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algebraic
expression
at least one
operation
2+n
r
w
q
1
Any letter can be
used as a variable.
combination of numbers and variables
DEFINE: A group of numbers, symbols, and variables that
represent an operation or series of operations.
EXAMPLE: The amount of money Jordan will need to
pay for 2 CD’s using a $5 off coupon can be
represented by the experession 2x - 5,
where x is the cost of each CD.
ASK: How would you write an expression to show
three times the number of pens?
1
2
area
DEFINE: The number of square units needed to cover the
inside of a region or plane figure.
EXAMPLE: When you color inside the lines of a coloring
book, you are filling in the area.
ASK: What is the area of a rectangle whose length is
7 feet and whose width is 6 feet?
2
3
coefficient
2y
2 is the coefficient of y.
DEFINE: The numerical factor of a term that contains a
variable.
EXAMPLE: In the expression 3x, the 3 is a coefficient.
ASK: What is the coefficient in the expression 4d?
3
congruent
angles
4
3
1
4
2
⬔1 ⬔4
⬔2 ⬔3
The symbol is used to show
that the angles are congruent.
DEFINE: Angles with the same measure.
EXAMPLE: All four angles of a square and a rectangle are
congruent angles.
ASK: What objects in the room have congruent
angles?
4
5
coordinate
plane
x-axis 3
2
1
y
y-axis
O
⫺3⫺2⫺1
1 2 3x
⫺1
origin
⫺2
⫺3
DEFINE: A plane in which a horizontal number line and
a vertical number line intersect at a right angle
at the point where each line is zero.
EXAMPLE: Maps use coordinate planes to make it easier
to locate places.
ASK: How would you find the point (5, 2) on a
coordinate plane?
5
decimal
Place-Value Chart
hundredths
thousandths
tenthousandths
0.01 0.001 0.0001
tenths
0.1
ones
1
tens
10
hundreds
1,000 100
thousands
6
0
0
0
1
3
4
0
0
whole number
less than one
decimal point
DEFINE: A number with one or more digits to the right of
the decimal point, such as 8.37 or 0.05.
EXAMPLE: Fifty eight cents represents 58 hundredths of a
dollar or $0.58.
ASK: When do you use decimals?
6
7
distributive
property
7 × (4 + 5) = (7 × 4) + (7 × 5)
DEFINE: To multiply a sum by a number, you can multiply
each addend by the same number and add the
products.
EXAMPLE: 8 × (9 + 5) = (8 × 9) + (8 × 5)
ASK: Does (4 × 3) + (4 × 5) equal 4 × (3 + 5)?
7
8
equation
The equation
is 2 + x = 9.
The value for the
variable that results in
a true sentence is 7.
So, 7 is the solution.
2+x=9
2+7=9
9=9
This sentence is true.
DEFINE: A mathematical sentence that contains an
equals sign, =, indicating that the left side of
the equals sign has the same value as the right
side.
EXAMPLE: x + 1 = 4
ASK: What value of x makes the example a true
statement?
8
equivalent
decimals
9
0.6 ⫽ 0.60
six tenths ⫽ sixty hundredths
=
0.6
0.60
DEFINE: Decimals that represent the same number.
EXAMPLE: 0.3 and 0.30
ASK: What is an equivalent decimal for 1.5?
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10
evaluate
Evaluate 16 + b if b = 25.
16 + b = 16 + 25 Replace b with 25.
Add 16 and 25.
= 41
DEFINE: To find the value of an algebraic expression.
EXAMPLE: The teacher asked Jody to evaluate 18 + d,
if d = 30.
ASK: What would Jody’s answer be after he evaluated
the expression?
10
exponent
5 factors
q
e
e
e
e
w
e
e
e
e
32 = 2 × 2 × 2 × 2 × 2 = 25
r
11
base
exponent
DEFINE: The number of times a base is used as a factor.
EXAMPLE: In 53, the exponent is three.
ASK: How would you write 3 × 3 × 3 × 3 with a base
and an exponent?
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12
factor
Factors of 32
32 × 1
16 × 2
8×4
DEFINE: A number that divides a whole number evenly.
Also a number that is multiplied by another
number.
EXAMPLE: 1 × 6 = 6 and 2 × 3 = 6
The factors of 6 are 1, 2, 3, and 6.
ASK: What are the factors of 14?
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13
formula
Use a formula to find the area
of a rectangle with length
12 feet and width 7 feet.
A = w
Area of a rectangle
A = 12 · 7 Replace with 12 and w with 7.
A = 84
Multiply.
The area is 84 square feet.
7 ft
12 ft
DEFINE: An equation that describes a relationship among
two or more quantities.
EXAMPLE: To find the area of a rectangle you can use the
area formula, A = w.
ASK: Use the area formula to find the area of a
rectangle with the length of 6 feet and a width
of 3 feet.
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function
14
Input (x)
Output (x + 4)
Input (x)
Output (x + 4)
10
䊏
10
14
12
䊏
12
16
14
䊏
14
18
DEFINE: A relationship in which each element of the
input is paired with exactly one element of the
output. In a linear function, the graph of a set of
ordered pairs forms a line.
EXAMPLE: The number of fish caught depends on how
many hours are spent fishing.
ASK: If you caught 5 fish per hour, how would you
make a function table to show the number of
fish that would be caught in 1, 2, 3, and 4 hours?
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graph
CDs Purchased
8
x-axis 3
2
1
6
4
⫺4⫺3 ⫺2 ⫺1 0 1 2 3 4
ya
l
ae
ich
M
Student
To
ro
Hi
Em
m
a
eg
0
o
2
Di
Number of CDs
15
y
y-axis
O
⫺3⫺2⫺1
1 2 3x
⫺1
origin
⫺2
⫺3
DEFINE: a. A visual way to display data.
b. To graph an integer on a number line, draw a
dot at the location on the number line that
corresponds to the integer.
c. Place a point named by an ordered pair on a
coordinate grid
EXAMPLE: To organize the number of points he scored each
game, Ronnie made a graph.
ASK: What kind of graph would be best for Ronnie to
display this information?
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histogram
Obstacle Course Finishing Times
12
10
Number of Students
16
8
6
4
2
0
60-80
80-100
100-120
Finishing Times (seconds)
DEFINE: A graph that uses bars to show frequency of
data organized in intervals.
EXAMPLE: Ten students finished the obstacle course
between 60 seconds and 80 seconds, 5 students
finished between 80 seconds and 100 seconds,
and 7 students finished between 100 and
120 seconds. Look at the front of the card to
see this information in a histogram.
ASK: What is one way to use a histogram to display
statistics from a football game?
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improper
fraction
17
1
2
0
0
1
8
2
8
3
8
4
8
1
12
1
5
8
6
8
The numerators are less
than the denominators. These
are called proper fractions.
7
8
8
8
9
8
10
8
11
8
12
8
2
13
8
14
8
15
8
The numerators are greater than
or equal to the denominators.
These are called improper fractions.
16
8
DEFINE: A fraction with a numerator that is greater than
or equal to the denominator.
EXAMPLE:
_5 is an improper fraction.
3
ASK: Which of the following is an improper
fraction:
_1 , _5 , or 2_3 ?
2 4
4
17
integer
18
negative numbers
Zero is neither negative nor positive.
6 5 4 3 2 1
positive numbers
0 1 2 3 4 5 6
Opposites are numbers that are the same
distance from zero in opposite directions
DEFINE: Whole numbers and their opposites, including
zero.
EXAMPLE:
…-3, -2, -1, 0, 1, 2, 3…
ASK: What are 3 integers between -5 and 5?
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19
intersecting
lines
DEFINE: Lines that meet or cross at a point.
EXAMPLE: When two streets come together, they form
intersecting lines.
ASK: What letter of the alphabet is formed by two
intersecting lines?
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20
least common
denominator (LCD)
The least common denominator of
_2 and _3 is the
3
5
least common multiple of 3 and 5. The LCD is 15.
Multiples of 3
Multiples of 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14 15
DEFINE: The least common multiple of the denominators
of two or more fractions, used as a denominator.
1 _
1
1
EXAMPLE: For the fractions _
, , and _; the LCD is 24.
8
12 6
ASK: What is the least common denominator
_1 _2 , and _3 ?
of ,
2
5
20
20
21
like fraction
1
5
2
5
4
5
Like fractions have the
same denominator.
DEFINE: Fractions that have the same denominator.
EXAMPLE:
_1 and _2
5
5
9
ASK: Which fraction below is a like fraction to _
:
10
_3 , _5 , or _6 ?
6 5
10
21
mean
22
Star Struck Movie Rental
Daily DVD Rentals
S
M
T
W
TH
F
S
55
34
35
34
57
78
106
55 + 34 + 35 + 34 + 57 + 78 + 106
399
___
=_
or 57
7
7
DEFINE: The quotient found by adding the numbers in a
set of data and dividing this sum by the number
of addends. A measure of central tendency.
EXAMPLE: The mean or average number of points a
basketball player scored after several games
was 22.
ASK: What would be the mean number of points a
basketball player scored if his points were as
follows: 12, 15, 9, and 18?
22
23
median
Book Costs ($)
20 7 10 15 11
20 25 15
8
g
7, 8, 10, 11, 15 , 15, 20, 20, 25 15 is in the middle.
DEFINE: The middle number in a set of numbers arranged
in order from least to greatest. If the set
contains an even number of numbers, the
median is the mean of the two numbers nearest
the middle.
EXAMPLE: 3, 4, 6, 8, 9, 9
The median is
(6 + 8)
_
2
or 7.
ASK: What is the median of the following set of data:
18, 19, 22, 22, 23, 25 ?
23
mixed number
24
5
17
5
Divide 17 by 5.
2
3_
5
5 17
- 15
−−−−
2
Use the remainder
as the numerator
and the divisor as
the denominator
of the fraction.
3
2
5
DEFINE: A number that has a whole number part and a
fraction part.
3
EXAMPLE: 6_
4
ASK: Which of the following is a mixed number:
_3 _8
1 , , or
6 5
_6 ?
10
24
mode
25
Temperature (°F)
Daily High Temperature
75
70
65
60
55
50
0
70
70
64
56
58
60
Sun. Mon. Tue. Wed. Thu. Fri.
Day
mode: 70°
DEFINE: The number(s) or item(s) that occurs most often
in a set of data. A set can have more than one
mode.
EXAMPLE: For the set of data including the numbers 7, 4, 7,
10, 7, and 2, the mode is 7.
ASK: What is the mode for the following set of
numbers: 2, 6, 10, 1, 2, 2, 10?
25
26
net
DEFINE: A flat pattern that can be folded to make a
three-dimensional, or solid, figure.
EXAMPLE: A cereal box is actually a net that has been
folded to make a rectangular prism.
ASK: What three-dimensional figure would the net
that is on the front of this card make?
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27
order of
operations
Evaluate 8 - 3 × 2 + 7.
8-3×2+7=8-6+7
Multiply 3 and 2.
=2+7
Subtract 6 from 8.
=9
Add 2 and 7.
DEFINE: Rules that tell what order to follow when
evaluating expressions
(1)
Evaluate within parentheses ( ).
(2)
Evaluate powers.
(3)
Multiply or divide left to right.
(4)
Add or subtract left to right.
EXAMPLE: 5 + 16 × (3 - 2) = 5 + 16 × 1
= 5 + 16
= 21
ASK: What is the value of the expression
(14 – 7) × 3 + 4?
27
28
ordered pair
8
7
6
5
4
3
2
1
0
(1, 5)
(3, 5)
(4, 0)
1 2 3 4 5 6 7
DEFINE: A pair of numbers that are used to locate points
in a coordinate plane or grid, written as
(x-coordinate, y-coordinate)
EXAMPLE: (4,0) (3,2) (1,5)
ASK: In the ordered pair (5, 9), which number
is the x-coordinate? Which number is the
y-coordinate?
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29
parallel lines
DEFINE: Lines that are the same distance apart. Parallel
lines do not intersect.
EXAMPLE: The equals sign (=) is made up of parallel lines.
ASK: What objects do you see in the room that have
parallel lines?
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30
parallelogram
DEFINE: A quadrilateral in which each pair of opposite
sides is parallel and congruent.
EXAMPLE: A parallelogram looks like a rectangle that been
stretched out by pulling on the opposite angles.
ASK: Is a triangle a parallelogram? Explain.
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31
percent
75% ⇒ 75 out of 100 or _
75
100
75%
DEFINE: A ratio that compares a number to 100.
EXAMPLE: If you answered
_8 of the questions on a quiz
10
correctly, it would be 80% because
_8
10
=
80
_
or 80%.
100
ASK: Where are some places that you see percents
being used?
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32
perimeter
3 units
5 units
4 units
P 3 4 5 12 units
DEFINE: The distance around a shape or region.
EXAMPLE: If you were to put a fence around your yard, that
fence would represent the perimeter.
ASK: How would you find the perimeter of your desk?
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33
perpendicular lines
DEFINE: Lines that meet or cross each other to form right
angles.
EXAMPLE: If you print the capital letter T, you are making
perpendicular lines.
ASK: Are there any other letters that form
perpendicular lines?
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34
25
32
103
powers
2 to the fifth power
3 to the second power or 3 squared
10 to the third power or 10 cubed
DEFINE: A number obtained by raising a base to
an exponent.
EXAMPLE: 5² = 25 25 is a power of 5.
ASK: What does 43 equal?
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35
prime
factorization
54
Write the number that is
being factored at the top.
54
2 × 27
Choose any pair of whole
number factors of 54.
3 × 18
2×3 × 9
Continue to factor any
number that is not prime.
3×2×9
2×3×3×3
Except for the order, the
prime factors are the same.
3×2×3×3
DEFINE: A way of expressing a composite number as a
product of its prime factors.
EXAMPLE: The prime factorization of 54 is 3 × 3 × 3 × 2
or 33 × 2.
ASK: What is the prime factorization of 36?
35
36
quadrants
Quadrant II
5
4
3
2
1
54321 O
1
2
Quadrant III 3
4
5
y
Quadrant I
1 2 3 4 5x
Quadrant IV
DEFINE: One of four sections of a coordinate graph
formed by two axes.
EXAMPLE: The ordered pair (2, 5) would be found in
Quadrant 1.
ASK: What do all the numbers in the ordered pairs
for Quadrant 3 have in common?
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37
quadrilateral
DEFINE: A shape that has 4 sides and 4 angles.
EXAMPLE: A square, rectangle, and parallelogram are all
quadrilaterals.
ASK: Why are squares and rectangles both classified
as quadrilaterals?
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38
rate
Dollars and pounds are
different kinds of units.
Miles and hours are
different kinds of units.
$12 for 3 pounds
60 miles in 3 hours
DEFINE: A ratio of two quantities that are measured with
different units.
EXAMPLE: $5.00 for 2 pounds of roast beef
ASK: In the example above, what would be the rate
for 1 pound (unit rate) of roast beef?
38
ratio
39
Cans of Concentrate
1
2
3
Cans of Water
3
6
9
The ratios _, _, and _ are equivalent
3 6
9
1
since each simplifies to a ratio of _.
1 2
3
3
DEFINE: A comparison of two numbers by division.
EXAMPLE:
1 cup of sugar
__
2 cups of flour
ASK: Using the ratio in the example above, how many
cups of flour would you need if you had
3 cups of sugar?
39
reciprocal
40
Numbers
_1 × _2 = 1
1
2
_1 and _2 are reciprocals.
2
1
Algebra
a
b
_
×_
= 1, where a and b ≠ 0
b
a
_a and _ba are reciprocals.
b
DEFINE: Two numbers whose product is 1.
3
5
EXAMPLE: The reciprocal of _
is _.
5
3
5
ASK: What is the reciprocal of _
?
7
40
41
rectangle
DEFINE: A quadrilateral with four right angles; opposite
sides are congruent and parallel.
EXAMPLE: The door of your classroom is a rectangle.
ASK: What other objects in the classroom would be
classified as a rectangle?
41
42
rectangular prism
DEFINE: A three-dimensional, or solid, figure with six
faces that are rectangles.
EXAMPLE: A cereal box is a rectangular prism.
ASK: What other objects in the classroom would be
classified as a rectangular prism?
42
solution
43
The equation
is 3 + x = 12.
3 + x = 12
3 + 9 = 12
The value for the
variable that results in
a true sentence is 9.
So, 9 is the solution.
12 = 12
This sentence is true.
DEFINE: The value of a variable that makes a sentence
true.
EXAMPLE: The solution of x + 10 = 15 is 5.
ASK:
What is the solution of 4x = 28?
43
44
surface area
5 ft
3 ft
7 ft
DEFINE: The area of the surface of a three-dimensional,
or solid, figure.
EXAMPLE: When you are wrapping a present you are
covering up the surface area with the paper.
ASK: What is the surface area of a rectangular
prism that is 7 meters long, 5 meters high,
and 3 meters wide?
44
45
threedimensional
figures
DEFINE: A solid figure that has length, width, and height.
EXAMPLE: A cube is different from a square because it has
height.
ASK: Which of the shapes below is a three-dimensional
figure?
a. circle
b. parallelagram
c. trapezoid
d. rectangular prism
45
46
unlike fraction
1
4
1
6
1
2
Unlike fractions have
unlike denominators.
DEFINE: Fractions with different denominators
EXAMPLE:
_3 and _1
5
7
ASK: Which of the following fractions is an unlike
_4
8
8
8
_
b. _
a.
fraction to ?
8
9
c.
_5
8
d.
_3
8
46
variable
at least one
operation
2+n
r
w
q
47
Any letter can be
used as a variable.
combination of numbers and variables
DEFINE: A letter or symbol used to represent an unknown
quantity.
EXAMPLE: In the expression 47 – p, the variable is p.
ASK: Evaluate the expression 47 – p if p = 8.
47
volume
48
2m
3m
6m
DEFINE: The number of cubic units needed to fill a
three-dimensional, or solid, figure.
EXAMPLE: If you were to fill a fish tank with base-ten
cubes, the amount of those cubes represents
the volume of the tank.
ASK: Would a square have volume?
48
49
x-coordinate
The x-coordinate corresponds
to a number on the x-axis.
(3, 6)
The y-coordinate corresponds
to a number on the y-axis.
DEFINE: The first number of an ordered pair that
indicates how far to the left or the right of
the y axis the corresponding point is.
EXAMPLE: In the ordered pair (-1, 2), -1 means to move
1 unit to the left of the y-axis.
ASK: Would you count over spaces to the left or to the
right of the y axis if (4, 6) were the ordered pair?
49
50
y-coordinate
The x-coordinate corresponds
to a number on the x-axis.
(3, 6)
The y-coordinate corresponds
to a number on the y-axis.
DEFINE: The second number of an ordered pair that
indicates how far up or down to move from
the x-axis.
EXAMPLE: In the ordered pair (-1, 2), 2 means to move 2
units up from the x-axis.
ASK: Would you count spaces up or down from the
x-axis if (4, 6) were the ordered pair?
50