Now for the hand-in portion of the first part. For each of the student invented

Question

Now for the hand-in portion of the first part. For each of the student invented algorithms, describe your opinion as to why each student may have come up with this algorithm, and discuss the validity of the algorithm. Describe how closely (or not) the student method corresponds to the usual base ten algorithm - in other words, whether it uses the usual place value ideas ata from largest to smallest or not. In addition, comment in each case on why the mathematics is correct or not (what is used - definitions? associativity? commutativity? the distributive laws?) 1, Robyn's invented algorithm for 896 ÷ 35 : 6-35 = 0 with 6 left over 90÷35 800 35 35 + 35 70 70 x 10 = 700 20 35s with 100 left over 35+3570 2 35s with 20 left over 2 more 35s with 30 left over 6 + 20 + 30 = 56 leftovers will make one more group of 35 with 21 left over 0+2+ 20+2+1-25 groups of 35 Figure 14- Robin's decomposing the dividend for 896 divided into groups of 35

Explanation / Answer

896/35 = (800 + 90 + 6)/35 which is the distributive law

Thus, we test for 6/35, 90/35 and 800/35

Then, we use the base 10 algorith and remainder theorem to find out remainders in each case and quotient in each case

6 = 0x35 + 6

90 = 2x35 + 20

800 = 22x35 + 30

Thus, we wll have 24 35s with 56 as remainder. But we can still subtract 35 from 56, leaving 21 as remainder.

So, we have a total of 25 35s and 21 remainder.

Or, 896 = 25x35 + 21

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