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12. a. For each of the following two subtraction problems, discuss two different ways a student could use reasoning to calculate the answer. For one way, view the subtraction as "taking from." For the other way, view the subtraction as an unknown addend problem (how much more one number is than the other). In each case, explain the reasoning in detail and include a number line (which need not be to scale) or other math drawing to illustrate. i. 405-397 ii. 405 - 7 b. Discuss which ways of reasoning were more difficult and which were less difficult in part (a).

12. a. For each of the following two subtraction problems, discuss two different ways a student could use reasoning to calculate the answer. For one way, view the subtraction as "taking from." For the other way, view the subtraction as an unknown addend problem (how much more one number is than the other). In each case, explain the reasoning in detail and include a number line (which need not be to scale) or other math drawing to illustrate. i. 405-397 ii. 405 - 7 b. Discuss which ways of reasoning were more difficult and which were less difficult in part (a).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**12.** **a.** For each of the following two subtraction problems, discuss two different ways a student could use reasoning to calculate the answer. For one way, view the subtraction as "taking from." For the other way, view the subtraction as an unknown addend problem (how much more one number is than the other). In each case, explain the reasoning in detail and include a number line (which need not be to scale) or other math drawing to illustrate. **i.** 405 – 397 **ii.** 405 – 7 **b.** Discuss which ways of reasoning were more difficult and which were less difficult in part (a).
Transcribed Image Text:**12.** **a.** For each of the following two subtraction problems, discuss two different ways a student could use reasoning to calculate the answer. For one way, view the subtraction as "taking from." For the other way, view the subtraction as an unknown addend problem (how much more one number is than the other). In each case, explain the reasoning in detail and include a number line (which need not be to scale) or other math drawing to illustrate. **i.** 405 – 397 **ii.** 405 – 7 **b.** Discuss which ways of reasoning were more difficult and which were less difficult in part (a).
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