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Unit 2, Week 1 -

Unit 2, Week 1 - . Ordering & Computing Numbers in Scientific Notation. Do Now – √81 / √25 + 5/ √144. Please pick up your guided notes, new tracker, and respond to the following SILENTLY & INDEPENDENTLY: What are you still confused about regarding scientific notation?

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Unit 2, Week 1 -

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  1. Unit 2, Week 1 - Ordering & Computing Numbers in Scientific Notation

  2. Do Now – √81 / √25 + 5/ √144 • Please pick up your guided notes, new tracker, and respond to the following SILENTLY & INDEPENDENTLY: • What are you still confused about regarding scientific notation? • What could you have done to better prepare for your quiz? • What are you going to do this week to improve your next quiz score?

  3. Quiz 1 Mathletes (85% of higher) • 3rd Period

  4. Quiz 1 All-Stars (!00%)

  5. Quiz 1 Class Averages

  6. Tracking Your Quiz • Please take out your tracker. • Independently, you will have to track your quiz & your class average. • You have 2 minutes to do this. • 3rd period – 70% • 5th period – 88% • 6th period – 70% • 7th period – 72%

  7. Student of the Week Kaylan is STUDENT OF THE WEEK because… • She is always participating! • Takes the time to truly understand what she is learning! • Has turned in 100% of her homework! • IS AWESOME at math! Kaylan Freeman

  8. Today’s Objective • SWBAT convert numbers into proper scientific notation. • SWBAT order numbers in scientific notation from least to greatest.

  9. Weekly Agenda - • Monday – Ordering Numbers in Scientific Notation/Scientific Notation Word Problems • Tuesday – Multiplying Numbers in Scientific Notation • Wednesday – Dividing Numbers in Scientific Notation • Progress Reports Issued • Thursday – Quiz • Parent Teacher Conferences 4-7 • Friday – NO SCHOOL! 

  10. Today’s Agenda • Do Now – 6 minutes • Shout Outs – 2 minutes • Class Averages/Tracking – 4 minutes • Today/ Weekly Agenda – 1 minute • Ordering Numbers INM – 15 minutes • Ordering Numbers GP – 10 minutes • Ordering Numbers IP – 5 minutes • Exit Ticket – 5 minutes

  11. Ordering Numbers in Scientific Notation • Today, we are going to order numbers in scientific notation in ascending or descending order. • Before we begin, you and your partner will work for 1 minute to come up with a real world situation where you would need to order really big and really small numbers in scientific notation.

  12. Ordering Numbers in Scientific Notation • Sometimes, when we are given numbers to order, they will not be properly written in scientific notation. • It will be up to you to put it in the correct form without changing the value of the number.

  13. Converting Numbers into Proper Form • You will work with your partner on examples 1 & 2 for 2 minutes and then we will review together. TRY YOUR HARDEST & use what we learned last week! • Example 1: Convert 56 x 10-7 into proper scientific notation. • Example 2: Convert .43 x 104 into proper scientific noation

  14. Converting Numbers into Proper Form • Did you notice anything about moving the decimals and changing the exponent? • Think with your partner for 1 minute and try to come up with a rule for moving the decimal and changing the exponents – fill this in on the box on your notes. • When you move a decimal left, you addthe number of places you moved the decimal to the exponent. • When you move the decimal right,you subtract the number of places you moved the decimal to the exponent.

  15. Converting Numbers into Proper Form • Example 3: Convert the following number into proper scientific notation: 2367 x 10-4 • Example 4: Convert the following into proper scientific notation: .875 x 10-2 • Example 5: Convert the following into proper scientific notation: 34.5 x 105 • Example 6: Convert the following into proper scientific notation: 781 x 107

  16. Ordering Numbers in Scientific Notation • Now that we understand how to properly convert numbers, we can now order them. • Example 7: Order the following numbers from least to greatest: 3.72 x104 .46 x105 4.2x108 82x105 • Make sure all numbers are in proper scientific notation form. • If not, convert them. • Turn into standard form. • Compare and order from least to greatest.

  17. Ordering Numbers in Scientific Notation • Example 8: Ordering the following numbers from least to greatest. 4.56x10-3 45.1x10-2 4.56x10-5 72x10-4 • Think with your partner now, did you notice anything about the exponents and the ordering? Try to come up with a rule that will help us ordering numbers without converting them into standard form. Write this in the box on your notes. You have 2 minutes!

  18. Ordering Numbers in Scientific Notation • After all numbers are correctly in scientific notation,: • The number with the smallest power is the smallest number. • The number with the largest power is the largest number. • If numbers are raised to the same power, the smaller factor 1 is the smaller number.

  19. Ordering Numbers in Scientific Notation • Example 9: The table lists the total value of music shipments for four years. List the years from least to greatest dollar amount. Work on this with your partner.

  20. Ordering Numbers in Scientific Notation • Example 10: Order the following numbers from greatest to least. Work on this with your partner. • 0.61 x 104 • 9.41 x 103 • 0.61 x 103 • 9.47 x 104

  21. Ordering Numbers in Scientific Notation • Example 11:Order the following numbers from least to greatest. Work on this with your partner. • 7.312 x 104 • 7.961 x104 • 7.7 x 107 • 7.423 x 102

  22. Ordering Numbers in Scientific Notation • Example 12: Order the numbers from least to greatest. Work on this on your own. • 5.43 x 107 • 6.012 x 105 • 6.3 x 105 • 5.324 x 109

  23. Ordering Numbers in Scientific Notation • Example 13: The following diameters are shown for different types of cells. Order these from greatest to least. Work on this on your own.

  24. Exit Ticket • Each of you will complete your exit ticket on a note card. • There are 2 problems. • You will complete the exit ticket in 5 minutes and it must be turned in before you can exit the classroom. • You must work SILENTLY and INDEPENDENTLY. • HOMEWORK –Worksheet! 

  25. Do Now – 32 / √121 / √400 - 8 • Please respond to the following on your guided notes SILENTLY & INDEPENDENTLY: • The following distances areshown for specific cities toMemphis. Order the distancesfrom least to greatest. • The following measurementsindicate the thickness ofdifferent currencies.Order the thicknessesfrom least to greatest.

  26. Today’s Objective • SWBAT multiply numbers in scientific notation.

  27. Today’s Agenda • Do Now – 8 minutes • Agenda – 1 minutes • Rules of Exponents – 5 minutes • Multiplying Numbers in Scientific Notation INM = 10 minutes • Multiplying Numbers in Scientific Notation GP & IP – 15 minutes • Exit Ticket – 5 minutes

  28. Computing with Scientific Notation • For the past week we’ve been working with numbers in standard form and scientific notation. • Today we will continue to work with scientific notation and standard form, but we will take it a step farther and multiply the numbers. • Before we can start that, we must understand the rules of multiplying numbers with exponents.

  29. Multiplying Exponents • When multiplying numbers with different exponents, you simply add the exponents together, if the base number is the same. • Example 1: 105x 1014 • If the base number is the same, you add the exponents. • Solution: ____________________ • Examples 2: 10-6x 107 • If the base number is the same, you add the exponents. • Solution: ____________________ • Examples 3: 10-20x 10-7 • If the base number is the same, you add the exponents. • Solution: ____________________

  30. Multiplying Numbers in Scientific Notation • If you remember, there are two factors to a number in scientific notation: • Factor 1: A number that is greater than 1, but less than 10. • Factor 2: A power of 10. • When you multiply numbers in scientific notation, we multiply all factor 1 numbers together, and then add the exponents of factor 2 together. • HAND MOTIONS!

  31. Multiplying Numbers in Scientific Notation • Example 4: (2.7 x 102) x (3.2 x 104) • First, we ID our factor 1 numbers. • 2.7 & 3.2 • Second, we multiply our factor 1 numbers together. • 2.7 x 3.2 = 8.64 • This is now our new factor 1 of our product. • Third, we multiply the numbers with exponents. • 102x 104 • Remember we add the exponents when the base is the same. • 10 (2+4) = 106 • Fourth, we combine our factors to get our final answer. • Factor 1: 8.64 • Factor 2: 106 • Final answer: 8.64 x 106

  32. Multiplying Numbers in Scientific Notation • Example 5: (4.3 x 10-4) x (3.6 x 10-3) • First, we ID our factor 1 numbers. • 4.3 & 3.6 • Second, we multiply our factor 1 numbers together. • 4.3 x 3.6 = 15.48 • This is now our new factor 1 of our product. • Third, we multiply the numbers with exponents. • 10-4x 10-3 • Remember we add the exponents when the base is the same. • 10 (-4+-3) = 10-7 • Fourth, we combine our factors to get our final answer. • Factor 1: 15.48 • Factor 2: 10-7 • Temporary Final answer: 15.48 x 10-7 • But your answer MUST BE IN CORRECT scientific notation form. • We need to move the decimal point one place to the left so our factor 1 is greater than 1, but less than 10  1.548 • When we do this, we must account for the change in factor 2. Factor 2 goes from 10-7to 10-6. • Actual final answer: 1.548 x 10-6

  33. Multiplying Numbers in Scientific Notation • Example 6: (3 x 106) (2.5 x 10-7) • First, we ID our factor 1 numbers. • 3 & 2.5 • Second, we multiply our factor 1 numbers together. • 3 x 2.5 = 7.5 • This is now our new factor 1 of our product. • Third, we multiply the numbers with exponents. • 106x 10-7 • Remember we add the exponents when the base is the same. • 10 (6+-7) = 10-1 • Fourth, we combine our factors to get our final answer. • Factor 1: 7.5 • Factor 2: 10-1 • Final answer: 7.5 x 10-1

  34. Multiplying Numbers in Scientific Notation • Example 7: (3.2 x 107) (1.75 x 10-10)

  35. Multiplying Numbers in Scientific Notation • Example 8: (5.4 x 105) (4.6 x 103)

  36. Multiplying Numbers in Scientific Notation • Work on this one with your partner. • Example 9: (6.4 x 10-3) (3.5 x 10-2)

  37. Multiplying Numbers in Scientific Notation • Work on this onewith your partner. • Example 10: (1.8 x 106) (7.5 x 10-2)

  38. Multiplying Numbers in Scientific Notation • Work on this one on your own. • Example 11: (7.3 x 108) (5.8 x 10-10)

  39. Multiplying Numbers in Scientific Notation • Work on this one on your own. • Example 12:(1.26 x 10-12) (4.78 x 10-13)

  40. Multiplying Numbers in Scientific Notation • Example 13: Which expression correctly indicates the product of these two numbers: 4.5x108 & 1.2 x 103 • (4.5 ÷ 1.2) x 10(8-3) • (4.5 x 1.2) x 10(8x3) • (4.5 x 1.2) x 10(8÷3) • (4.5 x 1.2) x 10(8+3)

  41. Ordering Numbers in Scientific Notation • Example 14:Which expression correctly indicates the product of these two numbers: 2.4x10-8 & 6.7 x105 • (2.4 x 6.7) x 10(-8x5) • (2.4 x 6.7) x 10(-8+5) • (2.4 x 6.7) x 10(-8÷5) • (2.4 ÷ 6.7) x 10(-8-5)

  42. Exit Ticket • Each of you will complete your exit ticket on a note card. • There are 3 problems. • You will complete the exit ticket in 5 minutes and it must be turned in before you can exit the classroom. • You must work SILENTLY and INDEPENDENTLY. • HOMEWORK – Math Book Page 120: #s 1-4 & 14-19! 

  43. Exit Ticket • (3.4 X 104) (2.1 X 103) = • (4.5 X 10-5) (5.2 X 10-6) = • (9.3 X 1024) ( 5 X 10-13) = • HOMEWORK – Math Book Page 120: #s 1-4 & 14-19! 

  44. Do Now – 22 + √25 / √144 / √100 + 2 • Please respond to the following SILENTLY & INDEPENDENTLY: • Write an expression for the product of these two numbers: (3.2x109) & (2.9x104) • Solve. (2.4x105) x (5.2x107)

  45. Today’s Objective • SWBAT divide numbers in scientific notation.

  46. Today’s Agenda • Do Now – 8 minutes • Agenda – 1 minutes • Rules of Exponents – 5 minutes • Dividing Numbers in Scientific Notation INM = 10 minutes • Dividing Numbers in Scientific Notation GP & IP – 15 minutes • Exit Ticket – 5 minutes

  47. Computing with Scientific Notation • Yesterday, we worked with adding numbers in scientific notation and today we will divide numbers in scientific notation. • Like yesterday, we will learn hand motions to help us remember the concept.

  48. Dividing Exponents • When divide numbers with different exponents, you simply subtract the exponents, if the base number is the same. • Example 1: 10315 ÷ 10-10 • If the base number is the same, you subtract the exponents. • Solution: ____________________ • Examples 2: 103 ÷ 10-4 • If the base number is the same, you subtract the exponents. • Solution: ____________________ • Examples 3: 10-20 ÷ 103 • If the base number is the same, you subtract the exponents. • Solution: ____________________

  49. Dividing Numbers in Scientific Notation • If you remember, there are two factors to a number in scientific notation: • Factor 1: A number that is greater than 1, but less than 10. • Factor 2: A power of 10. • When you divide numbers in scientific notation, we divide all factor 1 numbers, and then subtract the exponents of factor 2 together.

  50. Dividing Numbers in Scientific Notation • Example 4: (8.4 x 103) ÷ (2.1 x 10-4) • First, we ID our factor 1 numbers. • 8.4 & 2.1 • Second, we divide our factor 1 numbers. • 8.4 ÷ 2.1 = 4 • This is now our new factor 1 of our quotient. • Third, we divide the numbers with exponents. • 103 ÷ 10-4 • Remember we subtract the exponents when the base is the same. • 10 (3-(-4)) = 107 • Fourth, we combine our factors to get our final answer. • Factor 1: 4 • Factor 2: 107 • Final answer: 4 x 107

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