1 algebraic. expression. at least one operation. Any letter can be used as a variable. 2 + n. combination of numbers and variables

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1 1 algebraic expression at least one operation 2 + n r w q Any letter can be used as a variable. combination of numbers and variables

2 DEFINE: A group of numbers, symbols, and variables that represent an operation or series of operations. 1 EXAMPLE: ASK: 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. How would you write an expression to show three times the number of pens?

3 2 area

4 DEFINE: The number of square units needed to cover the inside of a region or plane figure. 2 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?

5 3 coefficient 2y 2 is the coefficient of y.

6 DEFINE: The numerical factor of a term that contains a variable. 3 EXAMPLE: In the expression 3x, the 3 is a coefficient. ASK: What is the coefficient in the expression 4d?

7 4 congruent angles The symbol is used to show that the angles are congruent.

8 DEFINE: Angles with the same measure. 4 EXAMPLE: All four angles of a square and a rectangle are congruent angles. ASK: What objects in the room have congruent angles?

9 5 coordinate plane y 3 x-axis y-axis 2 1 O x 1 origin 2 3

10 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. 5 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?

11 6 decimal Place-Value Chart 1, thousands hundreds tens ones tenths hundredths thousandths tenthousandths whole number less than one decimal point

12 DEFINE: A number with one or more digits to the right of the decimal point, such as 8.37 or EXAMPLE: Fifty eight cents represents 58 hundredths of a dollar or $0.58. ASK: When do you use decimals?

13 7 distributive property 7 (4 + 5) = (7 4) + (7 5)

14 DEFINE: To multiply a sum by a number, you can multiply each addend by the same number and add the products. 7 EXAMPLE: 8 (9 + 5) = (8 9) + (8 5) ASK: Does (4 3) + (4 5) equal 4 (3 + 5)?

15 8 equation The equation is 2 + x = x = = 9 The value for the variable that results in a true sentence is 7. So, 7 is the solution. 9 = 9 This sentence is true.

16 DEFINE: EXAMPLE: 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. x + 1 = 4 8 ASK: What value of x makes the example a true statement?

17 9 equivalent decimals = six tenths sixty hundredths

18 DEFINE: Decimals that represent the same number. 9 EXAMPLE: 0.3 and 0.30 ASK: What is an equivalent decimal for 1.5?

19 10 evaluate Evaluate 16 + b if b = b = = 41 Replace b with 25. Add 16 and 25.

20 DEFINE: To find the value of an algebraic expression. 10 EXAMPLE: The teacher asked Jody to evaluate 18 + d, if d = 30. ASK: What would Jody s answer be after he evaluated the expression?

21 11 exponent 32 = = 2 5 exponent r ee e e w e ee e q 5 factors base

22 DEFINE: The number of times a base is used as a factor. 11 EXAMPLE: In 5 3, the exponent is three. ASK: How would you write with a base and an exponent?

23 12 factor Factors of

24 DEFINE: A number that divides a whole number evenly. Also a number that is multiplied by another number. 12 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?

25 13 formula Use a formula to find the area of a rectangle with length 12 feet and width 7 feet. A = lw Area of a rectangle A = 12 7 Replace l with 12 and w with 7. A = 84 Multiply. The area is 84 square feet. 7 ft 12 ft

26 DEFINE: An equation that describes a relationship among two or more quantities. 13 EXAMPLE: To find the area of a rectangle you can use the area formula, A = lw. ASK: Use the area formula to find the area of a rectangle with the length of 6 feet and a width of 3 feet.

27 14 function Input (x) Output (x + 4) Input (x) Output (x + 4)

28 DEFINE: EXAMPLE: 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. The number of fish caught depends on how many hours are spent fishing. 14 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?

29 15 graph Number of CDs Diego CDs Purchased Emma Hiro Student Michael Toya y 3 x-axis y-axis 2 1 O x 1 origin 2 3

30 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 15 EXAMPLE: ASK: To organize the number of points he scored each game, Ronnie made a graph. What kind of graph would be best for Ronnie to display this information?

31 16 histogram Obstacle Course Finishing Times Number of Students Finishing Times (seconds)

32 DEFINE: A graph that uses bars to show frequency of data organized in intervals. 16 EXAMPLE: ASK: 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. What is one way to use a histogram to display statistics from a football game?

33 17 improper fraction The numerators are less than the denominators. These are called proper fractions. The numerators are greater than or equal to the denominators. These are called improper fractions.

34 DEFINE: A fraction with a numerator that is greater than or equal to the denominator. 17 EXAMPLE: 5_ 3 is an improper fraction. ASK: Which of the 1_ following is an improper 3_ fraction:, or 2 4 4? 2, 5_

35 18 integer negative numbers Zero is neither negative nor positive. positive numbers Opposites are numbers that are the same distance from zero in opposite directions

36 DEFINE: Whole numbers and their opposites, including zero. 18 EXAMPLE: -3, -2, -1, 0, 1, 2, 3 ASK: What are 3 integers between -5 and 5?

37 19 intersecting lines

38 DEFINE: Lines that meet or cross at a point. 19 EXAMPLE: When two streets come together, they form intersecting lines. ASK: What letter of the alphabet is formed by two intersecting lines?

39 20 least common denominator (LCD) 2_ The least common denominator of _ 3 and 3 is the 5 least common multiple of 3 and 5. The LCD is 15. Multiples of 3 Multiples of

40 DEFINE: The least common multiple of the denominators of two or more fractions, used as a denominator. 20 EXAMPLE: For the fractions 1_ 1_ 12, 6 1_, and ; the LCD is ASK: What 1_ is 2_ the least common denominator 3_ of 2,, and 5 20?

41 21 like fraction Like fractions have the same denominator.

42 DEFINE: Fractions that have the same denominator. 21 EXAMPLE: 1_ 5 and 2_ 5 ASK: 9_ Which fraction below is a like fraction to 10 : 3_ 5_ 6, 5, or 6_ 10?

43 22 mean Star Struck Movie Rental Daily DVD Rentals S M T W TH F S = _ 399 or 57 7

44 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. 22 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?

45 23 median Book Costs ($) , 8, 10, 11, 15, 15, 20, 20, is in the middle.

46 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. 23 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?

47 24 mixed number vide 17 y 5. 3 _ Use the remainder as the numerator and the divisor as the denominator of the fraction

48 DEFINE: A number that has a whole number part and a fraction part. 24 EXAMPLE: 6 3_ 4 ASK: Which 3_ 8_ of the following is a mixed number: 6_ 1 6,, or 5 10?

49 25 mode Daily High Temperature Temperature ( F) Sun. Mon Tue. Wed. Thu. Day 70 Fri. mode: 70

50 DEFINE: The number(s) or item(s) that occurs most often in a set of data. A set can have more than one mode. 25 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?

51 26 net

52 DEFINE: A flat pattern that can be folded to make a three-dimensional, or solid, figure. 26 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?

53 27 order of operations Evaluate = Multiply 3 and 2. = Subtract 6 from 8. = 9 Add 2 and 7.

54 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. 27 EXAMPLE: ASK: (3-2) = = = 21 What is the value of the expression (14 7) 3 + 4?

55 28 ordered pair (1, 5) (3, 5) 1 (4, 0)

56 DEFINE: A pair of numbers that are used to locate points in a coordinate plane or grid, written as (x-coordinate, y-coordinate) 28 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?

57 29 parallel lines

58 DEFINE: Lines that are the same distance apart. Parallel lines do not intersect. 29 EXAMPLE: The equals sign (=) is made up of parallel lines. ASK: What objects do you see in the room that have parallel lines?

59 30 parallelogram

60 DEFINE: A quadrilateral in which each pair of opposite sides is parallel and congruent. 30 EXAMPLE: A parallelogram looks like a rectangle that been stretched out by pulling on the opposite angles. ASK: Is a triangle a parallelogram? Explain.

61 31 percent 75% 75 out of 100 or 75 _ %

62 DEFINE: A ratio that compares a number to EXAMPLE: 8_ If you answered of the questions on a quiz 10 correctly, it would be 80% because 8_ 80_ 10 = or 80%. 100 ASK: Where are some places that you see percents being used?

63 32 perimeter 3 units 5 units 4 units P units

64 DEFINE: The distance around a shape or region. 32 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?

65 33 perpendicular lines

66 DEFINE: Lines that meet or cross each other to form right angles. 33 EXAMPLE: If you print the capital letter T, you are making perpendicular lines. ASK: Are there any other letters that form perpendicular lines?

67 34 powers to the fifth power to the second power or 3 squared to the third power or 10 cubed

68 DEFINE: A number obtained by raising a base to an exponent. 34 EXAMPLE: 5² = is a power of 5. ASK: What does 4 3 equal?

69 35 prime factorization Write the number that is being factored at the top. 54 Choose any pair of whole number factors of Continue to factor any number that is not prime Except for the order, the prime factors are the same

70 DEFINE: A way of expressing a composite number as a product of its prime factors. 35 EXAMPLE: The prime factorization of 54 is or ASK: What is the prime factorization of 36?

71 36 quadrants Quadrant II O x 1 2 Quadrant III 3 Quadrant IV 4 5 y Quadrant I

72 DEFINE: One of four sections of a coordinate graph formed by two axes. 36 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?

73 37 quadrilateral

74 DEFINE: A shape that has 4 sides and 4 angles. 37 EXAMPLE: A square, rectangle, and parallelogram are all quadrilaterals. ASK: Why are squares and rectangles both classified as quadrilaterals?

75 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

76 DEFINE: A ratio of two quantities that are measured with different units. 38 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?

77 39 ratio Cans of Concentrate Cans of Water The ratios _ 1 3, _ 2 6, and _ 3 are equivalent 9 since each simplifies to a ratio of _ 1 3.

78 DEFINE: A comparison of two numbers by division. 39 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?

79 40 reciprocal Numbers Algebra 1_ 2 _ 2 1 = 1 _ a b _ b a 1_ 2 and 2_ 1 are reciprocals. a_ b and b_ a = 1, where a and b 0 are reciprocals.

80 DEFINE: Two numbers whose product is EXAMPLE: The reciprocal of 3_ 5 is 5_ 3. ASK: What is the reciprocal of 5_ 7?

81 41 rectangle

82 DEFINE: A quadrilateral with four right angles; opposite sides are congruent and parallel. 41 EXAMPLE: The door of your classroom is a rectangle. ASK: What other objects in the classroom would be classified as a rectangle?

83 42 rectangular prism

84 DEFINE: A three-dimensional, or solid, figure with six faces that are rectangles. 42 EXAMPLE: A cereal box is a rectangular prism. ASK: What other objects in the classroom would be classified as a rectangular prism?

85 43 solution The equation is 3 + x = x = = 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.

86 DEFINE: The value of a variable that makes a sentence true. 43 EXAMPLE: The solution of x + 10 = 15 is 5. ASK: What is the solution of 4x = 28?

87 44 surface area 5 ft 7 ft 3 ft

88 DEFINE: The area of the surface of a three-dimensional, or solid, figure. 44 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?

89 45 threedimensional figures

90 DEFINE: A solid figure that has length, width, and height. 45 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 c. trapezoid b. parallelagram d. rectangular prism

91 46 unlike fraction Unlike fractions have unlike denominators.

92 DEFINE: Fractions with different denominators 46 EXAMPLE: 3_ 7 and 1_ 5 ASK: Which of the following fractions is an unlike fraction to 4_ 8? a. 8_ 8 b. 8_ 9 c. 5_ 8 d. 3_ 8

93 47 variable at least one operation 2 + n r w q Any letter can be used as a variable. combination of numbers and variables

94 DEFINE: A letter or symbol used to represent an unknown quantity. 47 EXAMPLE: In the expression 47 p, the variable is p. ASK: Evaluate the expression 47 p if p = 8.

95 48 volume 2 m 3 m 6 m

96 DEFINE: The number of cubic units needed to fill a three-dimensional, or solid, figure. 48 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?

97 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.

98 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. 49 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?

99 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.

100 DEFINE: The second number of an ordered pair that indicates how far up or down to move from the x-axis. 50 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?

1 SE = Student Edition - TG = Teacher s Guide

1 SE = Student Edition - TG = Teacher s Guide Mathematics State Goal 6: Number Sense Standard 6A Representations and Ordering Read, Write, and Represent Numbers 6.8.01 Read, write, and recognize equivalent representations of integer powers of 10.