Lesson 1
counting numbers: The numbers used to count;
ex. 1, 2, 3, 4, 5….12….37 are all counting numbers but 0.98 and ½ are not
sequence: A list of numbers arranged according to a certain rule.
Ex. the numbers 2, 4, 6, 8 form a sequence. This rule is “count up by twos”.
term: A number in a sequence.
Ex. 1, 3, 5, 7, 1… Each number in this sequence is a term.
digit: Any of the symbols used to write numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Ex. The last digit in the number 7862 is 2.
Lesson 2
whole numbers: All the numbers in this sequence: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,… The number 35 is a whole number but the number 35 ½ and 4.2 are not. Whole numbers are the counting numbers and zero.
even numbers: Numbers that can be divided by 2 without a remainder. Even numbers have 0, 2, 4, 6, or 8 in the ones place.
odd numbers: Numbers that have a remainder of 1 when divided by 2. Odd numbers have 1, 3, 5, 7 or 9 in the ones place.
half: One of two equal parts that together equal a whole.
Lesson 3
place value: The value of a digit based on the position within a number. Place value tells us that 4 in 341 is worth “4 tens”. In addition problems, we align digits with the same place values.
expanded form: A way of writing a number that shows the value of each digit. The expanded form of 234 is 200 + 30 + 4
Lesson 4:
comparison symbols: A mathematical symbol used to compare numbers. Comparison symbols include the equal sign (=) and the “greater than/less than” symbols (> or <). We read comparisons from left to right. Ex. 2 > 1 is read from left to right “two is greater than one”.
Lesson 5:
decimal point: A symbol used to separate the ones place from the tenths place in decimal numbers (or dollars from cents in money)
ex. 34.15
Lesson 6:
addends: Any one of the numbers added in an addition problem.
Ex. 7 + 3 = 10 The addends in this problem are 7 and 3.
sum: The result of addition. Ex. 7 + 6 = 13. The sum of 7 and 6 is 13.
Commutative Property of Addition: Changing the order of addends does not change their sum. In symbolic form, a + b = b + a. Unlike addition, subtraction is not commutative.
8 + 2 = 2 + 8 not commutative: 8 – 2 = 2 - 8
Identity Property of Addition: The sum of any number and 0 is equal to the initial number. In symbolic form, a + 0 = a. The number 0 is referred to as the additive identity. Ex. 13 + 0 = 13
algorithms: Any process for solving a mathematical problem. In the addition algorithm we add the ones first, then the tens, and then the hundreds.
Lesson 7:
ordinal numbers: Numbers that describe position or order. “First”, “second”, and “third” are all ordinal numbers
Lesson 8:
difference: The result of subtraction. 12 – 8 = 4. The difference in this problem is 4.
inverse operations: An operation that undoes another. Addition is the inverse operation of subtraction. Multiplication and division are inverse operations.
fact family: A group of three numbers related by addition and subtraction or by multiplication and division.
Ex. The numbers 3, 4, and 7 are a fact family. The make these four facts:
3 + 4 = 7 4 + 3 = 7 7 – 3 = 4 7 – 4 = 3
Lesson 10:
equations: A number sentence that uses the equal sign (=) to show that two quantities are equal.
Ex. x = 3 3 + 7 = 10 (not equations): 4 + 1 x < 7
Lesson 11:
formula: An expression that describes a method for solving a certain type of problem. These are often written with letters that stand for complete works.
Some + More = Total s+m=t
Lesson 12:
geometry: The study of shapes.
point: A dot on a line.
line: A line does not end.
line segment: The part of a line sometimes just called segment.
end points: A line segment has two endpoints.
ray: Sometimes called a half line, it begins at a point and continues without end.
horizontal: A line that is level with horizon, extending left and right.
vertical: A line that extends up and down.
oblique: A line that appears to be slanted. A line or segment that is neither horizontal nor vertical.
number line: A line that shows the numbers at a certain distance from zero.
negative numbers: Numbers to the left of zero and numbers with a negative sign
tick marks: The small mark above each number.
integers: The numbers shown on a number line.
Lesson 15:
multiplication table: Usually lists the first ten or more multiples of the first ten or more whole numbers.
multiples: A product of a given number and a counting number.
factors: Numbers that are multiplied together.
product: The answer to the multiplication problem.
Commutative Property: Applies to multiplication as well as addition, the order of factors may be chosen.
Property of Zero for multiplication: When a factor is multiplied by zero, the product is zero.
Identity Property of Multiplication: When the factor is multiplied by one, the product is that factor.
Lesson 19:
division: Is to search for a missing factor. A division problem is like a miniature multiplication table.
Division is an operation that separates a number into a given number of equal parts or into a number of parts of a given size.
Lesson 20:
dividend: The number being divided.
divisor: The number by which another number is divided.
quotient: The answer to the division.
Investigation 2
fraction: A number that names part of a whole.
numerator: The top number of a fraction; the number that tells how many parts of a whole are counted.
denominator: The bottom number of a fraction; the number that tells how many parts are in a whole.
Lesson 22:
remainder: The amount left over in a division problem.
Lesson 24:
operations of arithmetic: The operations are addition, subtraction, multiplication and division.
parentheses: When there is more than one operation in a problem, these show the order for doing the operations.
Associative Property of Addition: No matter which way the addends are grouped, the result is the same.
Associative Property of Multiplication: No matter which way the factors are grouped, the result is the same.
Lesson 25:
factors: A number where all the whole numbers that can divide it without leaving a remainder.
Lesson 27:
scale: One way to use a number line is for measuring temperature.
Fahrenheit: Is a scale, water freezes at 32 degrees F and boils at 212 degrees F.
Celsius: Is a centigrade scale, meaning there are one hundred gradations, or degrees, between the freezing and boiling points of water.
centigrade: There are one hundred gradations or degrees.
degrees: Points of temperature on the number line or scale.
Lesson 28:
common years: Three years in a row that have 365 days.
leap year: A year with 366 days.
decade: A period of ten years.
century: A period of one hundred years.
millennium: A period of one thousand years.
Lesson 29:
multiples: These are the answers when the number is multiplied by 1,2,3,4, and so on.
Lesson 30:
percents: One way to describe parts of a whole.
Lesson 31:
parallel lines: Lines that do not cross one another, stay the same distance apart and go the same direction.
intersecting lines: Lines on the same surface that are not parallel.
perpendicular: Lines that intersect and create 90 degree angles.
oblique: Lines and segments that are neither parallel nor perpendicular.
angle: An opening between intersecting lines, rays, or segments.
right angle: An angle like the corner of a square, opens in any direction, and means “square corner”.
acute angle: An angle whose opening is less than a right angle. Some remember this as “a cute” little angle.
obtuse angle: An angle whose opening is more than a right angle.
straight angle: An angle whose opening forms a straight line.
Lesson 32:
sides: Line segments that form a polygon.
vertex: A point of an angle, polygon, or solid where two or more lines, rays or line segments meet.
quadrilateral: Any four-sided polygon.
plane: A flat surface that extends without end.
polygons: A closed, flat shape with straight sides.
congruent: A shape having the same size and shape.
similar: A synonym for congruent.
Lesson 33:
estimate: To find an approximate value.
round numbers: A close number to a given number. Rounding a number can help us estimate
compatible numbers: Numbers that are close in value to the actual numbers and are easy to add, subtract, multiply and divide.
Lesson 35:
elapsed time: The difference between a starting time and an ending time.
Lesson 36:
triangle: A polygon with three sides and three angles.
acute triangle: A triangle whose largest angle measures less than 90 degrees.
right triangle: A triangle whose largest angle measures 90 degrees.
obtuse triangle: A triangle whose largest angle measures more than 90 degrees and less than 180 degrees.
equilateral triangle: A triangle in which all sides are the same length and all angles are the same measure.
isosceles triangle: A triangle with at least two sides of equal length and two angles of equal measure.
scalene triangle: A triangle with three sides of different lengths.
Lesson 38:
mixed numbers: A number expressed as a whole number plus fraction.
Investigation 4:
arithmetic sequence: A sequence in which each term is found by adding a fixed number to the previous term.
geometric sequence: A sequence in which each term is found by multiplying the previous term by a fixed amount.
Fibonacci sequence: A famous sequence in mathematics , which follows an addition pattern. 1,1,2,3,5,8 Each term equals the sum of the two terms before it.
function tables: A table that shows the relationship (or function) between related pairs of numbers.
Lesson 41:
common denominators: Denominators that are all the same.
Lesson 42:
short division: A form of division that differs from long division. In short division we keep track of some numbers in our head.
divisibility: The ability for a number to be divided by a whole number without a remainder.
Lesson 44:
length:A measure of distance between any two points.
centimeter:A metric unit of length equal to one hundredth of a meter.
millimeter:A metric unit of length equal to one thousandth of a meter.
metric system: An international system of measurement in which units are related by a power of ten. Also called the International System.
U.S. Customary System: A system of measurement used almost exclusively in the United States. Pounds, quarts, and feet are units in the U.S. Customary System.
Lesson 45:
parallelograms :A quadrilateral that has two pairs of parallel sides.
trapezoids: A quadrilateral with exactly one pair of parallel sides.
trapezium: A quadrilateral with no parallel sides.
rectangle: A quadrilateral that has four right angles.
rhombus: A parallelogram with all four sides of equal length.
square: A rectangle will all four sides of equal length.
Lesson 48:
expanded notation: A way of writing a number that shows the value of each digit.
Lesson 50:
triangular numbers: Numbers that can be represented by objects arranged in a triangular pattern.
average: The number found when the sum of two or more numbers is divided by the number of addends in the sum, also called the mean.
Investigation 5:
data:Information gathered from observations or calculations.
statistics:A branch of mathematics that deals with collections, analysis, organization, and display of numerical data.
frequency tables: A table that is used to tally and display the number of times an event or outcome occurs.
line plots:A method of plotting a set of numbers by placing a mark above a number on a number line each time is occurs in the set.
cluster: A group of data points that are very close together.
outlier: A number that is distant from most of the other numbers in a list of data.
mode: The number or numbers that appear most often in a list of data.
range: The difference between the largest number and the smallest number in a list.
median: The middle number (or the average of the two central numbers) of a list of data when the numbers are arranged in order from the least to the greatest.
pictograph: A graph that uses symbols to represent data.
Lesson 51:
Distributive Property: A number times the sum of two addends is equal to the sum of that same number times each addend.
Lesson 53:
circle: A closed, curved shape in which all points on the shape are the same distance from the center.
circumference: The distance around a circle; perimeter of a circle.
center: The point inside a circle from which all points on the circle are equally distant.
radius: (Plural: radii) The distance from the center of a circle to a point on the circle.
diameter: The distance across a circle through its center.
Lesson 57
probability: A way of describing the likelihood of an event; the ratio of favorable outcomes to all the possible outcomes.
certain: We say that an event is certain when the event’s probability is 1. This means the event will definitely occur.
impossible: We say that an event is impossible when the event’s probability if 0. This means the event will definitely not occur.
chance: A way of expressing the likelihood of an event; the probability of an event expressed as a percentage.
experiments: Tests to find or illustrate a rule.
outcomes: Any possible result of an experiment.
sector: A region bordered by part of a circle and two radii.
Investigation 6:
line graph: A graph that connects points to show how information changes over time.
horizontal axis: The scale of a graph that runs from left to right.
vertical axis: The scale of a graph that runs top to bottom.
Lesson 61
points: An exact position.
endpoints: The points at which a line segment ends.
Lesson 64
decimal places: Places to the right of the decimal point.
Lesson 65
meter: The basic unit of length in the metric system.
decimeter: A metric unit of measurement equal to one tenth of a meter.
centimeter: A metric unit of length equal to one hundredth of a meter.
millimeter: A metric unit of length equal to one thousandth of a meter.
Lesson 67
common fraction: A fraction will whole number terms.
Lesson 68
mill: An amount of money equal to one thousandth of a dollar. (one tenth of a penny)
Investigation 7
bar graph: A graph that uses rectangles (bars) to show numbers or measurements.
histogram: A method of displaying a range of data. A histogram is a special type of bar graph that displays data in intervals of equal size with no space between bars.
stem-and-leaf plots: A method of graphing a collection of numbers by placing the “stem” digits (or initial digits) in one column and the “leaf” digits (or remaining digits) out to the right.
pictograph: A graph that uses symbols to represent data.
icons: Symbols used in a pictograph to represent data.
legend: A notation on a map, graph, or diagram that describes the meaning of the symbols and/or the scale used.
circle graph: A graph made of a circle divided into sectors. Also called pie chart or pie graph.
mutually exclusive: Categories are mutually exclusive if each data point can be placed in one, and only one, of the categories.
Venn diagram: A diagram made of circles used to display data.
Lesson 72
area: The number of square units needed to cover a surface.
square inch: A measure of area equal to that of a square with 1-inch sides.
square centimeter: A measure of area equal to that of a square with 1-centimeter sides.
formula: An expression or equation that describes a method for solving a certain type of problem. We often write formulas with letters that stand for complete words.
Lesson 75
proper fraction: A fraction whose denominator is greater than its numerator.
improper fraction: A fraction with a numerator greater than or equal to the denominator.
Lesson 77
weight: The measure of the force of gravity on an object. Units of weight in the customary system include ounces, pounds, and tons.
mass: The amount of mass an object contains. A kilogram is a metric unit of mass.
Lesson 78
exponent: The upper number in an exponential expression; it shows how many times the base is to be used as a factor.
base: The lower number in an exponential expression.
power: The value of an exponential expression
exponential expressions: An expression that indicated that the base is to be used as a factor the number of times shown by the exponent.
square root: One of two equal factors of a number. The symbol for the principal or positive, square root of a number is √
perfect square: The product when a whole number is multiplied by itself. The number 9 is a perfect square because 3x3=9.
Lesson 79
equivalent fractions: Different fractions that name the same amount. ½ and 2/4 are equivalent fractions.
Lesson 80
prime numbers: Counting numbers greater than 1 whose only two factors are the number 1 and itself. 7 is a prime number . Its only factors are 1 and 7.
composite numbers: A counting number greater than 1 that is divisible by a number other than itself and 1. Every composite number has three or four more factors. Every composite number can be expressed as a product of two or more prime numbers.
Investigation 8
coordinate plane: A grid on which any point can be identified by its distances from the x- and y- axes. (axes is plural for axis)
x-axis: The horizontal number line of a coordinate plane.
y-axis: The vertical number line of a coordinate plane.
coordinates: 1. A number used to locate a point on a number line.
2. A pair of numbers used to locate a point on a coordinate plane.
origin: 1. The location of the number 0 on a number line.
2. The point (0,0) on a coordinate plane.
transformations: Changing a figure’s position to another without turning or flipping the figure.
Lesson 81
terms: 1. A number in a sequence. 1,3,5,7,9,...
2. A number that serves as a numerator or denominator of a fraction.
reducing: To rewrite a fraction in lowest terms.
Lesson 82
greatest common factor: The largest whole number that is a factor of two or more given numbers.
Lesson 83
plane figures: Flat shapes
geometric solids: A shape that takes up space.
faces: A flat surface of a geometric solid.
edge: A line segment formed where two faces of a solid intersect.
base: A designated side or face of a geometric figure.
Lesson 84
permutation: One possible arrangement of a set of objects.
mean: Average
median: The middle number of a list of data.
mode: The number or numbers that appear most in a list of data.
measures of central tendency: A value that describes a property of a list of data, such as the middle number of the list or the number that appears in the list most often.
spread: A value that describes how the data in a set are distributed.
range: The difference between the largest and the smallest numbers in a list of data.
Lesson 85
ounces: A unit of weight in the customary system.
liters: A unit of weight in the metric system.
Lesson 89
prism: A three-dimensional solid with two congruent bases.
Lesson 93
comparative graphs: A method of displaying data, usually used to compare two or more related sets of data.
Lesson 95
reciprocal: Two numbers whose product is 1.
invert: To switch the numerator and denominator of a fraction to form its reciprocal.
Lesson 97
ratio: A way of comparing numbers by division
Lesson 98
positive numbers: Numbers greater than zero.
Investigation 10
degrees: A unit for measuring angles.
protractor: A tool used to measure and draw angles.
Lesson 103
volume: The amount of space a geometric solid occupies. Volume is measured in cubic units.
cubic unit: A cube with edges of designated length. Cubic units are used to measure volume.
Lesson 105
line of symmetry: A line that divides a figure into two halves that are mirror images of each other.
reflective symmetry: A figure has reflective symmetry if it can be divided into two halves that are mirror images of each other.
rotational symmetry: A figure has rotational symmetry if it can be rotated less than a full turn and appear in its original orientation.
Lesson 108
schedule: A list of events organized by the times at which they are planned to occur.
itinerary: A type of schedule that lists locations and destinations together with departure and arrival times.
Investigation 11:
scale drawing: A two-dimensional representation of a larger or smaller object.
scale: 1) A type of number line used for measuring.
2) A ratio that shows the relationship between a scale model and the actual object.
Lesson 112
least common multiple (LCM): The smallest whole number that is a multiple of two or more given numbers.
