Placeholder, zero as, 205–215, 277 composite numbers compared, 337
Place value defined, 160
in addition, 8 division by, 337–341
commas and, 64, 65 Erathosthenes’ Sieve, 102
comparing numbers using, 47 factors of, 101, 106
in decimals, 8, 9, 178–181 greatest common factor (GCF), 106
and expanded notation, 169
powers of ten and, 64, 479, 593 Principal, 606
in subtraction, 9 Prisms
through trillions, 63–67
in whole numbers, 64 area of, 633
Place value chart, 64 drawing, 314, 315
Place value system, 65 rectangular. See Rectangular prisms
Plane, the coordinate, 363–367, 499–500, 581 triangular, 314, 316
Platonic solids, 315 volume of, 630–631
Please Excuse My Dear Aunt Sally, 480 Probability
Plots in word problems, 58–59 chance and, 299–305, 471
p.m., 170 compound experiments, 524–527
Points converting to decimals, 387
coordinates of, 363 of events, 471–473
decimal. See Decimal points events and their complement, 301–303, 400,
freezing and boiling, 51
on line graphs, 95 524–527
representing with letters, 353 experimental, 470–473
Polygons. See also specific polygons range of, 300
classifying, 311–312 theoretical, 470
common, 311 Problem solving
congruent, 408, 568 cross-curricular. See Math and other subjects
defined, 310–312 four-step process. See Four-step problem-
as faces of polyhedrons, 314
four-sided, 311 solving process
lines of symmetry, 574 real-world. See Real-world application problems
naming, 311 strategies. See Problem-solving strategies
perimeter of, 44 overview. See Problem-solving overview
regular, 44, 311 Problem-solving overview, 1–6
sides to vertices relationship, 311 Problem Solving problems (Power-Up)
similar, 568 Each lesson Power-Up presents a strategy
triangles as, 484
Polyhedrons, 314 problem that is solved using the four-step
Population, 55, 213 problem-solving process.
Positive numbers Problem-solving strategies
algebraic addition of, 543–547 Act it out or make a model, 50, 156, 178, 195,
on number lines, 73 Draw a picture or diagram 7, 73, 87, 105, 122, 127,
Sign Game, 543–545 150, 156, 187, 200, 250, 259, 358, 385, 404,
symbol for, 543, 587 408, 426, 460, 508, 553, 582, 592, 612
Powers. See also Exponents Find a pattern, 7, 23, 58, 63, 82, 368, 413, 488,
and fractions, 479–484 508, 528, 533, 543, 561, 566, 592
reading correctly, 380–381 Guess and check, 28, 32, 132, 164, 169, 205,
Powers of ten. See also Exponents 390, 395, 441, 573, 602
multiplying, 592–596 Make an organized list, 12, 136, 169, 195, 221,
268, 299, 493, 380, 447
678 Saxon Math Course 1 Make it simpler, 23, 63, 164, 187, 205, 272, 295,
329, 413, 431, 456, 465
Make or use a table, chart, or graph, 58, 73, 306,
320, 333, 421, 517, 548, 561

Problem-solving strategies (cont.) R INDEX
Use logical reasoning, 18, 28, 32, 36, 46, 68, 78,
99, 112, 122, 132, 136, 141, 145, 174, 178, 182, Radius (radii), 141–142, 190
191, 225, 231, 235, 239, 244, 254, 276, 285, Range, 266–267, 300, 308, 313
289, 310, 333, 337, 349, 353, 358, 375, 385, Rates, 122–126
390, 395, 431, 441, 452, 456, 460, 465, 479,
484, 493, 513, 517, 538, 548, 557, 573, 582, reducing before multiplying, 493–496
597, 612, 626 Ratio boxes, 456–458, 528–529, 548–550
Work backwards, 78, 285, 289, 342, 399, 404, Ratios
408, 413, 436, 497, 587
Write a number sentence or equation, 18, 87, 117, as comparisons, 494
191, 205, 216, 221, 259, 276, 280, 295, 306, converting to decimals, 385–389
324, 329, 342, 346, 353, 452, 474, 503, 553, defined, 122, 431, 494
557, 566, 597, 606, 617, 621 equivalent, 432, 442

Products. See also Multiplication writing, 385–389
defined, 12 fractional form of, 122–126
factors and, 12, 99 problems involving totals, 528–532
multiples and, 156 proportions and, 431–432, 442–443, 529
partial, 13 reducing, 153
of reciprocals, 157, 349 symbols for (:), 122
of signed numbers, 588 win-loss, 123
unknown numbers, 123 word problems

Proportions. See also Rates; Ratios using constant factors, 413–421
cipher to the rule of three, 452 using proportions, 456–459
in congruent figures, 568 using ratio boxes, 456–458
and crossproducts, 441–446 writing decimal equivalents, 385–389
defined, 431, 442, 443 Rays
ratios relationship to, 431–432, 442–443, 529 defined, 146
in ratio word problems, 456–459 lines and segments, 36–41
in scale drawings and models, 578–581 naming, 353
solving properties of, 37
percent problems with, 548–552 symbol for, 37, 353
using a constant factor, 457 Reading
using cross-products, 441–446 decimal points, 240
tables and, 39, 413–414, 497–501, 513–514, decimals, 182–186
548–550 exponents, 196, 380–381
unknown numbers in, 432, 442–443 graphs, 84
writing, 431–433 large numbers, commas in, 64–65
powers, 380–381
Protractors, measuring and drawing angles, 161–163 Reading math, 25, 31, 38, 47, 64, 65, 73, 79, 95, 110,
Pyramids, 314, 315, 630–636 133, 147, 150, 161, 175, 196, 197, 240, 246, 266,
343, 353, 368, 409, 423, 427, 462, 494, 544, 567
Q Real-world application problems 9, 11–13, 16, 17,
20–22, 26, 27, 30, 31, 32, 34, 37, 39, 40–44, 46,
Quadrilaterals 48, 51–62, 66, 67, 69–73, 75–77, 79, 80, 81, 83,
classifying, 311, 333–337 84, 86–88, 91–95, 98, 103, 104, 106–108, 114,
defined, 311, 333 116, 117, 119–121, 124–131, 134, 135, 138–140,
parallelograms as. See Parallelograms 143–145, 148–150, 153–155, 159, 160 163, 216,
rectangles. See Rectangles 218–220, 229, 230, 233, 234, 236–238, 242, 243,
squares. See Squares 247–250, 252–254, 256–264, 267, 268–275, 278,
sum of angle measures in, 508–512 280, 283, 284, 289, 290, 292–299, 301, 304,
306–309, 312, 313, 316, 317, 322, 323, 327, 330,
Qualitative data, 212–213, 264–265 332, 334, 335, 336, 340–342, 344, 345, 347, 351,
Quantitative data, 212–213, 266–267 355, 357, 360–362, 372, 374, 377–378, 382, 383,
Quart (qt.), 404–405 387–389, 391–393, 395–397, 399, 401–403, 404,
Quotients. See also Division 406–408, 410, 413, 414, 416, 421, 424–425, 428–
429, 431, 433–435, 438–440, 444–445, 449–451,
calculating, 22 453–454, 456–459, 462, 466–469, 474, 476–483,
in decimal division, 235–236, 272–273 485–487, 491–495, 501, 502, 505–507, 510–512,
as decimals, 385 513–515, 522–523, 530–532, 535–537, 540–541,
defined, 14 543, 545, 546, 548–552, 555, 556, 558, 560,
in equivalent division problems, 225 563, 564, 566, 569, 570–572, 575–577, 582–587,
missing, 25 589–594, 596–597, 599–601, 603–605, 607–611,
in operations of arithmetic, 65 613–615, 617–621, 624–625, 628–629, 634, 635
of signed numbers, 588

Index 679