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Standard 4.NBT.6 says “Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. ”
I know that would mean 7 divided by 3 is 2 remainder 1, but I don’t know if that is where a fourth grade teacher should stop or if you should explore the answer as 2 and 1/3. I am wondering if this is part of 5th grade in standard 5.NF.3 “Interpret a fraction as division of the numerator by the denominator a/b = a divided by b.”
(a/b=a÷b)
You are right, 7÷3 = 2 1/3 is really a Grade 5 understanding, although 7/3 = 2 1/3 is fine for Grade 4. Bear in mind also that writing something like 7÷3 = 2 R 1 is simply wrong … the thing on the right is not a number, and this usage leads to strange things like 7÷3 = 9÷4 (because they are both “equal” to 2 R 1). Correct usage would either use words like “3 goes into 7 twice with a remainder of 1” or, if you want to write a correct equation, you would write 7 = 2 × 3 + 1.
I am wondering if there is a way we can help teachers understand how to record the answer to a division problem with a remainder so that it will make sense to students. Most often, a division problem is being solved as a result of being in context. Therefore, we could interpret the remainder in terms of the context and not cause confusion with how to record our quotient. However, if a student is asked to solve a division problem out of context, such as the example above, is there a way that would be mathematically correct to record the answer symbolically other than using 2 1/3? Would you want students to write 7 = 2 x 3 + 1 as an equation to represent the solution to 7 ÷ 3? I understand why 2 R1 is not acceptable, but am looking for a way to help students see a connection to their work and the correct mathematics. Any thoughts would be appreciated.
I understand the desire for a compact notation here, but I don’t really have a great idea, and I would worry that introducing one would lead us into the same issues as 2R1. I think it is best to stick to something like a verbal statement “3 goes into 7 two times with a reminder of 1” and then express this mathematically using the equation 7 = 2 x 3 + 1.
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