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Place Value

Place Value. The place value chart below shows 1247.63. The number 1248.63 is one more than 1247.63 The number 1147.63 is one hundred less than 1247.63 The number 1247.83 is two tenths more than 1247.63. Review. Where is the decimal place? 34 $5698 508 67.89 HIDDEN DECIMAL. Review.

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Place Value

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  1. Place Value • The place value chart below shows 1247.63 • The number 1248.63 is one more than 1247.63 • The number 1147.63 is one hundred less than 1247.63 • The number 1247.83 is two tenths more than 1247.63

  2. Review • Where is the decimal place? • 34 • $5698 • 508 • 67.89 HIDDEN DECIMAL

  3. Review • Arrange each set of numbers from greatest to least! What strategy did you use? • A) 1.8, 2.8, 1.9 • B) 365.7, 358, 365.9

  4. Review – Learn Alberta Place Values http://www.learnalberta.ca/content/memg/index.html?term=Division02/Place_Value/index.html

  5. Review – Adding and Subtracting Decimals What do you need to do? • Line up the decimals • Add zeros into place values that are empty (if you wish) • Ex: 12.3 + 2. 4 = 12.3 12.3 + 2.4 + 02.4 14.7 14.7

  6. Review – Adding and Subtracting Decimals What do you need to do? • Line up the decimals • Add zeros into place values that are empty (if you wish) • Ex: 187.415 + 34.6 = 187.415 187.415 +34.6+ 034.600

  7. 2.1 Add and Subtract DecimalsStudent Outcome: I can use different strategies to estimate decimals. • Pg 44 Vocabulary: • Estimate: • to approximate an answer • Overestimate: • Estimate that is larger than the actual answer • Underestimate: • Estimate that is smaller than the actual answer

  8. Front-End Estimation Student Outcome: I can use different strategies to estimate decimals. Front End Estimation: keep the leading (front) digit and then add zeros behind Example #1 • 87.85 + 14.60 + 273.52 = 375.97 • 80.00 + 10.00 + 200.00 = 290.00 Using front-end estimation: 290 is an ok estimation

  9. Front-End Estimation Student Outcome: I can use different strategies to estimate decimals. Front End Estimation: keep the leading (front) digit and then add zeros behind Example #2 • 537.85 - 174.60 = 363.25 • 500.00 - 100.00 = 400.00 Using front-end estimation: 400 is a good estimation

  10. Front-End Estimation Student Outcome: I can use different strategies to estimate decimals. Front End Estimation: keep the leading (front) digit and then add zeros behind Example #3 49.45 + 239.99 + 87.06 = 376.50 ____ + _____ + ____ = _______ Example #4 708 – 45.89 = 662.11 ___ - ____ = _________

  11. Relative SizeStudent Outcome: I can use different strategies to estimate decimals. Use Relative Size: • Estimating each number to the nearest ten, hundred, thousand etc. Example #1 • 87.85 + 14.60 + 73.52 = 175.97 • 87.85 is between 80 and 90, and closer to 90.00 • 14.60 is between 10 and 20, and closer to 10.00 • 73.52 is between 70 and 80, and closer to 70.00 90.00 + 10.00 + 70.00 = 170.00 Using relative size: 170.00 is a good estimation

  12. Relative SizeStudent Outcome: I can use different strategies to estimate decimals. Use Relative Size: • Estimating each number to the nearest ten, hundred, thousand etc. Example #2 39.01 + 62.77 = 101.78 ____ + ____ = ________ Example #3 567.28 – 21.99 + 38.34 = 583.63 _____ - ____ + _____ = _______

  13. CompensationStudent Outcome: I can use different strategies to estimate decimals. Use Compensation: (try to round up - round down) • Estimating each number to the nearest ten, hundred, thousand etc. Example #1 • 87.85 + 14.60 + 73.52 = 175.97 • 87.85 is closer to 90.00 (round up) • 14.60 is closer to 10.00 (round down) • 73.52 is closer to 70.00 (round down) 90.00 + 10.00 + 70.00 = 170.00 Using compensation: 170 is a good estimation

  14. Compensation Student Outcome: I can use different strategies to estimate decimals. Use Compensation: (try to round up - round down) • Estimating each number to the nearest ten, hundred, thousand etc. Example #2 12.45 + 71.12 – 19.43 = 64.14 ____ + ____ - ____ = ____ Example #3 567.89 – 123.00 = 444.89 _____ - _____ = _____

  15. Compatible (Friendly) Numbers Student Outcome: I can use different strategies to estimate decimals. Use Compatible numbers: (5’s, 10’s 50’s 100’s 1000’s) Example #1 • 87.85 + 14.60 + 73.52 = 175.97 • 87.85 is closer to 90 or 85 • 14.60 is closer to 10 or 15 • 73.52 is closer to 70 or 75 • Two possible answers, but still others 90+10+70 = 170 or 85+15+75 = 175

  16. Try It On Your Own! • Rewrite each question using front-end estimation. • A) 45 + 33 + 92 = 170 ____ + ____ + ____ = ____ • B) $475.12 - $210.38 = $264.74 _________ - ________ = ________ Is your estimate higher or lower than the calculated answer? _____________

  17. Try It On Your Own! • Use any strategy to estimate the answers. • A) 45 + 33 + 92 = 170 ____ + ____ + ____ = ____ ____ + ____ + ____ = ____ • B) $475.12 - $210.38 = $264.74 ________ - ______ = _______ ________ - ______ = _______

  18. Try It On Your Own! • Using estimation, where would you put the decimal point in the answer? Why? • A) 631.5 + 902.4 + 217.83 = 175173 ______ + ______+ ______ = _______ • B) $475.12 - $210.38= $26474 _______ - _______ = _______

  19. Try These On Your Own! • For Homework Due Tomorrow! • Pg 48. #4, 7, 8ac, 10ac, 14, 20, 21 • Extend 22, 24, 25 • Page 2.1 worksheet

  20. Practical Quiz #1 Using Estimation, fill in the blanks where would you put the decimal point in the answer? • A) 81 + 14.074 + 201.897 = 296971 ______ + ______ + ______ = _______ • B) $782.56 - $258.76 = $5238 _______ - _______ = _______

  21. Assignment – Let’s go shopping Student’s will receive their handout to select their items and money to purchase merchandise. $500.00

  22. Multiplying Decimal NumbersStudent Outcome: I can estimate by +,-,x,÷ decimals. • Problem: Page 52 • Ashley and Marshall’s family keep busy travelling across the country by solving sudoku puzzles! During a stop, they look in a convenience store for more puzzles. • Marshall finds sudoku books on sale for $1.69. he wants to buy five books and has $9.00. • Help him estimate the total cost of the five puzzle books! • $1.69 x 5 = ______?

  23. Multiplying Decimal NumbersStudent Outcome: I can estimate by +,-,x,÷ decimals. • 1. Marshall estimates the total bill as $5.00 • a) How do you think Marshall got his estimate? • b) Is Marshall’s estimate over or under the total? • How do you know? • 2. Ashley estimates the total bill as $10.00 • a) How do you think Ashley got her estimate? • b) Is Ashley’s estimate over or under the total? • How do you know?

  24. DID YOU KNOW!!!! Sudoku • Sudoku was invented hundreds • of years ago, and traded around the world by ancient mathematicians. • Each digit from 1 to 9 must occur in: • Each row • Each column • Each 3 x 3 square.

  25. Multiplying DecimalsStudent Outcome: I can estimate by +,-,x,÷ decimals. • Use front-end estimation and relative size to estimate: • 2.65 x 3.72 • Front-End Estimation: • Relative Size:

  26. Multiplying DecimalsStudent Outcome: I can estimate by +,-,x,÷ decimals. Estimate to make sure your answer is reasonable! • Multiply 1.54 x 25 • What strategy will you use?

  27. Multiplying DecimalsStudent Outcome: I can estimate by +,-,x,÷ decimals. • Use a calculator to solve the equation: Multiply 1.54 x 25 • Things I know: 25 x 1 = 25 • Things I know 25 x 2 = 50 • Why would the answer lie between 25 and 50.

  28. Multiplying DecimalsStudent Outcome: I can estimate by +,-,x,÷ decimals. • Using paper and pencil • Multiply without decimals add decimals to product • Estimate an answer. Why? • Ex: 2.6 x 3.7= 26 x37 962

  29. Multiplying Decimals Learn Alberta http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=10 Slides 1-5

  30. Practice Makes Perfect • Page 57 • 3, 6ab, 9, 13, 14,17 • Extend 20, 21

  31. Dividing Decimal NumbersStudent Outcome: I can estimate by +,-,x,÷ decimals. • Example 1: • A) 15.4 ÷ 3.6 = 4.27778 Front-End Estimation: • Things I know: 15 ÷ 3 = 5 • The answer closest to 5 is 4.27778

  32. Dividing Decimal Numbers Using a Number Line Ex: 10 ÷ 2 =

  33. Use Estimation to Place the Decimal Point.Student Outcome: I can problem solve using decimals. • Example #2: Four friends buy 1.36L of pure orange juice and divide it equally. • A) Estimate each person’s share. • B) Calculate each person’s share.

  34. Use Estimation to Place the Decimal Point. • Solution: • A) To estimate, round 1.36L to a number that is easier to work with. • Try 1.2 • 1.2 ÷ 4 = 0.3 Underestimate • Try 1. • 1.6 ÷ 4 = 0.4 Overestimate • Things I know 12 ÷ 4 = 3 So 1.2 ÷ 4 = 0.3 16 ÷ 4 = 4 So 1.6 ÷ 4 = 0.4

  35. Dividing DecimalsStudent Outcome: I can problem solve using decimals. • Problem Questions: • 1. How many pens do you think you can buy with $6.00 if one pen costs $0.40 • Use both front-end estimation and relative size estimation to find your educated guess. Strategy Used:

  36. Working Together!! • Pg 66 #10 • A package of 7 fish hooks costs $17.99 • How much will one fish hook cost? • Estimate • Calculate- by hand and with calculator • Did you over/under estimate? ANSWER: $17.99 ÷ 7 = $2.57

  37. Working Together! • Pg 66 #11 • Ashley wants to find how many 355 mL cans of juice are in a 2-L bottle. • A) Show Ashley how to estimate the answer • B) Show Ashley how to calculate the answers

  38. Practical Quiz #2 What is the cost of each purchase before tax? Show your work!! 3 oatmeal cereal bars for $7.50

  39. Dividing Decimals Learn Alberta http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=10 Slides 6-10

  40. Assignment • Page 65 – 67 • #4, 8, 12, 13, 14, 17, 19 • Extend #21, 22

  41. BEDMASStudent Outcome: I can solve problems using order of operations. • Remember the order by the phrase • B - BRACKETS • E - EXPONENTS • D/M – DIVIDE OR MULTIPLY • A/S – ADD OR SUBTRACT

  42. The “B” and “E”Student Outcome: I can solve problems using order of operations. • The “B” stands for items in brackets • Do all items in the brackets first (2 + 3) The “E” stands for Exponents Do anything that has a exponent (power) 82

  43. The “DM”Student Outcome: I can solve problems using order of operations. • Represents divide and multiply • Do which ever one of these comes first in the problem Work these two operations from left to right

  44. The “AS”Student Outcome: I can solve problems using order of operations.. • Represents Add and Subtract • Do which ever one of these comes first • Work left to right • You can only work with 2 numbers at a time. 8 + 7 - 5 + 2

  45. 2) 8 – 3 x 2 + 7 8 - 6 + 7 2 + 7 9 1) 5 + (12 – 3) 5 + 9 14 3) 39 ÷ (9 + 4) 39 ÷ 13 3

  46. 15 x 103 15 x 1,000 15 000 • 10 + 8 ÷ 2 – 6 10 + 4 - 6 14 - 6 8 36 ÷ (1 + 2)2 36 ÷ 32 36 ÷ 9 4 7) 3 x 104 3 x 10 000 30 000

  47. (5 – 1)3 ÷ 4 43 ÷ 4 64 ÷ 4 16 14 + 3(7 -2) – 2 x 5 14 + 3 x 5 - 2 x 5 14 + 15 - 2 x 5 14 + 15 – 10 29 – 10 19

  48. Order of Operations – Learn Alberta • http://www.learnalberta.ca/content/mejhm/index.html?ID1=AB.MATH.JR.NUMB&ID2=AB.MATH.JR.NUMB.INTE&lesson=html/object_interactives/order_of_operations/use_it.html

  49. Let’s PracticeStudent Outcome: I can solve problems using order of operations. • Place the operations shown in square brackets to make each statement true. • 9__ 5__5 = 50 (+, x) • 15 __ 3 __2 = 24 (x,-)

  50. Let’s PracticeStudent Outcome: I can solve problems using order of operations. • What are the missing numbers? • A) _____ + 5 x 6 = 32 • B) _____ - 3.2 ÷ 0.5 = 5

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