Download Unit 1 Data Displays and Number Systems

Unit 1
Data Displays and Number Systems
1.1 Exploring Statistical Questions
 data – information that is gathered by counting,
measuring, questioning, or observing (pg. 416)
 statistical question – a question that would be
answered by collecting or analyzing data (pg. 435)
 statistics – (1) the study of numerical data: collecting,
organizing, and analyzing data to interpret it and answer
questions (2) the numerical data itself (pg. 435)
 range – the difference between the maximum and
minimum in a data set. The range is a measure of how
spread out a distribution is (pg. 431)
1.2 Creating Dot Plots
 dot plot – a sketch of data with dots marked above
a labeled line
 maximum – the greatest number in a set of data
 minimum – the smallest number in a set of data
 distribution – the arrangement and frequency of
data values in a data set
1.2 Creating Dot Plots
 variability – how spread out the values in a set of
data are
 median – the middle value in a set of numerical
data when the numbers are listed in order from
smallest to largest, or from largest to smallest
 mode – the value or values that occur most often in
a data set
1.3 Introducing the Mean
 average – a typical value for a set of numbers. The
word average usually refers to the mean of a set of
numbers
 mean – a typical value for a set of numerical data,
often called the average. The mean is found by
dividing the sum of the numbers by the number of
numbers in the set
1.4 Introducing the Mean as a Balance Point
 balance point – for data, it refers to the mean
1.5 Comparing Mean, Median, and Mode
 measure of center – a value representing what is
typical or central to a data set. Mean and median are
both measure of center
 outlier – a value far from most of the others in a
data set. Outliers are commonly much larger or
much smaller than other values
1.7 Introducing Histograms
 histogram – a bar graph of numerical data that are
grouped into intervals, called bins, along a number
line. The number of the values within an interval
determines the height of the bar. Many histograms
have fixed intervals, or equal-width bins
 bin – an interval for collecting, aggregating,
organizing, or graphing data
1.8 Examining Shapes of Graphs
 cluster -
1.10 Introducing Integers
 counting number – the numbers used to count things.
The set of counting numbers is {1,2,3,4…}
 whole number – the counting numbers, together with
0. The set of whole numbers is {0,1,2,3,4…}
 positive number – a number that is greater than zero;
a number that to the right of zero on a number line, or
above zero on a vertical number line. A positive number
may be written using the + symbol, but is usually written
without it. For example, +10 = 10
1.10 Introducing Integers
 negative number – a number that is less than
zero; a number to the left of zero on a horizontal
number line or below zero on a vertical number line.
The symbol – may be used to write a negative
number. For example, “negative 5” is written as -5
 integer – a number in the set {…, -4,-3,-2,-
1,0,1,2,3,4…}; a whole number or the opposite of a
whole number, where 0 is its own opposite
1.10 Introducing Integers
 rational number – any number that can be
written as an integer divided by a nonzero integer.
For example, 2/3, -2/3, 60% = 60/100, and -1.25 = 5/4
1.13 Locating Negative Rational Numbers on the
Number Line
 opposite – a number that is the same distance from
0 on the number line as a given number, but on the
opposite side of 0. For example, the opposite of +3 is
-3 and the opposite of -5 is +5
1.14 Plotting Ordered Pairs of Rational Numbers
in 4 Quadrants
 ordered pair – two numbers that are used to
locate a point on a rectangular coordinate grid. The
first number gives the position along the horizontal
axis, and the second number gives the position along
the vertical axis. The numbers in an ordered pair are
called coordinates. Ordered pairs are usually written
inside parentheses: (5,3)
 coordinate grid – a grid formed by two number
lines that intersect at their zero points and form right
angles. Each number lines is referred to as an axis
1.14 Plotting Ordered Pairs of Rational Numbers
in 4 Quadrants
 quadrant – one of the four sections of a rectangular
coordinate grid. The quadrants are typically
numbered I, II, III, IV counterclockwise beginning at
the upper right
 origin – (1.) the point (0,0) where the two axes of a
coordinate grid meet. (2.) The 0 point on a number
line
 x-axis – in a coordinate grid, the horizontal number
line
1.14 Plotting Ordered Pairs of Rational Numbers
in 4 Quadrants
 y-axis – in a coordinate grid, the vertical number
line
1.14 Plotting Ordered Pairs of Rational Numbers
in 4 Quadrants
 y-axis – in a coordinate grid, the vertical number
line
Unit 2
Fraction Operations and Ratios
2.1 The Greatest Common Factor
 Greatest common factor (GCF) - the largest factor
that two or more counting numbers have in common. For
example, the common factors of 24 and 36 are
1,2,3,4,6,and 12. The greatest common factor of 24 and
36 is 12.
 Prime number – a counting number that has exactly
two different factors: itself, and 1. For example, 5 is a
prime number because its only factors are 5 and 1
 Relatively prime - having no factors in common other
than 1. For example, 8 and 21 are relatively prime
because the only number that divides them both without
remainder is 1
2.2 The Least Common Multiple
 Least common multiple (LCM) - the smallest
number that is a multiple of two or more numbers.
For example, while some common multiples of 6 and
8 are 24, 48, and 72, the least common multiple of 6
and 8 is 24.
2.5 Comparing Strategies for Multiplying
Fractions
 Commutative Property of Multiplication – a
property of multiplication (but not division) that says
that changing the order of the numbers being multiplied
does not change the product. This property is often called
the turn-around rule. Ex. 8 x 3 = 3 x 8
 Associative Property of Multiplication – a property
of multiplication (but no division) that says that when
you multiply three numbers, you can change the
grouping without changing the product.
Ex. (5 x 8) x 9 = 5 x (8 x 9)
 Reciprocal – two numbers whose product is 1. Ex. 1/5
is the reciprocal of 5.
2.6 Dividing Fractions with Common
Denominators
 Divisor – the number that divides another number.
For example, in 35 ÷ 5 = 7, the divisor is 5
 Dividend – the number in division that is being
divided. For example, in 35 ÷ 5 = 7, the dividend is
35
 Quotient – the result of dividing one number by
another number. For example, in 35 ÷ 5 = 7, the
quotient is 7
2.8 Using Reciprocals to Divide Fractions
 Division of Fractions Property – a fact that
makes division with fractions easier: division by a
fraction that is the same as multiplication by the
fraction’s reciprocal.
2.9 Introducing Ratios
 Ratio – a comparison of two quantities using
division. Ratios can be expressed with fractions,
decimals, percents, or words. Sometimes they are
written with a colon between two numbers that are
being compared Ex. 3:5, 3/5, .6, 60%
2.11 Equivalent Ratios
 Equivalent ratios – ratios that make the same
comparison. Two or more ratios are equivalent if thet
can be renamed as equivalent fractions. Ex. 12 to 20,
or 6 to 10
 Unit ratio – a rate in which one of the quantities
being compared is 1. For example, 70 miles per hour
is a unit rate because it is the number of miles
traveled in 1 hr.
2.13 Using Ratios/Rate Tables
 Rate – a comparison by division of two quantities
with unlike units. For example, a speed such as 55
mph uses a rate that compares distance with time
 Unit rate – a rate in which one of the quantities
being compared is 1. For example, 70 mph is a unit
rate because it is the number of miles traveled in 1
hour.
Unit 3
Decimal Operations and Percents
3.1 Place Value and Expanded Form with
Decimals
 expanded form – a way of writing a number as the
sum of the values of each digit.
Ex. 356 is written 300 + 50 + 6
3.3 Reviewing Decimal Addition and Subtraction
 place value – system that gives a digit a value
according to its position in a number. In our baseten system for writing numbers, moving a digit one
place to the left makes that digit worth 10 times as
much. Moving a digit one place to the right makes
that digit worth one tenth as much
3.8 Introducing Percent
 percent – per one hundred or out of a hundred.
Ex. 48% of the students in the school are “boys”
means that 48 out of every 100 students in the school
are boys: 48% = 48/100, 0.48
3.10 Percents as Ratios
 Ratio – a comparison of two quantities using
division. Ratios can be expressed with fractions,
decimals, percents, or words. Sometimes they are
written with a colon between two numbers that are
being compared Ex. 3:5, 3/5, .6, 60%
 Rate table – a way of displaying ratio or rate
information. In a ratio/rate table, the fractions
formed by the two numbers in each column are
equivalent fractions
3.12 Introducing Box Plots
 Five number summary – a list containing the minimum,
first quartile, median, third quartile, and maximum of a data
set
 Lower quartile (Q1) – 1. first quartile, the middle value of
the numbers below the median in a data set 2. Informally, the
interval between this middle point of the lower half of the data
and the minimum of the data set
 Upper quartile (Q3) – 1. the middle value of the numbers
above the median in a data set. 2. Informally, the interval
between this middle point of the upper half of the data and the
median of the data set
3.13 Making Box Plots and Finding Interquartile
Range
 Interquartile range (IQR) – 1. the distance
between the lower and upper quartiles in a data set.
It is sometimes illustrated by a box-and-whiskers
plot. 2. The interval between the lower and upper
quartiles
Unit 4 Algebraic
Expressions and Equations
4.1 Parentheses, Exponents, and Calculations
 expression – (1.) a mathematical phrase made up of
numbers, variables, operation symbols, and/or grouping
symbols. An expression does not contain relation symbols
such as =, <, >, ≤, ≥. (2.) Either side of an equation or
inequality
 simplify – to rewrite an expression by clearing grouping
symbols and combining like terms and constants.
 base – a number that is raised to a power. Ex. 53, 5 is the base
 exponent - a number used in exponential notation to tell
how many times the base is used as a factor. 53, the exponent
is 3
4.2 Solving Problems with Order of Operations
 nested parentheses – parentheses within
parentheses in an expression. Expressions are
evaluated from innermost parentheses outward
4.3 Expressions and Patterns
 variable – (1.) a letter or other symbol that can be
replaced by any value from a set of possible values
 algebraic expression – an expression that
contains a variable
 substitute – (1.) to replace one thing with another.
(2.) to replace variables with numbers in an
expression or formula
4.4 Representing Unknown Quantities with
Algebraic Expressions
 coefficient – the number, or constant factor, in a
variable term in an expression, For example, in
3c + 8, 3 is the coefficient
4.5 Exploring Equations
 equation – a number sentence that contains an
equal sign. For example, 5 + 10 = 15 and P = 2l +2w
are equations
 open sentence – a number sentence with one or
more variables that is neither true or false. For
example, 9 + ___ = 15. ? – 24 < 1o, an 7 = x + y
4.6 The Distributive Property and Equivalent
Expressions
 Distributive property of Multiplication over
Addition – a x (b + c) = (a x b) + (a x c)
a(b + c) = ab +ac
 Distributive Property of Multiplication over
Subtraction – a x (b – c) = (a x b) – (a x c)
a(b – c) = ab – ac
4.9 Introduction to Inequalities
 inequality – a number sentence with a relation
symbol other than =, such as <, >,≤,≥, or ≠
 relation symbol – a symbol used to express a
relationship between two quantities
4.10 Finding and Graphing Solution Sets of
Inequalities
 solution set – the set of all values, or groups of
values, that make a number sentence true. For
example, 7 is a solution of 5 + n = 12.
 infinite - unlimited; continuing on forever
4.12 Absolute Value as Distance
 magnitude – the size of a number; the number’s
distance from 0. The absolute value of a number is
its magnitude.
 absolute value – the distance between a number
and 0 on a number line. The absolute value of n is
written as lnl. For example, the absolute value of -3,
or l-3l is 3 because it is 3 away from 0.
4.14 Mean Absolute Deviation
 mean absolute deviation (m.a.d.) – in a
numerical data set, the average between individual
data values and the mean of those values. It is a
measure of how spread out a distribution is.
Unit 5 Area and Volume
Explorations
5.1 Polygons on a Coordinate Grid
 polygon – a plane figure formed by line segments
(sides) that meet only at their endpoints (vertices) to
make a closed path. The sides may not cross one
another.
 line segment – a part of a line between and
including two points called enpoints of the segment
 endpoint – a point at the end of a line segment, ray,
arc, or curve
5.1 Polygons on a Coordinate Grid
 vertex – the point at which the sides of an angle or
polygon. Or the edges of a polyhedron meet.
Informally called the corner
 face – a flat surface on a closed 3-dimensional
figure. Some special faces are called bases
 interior - the set of all points in a plane by a closed
2-dimensional figure (2.) the set of all points in space
bounded by a closed 3-dimensional figure
5.2 Area of Parallelograms
 parallelogram –a trapezoid that has two pairs of
parallel sides
 quadrilateral – a 4-sided polygon
 base – the side of a polygon or face of a polyhedron
from which height is measured
 height – the length of a perpendicular segment
from one side of a geometric figure to a parallel side
or from a vertex to the opposite side
5.3 Area of Triangles
 Equilateral triangle – a triangle with all three side
equal in length. Each angle of an equilateral triangle
measures 60 degrees. It can also be called an equiangular
triangle. Equilateral triangles are also isosceles triangles
 Isosceles triangle – a triangle with at least two equal
length sides. Angles opposite the equal-length sides.
Angles opposite the equal-length sides are equal
 Scalene triangle – a triangle with sides of three
different lengths. The three angles of a scalene triangle
are different
5.3 Area of Triangles
 Right triangle – a triangle with a right angle that
measures 90 degrees
 Obtuse angle – an angle with a measure greater
than 90 degrees and less than 180 degrees
 Acute angle – an angle with a measure less than 90
degrees
5.4 Composing and Decomposing Polygons to
Find Area
 Decompose – to separate a number or shape into
smaller numbers or shapes. For ex. 14, 1 ten and 4
ones
 Compose – to make up or form a number or shape
by putting together smaller numbers or shapes. For
ex. 10 is composed by adding 1+1+1+1+1+1+1+1+1+1
5.5 Building 3-D Shapes with Nets
 Net – a 2-demensional figure created to represent a
3-dimensional figure by cutting and unfolding or
separating its faces and sides
 Geometric solid Edge-
 Congruent –
 Apex-
5.6 Using Nets to Find Surface Area
 Surface area –
5.9 Strategies for Finding Volume
 Volume –
 Cubic units –
5.11 Calculating the Volume of a Person
 Depth –