2 digit divisor into 3 digits
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I don't think that the common core "teaches" it. Students are supposed to learn it, but how a teacher does it is open to interpretation. How does your department at the school level prescribe it? However, what does the common core say about this skill? I wouldn't know.
As a K-4 math coach, I have been recently involved in curriculum and assessment writing for grades 5 and 6 in the school that my school feeds into. There is a CCSS standard that specifically refers to the standard algorithm for division (6.NS.2). It states "Fluently divide multi-digit numbers using the standard algorithm." The grade 5 standard (5.NBT.6) says "Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models." Grade 4 has a very similar standard (4.NBT.6) with one-digit divisors. I find it helpful to look closely at the language one grade above and one grade below in order to find what is specific to a certain grade (ie grade 5).
Here are some ways to approach it:
(1) Use area model (they are likely familiar with this for multiplication) - strategy based on place value
(2) Building up - using the relationship between multiplication and division:
Use multiplication to build up to 371 without going over, then see if there is a remainder. 15x10=150 (need more), 15x20=300, (closer) 15x30=450 (too much; quotient must be between 20 and 30) 15x25=375 (really close, but a bit too much), 15x24=360, so the quotient is 24, 371-360=21, so the remainder is 21; answer 371 divided by 15 = 24 r21
(3) Partial quotients
Video (start at 3:00 - end) https://www.khanacademy.org/math/arithmetic/multiplication-division/partial_quotient_division/v/partial-quotient-division
For (2) Building up, the problem in the example is 371 divided by 15
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