The Procedure For Math Vocabulary Index Cards
Math vocabulary will be a big part of math for all students this year. Being able to converse mathematically should become an integral part of a student's growth this year in math. In doing problems and projects, students need to demonstrate their knowledge of math by using proper math vocabulary in their written explanations. Math vocabulary will be stressed in all classes. There will be vocabulary quizzes. Math rules and formulas will be considered as vocabulary. Students should put all math vocabulary, math rules, and math formulas on index cards. Index cards are a great way to randomly review the vocabulary in large or small intervals. As vocabulary terms, rules, and formulas are introduced in class, they will be posted in the classroom and on my web site. Students are required to review math vocabulary every night for homework as much as needed in order to master the vocabulary.
These are some examples of how index cards should be filled out. The following 3 math items (area, area of a triangle, and changing a fraction to decimal) should be on separate index cards.
Example 1
What is area?
(This is a asking for a definition in the form of a question and must be on one side of the index card.)
The region enclosed by a figure. It is the number of square units it takes to cover the surface of an object. An example of how area is written is 100 sq. cm. or 100 cm.2
(This is the definition and an example of how it is written and must be on the other side of the index card.)
Example 2
What is the formula used for finding the area of a triangle?
(This is a asking for a formula in the form of a question and must be on one side of the index card.)
The formula used to find the area of a triangle is A = bh/2b = the base of the triangle and h = the height of the triangle.
For example: Find the area of the triangle with
Height of 4 cm. and base of 3cm.
A = bh/2
A = (3 cm.)(4 cm.)/2 = 6 cm.2
The area of the triangle is 6 cm.2
(This is the formula used and an example of how it is used and must be on the other side of the index card.)
Example 3
How do you change a fraction to a decimal?
(This is a asking for a rule in the form of a question and must be on one side of the index card.
The rule is to divide the numerator by the denominator.
3/8 changed to a decimal would be3 ÷ 8 = .375
and18/40 changed to a decimal would be18 ÷ 40 = .45
(This is the rule used and an example of how it is used and must be on the other side of the index card.)
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This page was last updated on 5/6/05.
1. Addends---A number to be added to another number---the 2 and 3 in (2 + 3 = 5).
2. Sum---The answer in an addition problem------the 5 in (2 + 3 = 5).
3. Minuend---The number from which another number is to be subtracted---the 5 in (5 - 2 = 3).
4. Subtrahend---The number to be subtracted from another number---the 2 in (5 - 2 = 3).
5. Difference---The answer in a subtraction problem---the 3 in (5 - 2 = 3).
6. Dividend---The number to be divided---the 13 in 13/4 = 3 R 1.
7. Divisor---The number by which the dividend is divided---the 4 in 13/4 = 3 R 1.
8. Quotient---The answer in a division problem---the 3 in 13/4 = 3 R 1
9. Remainder---What is left undivided when the dividend is divided by the divisor that is not one of its factors---the 1 in 13/4 = 3 R 1.
10. Factors---Numbers to be multiplied---the 2 and 3 in (2)(3) = 6.
11. Products---The answer in a multiplication problem---the 6 in (2)(3) = 6.
12. Commutative Property Of Addition--Changing the order of the numbers being added does not change the sum.a + b = b + a
13. Associative Property Of Addition--Changing the grouping of the numbers being added does not change the sum. (a + b) + c = a + (b + c)
14. Identity Property of Addition--When zero is added to any number, the sum is identical to the original number. For this reason, the number zero is called the Additive Identity.a + 0 = a
15. Commutative Property Of Multiplication--Changing the order of the numbers being multiplied does not change the product.ab = ba
16. Associative Property Of Multiplication--Changing the grouping of the numbers being multiplied does not change the product. (ab)c = a(bc)
17. Identity Property of Multiplication--When any number is multiplied by 1, the product is identical to the original number. For this reason, the number 1 is called the Multiplicative Identity.(a)(1) = a
18. Multiplication Property of Zero--When any number is multiplied by zero, the product is zero.(a)(0) = 0
19. Distributive Property--The property that allows you to multiply each number inside a set of parentheses by a factor outside the parentheses.a(b + c) = ab + ac and a(b - c) = ab - ac
20. Evaluate--To find the value of an expression.
21. Variable--A symbol, usually a letter, used to represent a number in a mathematical expression or sentence.
22. Order of Operations-- PEMDAS---The rules to follow when more than one operation is used. Do all operations inside the grouping symbols (Parentheses and brackets) first. Do all powers (Exponents) before other operations. Multiply and Divide in order from left to right. Add and Subtract in order from left to right.
23. Exponential Form---A shortened form of a multiplication expression in which all of the factors are the same. For example, (5)(5)(5) may be written in exponential form as 53.
24. Power---In exponential form, the entire expression is called the power. For example, 53 is a power of 5 and is read as "five to the third power."
25. Exponent---In exponential form, the number that tells you how many times a base is used as a factor. In 53, the exponent 3 tells you that the base is used as a factor 3 times.
26. Base---In exponential form, the number that is used as a factor.
27. Squared---For the exponent 2 in 52 is read "five to the second power" or "five squared."
28. Cubed---For the exponent 3 in 53 is read "five to the third power" or "five cubed."
29. Square Root---One of the two equal factors of a number. If a2 =b. the a is called the square root of b.(vis the square root symbol.)
30. Perfect Square--- The Square Numbers---A number whose square root is a whole number. The set of perfect squares is (02, 12, 22, 32, 42, 52, …) = (0, 1, 4, 9, 16, 25, …)
31. Polygon---A closed figure formed by joining 3 or more line segments in a plane at their endpoints with each line segment joining exactly two others.
32. Line Segment---A part of a line that consists of two endpoints and all the points between.
33. Line---A straight arrangement of points that extends forever in opposite directions.
34. Plane---A flat surface that extends forever.
35. Quadrilateral---A polygon with 4 sides.
36. Rectangle---A parallelogram with 4 right angles.
37. Right Angle---An angle that measure exactly 90 degrees.
38. Parallelogram---A quadrilateral with two pairs of parallel sides.
39. Parallel Lines---Two lines in the same plane that do not intersect.
40. Intersect---To meet or cross each other at one point.
41. Perimeter Of A Polygon---The sum of the lengths of all the sides of a polygon.
42. Height---For a parallelogram: the perpendicular distance between the bases.
43. Bases---For a parallelogram: either pair of parallel sides.
44. Perpendicular---Two lines that intersect to form 90 degree angles.
45. Area---The number of square units it takes to cover the surface of an object.
46. Area Of A Rectangle Formula---A = lw
47. Area Of A Parallelogram Formula---A = bh
48. The Four-Step Problem Solving Plan
Explore Determine what information is given and what you need to find. Paraphrase the question. Put the question in your own words.
PlanSelect strategies and operations for solving the problem. Make an estimate of what the answer should be.
Solve Do the math work needed to solve the problem. Label all parts of your work.
ExamineCheck your work. Did you answer the question? Does your answer make sense?
49. Equation---A mathematical sentence that contains an equal sign.
50. Inverse Operations---A pair of operations that undo each other.
51. Prime Number---A whole number that is divisible only by itself and 1.
52. Composite Number---A whole number that has more than two factors, including the number and itself.
53. Prime Factorization---a product of prime numbers that gives a certain whole number. For example, (2)(3)(5) = 30.---The greatest number in a list of common factors.
54. Divisible---A number is divisible by another number if the quotient is a whole number and the remainder is zero.
55. Divisibility Tests---A number is divisible by:
2 if the ones digit is divisible by 2
3 if the sum of the digits is divisible by 3
4 if the number formed by the last two digits is divisible by 4
5 if the ones digit is 0 or 5
6 if the number is divisible by 2 and 3
9 if the sum of the digits is divisible by 9
8 if the number formed by the last three digits is divisible by 8
10 if the ones digit is 0.
56. Common Factor---A number that is a factor of two or more numbers. For example, 2 is a factor of both 6 and 8, so 2 is a common factor of 6 and 8.
57. Greatest Common Factor (GCF)---The greatest number in a list of common factors.
58. Relatively Prime---Two numbers whose greatest common factor is one.
59. Ratio---A comparison of two numbers by division.
60. Lowest Terms Fraction---When the greatest common factor of the numerator and denominator is one.
61. Trapezoid---A quadrilateral with only one pair of parallel sides.
62. Pentagon---A polygon with five sides.
63. Hexagon---A polygon with six sides.
64. Rule For Changing A Fraction To A Decimal---Divide the numerator by the denominator.
65. Numerator---In this example a/b, a is called the numerator.
66. Denominator---In this example a/b, b is called the denominator
67. Terminating Decimal---The decimal obtained when the division of the numerator by the denominator results in a remainder of zero.
68. Repeating Decimal---The decimal obtained when the division of the numerator by the denominator results in a nonzero remainder, and a block of digits in the decimal repeats. Indicate the digits that repeat by putting a bar over those digits.
69. Repetend---The block of digits in a repeating decimal that repeats.
70. Place Value---…hundreds, tens, tenths, hundredths,…
71. Percent---A ratio that compares a number to 100.
72. Equivalent Ratios---Two ratios that have the same value.
73. Proportion--- An equation that shows that two ratios are equivalent.
74. Rule For Changing A Decimal To A Percent--- To write a decimal as a percent, multiply the decimal by 100 and add the percent symbol.
75. Rule For Changing A Percent To A Decimal--- To write a percent as a decimal, divide the percent by 100 and remove the percent symbol.
76. Cross Products---In a proportion, the product of the first numerator and the second denominator and the product of the first denominator and the second numerator. A proportion is only true if these cross products are equal.
77. Fish Rule------A method to find the unknown value in a proportion by solving an equation.
78. Percent Of Increase------The percent that an amount of increase is of the original amount.The percent of increase = (the amount of increase) divided by (the original amount).
79. Percent Of Decrease---The percent that an amount of decrease is of the original amount.The percent of decrease = (the amount of decrease) divided by (the original amount).
80. Mean---The sum of the numbers in a set of data divided by the number of pieces of data.
81. Median---The middle number in a set of data when the data is arranged in numerical order.
82. Mode---The number of numbers that appear most often in a set of data.
83. Range---The difference between the greatest and least number in a set of data.
84. Skew---Not symmetrical about the mean or extending to one side of the median value.
85. Reciprocals---Two numbers whose product is one.
86. The Rule For Changing A Percent To A Fraction ---To change a percent to a fraction divide the percent by 100 and read the decimal in place value.
87. The Rule For Changing A Fraction To A Percent ---To change a fraction to a percent, create a proportion using the fraction and n/100 and solve the proportion.
88. Is Over Of---"is/of " is the same relationship as "part of a whole" ("part/whole")
89. (R)(B) = (P)---Rate times Base equals Part. The equation used to find a percent of a number.
90. Integer---Any number in the following set: (...-3, -2, -1, 0, +1, +2, +3,.)
91. Additive Inverse--- Numbers that are on opposite sides of zero on a number line but are the same distance from zero. For example, 5 and -5 are opposites. To write "the opposite of the number m," you can write "-m."
92. Absolute Value--- The distance a number is from zero on the number line.
93. Adding Integers With The Same Sign---Add the absolute value of the two positive integers or two negative integers and the sum has the same sign as the integers you added.
94. Adding Integers With Different Signs---Find the absolute value of the positive and negative integer. Then subtract the lesser absolute value from the greater absolute value. Give the difference the sign of the integer with the greater absolute value. This will be the sum of the two integers.
95. Subtracting Integers---To subtract an integer, add its additive inverse.
96. Multiplying Integers---To find the product of two integers use the following rule: the product of two integers with the same sign is positive and the product of two integers with different signs is negative.
97. Dividing Integers---To find the quotient of two integers use the following rule: the quotient of two integers with the same sign is positive and the quotient of two integers with different signs is negative.
98. Coordinate Plane---A plane in which a horizontal number line and a vertical number line are perpendicular and intersect at their zero points.
99. Ordered Pair---Two numbers used together (x, y) to designate a particular point in a coordinate plane.
100. X-Coordinate---The first number of an ordered pair (x, y) used to designate a particular point in a coordinate plane.
101. Y-Coordinate---The second number of an ordered pair (x, y) used to designate a particular point in a coordinate plane.
102. Origin---The point of intersection (0, 0) of the x-axis and y-axis in a coordinate plane.
103. Quadrants---The four sections that are formed by the axes in the coordinate plane.
104. Right Triangle---A triangle in which one angle is a right angle.
105. Hypotenuse---In a right triangle, the side that is opposite the right angle. It is always the longest side.
106. Legs---In a right triangle, the shorter two sides.
107. Pythagorean Theorem---If the length of the hypotenuse of a right triangle isc and the lengths of the legs area andb, then the following relationship holds true.a2 + b2 = c2
108. Function---A relationship that pairs each number in a given set with exactly one number in a second set..
109. Function Rule---A description of a function that shows how to pair the numbers in a given set with numbers in a second set.
110. Graph---A picture that displays numerical facts.
111. Data---Numerical facts.
112. Pictograph---A graph that uses a symbol to represent a given number of items.
113. Key---A code on a graph that tells how many items each symbol represents
114. Bar Graphs---A graph that has bars to display numerical facts. It has one axis labeled with numbers and another axis labeled with categories.
115. Scale---The numbers appearing at fixed intervals along one axis that are used to measure amounts.
116. Legend---A key on a double bar graph used to identify the two types of bars.
117. Scattergram---A display that uses points to show the relationship between two sets of data.
118. Trend Line---The line that can be drawn near the points on a scattergram.
119. Positive Correlation---A relationship between two sets of data indicated by a trend line sloping upward to the right.
120. Negative Correlation---A relationship between two sets of data indicated by a trend line sloping downward to the right.
121. Line Plot---A graph that uses an X above a number on a number line each time that number occurs in a set of data
122. Line Graph---A graph in which data are represented by points that are connected.
123. Increasing Trend---Occurs over any interval on a line graph where a series of line segments slopes upward.
124. Decreasing Trend--- Occurs over any interval on a line graph where a series of line segments slopes downward.
125. Stem-and-Leaf Plot---A display of data that shows the digits of each number.
126. Leaf---The last digit on the right of a number.
127. Stem---The digit or digits that remain when the leaf is dropped.
128. Histogram---A bar graph used to show frequencies. There are no spaces between consecutive bars.
129. Frequency Polygon---A line graph used to show frequencies. It can be made by connecting the midpoints of the tops of the bars of a histogram.
130. Box-and-Whisker Plot---A display that shows the median, the quartiles, and the least and greatest values of data.
131. First Quartile---The median of the lower half of the set of data.
132. Third Quartile---The median of the upper half of the set of data.
133. Circle Graph---A display used to represent data expressed as parts of a whole.
134. Sector---A wedge of the circle that represents one part of the data.
135. Vertex---The common endpoint of the rays forming an angle.
136. Ray---A part of a line that has one endpoint and extends forever in one direction.
137. Angle---The figure formed when two rays share a common endpoint.
138. Compass---A geometric tool used to create a circle.
139. Protractor---A geometric tool used to measure an angle.
140. Degree---The unit commonly used to measure the size of an angle.
141. Central Angle---An angle whose vertex is at the center of a circle.
142. .Geometry---A branch of mathematics that deals with space and its relationships. It is derived from two Greek words, "metros" (measurement) and "geos" (earth) which means "the measurement of the earth."
143. Point---A point shows an exact location in space and has no size or shape.
144. Collinear Points---Points that lie on the same line (means "on the same line")
145. Endpoint---A point at the beginning or end of a part of a line.
146. Sides of an Angle---The rays that form an angle.
147. Acute Angle---An angle with measure greater than zero degrees and less than 90 degrees.
148. Obtuse Angle---An angle with measure greater than 90 degrees and less than 180 degrees.
149. Complementary Angles---Two angles for which the sum of their measures is 90 degrees.
150. Supplementary Angles---Two angles for which the sum of their measures is 180 degrees.
151. Adjacent Angles---Two angles that share a common side but do not overlap each other.
152. Vertical Angles---When two lines intersect, the angles that are not adjacent. Vertical angles are always equal in measure.
153. Transversal---A line that intersects two or more lines in the same plane at different points.
154. Alternate Interior Angles---Two angles on alternate sides of a transversal that intersects two lines in the same plane and interior to the two lines.