I explain to students that today we will be working with a T-Chart to calculate elapsed time. It will look different from the work we do on the number line but the thinking involved is actually the same.
In other words, my message to these students is that I am confident they can do this. Now, I am teaching them a different way to set the problem up for the same reason I teach alternative algorithms - this might suit some of them better than the other method.
As students are already familiar with elapsed time on a number line when I teach this lesson, what I am teaching them when I teach elapsed time with a T-Chart is primarily how to use a different tool, not the concept itself.
As with any method, there are different ways to use the tool. I choose one example that spans a short stretch of time (9:17 a.m. to 11:55 a.m.) and one example that spans a longer stretch of time (8:45 a.m. to 11:12 p.m.).
In the guided practice, I give students 3-6 problems to work through on their whiteboards and I have individual students work through the examples up on the board. Then I call upon students to critique their reasoning and/or explain what they (the person being called on, not the one who wrote the problem) understand about the process.
Examples for guided practice:
10:14 p.m. – 11:50 p.m.
4:25 a.m. – 11:11 a.m.
3:23 p.m. – 9:17 p.m.
9:15 a.m. - 2:45 p.m.
6:16 a.m. – 2:30 p.m.
2:12 p.m. – 5:36 a.m.
This student is able to uncover an error in her own thinking when she critiqued the work of another student. Something that I find very interesting when students are critiquing the reasoning of others is their underlying assumptions. One common assumption is that the work must be incorrect, or they wouldn't be critiquing it. Another common assumption is that if there was child who spoke prior to them, that this person must have been correct.
In the active engagement portion of this lesson, most students are working on their own or with a peer to solve elapsed time problems using a T-Chart. I found that the students who struggle with elapsed time on the number line also struggle with this initially, and it often came back to the the fundamental strangeness of living in a base ten world but operating with 60 minutes in an hour.
I work with students who need more assistance but also leave them to confer with the students who are working more independently elsewhere in the room.
I write the problems on the board and they solved them on scrap paper but they could also be done on this page.
I ask students to voluntarily place themselves in three groups for our concluding discussion:
In my classroom there is a lot of support and encouragement for students being honest about their learning and how much they understand. I make a marked point of frequently talking about and pointing out the very important truth that mistakes are what help us learn, as long as we move through them.
Therefore, my students do not have trouble placing themselves in these groups. If this were an unfamiliar group of children I might only have them choose two groups:
That is less likely to make them self-conscious.
Then, within their groups, I ask students reflect to find a positive and a concern that they have in common. In other words, something they all liked or understood and something they all had some kind of struggle with.