1. 6 th Grade Review

3. Whole Number Operations 1. 4137 + 739 2. 567 +139 3. 5602 +8835 4. 65391 + 87 5. 941372 + 128343

4. 1.4,876 2.706 3.14,437 4.65,478 5.1,069,715

5. Whole Number Operations 1.345 - 278 57 2. 9864 - 671 9193 3. 149856 - 51743 97113 4. 7548362 - 969457 6678905 Can you find the mistake?

6. Whole Number Operations 1.65 x 32 2.345 x 123 3.265 x 524 Be Sure To Show All Your Work!!

7. Solutions To Multiplication Problems: 1.2,080 2.42,435 3.138,860

8. Whole Number Operations 1.9954 ÷ 63 2.2571 3 3.48026 ÷ 37

9. 1. 158 2. 857 3. 1298

10. Powers A POWER is a way of writing repeated multiplication. The BASE of a power is the factor, and the EXPONENT of a power is the number of times the factor is used.

11. Power Examples

12. Your Turn to Try a Few Powers

13. Real World Apps with Powers

14. Lesson 1 EQ: How do I solve numerical expressions?

15. Draw a real world example of an event that must be done in a certain order

16. Vocabulary Expression – a collection of numbers and operations 11 – 14 ÷ 2 + 6

17. PEMDAS P - parentheses E - exponents M - multiply D - divide A – add S - subtract 11 – 14 ÷ 2 + 6 Order of Operations – the rules we follow when simplifying a numerical expression

18. Order of Operations BenSusie 3 + 4 x 2 = 7 x 2 = 14 3 + 4 x 2 = 3 + 8 = 11 Which student evaluated the arithmetic expression correctly?

19. Simplify the expression. Using the Order of Operations 3 + 15 ÷ 5 3 + 3 6 Divide. Add.

20. Simplify the expression. Using the Order of Operations 44 – 14 ÷ 2 · 4 + 6 44 – 7 · 4 + 6 44 – 28 + 6 16 + 6 22 Divide and multiply from left to right. Subtract and add from left to right.

21. Simplify the expression. Using the Order of Operations 3 + 2 3 · 5 3 + 8 · 5 3 + 40 43 Evaluate the power. Multiply. Add.

22. Using the Order of Operations Simplify the expression. 28 – 21 ÷ 3 · 4 + 5 28 – 7 · 4 + 5 28 – 28 + 5 0 + 5 5 Divide and multiply from left to right. Subtract and add from left to right.

23. When an expression has a set of grouping symbols within a second set of grouping symbols, begin with the innermost set. Helpful Hint

24. Simplify the expression. Using the Order of Operations with Grouping Symbols 42 – (3 · 4) ÷ 6 42 – 12 ÷ 6 42 – 2 40 Perform the operation inside the parentheses. Divide. Subtract.

25. Using the Order of Operations with Grouping Symbols [(26 – 4 · 5) + 6] 2 [(26 – 20) + 6] 2 [6 + 6] 2 12 2 144 The parentheses are inside the brackets, so perform the operations inside the parentheses first. Simplify the expression.

26. Try this one on your own! 3 + 6 x (5+4) ÷ 3 - 7 Step 1: Parentheses 3 + 6 x (5+4) ÷ 3 – 7 Step 2: Multiply and Divide in order from left to right 3 + 6 x 9 ÷ 3 – 7 3 + 54 ÷ 3 – 7 Step 3: Add and Subtract in order from left to right 3 + 18 - 7

27. Try another! 150 ÷ (6 +3 x 8) - 5 Step 1: Parentheses 150 ÷ (6 +3 x 8) – 5 Step 2: Division 150 ÷ 30 – 5 Step 3: Subtraction 5 – 5

28. Challenge! Classify each statement as true or false. If the statement is false, insert parentheses to make it true. false 1. 4  5 + 6 = 44 () 2. 24 – 4  2 = 40 () false 3. 25 ÷ 5 + 6  3 = 23 4. 14 – 2 2 ÷ 2 = 12 true

29. Application Sandy runs 4 miles per day. She ran 5 days during the first week of the month. She ran only 3 days each week for the next 3 weeks. Simplify the expression (5 + 3 · 3) · 4 to find how many miles she ran last month. WeekDays Week 15 Week 23 Week 33 Week 43 (5 + 3 · 3) · 4 (5 + 9) · 4 14 · 4 56Sandy ran 56 miles last month. Perform the operations in parentheses first. Add. Multiply.

30. Application* Jill is learning vocabulary words for a test. From the list, she already knew 30 words. She is learning 4 new words a day for 3 days each week. Evaluate how many words will she know at the end of seven weeks. DayWords Initially30 Day 14 Day 24 Day 34 (3 · 4 · 7) + 30 (12 · 7) + 30 84 + 30 114 Perform the operations in parentheses first. Jill will know 114 words at the end of 7 weeks. Multiply. Add.

31. Application* Denzel paid a basic fee of $35 per month plus $2 for each phone call beyond his basic plan. Write an expression and simplify to find how much Denzel paid for a month with 8 calls beyond the basic plan. $51

32. Simplify each expression. 1. 27 + 56 ÷ 7 2. 9 · 7 – 5 3. (28 – 8) ÷ 4 4. 136 – 10 2 ÷ 5 5. (9 – 5) 3 · (7 + 1) 2 ÷ 4 58 35 5 116 1,024

33. EQ: How can I perform operations with fractions?

34. Fraction Action Vocabulary FractionA number that names a part of a whole and has a numerator and denominator Simplest formWhen the numerator and denominator have no common factor other than 1 NumeratorThe top portion of a fraction DenominatorThe bottom portion of a fraction

35. Least Common Denominator The least common multiple (LCM) of the denominators of two or more fractions Greatest Common Factor The largest number that factors evenly into two or more larger numbers Fraction Action Vocabulary

36. Adding Fractions 1. 1/5 + 2/5 2. 7/12 + 1/12 3. 3/26 + 5/26 With Like Denominators!

37. Adding Fractions 1. 2/3 + 1/5 2. 1/15 + 4/21 3. 2/9 + 3/12 With Different Denominators! Steps: 1.Find the LCD 2.Rename the fractions to have the same LCD 3.Add the numerators 4.Simplify the fraction

38. Subtracting Fractions 1. 3/5 - 2/5 2. 7/10 – 2/10 3. 21/24 – 15/24 With Like Denominators!

39. Subtracting Fractions 1. 2/3 – 4/12 2. 4/6 – 1/15 3. 2/12 – 1/8 With Different Denominators! Steps: 1.Find the LCD 2.Rename the fractions to have the same LCD 3.Subtract the numerators 4.Simplify the fraction

41. Multiplying Fractions 1. 2/9 x 3/12 2. ½ x 4/8 3. 1/6 x 5/8 Steps: 1.Multiply the numerators 2.Multiply the denominators 3.Simplify the fraction

42. Dividing Fractions 1. 2/10 ÷ 2/12 2. 1/8 ÷ 2/10 3. 1/6 ÷ 3/15 Steps: 1.Keep it, change it, flip it! 2.Multiply the numerators 3.Multiply the denominators 4.Simplify the fraction

44. Fraction Action Vocabulary Equivalent fractionsFractions that name the same number or are of equal value Proper fractionNumerator is smaller than the denominator Improper fractionWhen the numerator is larger than the numerator Mixed NumberA whole number and a fraction

45. Changing Improper Fractions to Mixed Numbers 1. 55/9 2. 39/4 3. 77/12 Steps: 1.Divide 2.Remember…First come, first serve

46. Changing Mixed Numbers to Improper Fractions 1. 2. 3. Steps: 1.Multiply the whole number by the denominator 2.Add the result to the numerator (that will be your new numerator) 3.The denominator stays the same

47. Operations with Mixed Numbers 1. 2. Steps: 1.Convert both mixed numbers to an improper fraction 2.Follow the necessary steps for the given operation 3.Simplify

48. Equivalent Fractions 1. 3/8 = 375/1000 2. 18/54 = 23/69 3. 6/10 = 6000/1000

49. 1. True 2. True 3. False

50. Homework: handout

51. EQ: How do I perform operations with decimals?

52. Decimals A way to represent fractions EX: 1.Look at the last decimal place…that place value is the denominator of the fraction 2. The numbers to the right of the decimal are the numerator

53. Place Value The value of a digit based on its position in a number

55. Place Value Game FunBrain - Place Value Puzzler

56. Ordering Order from least to greatest 3.84, 4.4, 4.83, 3.48, 4.38 Order from greatest to least 5.71, 5.8, 5.68, 5.79, 5.6

57. Comparing Decimals: Use, or = to complete the following. 1. 6.5 ____ 6.45 2. 12.4312 _____ 12.43112 3..6 ____.61

58. Rounding – “4 or less let it rest 5 or more let it score” 1. Round to the nearest one 17.6 2. Nearest thousandth 12.5503 3. Nearest hundredth 2.2959

59. Decimal Operation Chant Do you know your decimals? Add or Subtract, line it up, line it up! Multiply, Count it out, count it out! Division, step it out! Now you know your decimals!

60. Adding and Subtracting Decimals Just make sure to line up the decimal points so that all the decimal points are on a vertical line HINT:

61. Try some! 156.7 + 23.14 = 57.123 – 14.25 =

62. Multiplying Decimals Multiply the numbers like normal Move the decimal to the right the exact number of place values in the numbers being multiplied

63. Try One! 45.68 x 3.5=

64. Dividing Decimals Stranger Story The stranger moves toward the door, so you move the same amount back The stranger gets to the door! GET AWAY! Go to the ROOF!

65. Dividing Decimals Then, divide like normal

66. Try these! 16.9 ÷ 6.5 55.318 ÷ 3.4

68. EQ: How are percents, ratios, and proportions related?

69. Percent: A ratio that compares a number to 100 Out of 100 Part/whole

70. Ratio: A comparison of two numbers Part What is the ratio of pink circles to white circles?

71. Proportion: An equation that shows two ratios are equal

72. Convert to a fraction and a percent… 1..25 2..003

73. Convert to a percent and decimal… 1. 3/4 2. 23/50

74. Convert to a fraction and a decimal… 1. 25% 2. 104%

75. Sales Tax, Discount & Mark-Up Vocabulary Discount – the amount taken off the price, this is a savings Sales Tax & Tip– amounts added to the price of a purchase that are calculated by using a percent of the purchase price. Sale Price –the price of an item before a discount or mark-up is applied Mark-up- the increase from the wholesale price to the retail price Wholesale price – the price the manufacturer charges the store who will sell its item Retail price - the price the store you buy the item from charges

76. Sales Tax & Tip Example

77. Discount Example

78. Mark-up Example

79. Practice with discounts, mark-ups, & tax.

81. EQ: How can I evaluate algebraic expressions? Card activity

83. Variable -- An unknown quantity

84. Expression -- A collection of numbers, variables, and symbols NO equal sign!! 10 (x+3) + 2

85. Simplify -- To reduce to the most basic form Make it simple! 1. 3 + 5 (3*5) 2.

86. Find the variable, replace it Simplify the expression Now your all done Just remember to… PLUG IT IN!

87. Learning Partner Class Work

88. Lesson 6 Area & Perimeter EQ: How can I solve mathematical problems that involve finding the area and perimeter of various shapes?

89. Vocabulary Perimeter – the distance around a figure Area – the amount of space inside a figure Circumference – the distance around a circle. The ratio of the circle’s circumference to its diameter is represented by (3.14 or 22/7).

90. Triangle Area Formula

91. Example

92. Parallelogram Area Formula

93. Example

94. Trapezoid Area Formula

95. Example

96. Circumference Formula

97. Example

98. Your Turn…

99. Your Turn