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State in Exponential Form

Lesson 8: I can fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product. State in Exponential Form. 10 2. Say it as a number sentence without using a multiplication sentence.

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State in Exponential Form

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  1. Lesson 8: I can fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product 5th Grade Module 2 – Lesson 8

  2. State in Exponential Form 102 Say it as a number sentence without using a multiplication sentence Say 10 squared as a multiplication sentence starting with 10 Say the base. Say the exponent. 10 squared = 100 10 x 10 = 100 5th Grade Module 2 – Lesson 8

  3. State in Exponential Form 103 Say it as a number sentence without using a multiplication sentence Say 10 to the third as a multiplication sentence starting with 10 10 to the third = 1000 Say the base. Say the exponent. 10 x 10 x 10 = 100 5th Grade Module 2 – Lesson 8

  4. State in Exponential Form 104 Say it as a number sentence without using a multiplication sentence Say 10 to the fourth as a multiplication sentence starting with 10 10 to the fourth = 10,000 Say the base. Say the exponent. 10 x 10 x10 x 10 = 10,000 5th Grade Module 2 – Lesson 8

  5. State in Exponential Form 105 Say it as a number sentence without using a multiplication sentence Say 10 to the fifth as a multiplication sentence starting with 10 10 to the fifth = 100,000 Say the base. Say the exponent. 10 x 10 x 10 x 10 x 10 = 100 5th Grade Module 2 – Lesson 8

  6. State in Exponential Form 107 Say 10 to the seventh as a multiplication sentence starting with 10 Say it as a number sentence without using a multiplication sentence 10 to the seventh = 10,000,000 Say the base. Say the exponent. 10 x 10 x 10 x 10 x 10 x 10 x 10= 100 5th Grade Module 2 – Lesson 8

  7. Multiply Using the Area Model with a Zero in One Factor 287 x 64 ≈ ___ x ___ = ____ 300 60 18,000 On your boards, write the multiplication sentence rounding each factor to arrive at a reasonable estimate of the product. 5th Grade Module 2 – Lesson 8

  8. Application Problem Erin and Frannie entered a rug design contest. The rules stated that the rug’s dimensions must be 32 inches x 45 inches and that they must use rectangles. They drew the following for their entries. Show at least 3 other designs they could have entered in the contest and calculate the area of each section and the total of your rugs. 5th Grade Module 2 – Lesson 8

  9. 5th Grade Module 2 – Lesson 8

  10. 314 x 236 300 x 200 = 60,000 Multiply your rounded factors to estimate the product. What is 300 x 200? Round each factor to estimate the product. Turn and talk. 6 x 104 Express 60,000 as a multiplication expression with an exponent. The answer should be more because our actual factors are more than what we rounded to! Solve using the standard algorithm. Look back at our estimate. Is our answer reasonable? I noticed that we rounded both of our factors down to the nearest hundred. Will our actual product be more than or less than our estimated product? 5th Grade Module 2 – Lesson 8

  11. 1,882 x 296 Round each factor and estimate the product. 2,000 x 300 Will the actual answer be greater than or less than your estimate? Work independently to solve for the actual answer. Is the product reasonable? 5th Grade Module 2 – Lesson 8

  12. 4,902 x 408 Should our actual product be more or less than our actual product? Turn and talk! Some of you estimated the product to be 200,000. What is the error? Find the estimated product for this problem. Let’s read the estimated multiplication sentence without the product. We cannot simply count the zeros! You must think about your units! 4,902 x 408 is about as much as 5,000 x 400 We rounded one factor up and one factor down. We can’t really tell but it should be close! 5th Grade Module 2 – Lesson 8

  13. Get Ready to Complete theProblem Set on Your Own! Complete Pages 2.B.75 - 2.B.76 You will have 10 minutes to work. Try your Best! 5th Grade Module 2 – Lesson 8

  14. Debrief • How can estimating before solving help us? • Look at Problem 1(b) and (c). What do you notice about estimated products? Analyze why the estimates are the same but the products are so different. • How could the cost of the chairs have been found using the unit form mental math strategy? 5th Grade Module 2 – Lesson 8

  15. Debrief • In Problem 3, Carmella estimated that she had 3,000 cards. • How did she most likely round her factors? • Would rounding the number of boxes of cards to 20 have been a better choice? Why or why not? • Do we always have to round to a multiple of 10, 100, or 1,000? Is there a number between 10 and 20 that would have been a better choice for Carmella? 5th Grade Module 2 – Lesson 8

  16. Debrief • Can you identify a situation in the real world where overestimating would be most appropriate? • Can you identify a situation in the real world where underestimation would be most appropriate? 5th Grade Module 2 – Lesson 8

  17. EXIT TICKET Page 2.B.77 5th Grade Module 2 – Lesson 11

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