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Bill,
Standard 3.MD.1 says, “Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.”
Standard 4.MD.2 says, “Use the four operations to solve word problems involving distances, intervals of time, …”
What is the distinction between these two standards?
One interpretation has been that the phrase used twice in 3.MD.1, “time intervals in minutes” is meant to limit the intervals to less than 60 minutes (it does not say “time intervals in hours and minutes”) and leave intervals of time over 60 minutes for fourth grade.
Another interpretation has been that third graders could solve word problems with intervals of greater than 60 minutes, but that the word problems are limited to addition and subtraction. Fourth grade word problems could involve all four operations.
Please clarify which interpretation, if either, was the intent of the authors.
Thanks,
Brian
Brian, your second interpretation is closer to the truth. “Time intervals in minutes” doesn’t have to mean “less than an hour.” For example, there’s no reason why Grade 3 students can’t say how many minutes it is from 3:30 to 5:00. But multiplication, fractions and decimals, and unit conversion open up the scope on Grade 4. The one of these you didn’t mention was the inclusion of fractions and decimals in Grade 4. Students in Grade 4 might be expected to be able to answer a question like “If Don can peel 3 potatoes in a 5 minutes, how many can he peel in 3/4 of an hour?” (Not saying this is a great problem, but you get the idea.)
Building on this question, if you did say “How many minutes is the interval from 3:00 pm to 5:30 pm?” Would 3rd graders need only answer in minutes Ex: 150 minutes or using a number line, would they answer “2 hours and 30 minutes?” Or do we not expect that conversion at this grade? I figured with number lines it would be easier for them to see the number of hours and minutes, but wanted to ask if that was up to interpretation or if we want them specifically answering in minutes. Or if both answers are acceptable?
Thanks!
CarrieAlso, I meant to ask, do students need to do intervals in 5s, or more specific like 12:37 pm to 2:34 pm? Thanks! Trying to figure out how to format the number lines.
Cheers!
CarrieStudents aren’t expected to do measurement conversions until grades 4 and 5.
From NF progression:
At Grades 4 and 5, expectations for conversion of measurements parallel expectations for multiplication by whole numbers and by fractions. In 4.MD.1, the emphasis is on
times as much” ortimes as many, conversions that involve viewing a larger unit as superordinate to a smaller unit and multiplying the number of larger units by a whole number to find the number of smaller units.4.MD.1, 5.MD.1For example, conversion from feet to inches involves viewing a foot as superordinate to an inch, e.g., viewing a foot as 12 inches or as 12 times as long as an inch, so a measurement in inches is 12 times what it is in feet. In 5.MD.1, conversions also involve viewing a smaller unit as subordinate to a larger one, e.g., an inch is 1/12 foot, so a measurement in feet is 1/12 times what it is in inches and conversions require multiplication by a fraction (5.NF.4).
Using a number line to represent hours and minutes seems complicated because it doesn’t arise from measurement experience with physical units (e.g., rulers) and wouldn’t be in base 10. Students aren’t expected to use number lines to represent feet and inches though they might use drawings of rulers.
Thank you for the info, Cathy.
So they do need to use a number line diagram to calculate the minutes, right? (Because it isn’t in base ten and they aren’t converting units yet.) Are they doing any straight addition/subtraction calculations, or is it all on number lines? I was wondering about the hours vs. minutes because a lot of time number lines have the hours marked on them so students can find one time on a number line and jump up or down to the other given time. Some students may see that they have jumped 1 hour and 30 minutes and write that instead of 90 minutes. So I just wanted to be sure that we emphasize that their answers should strictly be in minutes, right?
Sorry, hope that makes sense!
Cheers!
CarrieMy guess is that what Bill was thinking was along the lines of “3:30 to 4:00 is 30 minutes (perhaps looking at analogue clock face), 4:00 to 5:00 is 60 minutes. 30 plus 60 is 90, so it’s 90 minutes from 330 to 5:00.” No unit conversion. No number line.
Using a number line to calculate in hours and minutes would be complicated if “1 hour” were also labeled “60 minutes.” That’s what I mean by “not in base 10”—there’s something labeled “1” but it’s not made of 10 subunits but 60 subunits, which would be 1, 2, 3, . . . if subunits were minutes or 1/60, 2/60, . . . if subunits were hours. In the first case, the situation might be better represented by a double number line (which is introduced in middle grades, see RP Progression). In the second case, the denominators are large (not in grade expectations) and students would need to convert minutes to hours anyway.
Okay, I get the 3:30 – 4 is 30, and 4 – 5 is 60 more, etc… But I think I’m getting confused on the “no number line” part. The standards example given says to use a number line, so that’s why I was thinking you needed to use one.
“…Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.”
I figure they can also use the clock face itself, like you had mentioned, but I figured since it was the prime example given, that you should use number lines. Is that not necessary? If it can be done in the way you suggested (30 minute jump + 60 minute jump = 90 minutes total) that’s fine, and I can see them using a clock face to help. So does that mean you do not need to use a number line?
Sorry, just clarifying to be sure!!! Thanks again for the help, Cathy! I appreciate it!
Cheers!
Carrie“e.g.” doesn’t mean one
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use it. In this particular example, drawing or using a number line seems like a lot of work for students who have learned strategies for finding sums of multiples of 10 in previous grades. (Use appropriate tools strategically.) As you note, there are decisions to be made about how to format a number line that goes up to 90. For finding sums of smaller numbers of minutes that are not multiples of 10 a number line might be more appropriate.
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