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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.’

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!

Station Teaching

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!

Algebra Example             Geometry Example

Here are the documents we used in one workshop with high school math teachers:

photo 1

At the Application Station, teachers considered embedding authentic, real world situations into math tasks. Collaborating with the Physics teachers is on this group’s list of next steps.

photo 2

After setting a purpose for their work, these math teachers watched the videos linked to in this post looking for strategies they could use in their own classrooms.

photo 3

Here at the Manipulation Station, teachers investigated new math kits they will have access to in their classrooms. They focused on incorporating manipulatives into as many concepts as possible. The green tent card lets the facilitators know they are “going strong and need no assistance.” Some teachers plan to use the green, yellow and red tent cards during their stations to increase students’ independence.

  Signs for Stations           Station Descriptions & Planning Sheets

Norms to Post               Sample Rotation/ Map      10 Principles

Here are some great links to resources that may support your work:

Math Coaches Consortium       Dare to Differentiate    Mathematics Assessment Project

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