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.
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.
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.’
How do you capture all of the learning that occurs during discussions, hands-on exploration and collaborative group work? When there is a written product… we know we can collect and correct (ugh)… but that’s not always my first choice. When I collect and correct too much, I lose the ability to catalog and analyze and make instructional decisions based on the evidence. Instead, my school bag gets heavy Read More
So, your school department actually has a manual for you and it’s full of printables… They were designed by educators and statisticians… and people that must know more about teaching this content than you do… so why aren’t you students engaged? Well, I am writing this post to make sure you don’t “throw out the baby with the bath water!” Before you throw away every workbook and ditto in your classroom… let’s put our heads together.
You are right, experts did design these materials, so there’s probably something that works in here…
Don’t reinvent the wheel- Re-purpose it instead!
Here’s a template for a cube (as well as other amazing ideas- amazing wiki). Why not put the best questions from your packet on the 6 sides of the cube and let students roll and discuss in pairs? Your goal (with the packet) was for students to think about the questions, right? Imagine all the ideas they’ll get from their partner when rolling the cube??!! Two heads are always better than one.
You could listen in on student conversations and assess their Speaking & Listening Skills or their content knowledge. Another idea is to assess student learning with an exit slip at the end of class. When you encourage students to have conversations, arm them with sentence stems and accountable talk to make it as productive as possible.
What will you re-purpose this week? Let us know in the comments & you may inspire someone else to take a similar risk!
PS… I’m looking to give away a TpT gift certificate to a lucky blog commenter this week! Spread the word- bring a friend!
Regardless of the subject, brain research tells us we need many rehearsals (+20…yikes!) for new learning to stick! Learners rehearse learning when they are actually engaged in it. And, just to be clear… a worksheet with 20 math problems does not equal 20 rehearsals…( awwww, maaaan!) So, let’s consider the value of a jigsaw!
Dear Fellow Teachers,
Let’s roll up our sleeves, take some risks and be proud of the outcomes! It’s February and by now you have a good idea where you want to focus your attention. Maybe you’ve been observed by a colleague or administrator and you have some actual feedback to guide you (yes!!) or maybe you’ve known for months and have finally dug yourself out of that pile of paperwork and are ready to go!
However you got to this place of wanting to grow- I’m glad you did. All we need is some focus and a little bit of persistence and together we will make change happen! Over the next four weeks, I will post practical tips you can use right away to make change happen in your classroom! We will focus on a different area each of the four weeks, and connect the work directly to the RI Teacher Evaluation System (based on the domains of Danielson’s Framework for Teaching). We will self-assess, implement a strategy and reflect. Any comments or feedback you leave will help me to generate the next post. I will respond to your needs… Based on teacher requests, we will start with Questioning/ Prompts and Discussion Techniques.
There are lots of rubrics out there! Here are two you can use to self-assess, reflect and set a purpose for our work together around questioning!
Let’s support each other and celebrate success using feedback, comments, Facebook & Twitter. Subscribers will receive additional tips along the way, so if you haven’t already subscribed- make today the day!
So excited to get started!!
Lately, many of the teachers I support have been expressing a desire to take risks with new and different teaching strategies. One strategy many teachers are investigating is station teaching. Over the next two weeks I will attempt to respond to their needs as best I can through group work sessions, classroom observations and modeling.
Here are some videos from Teaching Channel.com that provide examples!
Here are the documents we used in one workshop with high school math teachers:
Here are some great links to resources that may support your work:
I was first introduced to the idea of a writer’s notebook by my tenth grade English teacher, Mrs. Catamaro. I loved that notebook! My notebook helped me see who I was as a writer, and focus on the writer I wanted to become. It met my needs as a learner the way nothing before had. I was impulsive and unfocused, and in my writer’s notebook my ideas and Mrs. Catamaro’s feedback would wait for me. I could read and reread. I could process what I wanted, when I was ready. I’ve used the writer’s notebook with my own students and hope I provided them with opportunity to navigate their learning that Mrs. Catamaro did for me.
My Blogging Territories (Like in A Writer’s Notebook, these are ideas I want to remember so I can write about them later)
Common Frustrations & Pitfalls of New Teachers
Educational Issues that keep me up at night