Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobe
Lesson 35
1. Chapter 7 Lesson 35 Testing for Divisibility WO.17 Use long division to determine if one number is divisible by another. WO.23 Use divisibility rules to determine if a number is divisible by 2, 3, 5, or 9 and understand the justification for these rules.
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6. Is 36 divisible by 2? Let’s try to express 36 as repeated addition of 2.
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11. Check for Understanding 1. Determine whether the number is divisible by 2. a. 23 b. 78 c. 504 d. 8,241 e. 6,794 Not divisible by 2. Divisible by 2. Not divisible by 2. Divisible by 2. Divisible by 2.
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14. Check for Understanding 2. Determine if the number is divisible by 5. a. 70 b. 553 d. 72865 c. 10003 e. 8003000 Divisible by 5. Divisible by 5. Divisible by 5. Not divisible by 5. Not divisible by 5.
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18. 7 + 5 + 6 = 18 Since 18 is divisible by 9, we conclude that 756 is also divisible by 9. What about larger numbers? Is 756 divisible by 9?
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20. Check for Understanding 3. Determine whether the number is divisible by 9. a. 73 b. 108 c. 7812 d. 6873 e. 98016 Not divisible by 9. Not divisible by 9. Not divisible by 9. Divisible by 9. Divisible by 9.
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24. Check for Understanding 4. Test whether the number is divisible by 3. Verify the result using long division. 5. Using what you learned in this lesson, how can you quickly determine if 1,335 is divisible by 15? Is it? 6. What is the smallest number you can add to 7,120 to make it divisible by 3? 7. When you divide 2,349,684 by 5, will there be a remainder? What will the remainder be? a. 84 b. 275 c. 1086 d. 23938 e. 62505 Yes Yes Yes No No You check to see if it is divisible by 3 and divisible by 5. Thus 1,335 is divisible by 15. Add 2. 7,122 is divisible by 3. Yes; 4
26. A student made the following claims about divisibility. What is the student misunderstanding? What would you tell this student to correct their understanding? Find the Errors The student was able to correctly determine if a number is divisible by 2 or 5, but misunderstood how to test for divisibility of 3. You cannot in general look at the last digit to determine if it is divisible by 3, you must add all the digits together and check if the number is a multiple of 3. 5 + 2 + 3 = 10, which is not a multiple of 3. Therefore, 523 is not divisible by 3.
Hinweis der Redaktion
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Page 342 -Each stack of 10 turns into (2 + 2 + 2 + 2 + 2):
Page 342 -Let’s represent 100 as repeated addition of 10:
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Page 343 -Let’s verify using long division:
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Page 344 -This means we simply have to check if 5 + 2 is divisible by 9.
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Page 345 -Let’s verify using long division:
Page 345 -By generalizing the above arguments, we arrive at the following rule:
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Page 346 -Using the same logic as the divisibility test for 9, we arrive at the following rule:
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