Priorities for the Year

The first two months of the school year are almost over. I’m at a new school (new for me; it’s been around for many years), and I’m very happy with my move, in general. I’m finding teaching two totally new curricula to be a bit of a challenge, but I’m confident that I’ll do an even better job next year than I’m doing this year.

In talking with some of my math colleagues, I’ve shared different things I’m trying out this year, and some of them have been impressed/shocked at “how many” things I’m doing with my students. So I wanted to articulate for myself some of the ones which I want to prioritize and ensure I don’t lose/forget about as I go from unit to unit. I also realized there are some things I want to emphasize more that I haven’t focused enough on yet, and I need to do something to change that soon.

Things I’m already doing that I want to keep doing:

Visibly Random Groupings – mostly daily. Sometimes, we need to finish a project in groups, so we stay in the same groups as yesterday, but for the most part, students enter each day with new seats, and new partners. They’re mostly enjoying it so far, I think, but I did give assigned seats the other day (for one grade, based on an exit slip for a leveled activity, and in the other grade, for a partner project that will be graded).

Notice/Wonder – I’ve done these regularly, but I worry that my students aren’t “wondering” enough – and I’m not sure yet how to model for them what they should/could be wondering. I’m wondering if anyone has any good problems to use this routine with. I worry that I’m overusing it on things that aren’t worthy of it; in one class, I had a student express that he didn’t feel like the task was worthwhile (while in another class, a student expressed that she liked sharing her answers for notice/wonder, where there wasn’t “one right answer”). I’m not getting rid of this, but I definitely want to step it up a notch.

Partner talk daily – students talk with their mirror partners (the kids they sit across from) and their elbow partners (the students they sit next to), as well as in whole groups. Students have become proficient at talking, but I worry that the kids still don’t know each other well (especially in the 7th grade classes – or even the 6th grade class that’s not my homeroom). I want to do some middle-of-the-year ice-breakers. I need to decide which ones would be good!

Share/Check, Discuss – this is a small group routine I created to share answers to a handout and discuss misconceptions/mistakes in small groups (rather than as a whole class). I find it particularly useful with handouts that have a lot of small exercises/problems for students to work on that would be tedious to check as a whole group, but where misconceptions might cause disagreement about certain ones. I have students go around and share their answers for each problem in rounds, while the listeners circle ones they disagree about and check ones they agree on. After reading all of the answers, they go back to the ones they circled and discuss those.

Things I’ve started doing, but I am not doing consistently enough yet:

Naming routines & their structures  – and then using them repeatedly so students can get used to doing “a share/check, discuss” and not need the directions renamed every time. I learned this idea from Rhonda Bondie at MfA, and it’s reinforced in the Instruction Routines book I’ve been reading, but I want to be more and more thoughtful about the routines that I name for the kids and doing them repeatedly.

Number Talks – every class has done several dot talks. The two sixth grade classes have done several subtraction number talks, including a few with integers. The seventh grade classes haven’t really done any more number talks – one did a percent talk, but I didn’t get far with it. I want to incorporate more of these, but I’m struggling with choosing which number talk to do when – and with ensuring that there’s ACTUALLY enough time to do it!

Which One Doesn’t Belong – I almost want to include this in the category of “want to being but haven’t yet” because I’ve really only done it once or twice in each of my classes. I think this is a valuable task, but I haven’t been able to work out when to do it – perhaps as a starter instead of a warm-up once per week? I wanted to find WODB’s that matched our content (like ones with numbers or pictures, etc.), but I haven’t been working on creating those yet. Maybe I can make incorporating this my November goal.

Convince yourself, convince a mathematical friend, convince a skeptic – I need to create a new poster, so I can remember to reference it in class. I’ve definitely said “who can convince our skeptics?” a bunch, but I want this idea to be internalized by the students, and I’m not referring to it often enough for that to happen yet.

Things I want to be doing, but I haven’t yet:

Would you rather? – I want to incorporate these, but I haven’t had an opportunity to do so yet. I think it will work out really well in my ratios/proportions unit, but I might even be able to incorporate one or two of the probability ones in my probability unit (especially as we turn towards review for the end-of-unit).

Fraction Talks – I think my next unit in each grade involves fractions, so I’ll make sure to incorporate some of this in there!

Problem solving – we haven’t done nearly as much problem solving as I would like to!

Visual Patterns – I did ONE in the 6th grade (the one from Jo Boaler), and I haven’t had any opportunity to do one with the 7th graders yet! I know we’ve got a unit on expressions and equations – I plan to use these heavily in there and in the linear unit!

Vertical, Non-Permanent Surfaces – I heard about this at the same time as the visibly random groupings, but I need the right kinds of problems to have students working at these surfaces AND I need to ensure that I actually have the right kind of space for this! My white boards are way to small for this idea, and I haven’t figured out the logistics of enacting it yet.

Naming the classroom mode we’re in – for example, “whole class instruction/discussion” and what the expectations for them are right now vs “table talk” and how those expectations are different. I want to create posters that explain each of these in detail, but I need to finish formalizing it in my mind first. I got the idea from Rhonda Bondie again, and I mentioned it in more detail in a much earlier post, but I haven’t gotten around to this yet (though perhaps this is something I should begin sooner rather than later).

Open Middle problems – I’ve used these as an extension, but I haven’t had a whole class discussion about more than one or two of these yet, and I really want to encourage my students to do this kind of thinking.

*Deep Breath* I know there’s a lot here, and I have to keep reminding myself not to try to do too many things all at once. I would rather do only three of these things, but do them REALLY WELL than to attempt all of these things, and do none of them well. So I need to keep reminding myself of that as I move forward with my classes – it’s okay if I don’t do all of them this year; there will be future years.





Probability Practice @alittlestats

On Friday, I gave my 7th graders a quiz on two topics related to probability. In the first set of problems, I gave them a table with the unequal probabilities for some outcomes and students had to determine the probability of certain events: one which was just one of the outcomes and one which was two or more of the outcomes (requiring the students to add the probabilities). Most students got this section correct, but a few thought they were supposed to multiply the probabilities instead of add.

The place that concerned me more, however, was in the second section of the quiz. I gave a scenario that was a two-step chance experiment: drawing two marbles from a bag with replacement. In the bag, there are two, four and six of each color marble (red, yellow, and blue). Students had to draw a tree diagram and label it with the probability of each outcome, and then list the 9 possible outcomes (preferably with the 9 different probabilities, which they could find by multiplying along each branch of the tree diagram). They had to find some probabilities based on the tree diagram which required them to add some of those probabilities.

Many of the students got confused in this section and used the probability of 1/9 for each of the possible outcomes instead of the actual ones, like 1/36 or 1/12, based on the probability of the two marbles individually. A few kids tried to add the probabilities instead of multiplying.

I have to confess: it’s been years since I took a statistics and probability course, and honestly, other than a HORRIBLE one in grad school, I don’t think I took any courses past HS that included probability. I’ve been keeping up on the material by teaching myself a few days in advance, and then implementing the Engage NY lessons modified by my department head (and tweaking them for my own classes).

In the past, I might’ve interpreted the results of my exam as meaning that “I did a good job with some of my students and that some of these kids just didn’t want to study or put in the effort” – but now I recognize that the kids who did well on this probably already were familiar with this to some extent, and that many of the kids who did poorly had questions they weren’t asking in class – which concerns me. I also recognize that in retrospect, I probably should’ve given an exit ticket that I collected before giving a graded quiz.

Now I need to give back the quiz to the students and figure out a way to reteach the material to the students who didn’t get it the first time, but do an extension for the kids who did get it – OR do an activity where I have the students who got 100% help teach the kids who were struggling? I’m not sure exactly how I want to handle it. Nor do I know what a good activity would be! Guess I’ve gotta do some research for this week. Any advice?

Day in the Life: October 13

Today started in a blur. I overslept a bit, so instead of getting up at 520, I woke up at 610! I had trouble falling asleep last night, so I didn’t get enough shut eye, clearly. I should’ve skipped trimming my beard, but I felt like a wild man, so I used the electric clippers to shorten my goatee. I hopped in for a quick 12 minute shower and dried off. I let Stormy out for his breakfast and went to make my food. I decided to make a whole pot of tea today so I would have tea ready for tomorrow. While I waited for the water to boil, I toasted an English muffin for my sandwich and used the microwave to nuke the last breakfast sandwich. I scarffed down a banana while I put together the other items for my lunch: mandarin oranges, carrots and peppers, kashi cookie, pudding, and blackberries. I made my sandwich and prepared my tea while eating the breakfast sandwich.

After I ate, I picked out a tie and conferred with my partner about the pants and shirt to go with it. I’ve being doing weight watchers to lose some weight and not all of my clothing fits me right now. I have MfA tonight from 530-730pm, so I decided I needed to wear pants that would be comfortable all day and went with a pair that my partner for me for Christmas last year. I added in a blue button down from old Navy and went to walk Stormy. while waiting for the elevator, I noticed it was already after 7am, so I rushed my dog through his walk: walking around to the front of the building and going in the main entrance to avoid having to wait for the elevator in the basement.

Finally left by 715, and knew it was gonna be tight to make my 725 train. I got across the street and realized I left my tie at home (after all that, my whole outfit designed around wearing that tie!). No time to go back, so I shook my head and carried on. got to the corner and saw a bus coming: even more exciting, he seemed like he was actually gonna stop and pick up passengers (the busses often skip my stop, because they think they’re too full, even though there’d be room of people moved back). I did a silent happy dance and got on. I moved in a bit and then noticed we stopped at the corner where the bus normally turns,  and the light was still green. I groaned: garbage truck, again!?! What bad luck. I tried to urge my driver to go around, as many of the bus drivers do,  going to 73rd and then slipping this one block, but he refused, saying he wasn’t authorized. I asked him to open the door and let me off, but he wouldn’t do so until he had room to straighten out. I told him I had 4 minutes to make my subway (and we were at a place that normally takes me at least 7 minutes to walk, if not 10), and he still wouldn’t open the door until the whole row of traffic moved up. finally, he let me out, and my paying comment was that he needed to talk to his supervisor about authoring them to go around the garbage truck because this happens at least twice a week! As I ran down the block toward the subway, I told the garbage collectors essentially the same thing: they needed to not go down a bus route during rush hour! and they hold traffic write a while: I passed a second bus as I was going toward the subway! Anyway, I ran and I got into the subway station right at 724. got down to the platform just in time to see my e pull away! 😦 luckily, the next train was another e (instead of an f, as it usually is), so I managed to get on. I’ve got 3 more stops and ten minutes to get to work on time, and I teach first period. I hate being rushed like this: when I don’t have a chance to settle in, it means I’m not at the top of my game.

Anyway, I’ll finish this draft after school. I used my subway commute to begin my “day in the life” post for October. I realized it’s the only way, as I’ve got an incredibly long day today! I’ve got a Math for America PD this evening until 730PM.

Alright, so luck was with me, and I managed to make it to school at 755, get upstairs by 758, and put my bags in the closet before letting my kids in at 8AM.  First period, I taught my split 7th grade class (or as I like to call them, 007, pronounced double-oh seven). My student teacher met the class at the door with their random cards while I came around and handed out HW, collected the cards, and got them settled into our opening routine: take out last night’s HW to be checked by my student teacher, copy tonight’s HW and put it away in their folders, and open their NB to a page for today, write the date and a “shortened FQ” (focus question) and then begin the warm-up. Since we have a quiz tomorrow, I also made sure to tell the students the topics for the quiz (which I meant to post online, but I forgot until just now, at 8:12PM!). Some of them copied the topics down, while others didn’t.

I started with a warm up of drawing a tree diagram for making a choice about ice cream cones: two cone types and three favors made for 6 possible outcomes. I got a student to share their tree diagram on the board – I paid special attention to select a young lady who rarely participates verbally in class, but is always working hard and accomplishing a lot. She had labeled her branches with fractions (which not everyone remembered to do) so I made sure to emphasize that being drawn in on their work.Then we listed the 6 outcomes on the board, determined the probability for each (and established two ways we could know it was 1/6 – by multiplying each pair of branches to get 1/2 x 1/3 = 1/6 OR, since all outcomes were equally likely, we could just count number of branches and  say each one was 1/6).

Since we only had a single today, I immediately handed out the practice handout, with 4 problems & tree diagrams for them to create. I had them start independently, but then share in partners, by comparing their tree diagrams and discussing the possibilities. I had a student I selected (again, choosing someone  whose voice we don’t hear much) go to the board and draw it while we continued to compare. We shared our answers to the questions about that problem, and dealt with some mistakes/confusion.We took a look together at number 2 9which had students considering a situation with 81 branches!) and discussing why we wouldn’t want to make a tree diagram for that. We didn’t have a chance to work on the other 4 problems, but it let me know how long my students need for this type of work.

Second period is my only prep on Thursdays, when I teach 6 periods. Since my student teacher was being observed 3rd period by his supervisor, we spent the first part of our prep rehearsing/preparing for his lesson. I sent him to go meet his supervisor about three quarters of the way through the period and I printed myself a copy of the quiz for tomorrow’s 7th grade classes. I worked on answering it, to see whether I was asking the types of questions I wanted to or if I needed to make any edits. I also started thinking about point values of the questions: I like quizzes to be out of a number that’s a factor of 100, so it’s easy to convert to percents.

During second period, the department head, M, stopped by to tell me that we couldn’t meet tomorrow during our normal 7th period meeting time because she had a coverage, but was there anything we needed to discuss in particular? I asked her about the second question on the handout I’d just used where the kids needed to make 81 branches (which is absurd), and I shared with her how I modified it (to be a discussion of when NOT to make a tree diagram!). She wasn’t sure if she had the same problem on her handout, so she planned to check it against her document. I also ran my timeline by her for the rest of my unit, in terms of planning when I’m going to be doing simulations and when I’m going to be doing the project in class.

Before. it, third period was upon us. My homeroom was a bit late because the art teacher let them go a little late (my school doesn’t have bells, so it’s all about the teachers paying attention to the clock!), but my student teacher handed out the cards and got them settled and started immediately. I checked HW and I noticed that many of the students were missing specific examples from their My Understanding reflection from Tuesday night (where they were supposed to compare the difference between predicting the sign for a product with figuring out the sign for adding or subtracting), so I gave out a lot of feedback on giving them 85% and telling the ones who seemed to genuinely be confused about their work that they would get a chance to redo their HW for credit for the next day if they went home and revised their work tonight.

In 6th grade, I’m teaching a unit on integers (though we go into operations fully, which is technically a 7th grade standard, but we accelerate). Today we formally introduced division with negatives to the students. We pulled resources from Accentuate the Negative (CMP3’s text) and combined it with our own ideas. The warm-up was four “open number sentences” where students had to determine the missing factor for a multiplication problem (we’ve just finished working on multiplication with integers on Tuesday). Students explained how they knew what number to fill in the blank, and some of them referenced the idea of using division to undo the multiplication, and the idea that multiplication and division were inverse operations (so we added that to our notebooks). The follow-up to the warm-up that my student teacher led was about rewriting each number sentence as a division problem – and we introduced “fraction notation” to mean division today.

My student teacher clearly felt rushed after spending so long on the warm-up, because he rushed through his directions for the second part of class. We had decided to do a “notice/wonder” with students about three multiplication/division fact families (where students saw four number sentences using the same three numbers – two multiplication and two division); however, instead of having students write their own individual notice/wonder chart in their NBs, we had them write it on post-it notes and then group them onto a “poster” paper where students shared some of their ideas  The directions got a little jumbled and he overloaded them a bit by giving it to them ALL at once, but in the end, I think it wound up okay – we went around, table-by-table, and made sure the groups knew what to do. They shared a bit, and then he had them create their own fact families in groups – this was also a little bit jumbled (again because of his rushed/clustered directions), but again, the students muddled through and we supported them in small groups. Finally, he gave the students a practice handout with some division problems to try out. Last thing he managed to fit in was going over the first ten questions (the “regular” division problems, as opposed to the open number sentences). Then it was time to say good bye!

I realized in that moment that I didn’t have the multiplication fact fluency quiz ready that I planned to give my doubles that afternoon, so I asked my student teacher to do me a favor and run down to our parent coordinator (who does all of our copies) and see if she’d finished them yet and if so, to bring it up to me. I couldn’t even find the file in my computer, so I wasn’t sure if I’d be able to print it if he didn’t come back with it. Luckily, she’d finished, so he quickly returned with it and went off to his debrief with his supervisor.

Meanwhile, I got 704 on track with copying their HW into their planners and getting started on the same warm-up as 007. I passed out HW and collected the cards. We’d already discussed the topics for the quiz on Tuesday, so we started going over the tree diagram immediately. I had students put up the tree diagram on the board, but unfortunately, this time, I didn’t notice students writing in the fractions on the branches, so while I still chose a student who we didn’t hear from much, I emphasized that I chose them because they were missing a key detail that I didn’t want to see anyone forget on tomorrow’s quiz and we edited the ones in our notebook. At this point, I made sure we listed out the possible outcomes and their probabilities (same as before), and then we discussed how to calculate the probability of each one.

Unlike earlier, this class was a double period, so before giving them the handout, we did a problem from the board. This problem had an unequal probability because they were picking marbles from a bag where there were 4 green and 6 red (for a total of 10). They created their tree diagram – this time, I drew the diagram on the board (for neatness sakes) and asked a quiet student to write in the fractions for each branch. He did so, and then we discussed the outcomes. This time, there were only 8 outcomes  (2^3), but they were unequally likely. So when we calculated each probability, it was a bit more complex – I could see that the students definitely needed a bit more work on this topic, and I was glad we had an example like this before tomorrow’s quiz, since there will be a question just like it on the quiz!

We compared tree diagrams, we calculated probabilities, we used the probabilities of each branch to discuss some of the particular probabilities (such as getting at least one red or getting a red and a green). We spent a lot of time focused on the details of this tree diagram, and I’m hoping it made a difference for the students in this class. This is one of my larger classes (30 students), and I feel less connected to them than any of my other four classes. I worry that the students have more room to “hide” in here, and there are definitely students who I rarely hear from (in terms of raising their hands), and there are even a few students who I doubt are talking during partner talk (and I’ve had to prompt them or hover over some of them), but academically, they’re all doing okay or better (i.e. no one’s really failing!).

Before we moved into the tree diagram handout, I decided to pause and do the multiplication fact fluency (practice) quiz with them. I am required to give timed quizzes to all of my classes and it’s supposed to count for 10% of their grade. I haven’t begun fact quizzes yet because I’ve been really hesitant about how I want to roll it out, and which facts I wanted to quiz. I decided to start with multiplication facts because I felt it was somewhat likely that my students would already know most (if not all) of their multiplication facts, so hopefully, they would feel pretty successful. I hate the idea of the timed quizzes (especially given that we’re supposed to only give 30 seconds!), so I’m combatting it (at least at first) with starting with the most basic of the facts they’re supposed to be tested on – the multiplication facts. Afterward, we’ll do division facts, and then we’ll make our way to decimal/fraction/percent conversion facts, and eventually to the perfect squares up to 30! We’ll include square roots at the end if there’s time. I’m supposed to give a timed quiz every week, as the more often I give them, the less each individual quiz will count in their overall grade. I’m going to allow any student who fails a fact quiz to make it up during homeroom so they can improve their grade. I’m also thinking that I’m going to give each skill two to three times before moving on to the next skill. I’m also going to try to have a few variations (in part to avoid copying/cheating problems, but also to avoid giving the students the exact same quiz a few weeks in a row). The only tricky thing is since everyone’s sitting randomly every day, I have no way of ensuring that every person does all of the variants. I’ll have to think about this some more.

Anyway, we did three rounds of this practice quiz, though it was obvious to me that most of the kids only needed one round. I gave them 12 multiplication facts and 30 seconds. Then they circled any they hadn’t completed, and I gave them an additional 30 seconds. Afterward, I had them work for another 30 seconds, and star anything they STILL hadn’t been able to complete. Finally, they checked off either they just knew a fact or they used a particular strategy. On the back, I asked them to tell me about how confident they felt on these facts and which math facts they felt they needed to practice more.

In the last part of this double, we began working on the same tree diagram handout as 007 had this morning. We didn’t get very far: most students only finished #1 and answering those questions. I had them converse/compare in their groups, and share our some of their questions. We discussed how to list out the possibilities and answer the questions as the class ended – I had to force them back to their seats for a minute because they started packing up the moment they heard students in the hallway.

After 5th period is homeroom, so my kids came back. I decided today would be a silent reading day (I have a few different types of homeroom days). When the kids came in, my student teacher directed them to take out their independent reading books because it was a silent reading day. I noticed many of the kids needed to borrow a book, and I had to help one student select a book they liked (my library is somewhat limited since it’s mostly my own personal books!). Homeroom normally goes from 11:50 – 12:05. At 12:04, I realized I’d forgotten to hand out the two papers I was supposed to distribute to my homeroom, so I wound up making everyone a little late to lunch! I handed out a permission slip for our first field trip (to Chelsea Piers, totally fun the day before thanksgiving – not at all intended to be educational – just a spirit building activity) as well as an envelope to remind students to bring in their payment for the school planners.

I sent the kids to lunch and I sat down with my student teacher at lunch. We talked a bit about his feedback from his supervisor, and he asked me to support him in the other 6th grade class and co-teach it with him, so that the directions would be more clear. We talked about a few ideas of what to do when you’re not sure if the kids understand the directions (having them turn to a neighbor and tell each other the directions or asking them to repeat the directions aloud or asking them to do a thumb vote about whether they understood or not). We also talked a bit more socially – he asked me what board games I didn’t have (since he knew I had 89 board games!). I told him about Firefly Clue, a variant of the clue game that involves the firefly characters and the space ship serenity. We also chatted a bit about favorite TV shows and movie types/genres. I’m sad that he’s only with me about another week and a half before he goes off to his high school placement. He’s been a really great student teacher.

I ran to the bathroom near the end of lunch, before the students returned, and I filled up my water bottle. It’s so important to make sure both of those tasks get accomplished before the kids return, and even though lunch is SUPPOSED to end at 12:48PM, most days, students start arriving upstairs as early as 12:35 or 12:40! I wind up half waiting in the hallway with them, because I don’t want them to be out there unsupervised – it’s really not a great plan, and I’m waiting for the day a student gets hurt and no one was responsible for them. I hope it doesn’t happen, but I don’t know how to keep the kids downstairs longer.

Anyway, after lunch, my student teacher and I did a repeat of the 6th grade lesson – but again spread out in a double. This time, he did the warm-up again and I checked HW again, but I think he felt less rushed, so it went even better. Since he wasn’t being observed, I felt comfortable enough to call out “You should be writing this down in  your notebook” when he wrote up the relationship between multiplication and division being inverse operations. I like that we sometimes co-teach (like I did last year with my co-teacher!) rather than always have it be him or me. I think that takes better advantage of our set-up with two adults in the room available to facilitate.

This time, after he finished the warm-up, he turned it over to me for the notice/wonder, and I did the directions in much smaller chunks – first, take three post-it notes. Then write at least 2 noticings and 1 wondering about these fact families. Then I had them go around their groups, one at a time, placing their post-its on the poster and reading them aloud to their group members. If they had related ideas, I asked them to group the post-its; if the ideas were different, the post-its should be separated but in the correct column.

Then we did a gallery walk – each group rotated through the other 6 group’s “posters”. I gave each group about 30 seconds to read silently to themselves and 30 seconds to discuss in their groups. Before they moved, I told them I wanted them to look for patterns in what people wrote on the post-it notes, and if there were any surprises. I got this routine from Rhonda Bondie, but I’m not super impressed by what my students have done with it so far – the patterns part works, but they rarely seem to admit being surprised. Once they got back to their own group, they sat down and we did a silent write for two minutes where they responded to those two questions: “What patterns did you see?” and “What surprised you?”

In this case, we got a few really important observations out – they noticed that people had commented on the same three numbers being used in each fact family, they commented on how it only involved multiplication and division, and there were a few other observations too. In the surprises, one group had written a post-it note “What’s the point of this?” in the wonder column, and two kids were (in their words): “appalled” that someone had written that. I addressed the fact that it’s actually helpful for them to be honest like that because it lets me know that the purpose of the activity isn’t clear to everyone, and that we learn better when we understand the point of an assignment. So I asked them to reflect for a moment on why we had done this notice/wonder activity, and we shared out. A few students said it was really helpful to see how the multiplication and division facts were related, and how they thought that was going to help them when they started figuring out the division rules for negative numbers.

After this, we had students create their own fact families in their notebooks and then share with their elbow partners and add one new fact family to their notebook. We had two kids go up and put their fact families on the board – it was interesting, because one of the kids chose numbers with the same absolute value for both families (we gave the constraints that one family had to have two negative factors, while the other family had to have one positive and one negative factor). We pulled out some of our vocabulary here – absolute value and additive inverse and discussed the relationship between the numbers.

Next, we gave students the same practice handout. I was really proud of myself for this idea: when we created this handout, I added an extension where the students got four numbers and they had to use all four of them to create a target number with any operation. They HAD to use all four numbers. I have one student who always finishes everything ridiculously quickly (his dad is a math professor, and I don’t think this student has learned much new from me this year) – but today, he told me it was a good challenge, and when I checked in on him near the end of this work time, he had only completed two of the five extensions! I considered that a score!

We gave the students some time to work. During this time, one of my strugglers called me over and asked me to explain the division problem to her: -18 / 6 = ? I connected it back to the warm-up for the day, where we had rewritten the open multiplication number sentences as division sentences, and we read it backwards – so instead of reading it as -18 divided by 6, we read it as “What number times 6 will give us -18?” She thought for a moment, and then was able to successfully answer -3. I left her to keep working, and I circulated through the room. After I gave most students enough time to finish A and B, we put up the answers on the board. We didn’t go over them much because it was mostly just calculations: just putting up answers and checking or correcting. I asked them to give themselves a score out of 10 so they would know which ones they needed to work on more.

Finally, the last thing I did with them today was the multiplication fact fluency quiz that I did in 704. I gave them the same rules about the rounds. I noticed that the 6th graders definitely had many more students who needed a minute (as opposed to 30 seconds) to complete all of the facts. We did our three rounds, and once again, I asked them to write to me about which facts they felt confident about and which facts they felt they needed to work on. When they had submitted their fluency quizzes to me or Mr. Diaz, we dismissed them to go home.

School day ends officially for the students at 2:20PM. I said good bye and I sat down to fill out my period attendance for the day before running it over to the pupil accounting secretary in the principal’s office. I ran to the bathroom again – six periods in one day is hard on my bladder!

When I returned, my student teacher and I debriefed his lesson and I gave him some feedback and advice on the things he was concerned about. I also emphasized how awesome some of the things he was saying went well were – he takes some of them for granted right now, but the fact that he’s successfully using talk moves like “Can someone else restate <So-and-so’s> idea?” and then waiting and calling on kids who do it is actually a big deal and not something I would normally expect a pre-service teacher to do with the ease I see him use that technique he learned from me.

After that, I gave him a task of hunting some problems down for tomorrow’s 6th grade lesson while I wrote myself a debrief to remember where each class left off and how I wanted to pick up tomorrow.

I sent him on another errand, bringing the quizzes to be copied by the parent coordinator while I timed myself on making the answer keys for them. It took me 6 minutes, which probably means it’ll take my slowest student three times as long. I decided to round up to 20 minutes of class time. In creating my debrief, I realized that my two seventh grade classes each had parts of the lessons the last two days that were missing from the other class. So I made myself a list of the activities/lesson items each class needed to go over tomorrow.

Unfortunately, on Thursdays, Manhattan Youth, the organization that runs an afterschool program in my building with my students (and other students from my middle school) uses my classroom for one of their classes. The kids were somewhat loud while my student teacher and I tried to plan in my little nook, but I refused to cede my classroom to them. We just faced the corner and ignored!

Anyway, we started with a plan for tomorrow that involved word problems, but then I realized we hadn’t even brainstormed OTHER situations that involve negatives (which I guess we should’ve!), and that the real world application word problems should probably wait until after we’ve talked about other situations! Then I got worried that if we tried to cram all of that in before our quiz on mixed operations, it might delay our quiz more than I wanted to. I decided that meant we should JUST do more work with the four operations and the other topics we’ve learned so far (comparing the size of two numbers, finding absolute value and additive inverses). We sketched out the overall lesson plan for tomorrow in the concise lesson plan format that I’ve created. I gave my student teacher tasks: to create the HW, the power point, and the CW review handout for tomorrow.

We spent so long talking, and I wanted to make sure he really understood what to do very well, that it was close to 5:10 before I left my classroom. Luckily, google tells me it will only take about 14 minutes to get to MfA (more like 20, but that’s okay, I still make it before 5:30PM!). I pack up my bags quickly and we hurriedly take the elevator downstairs together. I stop by the office: my time card has been moved back, and in my mailbox I discover the parent coordinator has already photocopied my quizzes for tomorrow – she’s awesome at her turn-around time!

I walk swiftly to the subway, saying good bye from a distance to my student teacher as I run to the south end of the train station to catch a Brooklyn-bound L train. I take it two stops to Union Square, where I get off and walking around a maze I head north. I exit at 16th and Broadway, and I walk up Broadway, past 21st St, heading in to MfA’s building on Broadway. I give my name to the guard in the lobby and I head up to the 17th floor. I check in at the digital iPad and I check for snacks in the kitchen. I don’t want to eat pizza because of my diet, but I should’ve because all the snacks I wound up eating put me over my points! I took two flavored seltzer waters (both sugar free), and a bag of pretzels (that I later regretted!). I hit the bathroom before heading downstairs to my workshop: Contemplate then Calculate with Jasper and Constance.

They started the workshop with demonstrating another “C-then-C”. I found the problem they used somewhat interesting, because I felt confused why there were so many details in the picture that seemed unnecessary. My partner and I had an opportunity to discuss strategies and come up with a few, before we shared out as a group. We then had a chance to debrief the CthenC routine a bit, and begin planning. We broke up into groups by grade level – sadly, I’m literally the only middle school teacher in this workshop, so one of the facilitators worked with me, since she’s had experience teaching every grade from 5 – 10 (even though she’s currently teaching HS). We looked through the tasks on the New Visions website and found an algebra 1 task that would be appropriate when I was beginning a unit on solving equations. We started working on one, and then we decided it might be too easy for some of my kids, so we decided to look at a second one – and I love them both! ( and

She worked with me a bit on planning the possible ways students could find shortcuts to solve the problems, and I worked on filling out the planning template for it. I really liked some of the reasoning skills involved. Although I’ve always been a BIG proponent of students showing their work (using inverse operations and other properties of equality), I recognize now that there’s a lot more power behind those moves if students understand how to reason about equations mentally first. These two diagrams sort of reminded me of the frog jumping problems I did last year with Kara Imm.

Anyway, long before I finished planning, we ran low on time, and Jasper called another group to present/practice their CthenC. I was excited because I had a simple method for calculating the angle that wasn’t mentioned (using slope!), and I felt like my solution was particularly elegant in comparison with the unwieldy use of right triangles and such in the diagram. At MfA, I often wind up feeling less than adequate in my math abilities simply because I’m a middle school teacher without a lot of practice in higher levels of math, so I’ve forgotten some of the skills I used to know (i.e. I could tell you about the laws of sines or cosines, but I don’t know that I still have the formulas memorized or that I could tell you exactly which situations to use them in! And there are even more topics I don’t remember enough about to even tell you this much!). So it’s always satisfying to me when I’m able to see something in a way that I think is more efficient or sophisticated than the other teachers – not because I feel like I’m competing with them and I have to be better, but rather because I feel like I don’t measure up very often, and it’s validating to know I actually do (and that helps me feel like “Oh right, I do belong!”).

Anyway, MfA finished around 7:30, but we almost ran late (we had to cut off our conversation). I asked Jasper and Constance about sharing their materials so I could turn-key the routine at my school. We started an email thread so they could share those resources with me, and I’m excited, because I feel like my school has so many really great things going for it that they neglect the PD because they can get away with it and because they don’t have the budget to bring in tons of outside people. So I’m planning ways I can bring back the awesome things I’m learning at MfA to my school.

Afterward, I headed upstairs to use the bathroom on the 17th floor, because we didn’t know the code for the men’s room on the 10th floor (where my class was). While upstairs, I saw Kara and some MfA people, but I didn’t stop to say hello, as I was exhausted! I opened my iPad to load this draft so I could keep working on the subway (and no, I still didn’t finish it there – I’m still working on it now, at 11:50PM!). I headed out to the subway and hopped on an R train. I had to wait for a bit though, because an N train came first.

I got a seat immediately, and took out my iPad and wrote part of this draft the whole subway ride home. When we pulled into Queens Plaza, an E train was pulling in across the platform, so I “jumped ship” and crossed for the express. I got a new seat and kept writing until Jackson Heights station. I got off and saved my draft (and accidentally uploaded it, instead of just saving it as a draft – whoops!). I opened up my kindle and read my book, Cobra by Timothy Zahn (which I’m borrowing from the Kindle Prime library) on the 15 minute walk home. I got home and I checked the mail – clearly no one has checked it in a few days! There were two packages in there – one for me (my book on groupwork) and one for my partner (her tights apparently). I headed upstairs where my dog, Stormy barked excitedly to say hi to me! I came inside and I pulled out the turkey club my partner had for dinner and put the leftovers back together for me. I ate it along with two mandarin oranges and some strawberries.

After I finished eating (and half reading/ half watching Flip or Flop on HGTV with my partner), I hid in the bedroom with my laptop to finish working on my lessons for tomorrow. I started with answering a few emails from students/parents. Then I checked the lessons my student teacher created for 6th grade. Overall, they were pretty good, but they needed a few tweaks. I made the edits and I moved on to 7th grade math. I followed the notes from my debrief and I created the lessons I wanted to do before the quiz tomorrow. I was half falling asleep by 10PM, but I wanted to make sure I finished my Day in the Life post, so I took the last hour and a half or so to type it up – whoops! That took me a bit longer than I meant to! I’d better head to bed now, or I’ll never be able to get up in the morning!

1) Teachers make a lot of decisions throughout the day.  Sometimes we make so many it feels overwhelming.  When you think about today, what is a decision/teacher move you made that you are proud of?  What is one you are worried wasn’t ideal?

I’m proud of the way I chose to emphasize the “what went well?” part of my student teacher’s debrief. I think he’s taking for granted some of the really important things he’s doing, and focusing too much on how much room he’s still got to grow, and I had to give him a reality check that for a pre-service teacher, he’s actually got a lot of skills down and it’s important.

For vets: what is one teacher move you made today that you wouldn’t have made your first year?

I called my 704 class on their packing up before I dismissed them. I don’t think I would’ve done that my first year teaching, and I think it was really important to set the tone that I dismiss the class, not the noise in the hallway.

When you close your eyes and picture yourself in five years, what part of today’s lesson would be same/different?

I think in five years from now, I’ll be much more proficient with the content of the 7th grade statistics/probability that I’m teaching, so the problems will be more interesting and engaging instead of boring (which is how it feels now!).

Did your lesson how how you planned? Did you or your student deviate? How did that work for the learning you had planned?

My lesson basically went as planned, but I deviated a little bit in each of my classes. For the most part, I feel like it was for the betterment of the lesson, in terms of fitting in the lesson in the allotted time.


2) Every person’s life is full of highs and lows.  Share with us some of what that is like for a teacher.  What are you looking forward to?  What has been a challenge for you lately?

I’m looking forward to this weekend and catching up on sleep. Both of our days off this last week were spent sleeping, and even though I’m feeling a lot better from when I was feeling sick a few weeks ago, I worry  that I’m still in the midst of fighting off a bug, and I don’t want to get sick.

I’ve been finding planning my 7th grade lessons a challenge, because I don’t feel as comfortable in my knowledge of statistics and probability as I am in my knowledge of integers, so I feel like I’m doing a much better job at facilitating my 6th grade classes than my 7th grade classes.

What was the most negative/positive part of your day?

I think in many ways teaching 6 periods in one day is the most negative part of my day. It’s so exhausting, and having MfA in the evening meant my day didn’t end until after 8PM – and I’m feeling like I’m running on fumes.


3) We are reminded constantly of how relational teaching is.  As teachers we work to build relationships with our coworkers and students.  Describe a relational moment you had with someone recently.

My student teacher and I spent time chatting socially today at lunch, and that was nice. I feel like so often, even though we eat lunch together daily, we either are so tired/wrapped up in our own world, that we don’t talk at all, or we talk about lesson-related stuff. It was nice to chat about board games, and TV shows and movies.

I also had a relational moment with one of my challenging students today. I know he normally finished the CW incredibly quickly, and I keep trying to find more and more challenging problems to keep him engaged. I went over to him today when I handed out the practice handout, and I told him that I was thinking of him when I included the extension, so I wanted to know what he thought of it. When I visited him again later, he was so engrossed in the extension problem that he barely looked up at me, but he told me it was a great level of challenge for him. He was more engaged during that part of the lesson than he normally is because he didn’t feel bored. I feel like we built our relationship because I let him know that I’ve heard his complaint about being bored, and he saw that I was able to find something the right level of challenging for him to think about.

How did someone help you today?

My co-worker who’s head of the math department stopped by today and gave me some advice about the lessons in the unit.


4) Teachers are always working on improving, and often have specific goals for things to work on throughout a year.  Subsequent posts: What have you been doing to work toward your goal?  How do you feel you are doing?

I set four goals for myself this year: learn the topics in 6th and 7th grade, prioritize student-to-student talk in my classroom, work on the close of the lesson, and build relationships with my students.

I’ve definitely still got a long way to go with learning the curriculum, but I’m definitely on the right track. I’ve been thinking more about the 7th grade curriculum in particular (since that’s the one I currently feel least comfortable with) about how to do things differently next year, and thinking about how different ideas are tied together so I can foreshadow ideas before they arise specifically.

I think I’ve done a GREAT job at prioritizing the student-to-student talk, as my kids are talking to each other multiple times per day, and we’re doing both “elbow partners” and “mirror partners” (since they sit in groups of four!). I also think the random grouping is helping to get students talking more to students they don’t know as well because they’re having an opportunity to speak to new people every day, so there’s something novel about hearing from someone they haven’t spoken to yet. I do think there’s still work to be done here, both because there are certain students who are VERY quiet and rarely open up, even in partner talk, but also because there are kids who ONLY speak during partner talk and never speak to the whole class – and I’m still thinking about how to engage them more in the whole class conversations.

I think in general, I’ve been doing okay with the close of my lessons, but not as good as I’d like to be yet. I rarely get cut off too much in the middle, and I’m not finding myself having to majorly cut parts of my lesson (unless I know I planned too much in advance). I am finding that I don’t always have a good closure activity for the students – some days, we do an exit ticket or a reflection with partners, but more often than not lately, the close has been concluding the last question that we’re going over from the handout/activity that the kids were working on. I want to think more about how to improve this; I wish there were some books/articles/videos on good closes of lessons, with ideas of what’s come before in that lesson!

Finally, the last thing is about building relationships. I think I did some really important work in the beginning, in terms of writing the name tents (and the fact that kids asked about whether we were going to continue them or not made me think they thought of them as special too), but I feel like my relationship building needs a bit of a pick-me-up. I think my efforts have been flagging lately – I asked my track kids about their meet on Tuesday (for which they missed math class), and I got mostly bland answers. And other than that, I don’t think I’ve interacted in a personal manner with any of my other students since at least last week! I need to think up ways to incorporate these types of interactions or to think up ways to survey my kids for information I can use to build a relationship with them. I think some of my own awkwardness gets in the way of this to some extent.

As an aside: I love doing these day in the life posts, but I missed September 13’s post because these take me so long to write! I’ve literally been writing for over three full hours, including my time on the train this morning and this evening and the late-night typing I’ve been doing for the last two hours. I need to figure out a way to make this more succinct and shorter if I’m going to be able to sustain this. I also don’t remember if I did a post for curriculum night with the parents. The thing that sorta sucks about missing those is that I did a half-post and saved a draft, so I could probably reconstruct it – but I keep feeling so busy (and I keep winding up having specific things I want to blog about) that I don’t get a chance to go back and write those two days up. On that note, I’m going to go fall asleep now!


Number Strings @pwharris @Kara Imm

Last week, I took a week off from doing any number talks/number strings. I had a visit from the superintendent to work in, and I felt like I was juggling too many other new things. One of my coworkers seems to be able to do number strings intuitively with her kids, based on questions that come up in the moment. For example, when she introduced her students to probability, they asked about a roulette wheel, and so she asked them to consider the chances of getting 00 (which is 1/38). To estimate that percent, she had them first do 1/4 >> 1/40 and notice a relationship, then 1/2 to 1/20, 1/3 to 1/30, and a few others before she had them estimate the 1/38 and then check via a calculator. I was impressed, but I don’t think I’m ready to do it without planning it yet.

I’m trying to figure out how to incorporate some number strings this week for my students. I’m struggling in some ways because I want to be sure that I’m addressing the skills that the kids need in my current unit, but also not giving them strings that require them to make use of strategies from strings we haven’t looked at yet…

In 6th grade, we’ve “finished” our addition and subtraction of integers and we’re in the midst of multiplying and dividing with integers. We’ve done multiplication so far and we’re about to introduce division this week. I’m wondering if there’s a multiplication string that would be appropriate for me to use with them. And I’m also wondering if there’s a problem if I introduce some of the strings with negative factors! Or if I should keep the focus of the multiplication strings on the products themselves, and leave the signs to the day’s lesson.

In 7th grade, we’re working on probability, and there are a few things that have come up that I think could be good for number string work. First, I noticed that while my students have fluency with converting some fractions into percents (more than most kids – not only do they know their 1/4s and 1/2s, they also know their 1/3s, and 1/9s and even their 1/8s!), but the students aren’t fluency with multiple eighths, nor are they fluent with some of the “odder” fractions into decimals/percents yet. I’m wondering if there’s a way to get the students to be able to calculate the percents of 3/8, 5/8 and 7/8 easily (i.e. noticing that 1/8 + 1/4 = 3/8, or that 5/8 = 1/2 + 1/8 and leveraging those skills somehow – or multiplying 12.5 x 3 or x 5).

Second, tomorrow, we’re going to begin proportional reasoning with percents, so I’m wondering if I should do a string where we find “friendly” percents of a number to build a more complex one.

Third, we’ve had to multiply fractions by each other (but mostly “easy” ones), so I don’t know if this is worthy of a whole string right now.

I’m still struggling not only with how to implement these strings, but also how to design and decide on the best string for a given lesson. I know there’s been some back-and-forth about whether the strings should relate to the day’s content or not, and while I’m okay with it not relating directly to that day’s content, I do feel it necessary to relate it to the general topic of the week/unit.

Visibly Random Groupings

I am a total convert! I read the research this summer and I wasn’t quite convinced, but I rolled it out yesterday and it’s gone fabulously so far! I don’t think I’ve had any kids try to switch cards or complain about their seats. 

I did have four students wind up sitting together two days in a row, but that CAN happen (wow! What are the chances?! 31 cards, 31 students, and two days in a row, 4 of them got the same number as each other! They told me about it, which is why I believe it really happened randomly).

I do think the first month, in September, of sitting alphabetically with name tents so I can learn all of their names FIRST is vital;  I don’t think I could’ve done it otherwise! Calling on students has tested my memory today and yesterday, but the more they’re in different seats, the better I’ll get, I’m sure. 

I think the way I rolled it out has to do with its success so far. At the beginning of the year when we made our name tents, I told the students that one of my goals for us was to be a community of learners together and that I wanted everyone to learn each other’s names. In my sixth grade classes, I did a poll and no one knew more than 5 other kids; in 7 th grade, there was obviously a little bit more familiarity, but no one knew more than 2/3 of the people. Plus, two of my classes, one 6th and one 7th, are “split classes” – kids from different homerooms go to math with me together, but there’s no other class where they have exactly that configuration of people. 

Anyway, I rolled it out yesterday with every class (except my homeroom who I prepped it with on Friday last week). I started by handing the random cards to each student when they walked in and said “find the desk with this card on it” – and the desks are systematically arranged in groups of four and then numbered A-8 (with the four suits in the same relative position). 

Once everyone was seated and starting the warm up/copying down their HW), I paused them and pointed out that we had a new seating arrangement and asked them how I assigned it. We established that it was random, and they saw the cards were shuffled. I told them I would give them a new card and a new seat the next day and the next day and next week. I asked them why they thought I was giving them so many new seats and THEY remembered my goal of learning everyone’s names and working together. I told the kids this would ensure they have lots of opportunities to work with everyone in their classes. I reinforced that their seat would be new each day, though sometimes they might work with the same people or at the same table, that was ok because their seats were only for a day. 

I then give each student an “A#” – an alphabetical number so checking HW will be easier (since we can find them easily on the alphabetical list when they tell us their numbers). 

In my classes, I’ve already noticed some changes: students are talking in partnerships more because it’s a new person each day and some of that is even translating to sharing in the whole class because they feel more confident as they get to know more kids personally. 

Now, tomorrow, my two 7th grade classes will have to sit in the same seats because they were in the midst of debriefing an experiment that they designed in their groups today, and they can’t talk about those experiments with other groups in the same way! But next week, we’ll be back to new seats! 

I can’t wait to spread this practice to everyone! Try it out!