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Subtraction with Renaming

Trading to Rename

Standards for Math Practice 4

We have moved on to subtraction with renaming (2.NBT.7). I’ve been doing a lot of this work with students in small groups and it’s amazing  to see students talking and thinking about making trades, or renaming numbers. In a small group full of dialogue, students physically traded one of the ten rods that makes up 60 for 10 unit so they can more easily subtract 13. We talked about the value of 60 at the start, during and after the trade. Students giggled about how I could still buy exactly 60 $1 ice cream cones- no more, no less; at every phase of the trade. They knew that whether 60 was composed of 6 ten rods (60+0) or 5 ten rods and 10 unit cubes (50+10), its value remained constant. We worked through a few more bare number problems that also required renaming to get more ones and I really emphasized how accurately our recording matched their physical manipulation of the base ten blocks as well as their thinking. Students recorded on white boards, just as I had… and I expected we were good to go! Not so fast. About 1/3 of my students were not able to demonstrate their learning with much independence… even with 60-13. Even if I talked about ice cream cones. These students seemed to rely heavily on the scaffolding that came from our discussion throughout the trading process.  So, I decided they needed a trading center- a place where they could be successful and independent with the skills that this high level work demanded. Here are some of the recording sheets that are guiding their work. I needed them to build confidence and more deeply conceptualize the equality of the value of the numbers they were composing, both before and after renaming. They needed to deepen their understanding that values can be represented in multiple ways. After observing students’ success with this work in centers, I realized this center had potential value for all of my students. It provides an opportunity for students to focus on and practice their recording, outside of the context of the subtraction problem itself.  Additionally, it is forcing some of my higher level students to build, revisiting a more concrete experience with numbers. This helps me prepare them to rename to get more tens, hundreds etc. They are finding the challenge numbers particularly fun to work with, and I appreciate the opportunity for students to grapple with these situations in isolation, as opposed to in the context of a subtraction problem. Having this more isolated experience, makes them more confident, and less distracted by the challenge in the midst of a problem.

Concerns About Counting

In my second grade classroom, I’ve recently identified a troubling gap in my students’ learning… Counting. I know how important counting is… and we have been counting all year. We count while we wait in line, we count backwards and forwards, by 2s, 3s, 5s, 10s and more. We start in the hundreds, we start in the teens… So, why (I’ve asked myself and anyone who will listen) am I observing students struggle to cross decades when counting in the midst of double digit addition and subtraction?!?! Here’s what I mean: We are working on adding multidigit numbers and I stumble upon a student who is heading toward the wrong answer. As I listen to her explain her thinking, I realize when she counts from 19 to 20, there is a question mark in her voice and she looks up at me for reassurance. From 38, 39 she heads to 60 with the same inflection and eye contact. The scariest part… she’s not the only one. I’ve realized this is a symptom of a few more serious issues, one of which is patterning in base ten… and conceptualizing the magnitude and difference of numbers.

So what are we doing about it? After consulting with some of my favorite math teachers… here’s the plan. First, I’ve been doing an activity we call Sound of a Number for a few minutes each day.The kids love it and they are exercising an important part of their math brain. For this activity, I hide behind a cardboard study carrel with a pile of base ten blocks. Students listen hard to attempt to identify the value of the blocks I drop. We start each lesson with a quick review. I drop of each of the pieces, unit, ten rod and hundred flat; a student identifies each by sound and explains some of the different ways each could be made. For example, we could make a hundred flat with ten ten rods or 100 unit cubes etc. This helps to deepen the concept of base ten.

Next, I drop different quantities and students listen intently to try to name it. This feels like a game and I learn a lot about students’ thinking. For example, when I dropped 21 (two ten rods and one unit cube), a wrong answer of 23 or 25 was different than 201. Most answers are accurate though, during this quick activity.


*Side note: This activity brings me back to my sixth grade teaching days, when I used this to introduce rational numbers. In that context, we’d establish that a 100 flat had a value of 1, and the ten rod was a tenth of that etc…

What else seems to be helping? Here’s a center I threw together that my students are loving! Other bonuses… it practically differentiates itself and gives me great information about my students’ thinking.

These center directions got kids started.

These center directions got kids started.

This student rolled a 1 and a 2 and decided to start at 21.

This student rolled a 1 and a 2 and decided to start at 21.

At the center, students had three dice, white boards, markers and socks (for erasing). Students could decide on their own if they wanted to roll two dice to get a 2-digit starting number, or three dice to get a 3-digit starting number. I was impressed with the choices students made for themselves.



I circulated and checked students’ work as they made their number lists. Some of my strugglers needed the scafffold of hearing me ‘count on’ when they seemed stuck, and then were able to continue on their own. I asked some students to use another marker color to identify patterns or talk with a partner about patterns. This was great as students articulated patterns in the ones place throughout their lists. I challenged some fast finishers to roll a new number and count backwards by 2. I plan to keep this center going for a while and mix up what students are ‘counting by.’

Classroom Teacher: Reality Check

The view from down here.
“It all falls on the classroom teacher, it always does” she reminded me. This was my mother. A retired elementary school teacher, who had made it the long haul. In the classroom for her entire career, advocating for kids, mentoring new teachers- reminding me when I express frustration in the system that, I shouldn’t be surprised because “other people just don’t get it. Everything is the responsibility of the classroom teacher.” In other words- s#!t rolls down hill. I’ve been hearing it for years. But, honestly I didn’t quite get it until recently.
I’ve spent most of my career as a middle school teacher. I guess I have that genetic mutation that appreciates the sass and limit-testing of the adolescent. Anyway, after a few years of moving around, including coaching and mentoring new hires to “fight the good fight,” I opted for a change. Something I admired about so many of the elementary classrooms I had visited as a coach, was the deep sense of community that I watched develop within those four cheerfully decorated walls. In my ever idealistic dreams of the next chapter of my life as a teacher, I thought- that is where I belong. If I teach in an elementary school classroom, I can have so much more of an impact! I can foster a sense of community, encourage students to work together, develop their character, their leadership skills, and of course… differentiate instruction so they don’t end up in middle school with so many gaps in their learning. Yes- if I meet them each exactly where they are (in grade 2) and do my job, I will change the course of the future.

Last night at dinner, a friend was telling us about the new job she’d be starting as her maternity leave comes to an end. She is taking a position where she will work three 10 hour days, instead of five 8 hour days. While it will be a decrease in hours, it will work for her family, and for that we were celebrating. My mind wondered… thinking about all of the ten hour days I had been working since September… Someone interrupted my thoughts with a question. “So… I know teachers work a lot more than the hours they have to be at school… but how many hours is the actual school week anyway?” As I answered, “Umm… 35ish, I guess…”  my mind raced with the math of my typical work week. 7-5 most days, 7-6 some… there was that day I made it to my 4:00 dentist appointment on time. That felt like a holiday.

And yet, almost every morning (while I race around hoping that the hour before my students arrive will tick by more slowly) I chastise myself for my lack of preparation, for everything I’m not doing. And most afternoons, I leave wishing I could just find three more hours to prep, to  plan… or maybe even (dare I say?) to think. On the way home, I beat myself up about the administrative tasks I’ve pushed off yet again- logging those scores into the database, filing last week’s evidences into student folders. And then I offer myself some consolation- if something’s gotta give, at least it’s not your face time with kids… But let’s face it- I judge myself solely on what I haven’t accomplished in my classroom. Don’t we all?

So during the rest of that celebratory dinner, I multitasked, making some mental lists, doing some serious math. What was it that was getting in the way of the real work I wanted to do with kids? Why hadn’t I helped every student choose a “just right” book from our classroom library yet, met with reading groups regularly, held enough writing conferences and completed a running record for every student? I found my answer in the math. My students are at school for 6 hours and 15 minutes each day. They attend a specialist class, eat lunch, and have recess- all outside of our classroom. This brings our time together for teaching and learning down to just 4 hours and 25 minutes. Next, we visit the lav as a class- twice a day. While I wish it were faster, it takes a solid 15 minutes each time. We practice our math facts in the hall because I’m trying to squeeze every educationally productive minute out of the day possible, but these necessary bio breaks bring our time together to 3 hours 55 minutes. Next is snack. Seven and eight year-olds need a healthy snack during the day. I dreamed of protecting this time for reading aloud while students munched. I imagined kids eating their snacks on the edges of their seats waiting to hear what would happen next to Junie B. Jones or Charlotte, the spider.



Fruit cups however, are killing me. Every day at least three kids bring a fruit cup for snack- a very healthy option for sure. The seal though… they can’t open it themselves. And even when I open it for them and suggest they drink the extra juice first- the end of our snack time always brings the “sticky desk sweep.” I race around the room spraying down the desks of every student who had a fruit cup or yogurt. This is a new routine for me- and quite genius, I think. It saves me instructional minutes later, when students would regularly raise their hands mid lesson to say, “my desk is sticky. I don’t know why.” This would cause a much more serious loss of instructional time… but alas- the read aloud snack time dream was just that- a dream. After accounting for snack time, we’re left with 3 hours 40 minutes, on a good day. Let’s subtract 15 minutes for classroom jobs and cleanup at the end of the day, and 15 minutes for the morning meeting that helps us remember we are all individuals, that matter- and care about each other. (I will foster a sense community!!)

I have 3 hours and 10 minutes. And thank goodness- because I am going to need every single one of those minutes! My “job” is to design opportunities for these amazing second graders to learn math, reading, writing and science or social studies concepts each day. Oh yeah, and I have to deliver a 40 minute phonics lesson each day- that luckily I don’t have to design…so… 2:30 it is!

What did I do so irresponsibly with those minutes this week? How is it that my “to teach” still feels so long?? Monday we had an assembly… one hour gone. Tuesday, I was out learning about the phonics program. Enlightening? Yes. Necessary? Definitely. Wednesday was picture day. Thursday, we had chorus rehearsal and our hearing tested. And Friday… why was Friday so hectic? Oh right… it was Halloween, hat day and we met with our fourth grade reading buddies. And thank goodness we did- because I definitely did not sit and listen to each student read this week.

So, kudos to all of the elementary school teachers who have the systems in place to juggle these demands. Those of you that juggle them and don’t sleep at school- you are my heroes! I’m watching and learning from every single one of you, every single day!


Using Google Presentations for What??

Using Google Draw

Place Value in Second Grade

Here’s how we’re getting our senses involved as we determine the value of base ten blocks in second grade!

Using Screencastify

Teaching with Online Discussions

I decided early this year that I have a responsibility to improve the quality of online discussions. As a teacher, I often feel responsible to improve the world I live in. Knowing each year, that I will spend so many hours every day with so many impressionable, mold-able citizens of the future- can sometimes feel like a lot of pressure. I know my time working on digital citizenship is well spent though, because my students have digital footprints that are growing faster than they are!

Teaching students to have respectful, productive academic discussions online follows the same construct as teaching anything else. Students need to be taught explicitly. Students need clear, timely feedback. Students need to play an active role in creating/ designing the expectations. Students need to be exposed to and evaluate samples of the work they are being asked to create.
My students used Edmodo a great deal this year to have online discussions. Sometimes we discussed a current event, other times a shared novel. One reason I liked using Edmodo was that I had the ability to give students feedback on their posts. I also liked that I could create small discussion groups. Here is a snapshot of a reading group discussion.

Edmodo Screen Shot
I found this threaded discussion rubric online and love it! It came from Educational Origami, a blog and wiki dedicated to 21st Century Teaching & Learning. You’ll want to bookmark their page!
Based on this rubric, threaded discussion posts should:

  • Refer to posts and thread
  • Enhance the discussion
  • Be clear and concise
  • Add own opinion based on thread
  • Develop an argument (supportive or opposed)
  • Develop suitable questions
  • Critique other posts
  • Answer questions and defends stance or position

If I could go back in time, I’d have this list in mind as my goal, as I elicited student ideas about what threaded discussions should look like. We revised and narrowed our expectations as a group this year, and ended up with a similar list, but starting with the end in mind always helps!

Do you have any advice for teachers who plan to dive into online discussions this year? Have a rubric to share?

7 Ways I’ll Work Smarter in my Next 1:1 Classroom

After using a class set of Chromebooks for the whole second semester of the school year in my sixth grade Humanities class, my brain is spinning with all of the “next time I’ll…” ideas. Here are a few:
1. Simplify & standardize the creation of students’ usernames and passwords. If students are creating an account that is linked to their Google account (GAFE), having them sign in with Google was great! No password or username needed. However, it wasn’t until we had dealt with the annoying, “Um… Mrs. Sullivan, my password’s not working” too many times that one of my students mentioned that there’s a  rule in the library. My school’s amazing media specialist had already trained my students that when creating any online account they had to use their email prefix for the username (complete w/ a sequence of numbers, so no one ever got a message that their username of choice was already taken) and their lunch number for their password. As often happens in middle school- once my students walked out of the Media Center and into my classroom, they disconnected the part of their brain that they used in the Media Center. Luckily, someone had a moment of clarity… followed by a collective, “Oh yeah…” from her classmates!
2. Collaborate in product and credit. Very often I’d assign students to work together on a digital creation. As a partnership or small group they’d present their analysis of a character or pitch a new idea. While working, the students would be using one person’s account, which meant that later if one of the group members wanted to access that product they wouldn’t be able to log in and see it. This really didn’t pose many problems, however at the end of the year it occurred to me that we could avoid problems with a simple procedure. Each time students work collaboratively, they sent an email with the link and embed code to me and all group members. In the subject line, they wrote the assignment title. This was helpful because many students wanted to embed a Powtoon or Amimoto video on their blog or in their digital portfolio, and would need the embed code to do that. Note: this was not an issue when working in Google Docs, as students can easily share access.

3. Classroom Jobs: Technology Managers pass out and collect Chrome books and manage easy to tangle plugs. Help Desk Staff- These are students you can go to for help and who manage a Help Desk webpage to answer Frequently Asked Questions through text/ video tutorials.
4. Have students create and keep a Digital Portfolio Page on their website as a place to display (and reflect on) all of the digital creations they make throughout the year. I wish I had done that along the way, instead my students added it at the end of the year. I’m sure they missed some of their creations.
5. Comment on each others blog posts more often. Next time, I think I’d establish a time frame to keep this going all year. This year on a few different occasions I grouped students (across classes) into groups of 4 students. Each was responsible to comment on each of their fellow group members posts and respond to a certain number of comments. They LOVED doing this and I wish I had done it more. It increased the pride students took in their own published work when they knew they would actually have an audience, and they loved checking the stats to see how many visitors they had, which posts were most popular etc. The possibilities are endless here!
6. Encourage students to be each others’ editors more often. Here’s a rubric that students used to peer assess websites. Here’s a digital presentation rubric that my students used to both peer and self-assess their Genius Hour projects. (I adapted these from others that I found somewhere on the web… sorry that I don’t remember where! If you are the original author- thank you! I love your work, please get in touch so I may credit you!)
7. Don’t reinvent the wheel! Essay questions make great platforms for digital creations. Instead of adding an assignment, try replacing one that’s tried and true. For example, I love this assignment that I’ve been giving for a few years now, where students have to take the perspective of either the North or the South the day after the election of 1860. They used to write an editorial that would have appeared in the local newspaper. At the end of the unit, my students would also find a similar essay question on their test. I still love the assignment, the thinking and the discussions! This year though, they worked in groups… and instead of writing an editorial, they created a video that would have gone viral in either the North or the South the day after the election. They still found the same essay question on their test. This was by far- my favorite assignment of the year.

What advice do you have for someone ready to take the edtech plunge?

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