(Lesson Notes)
You can watch a full video recording of this lesson through Edthena at
https://app.edthena.com/conversations/esEecmc5gQBuNAASv
https://app.edthena.com/conversations/esEecmc5gQBuNAASv
My Observation Notes from Edthena:
0:11 I look Rachel's advice and I assigned seats and partners this time.
0:28 Going over expectations
0:51 Practice expectations
1:01 Everyone put their thumbs up to signal that they think they can meet those expectations.
1:13 Go over consequences for not behaving in line with the expectations and have a visual.
1:48 First I'm going to read you a math problem and we're going to think about it in our heads.
1:52 Maybe I shouldn't have put the pencils on the table just yet. If I don't want them to use them/play with them, don't give it to them!
2:20 "For right now we're not going to worry about the answers. We're going to worry about how we solve it."
2:24 Changed it to four students, since there were four students that day.
2:40 Like I said before, I started off with some directly modeling of the problem, but given where these students are in their understanding of subtraction, is direct modeling even necessary?
2:49 Stephen and DeSean were able to identify how many students we started with and how many left. However, the other two students didn't hear this because they were standing by the door like I asked them to.
2:57 Stephen asks, "Where are we supposed to write it?" I say, "We're not writing yet."
3:18 Maybe I should have introduced all of the steps before asking them to follow the steps.
3:35 Stephen warning #1 "One person talks at a time."
3:42 Ask student to repeat what Dana just said.
4:30 DeSean reminds us that we're trying to figure out "how many are left".
4:31 I shouldn't have used the word "left" in both. I said some students left and how many do we have left. That could get confusing.
5:06 Matthew: "It's going to be smaller because two are not there anymore."
5:09 Thumbs up if you agree/thumbs down if you disagree with Matthew
5:25 Encourage DeSean to talk to Matthew to remind him about what he said.
5:57 Tell students to write a number sentence based on what we know.
6:37 "We're doing it by ourselves first."
7:07 Should have reminded students that we're not worried about finding/writing down the answer.
7:28 Waited until all 4 thumbs were up. Then told them to talk to their partner about their number sentences.
8:01 I'm conferencing with the pairs. Should I have just walked around and listened to them instead of encouraging them to share with each other?
8:31 Stephen said number sentence and then "We both got two." I reminded him that 2 is the answer and that we're thinking about the whole number sentence right now.
8:59 Should I have written a model number sentence first?
9:11 Dana starts retelling the problem when asked to give our number sentence. This kind of suggests to me that they didn't get what a number sentence is and perhaps I should have reviewed.
9:28 I told them that that's all we know from the problem instead if letting them figure out that that's all we know so far.
9:50 When we have 4-2, what is this right here? (I point to the space to the right of the equals sign)
9:58 Dana says that it's the number that's the last number that we found.
10:02 Me: "This is the number that we're trying to find, but from this problem, do we know that number yet?"
10:08 I asked "Does it say this number in the problem?" except that it DOES say that number, 2, in the problem. This is why I realized my new problem was a bad one because the change and the result were the same number!
10:23 Students realize that we don't see the answer in the question yet.
10:33 Ask students if I can tell them what mathematicians do when they don't know what goes there yet.
10:39 Warning #2 for Stephen. "We're not calling out. Can you move right here please?"
10:43 Did I maybe jump too soon on moving Stephen's seat? I feel like I did except I also gave him warning number 2 which means you move your seat so I felt like I had to once I started.
10:58 Introduce [ ] and ? as things that mathematicians put when they don't know the number that goes there.
11:06 Ask students which they would like to use. [ ] or ?
11:46 All 4 students agree to use a ? when we don't know what number goes there.
11:55 Filling out table to show the same thing in a different way.
12:26 Directly model the worksheet and what they should write on it.
12:49 Allow all students to share by saying it at the same time. (Subtracting)
13:27 "I love how you're revising that Stephen and DeSean."
13:35 "What did we agree we're going to put in the box when we don't know the number?"
13:50 Reminder that "Right now we're not even worried about the answer, we're worrying about the problem."
13:56 Do you think it would have helped to have picked numbers that were really big? Like 243 and 38? So that they don't get distracted by figuring out the answer and instead can focus on thinking about what we know and what we're trying to find out.
14:17 Being overly prepared really didn't help me in this situation...
14:32 Ahhh. I didn't even realize that I said, "Yeah, so we got it right." I didn't mean to use that word and make it seem like we're still trying to find a "right" answer.
14:33 Should I have asked the students to name what kind of problem this is instead of telling them we're going to call it an "end unknown" problem. Maybe it will make more sense to them if they name it themselves.
14:49 Asks DeSean to explain why we might call it an end unknown problem.
15:10 I think they said because "we don't know the number that goes right there" [the end].
15:17 Moving on to the second word problem.
15:25 Stephen is excited that we're doing the second word problem by ourselves.
16:49 Reading the problem another time because I changed the word problem and it might have been confusing.
17:21 Going back to the same questions on the poster.
17:39 Stephen says he knows there are two people left in the library.
17:47 DeSean tells us that we started with 4 students.
18:21 Matthew doesn't know what the question is asking. DeSean tells us it's asking "How many students left to find Ms. V?"
18:42 Dana thinks it's going to be smaller.
19:07 Reading the problem one more time and then filling the table out by ourselves.
19:52 Reminder to put the question mark when we don't know the number.
20:04 Maybe I should have done one end unknown and one change unknown problem together before having them do problems individually.
20:12 Remind them that we're not worried about solving the math. We're worried about what we know and what we don't know. I remind them to think about where to put the question mark.
20:34 Instead of approaching it by asking what we're trying to find first, I should have asked DeSean what we know for sure from reading the problem.
20:50 Matthew: "I just wrote a question mark, because you're supposed to."
21:32 Matthew says some is two because he keeps solving the math problem.
21:46 Me: "There are two students left in the library now. Where do you think that 2 would go?" Matthew: "At the end."
22:30 Me: "How do you know there were 4 at the start?" Dana: "Because there were 4 in the library."
22:42 I keep reminding the students to refer back to the word problem. How can I get them to refer to the word problem on their own?
22:58 Did I really need Stephen to keep his paper on the table? Or was I just doing that because students usually write on the table and that's what's expected?
23:24 Don't forget to tell students what to do when they finish their task!
24:06 Refer back to our original direct modeling of the situation
25:13 DeSean put his question mark at the end. I decided that we were going to have students share at this point. (Knowing that two had put the ? in the "change" place with my help and knowing that the other two put the ? in the "end" place.
25:57 Some students put their thumbs down because they had different numbers in their boxes.
26:27 Matthew: "I just wrote this because I have to". He clearly doesn't get why it is there, he put it there because he thought that's where I wanted him to put it! This is not what I intended! I wanted them to stop seeing math as something that means doing "because you're supposed to".
26:56 Give more wait time to Dana!
27:17 I asked for the question and Justin starts retelling.
27:23 Stephen: "The answer is two."
28:16 "It looks like some people are getting confused. We're going to try to learn this as a group."
28:48 Fix the poster! To some kids, it looked like it did say "two" there.
29:40 Was I being too harsh on Stephen? Did I need to jump to #3 for that?
29:52 I did give him something to do over there during his cool down. (Draw the problem. I know he likes to draw.)
30:54 "Do we know the change?" DeSean shakes head no. Matthew: "Yes. I do."
31:38 Remind Matthew again that we're not worried about the answer.
32:32 It seems like Matthew understands now that we're trying to find the change, or how many students left to find Ms. V.
33:06 Put the two posters next to each other so that the students can see the difference.
33:45 I should have kept the scenario consistent instead of making the first one about the bathroom and the second one about Ms. V.
34:15 Stephen: "Some means three. A couple means two."
34:33 Instead of rushing to write the word problems, we should have just reviewed what we already did. I was trying to fit too much in not enough time.
35:30 Don't give a 5 minute warning when we don't have 5 minutes!
36:27 One more minute to work on your problem.
36:47 Pencils down.
37:26 End of lesson was very abrupt. I need a watch or clock!
37:35 Matthew: "Are we going to get to finish it?"
0:28 Going over expectations
0:51 Practice expectations
1:01 Everyone put their thumbs up to signal that they think they can meet those expectations.
1:13 Go over consequences for not behaving in line with the expectations and have a visual.
1:48 First I'm going to read you a math problem and we're going to think about it in our heads.
1:52 Maybe I shouldn't have put the pencils on the table just yet. If I don't want them to use them/play with them, don't give it to them!
2:20 "For right now we're not going to worry about the answers. We're going to worry about how we solve it."
2:24 Changed it to four students, since there were four students that day.
2:40 Like I said before, I started off with some directly modeling of the problem, but given where these students are in their understanding of subtraction, is direct modeling even necessary?
2:49 Stephen and DeSean were able to identify how many students we started with and how many left. However, the other two students didn't hear this because they were standing by the door like I asked them to.
2:57 Stephen asks, "Where are we supposed to write it?" I say, "We're not writing yet."
3:18 Maybe I should have introduced all of the steps before asking them to follow the steps.
3:35 Stephen warning #1 "One person talks at a time."
3:42 Ask student to repeat what Dana just said.
4:30 DeSean reminds us that we're trying to figure out "how many are left".
4:31 I shouldn't have used the word "left" in both. I said some students left and how many do we have left. That could get confusing.
5:06 Matthew: "It's going to be smaller because two are not there anymore."
5:09 Thumbs up if you agree/thumbs down if you disagree with Matthew
5:25 Encourage DeSean to talk to Matthew to remind him about what he said.
5:57 Tell students to write a number sentence based on what we know.
6:37 "We're doing it by ourselves first."
7:07 Should have reminded students that we're not worried about finding/writing down the answer.
7:28 Waited until all 4 thumbs were up. Then told them to talk to their partner about their number sentences.
8:01 I'm conferencing with the pairs. Should I have just walked around and listened to them instead of encouraging them to share with each other?
8:31 Stephen said number sentence and then "We both got two." I reminded him that 2 is the answer and that we're thinking about the whole number sentence right now.
8:59 Should I have written a model number sentence first?
9:11 Dana starts retelling the problem when asked to give our number sentence. This kind of suggests to me that they didn't get what a number sentence is and perhaps I should have reviewed.
9:28 I told them that that's all we know from the problem instead if letting them figure out that that's all we know so far.
9:50 When we have 4-2, what is this right here? (I point to the space to the right of the equals sign)
9:58 Dana says that it's the number that's the last number that we found.
10:02 Me: "This is the number that we're trying to find, but from this problem, do we know that number yet?"
10:08 I asked "Does it say this number in the problem?" except that it DOES say that number, 2, in the problem. This is why I realized my new problem was a bad one because the change and the result were the same number!
10:23 Students realize that we don't see the answer in the question yet.
10:33 Ask students if I can tell them what mathematicians do when they don't know what goes there yet.
10:39 Warning #2 for Stephen. "We're not calling out. Can you move right here please?"
10:43 Did I maybe jump too soon on moving Stephen's seat? I feel like I did except I also gave him warning number 2 which means you move your seat so I felt like I had to once I started.
10:58 Introduce [ ] and ? as things that mathematicians put when they don't know the number that goes there.
11:06 Ask students which they would like to use. [ ] or ?
11:46 All 4 students agree to use a ? when we don't know what number goes there.
11:55 Filling out table to show the same thing in a different way.
12:26 Directly model the worksheet and what they should write on it.
12:49 Allow all students to share by saying it at the same time. (Subtracting)
13:27 "I love how you're revising that Stephen and DeSean."
13:35 "What did we agree we're going to put in the box when we don't know the number?"
13:50 Reminder that "Right now we're not even worried about the answer, we're worrying about the problem."
13:56 Do you think it would have helped to have picked numbers that were really big? Like 243 and 38? So that they don't get distracted by figuring out the answer and instead can focus on thinking about what we know and what we're trying to find out.
14:17 Being overly prepared really didn't help me in this situation...
14:32 Ahhh. I didn't even realize that I said, "Yeah, so we got it right." I didn't mean to use that word and make it seem like we're still trying to find a "right" answer.
14:33 Should I have asked the students to name what kind of problem this is instead of telling them we're going to call it an "end unknown" problem. Maybe it will make more sense to them if they name it themselves.
14:49 Asks DeSean to explain why we might call it an end unknown problem.
15:10 I think they said because "we don't know the number that goes right there" [the end].
15:17 Moving on to the second word problem.
15:25 Stephen is excited that we're doing the second word problem by ourselves.
16:49 Reading the problem another time because I changed the word problem and it might have been confusing.
17:21 Going back to the same questions on the poster.
17:39 Stephen says he knows there are two people left in the library.
17:47 DeSean tells us that we started with 4 students.
18:21 Matthew doesn't know what the question is asking. DeSean tells us it's asking "How many students left to find Ms. V?"
18:42 Dana thinks it's going to be smaller.
19:07 Reading the problem one more time and then filling the table out by ourselves.
19:52 Reminder to put the question mark when we don't know the number.
20:04 Maybe I should have done one end unknown and one change unknown problem together before having them do problems individually.
20:12 Remind them that we're not worried about solving the math. We're worried about what we know and what we don't know. I remind them to think about where to put the question mark.
20:34 Instead of approaching it by asking what we're trying to find first, I should have asked DeSean what we know for sure from reading the problem.
20:50 Matthew: "I just wrote a question mark, because you're supposed to."
21:32 Matthew says some is two because he keeps solving the math problem.
21:46 Me: "There are two students left in the library now. Where do you think that 2 would go?" Matthew: "At the end."
22:30 Me: "How do you know there were 4 at the start?" Dana: "Because there were 4 in the library."
22:42 I keep reminding the students to refer back to the word problem. How can I get them to refer to the word problem on their own?
22:58 Did I really need Stephen to keep his paper on the table? Or was I just doing that because students usually write on the table and that's what's expected?
23:24 Don't forget to tell students what to do when they finish their task!
24:06 Refer back to our original direct modeling of the situation
25:13 DeSean put his question mark at the end. I decided that we were going to have students share at this point. (Knowing that two had put the ? in the "change" place with my help and knowing that the other two put the ? in the "end" place.
25:57 Some students put their thumbs down because they had different numbers in their boxes.
26:27 Matthew: "I just wrote this because I have to". He clearly doesn't get why it is there, he put it there because he thought that's where I wanted him to put it! This is not what I intended! I wanted them to stop seeing math as something that means doing "because you're supposed to".
26:56 Give more wait time to Dana!
27:17 I asked for the question and Justin starts retelling.
27:23 Stephen: "The answer is two."
28:16 "It looks like some people are getting confused. We're going to try to learn this as a group."
28:48 Fix the poster! To some kids, it looked like it did say "two" there.
29:40 Was I being too harsh on Stephen? Did I need to jump to #3 for that?
29:52 I did give him something to do over there during his cool down. (Draw the problem. I know he likes to draw.)
30:54 "Do we know the change?" DeSean shakes head no. Matthew: "Yes. I do."
31:38 Remind Matthew again that we're not worried about the answer.
32:32 It seems like Matthew understands now that we're trying to find the change, or how many students left to find Ms. V.
33:06 Put the two posters next to each other so that the students can see the difference.
33:45 I should have kept the scenario consistent instead of making the first one about the bathroom and the second one about Ms. V.
34:15 Stephen: "Some means three. A couple means two."
34:33 Instead of rushing to write the word problems, we should have just reviewed what we already did. I was trying to fit too much in not enough time.
35:30 Don't give a 5 minute warning when we don't have 5 minutes!
36:27 One more minute to work on your problem.
36:47 Pencils down.
37:26 End of lesson was very abrupt. I need a watch or clock!
37:35 Matthew: "Are we going to get to finish it?"
Observation Notes from my Penn Mentor: