3. Chapter 1: Variables and Patterns

4. Chapter 1: Patterns and Variables Definition of a Pattern A list of numbers that follow a certain sequence or patterns. Definition of a Variable A symbol or number that is unknown, therefore it needs to be solved.

5. Examples: StudentsAmount of Dollars $ 110 220 330 440 550 The student column is the “input” area and the amount of dollars is the “output” area. Expression: 10 D D is the variable. For an example, when we put 1 student representing D, there is 10 dollars. For an example, when we put 2 students representing D, there is 20 dollars.

6. Definition  Coordinate grid –  A coordinate grid, is a grid that is used to locate a point by its distances from 2 intersecting straight lines. A B C D E 12345 What are the coordinates of the house?

7. Definition  x axis – a horizontal number line on a coordinate grid. 1234506 x

8. Definition  y axis – a vertical number line on a coordinate grid. 1 2 3 4 5 0 6 y

9. Hint  y is the tallest and stands upright or vertically. 1 2 3 4 5 0 6 y

10. Definition  Coordinates – an ordered pair of numbers that give the location of a point on a grid. (3, 4) 1 2 3 4 5 0 6 1234506 (3,4)

11. Hint  The first number is always the x or first letter in the alphabet. The second number is always the y the second letter in the alphabet. 1 3 2 4 5 0 6 1234506 (3,4)

12. How to Plot Ordered Pairs  Step 1 –  Always find the x value first, moving horizontally either right (positive) or left (negative). 1 3 2 4 5 0 6 1234506 (2, 3) y x

13. What is the ordered pair? 1 3 2 4 5 0 6 1234506 (3,5) y x

14. Chapter 2; Whole Numbers

15. Chapter 2: Whole Numbers Whole Number A Whole Number is a number that is an integer. It can be positive or negative and it does not include a decimal. Prime Number A Prime Number is a number that has only itself and one as its factors. Example: 2, 1 and 2 are its factors. Composite Numbers Composite Numbers are numbers that have more than 2 factors. Example: 9: 1, 3, and 9 are its factors.

16. Chapter 2: Whole Numbers Factors Factors are numbers that make up a whole number. Example: 3 is one of the factors that 9 has. Multiples Multiples are what you get when multiply are prime number or a composite number by a whole number Example: 5 X 2 = 10; 11 is not a multiple of 5 because you cannot multiply a whole number by 5 to get to 11.

17. Chapter 3; Decimals

18. Chapter 3: Decimals  Definition of a Decimal:  A decimal is similar to a fraction in that it is not a whole number. It is a part of a number.

19. Let’s Look at Some Place Value: The Example is 137 dollars and 82 cents. One Hundred Dollars Ten Dollars One Dollar Ten Cents Cents 13782 HundredsTensOnesTenthsHundredths 13782

20. Example: Estimate the sum of 10.93 and 3.25. 10.93 + 3.25 11 11.00 3.003 14

21. Multiplying Decimals  Multiply decimals the same way as you would with whole numbers.  Then place the decimal point in the product.  The number of decimal places in the product is equal to the sum of the number of decimal places in the factors.

22. Example: Multiply 5.63 x 7 5. 63 7 x 1 2 4 4 39 two.

23. Multiplying by 10,100, 1000 :  When you multiply by 10, 100, or 1,000, you can move the decimal point to the right.  The number of decimal places you move is the same as the number of zeroes you are multiplying by.  When you divide by 10, 100, or 1,000, you can move the decimal point to the left. Move the decimal point once for each zero that you are dividing by.

24. 1.492 x 100 Move the decimal to the right: two spaces. 149.2

25. 2,124.94 ÷ 1,000 Move the decimal to the left: three spaces. 2.12494

26. 4.2 ÷ 100 Move the decimal point to the left: two spaces. Add a zero for the second space..042

27. 15.36 x 1,000 Move the decimal point to the right: three spaces. Add a zero for the third space. 15,360

28. Chapter 4; Angles

29. Keywords to Know  An angle has two sides and a vertex.  The sides of the angles are rays. The rays share a common endpoint (the vertex).  Angles are measured in units called degrees.

30. Types of Angles When lines intersect to form right angles, then they are classified as perpendicular lines.

31. Right angles  Right Angles measure between 90 degrees.

32. Obtuse Angles  Obtuse Angles measure between 90 and 180 degrees.

33. Acute Angles  Acute Angles measure between 0 and 90 degrees.

34. Reflex Angle  A Reflex angle is an angle between 180 and 360 degrees.

35. Straight Angle  A straight angle is an exactly 180 degrees.

36. All of the Angles  Acute Angle  Right Angle  Obtuse angle  Straight Angle  Reflex Angle  * All are listed in order to the measures that they follow.

37. Finding Missing Angles The three angles of a triangle always add to 180°. Use a variable to stand for the missing angle and set an equation equal to 180. x + 49 + 47 = 180 x + 96 = 180 180-96= x = 84

38. Drawing Angles With a Protractor

39. Drawing Angles 1. Draw a ray.

40. Drawing Angles 2. Line up protractor with rays endpoint; have ray pointing to zero degrees.

41. Drawing Angles 3. Draw ray from endpoint of first ray though second point.

42. Draw a 75 degree angle.

43. Draw a 100 degree angle.

44. Measuring Angles

45. Finding Angle Measures: What is measure of D Line up angle vertex with center of protractor ; have one side at 0° Center of protractor Ray D is at 0°

46. Look at where non-zeroed ray crosses…….. Approximately 34°

47. What is the angle measure? Approximately 80°

48. A Review of Some Shapes

49. What is a quadrilateral? A quadrilateral is a closed 2 dimensional figure with that are line segments. four sides

50. What is a parallelogram?  Quadrilateral – 4 sides  Opposite sides congruent  Opposite sides parallel

51. What is a rectangle?  Quadrilateral- 4 sides  Parallelogram- opposite sides parallel  Four right angles.

52. What is a rhombus?  Quadrilateral- 4 sides  Parallelogram- opposite sides parallel  Four congruent sides.

53. What is a square?  Quadrilateral – 4 sides  Parallelogram- opposite sides parallel  Rectangle- 4 right angles  Rhombus- 4 sides congruent

54. What is a trapezoid?  Quadrilateral – 4 sides  Exactly one pair of parallel sides

55. Quadrilateral Parallelogram Trapezoid Rhombus Rectangle Square

56. What are all of the names for this polygon?  Quadrilateral  Parallelogram  Rectangle Which name best describes the shape?

57. chapter 4 Property of quadrilaterals  The sum of all the angles equals 360º degrees. 90º

58. chapter 4 Property of Quadrilaterals  The sum of all the angles equals 360º degrees. 70º 110º 70º 110º 70º 110º + 360 º

59. chapter 4 What is the missing angle? 58º 81º 109º ? + 360º 81º58º 109º ?

60. Chapter 5: Percents and Ratios etc.

61. Vocabulary  A percent is a ratio that compares a number to 100. It means “per 100.”  49 out of 100 is 49%.

62. Writing Percents as Fractions  Place the percent in a fraction with a denominator of 100.  Simplify the fraction. 26% 26 100 13 50 75% 75 100 3 4

63. Writing Fractions as Percents  Write a proportion with a denominator of 100 if possible (easiest way). Then write as a percent. OR  Divide the numerator by the denominator to get a decimal. Then change the decimal to a percent by moving the decimal point to the right (multiply by 100). 6 25 ? 24% 100

64. What is a Percent Classification of a percent A percent is the number of parts per 100; the numerator of a fraction with the denominator of 100. A percentage sign: %

65. Percent to Decimal  45 %  0.45 Percent Decimal

66. A Conversion from Decimal to Percent  To convert decimals to percents, you have to multiply by 100. 0.45 X 100 45%

67. A Conversion from Percent to Decimal  To convert percents to decimals, you have to divide by 100. 45 % / 100 0.45

68. Ratios

69. Ratio’s Part to Part Ratio Part-to-part ratio: A ratio that compares a part if a whole to another part of the whole. For example there are 7 brown rabbits and 6 white rabbits. The ratio of brown rabbits to white rabbits are 7:6. Part to Part Ratio Part-to-whole ratio: a ratio that compares a part of a whole to the whole. For example if there are 7 brown and 6 white rabbits, the ratio for brown rabbits to all rabbits is: 7: 13. Term of a Ratio Term of a ratio: The quantities that make up the total ratio. For example in a ratio 4:5 the terms are 4 and 5.

70. Ratios  A ratio is a comparison between two numbers by division.  It can be written in three different ways: 5 to 2 5 : 2 5 2

71. Equal Ratios  When two ratios name the same number, they are equal. It ’ s like writing an equivalent fraction. 20 : 30 Equal Ratios: 10 : 15 2 : 3 80 : 120

72. Fractions

73. Improper Fractions and Mixed Numbers

74. Improper Fractions

75. Mixed Numbers and Improper Fractions

76. Conversion: The Steps The Steps to Converting a Mixed Number to An Improper Fraction. Step 3: When finished, put the final result as the numerator, and keep the denominator the same way. Step 2: Add the result to the numerator. Step 1: Multiply the whole number by the denominator.

77. Conversion: The Steps Step 1: Divide the numerator by the denominator. Step 2: Write down the whole number answer. Step 3: Then write down any remainder above the denominator. The Steps for Converting an Improper Fraction to a Mixed Numbers

78. Example 1 5 8 x 3 4 = 15 32 There are no common factors for 15 and 32, so this fraction cannot be simplified.

79. Example 2 3 4 x 2 9 = 6 36 This fraction can be reduced. Divide the numerator and denominator by the GCF, which is 6. = 1 6 Or Use Cross Canceling from the beginning!!!

80. Multiplying by a Whole Number If you want to multiply a fraction by a whole number, turn your whole number into a fraction by placing a 1 as the denominator. If your answer is improper, divide the bottom into the top. 4 5 x 20 1 = 80 5 = 16

81. Example 3 15 x 1 6 1 = Cross Cancel. 5 2 Five halves is improper, so we divide the bottom into the top. 25 2 4 1 2 1 2

82. Data Management and Probabity

83. Overview Probability is the study of random events. The probability, or chance, that an event will happen can be described by a number between 0 and 1: A probability of 0, or 0%, means the event has no chance of happening. A probability of 1/2, or 50%, means the event is just as likely to happen as not to happen. A probability of 1, or 100%, means the event is certain to happen. For instance, the probability of a coin landing heads up is ½, or 50%, This means you would expect a coin to land “heads up” half of the time.

84. Overview The language of probability includes: Experiment – a systematic investigation where the answer is unknown You can represent the probability of an event by marking it on a number line like this one Impossible 0 = 0% Certain 1 = 100% 50 – 50 Chance ½,.5, 50% number of possible outcomes Probability = number of favorable outcomes

85. Ways to write Probability Fractions Percent Or Decimal Most Common Way: Fraction or Percent

86. 1. What is the probability that the spinner will stop on part A? 2.What is the probability that the spinner will stop on (a)An even number? (b)An odd number? 3. What fraction names the probability that the spinner will stop in the area marked A? AB CD 3 1 2 A CB

87. References: Yuskaitis, M.chapter 4 © 2000 http://leahbrownell.escuelacampoa legre.wikispaces.net/6th+Grade+Ma th+Class+Notes http://leahbrownell.escuelacampoa legre.wikispaces.net/6th+Grade+Ma th+Class+Notes