March 21, 2013 at 8:15 pm #1824
I’m wondering about the expected limits for division in Grade 5. Fluency in the standard algorithm is not expected until Grade 6 (6.NS.2) though I’m assuming that, based on Bill’s comments about other algorithms, some foundational work with the standard algorithm before that time would be useful.
Bearing that in mind, and looking at 5.NBT.6 and 5.NBT.7 together, what are the expectations for using the standard algorithm with questions that involve decimal fractions in some way? I’m looking for specific guidance on each type given by these examples:
a) 29 / 4 = 7.25
b) 1.20 / 6 = 0.20
c) 10 / 0.2 = 50
d) 3.6 / 0.9 = 4
I know that what is not mentioned is not thereby forbidden, but most of the discussion on page 18 of the NBT Progressions seems to focus on examples B, C, and D and using reasoning to get the quotients, rather than following an algorithm. An example like A above does not seem to be mentioned anywhere, for any method.March 25, 2013 at 1:30 pm #1838
Examples A, B, and D doesn’t seem to fall under either 5.NBT.6 or 5.NBT.7. The former requires whole number quotients of whole numbers, and the latter is limited to the fraction divisions under 5.NF.7, unit fractions by whole numbers and whole numbers by unit fractions. But I agree that any of them could arise at by reasoning about the corresponding multiplication problem.March 25, 2013 at 1:30 pm #1839
Examples A, B, and D doesn’t seem to fall under either 5.NBT.6 or 5.NBT.7. The former requires whole number quotients of whole numbers, and the latter is limited to the fraction divisions under 5.NF.7, unit fractions by whole numbers and whole numbers by unit fractions. But I agree that any of them could arise at by reasoning about the corresponding multiplication problem.April 7, 2013 at 7:00 pm #1877
Thanks Bill. Just to clarify – is example C okay? It’s similar to an example on p.18 of the NBT Progressions (7 / 0.2) because it has 0.2 as the divisor. But would 0.2 really be considered a unit fraction (i.e. 1/5) and, if so, how does 0.125 (i.e. 1/8) fare?April 7, 2013 at 10:29 pm #1879
I was thinking C was o.k. because 0.2 is a unit fraction, but of course you are right that this requires a conversion. That conversion is fairly simple, and well within the purview of Grade 5; your example of 0.125 is somewhat trickier.February 9, 2014 at 8:42 am #2489
Regarding 5.NBT.7, please clarify …and divide decimals to hundredths. Does this mean divisors, dividends and quotients to hundredths? I’ve used drawings and models, but using 5.NBT.1’s understanding of place value seems to help my students.February 16, 2014 at 2:34 pm #2565
Yes, I would say that this limits the division problems to ones where divisors, dividends and quotients all be decimals that with no non-zero digits beyond the 100ths place.March 1, 2016 at 3:09 pm #3543
I’m still confused about 5.NBT.7 based on the posts. Your last post says that “dividends, divisors, and quotients” can all be decimals limited to the hundredths place. Should it be dividend or divisor (e.g., 4 / 0.25 or 0.25/4) as opposed to dividend and divisor (0.16/0.4)?
Also, does 5.NF.7
“Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions” constrain 5.NBT.7 at all?March 7, 2016 at 11:56 am #3544
Bill’s reply in this thread (from 3/25/13) states that 5.NBT.7 is limited to the fraction divisions under 5.NF.7: unit fractions by whole numbers and whole numbers by unit fractions. So, it seems like the example of 0.16/0.4 would not fall under 5.NBT.7, but the other examples (4/0.25 and 0.25/4) would.