How To Teach Regrouping So They Really Understand

Teaching second and third grade, I come across a lot of kids who have trouble making the jump from concrete representations of regrouping to the abstract algorithm. That's not because they aren't smart enough or developmentally ready. It's because in making the jump to the standard algorithm, they are missing a crucial step... converting between place values.

I bet many of your students are weak in this skill too. Just last week, I had to take a detour from my planned math lessons and revisit something they should have learned in second grade - how many tens are in a 3-digit number. It was a simple question, or so I thought...

"What is the total number of tens in the number 238?"

All of their hands shot up in the air and all of them thought the answer was 3.

"No, I don't want to know what number is in the tens place. If we were going to build the number 138 and we only had tens rods and ones blocks, how many tens would we need?"

They stared at me like I was speaking in tongues. No one had an understanding that 2 hundreds is the same as 20 tens. So I got out the math blocks. We counted by tens. We figured it out. We practiced with pictures of math blocks, We did it forwards and backwards. They were ready, right?

So, I wrote a problem on the white board... 

238 - 57

I asked them how we could solve this problem. Note that I did not ask them to find the answer. I wanted to know how they would tackle the problem itself. Not one of them could verbalize the idea that you would need to move one of the hundreds from the hundreds place and convert it into tens in order to subtract the 50. Nor did anyone see that there were 23 tens from which you could subtract 5 tens. I got all kinds of things like...

"Cross off the two and cross off the three and put a one above it and then you have thirteen which is bigger than five." 

I prodded them to explain their ideas and again, they just stared at me. Clearly they had been shown the algorithm either by a parent or a teacher, but they had no understanding of what the procedure meant or why they were doing it.

I'm sure my class isn't the only group of 8-year olds who get stuck when it comes to understanding what regrouping means. That's where expanded form comes in. When you break a problem down into expanded form before subtracting, it all becomes very clear. This is what it looks like...

Now students are forced to see the value of each digit and therefore, understand what is being moved from one column to the next. It's the logical step between concrete and abstract and it's missing from a lot of math instruction. If your kids don't have a solid understanding of regrouping and why they are doing it, try using the expanded form model before the standard algorithm. I think you'll find that it really helps!

A few resources you might like:

  

Engaging Kids in Informational Writing

The end of the school year is such a busy time, isn't it? I know most of you probably feel like me... worn out by testing and ready for summer but still looking at a to-do list a mile long!  Add to that student behavior that is, well, less than stellar. Ugh!

I've been finding reading centers to be particularly hard lately. These third graders have nothing on their minds except socializing and acting like the fourth graders they haven't quite become yet. So I took the drastic measure of canceling reading centers. That's right... I canceled them. No more centers! 

So, what are these children doing for an hour every day? Research and writing. Wow, that sound boring... zzzzz. But check out some of their finished work and you tell me, does this look boring?

These are the students' self-published "Time For Kids" magazines. After using TFK in our guided reading groups for awhile, I decided to use them as a way to get the kids writing.

First, we brainstormed ideas for topics and created a "topic menu". They came up with things like the San Francisco earthquake, the Titanic, Pompeii, the New York Yankees, Martin Luther King Jr., and the Apollo Space Mission. They were all VERY excited to contribute to the menu.

Then we closely analyzed TFK to figure out what makes them so interesting. The kids noticed that the paragraphs were short with text features to go with them. They noted that there were a lot of very interesting facts and that each section had its own heading. They pointed out the colorful illustrations and interactive features like links to videos. We decided it would be a good idea to use index cards for each paragraph or sub-topic.

Next, we talked about how to conduct research including how to paraphrase, how to cite your source (which we've been working on for awhile), and how to take notes. I also made a list of acceptable websites that they could access on the computer or ipads.

Finally, they were ready to go and boy, did they dive right in! Most of them chose to partner up for their first topic. They spent several days researching with some of them asking to visit the media center to find even more information. During reading groups, I looked over what they had done so far and offered guidance as needed. Some things they had trouble with at first were writing good headings for each paragraph and forgetting topic sentences.

After our first round of TFK publishing, the kids decided they wanted to do more, so they all chose a new topic! Some decided to work on their own because they were excited to research something specific. It was great seeing them so absorbed in their writing. Most of them spent a full week doing research and another week writing, illustrating, and editing. Their hard work really paid off! Take a look at some of these finished pieces...

Now that the school year is coming to an end, I wish we had more time for projects like these. But hey, I'm still ready for summer to start!

Don't forget to check out TpT's big Teacher Appreciation Sale starting tonight at midnight!

You Oughta Know About...Learn Zillion

For this month's "You Oughta Know" blog hop, I want to share one of my favorite websites for teachers. It's called Learn Zillion. If you saw September's hop, you might be thinking, "Hey, didn't you already recommend your favorite teacher site?" Well yes... EngageNY is my favorite for detailed, standards-based lesson plans. But Learn Zillion is where you can go for interactive, student-oriented lesson support.

• Lessons - Learn Zillion provides a lesson for every math and ELA standard. They are not the in-depth, scripted type you will find on EngageNY. These lessons use visuals that you can project for the students to see. Each one begins with a short opening question called a "Launch" to get students thinking. You can solve this together whole-group or model it. I like to show the launch, have partners talk about strategies they could use to solve it, and then model it myself. Here is an example of a math Launch question for third grade:

The Launch problem is then followed a "Task" and "Task Debrief" which gives students the opportunity to apply the skill that you're working on and see the steps for solving. 

One of my favorite parts of the Learn Zillion presentations are the "Common Misunderstanding" slides. They show students why a certain strategy or idea won't work:

The rest of the presentation shows the Big Ideas students will take away from the lesson, a formative assessment (great for exit tickets!), and then problem sets that can be printed out. At the very end is a video that goes with the lesson, which leads to the BEST part of the website...

• Videos - This is the part of Learn Zillion that you absolutely MUST try! There are so many possible uses for the videos. First, you can use them for direct instruction. The videos are well-paced, clear and easy to understand, and they really break the steps down into manageable pieces. You could also use them for doing flipped classroom by having students view them prior to your own lesson. If you have above or below-level students, you can use the videos for other grade levels to meet their instructional needs. 

There are also teacher-created video "Lesson Sets". These are short series of videos around a particular topic. For example, this week I used the 3rd Grade Opinion Writing video set during my guided reading groups. In one group, I have a student who had gotten far ahead of the others. She needed something to work on while I caught the rest of them up. So, I pulled out the iPad and selected the video from this series called "Make a Brave Statement" to help her develop stronger openings for her writing. We had just read an article in Time For Kids called "Should Soda Be Taxed?" After watching the video, the student used what she learned to write an opening paragraph for her opinion on the TFK article. It allowed her to independently extend her learning and practice an important skill with very little involvement from me.

Next week, my reading groups will all be watching video lessons during their computer time. I set up a "class" so each student has a username and password and assigned specific videos for them to view before we meet at reading table. I can't wait to see how it jump starts their learning!

So that's a little overview of Learn Zillion. Go check it out!

The Trouble With Toothpicks

Next week is the big day... formal evaluation time. Ugh, I just hate this time of year. Not because I question my own teaching skills. It's the kids and their inability to act like humans when another adult enters the room. Why is it that they all turn into lunatics as soon as the principal shows her face? Don't get me wrong... I have a lovely class this year. In fact, I like them so much that I'm hoping to loop up to third grade with them. They are sweet and cute and pretty darn smart! But Lord help me, as soon as the Big Boss comes in, you'd think they'd been raised in barns.

So as I sit here planning my lesson for the big horse and pony show (aka Formal Evaluation), I'm second guessing myself. We are starting a unit on shapes in math and that is what I will be teaching. My plan is this...

1. Read "The Greedy Triangle" to generate interest and introduce vocabulary.
2. Explicitly teach vocabulary using my Properties of Shapes Posters.
3. Model how to use a circle map to describe a shape and then have the kids do their own in small groups.
4. Come back to whole group and create a table showing each shape and their defining attributes.
5. Based on the information generated, determine which shapes are quadrilaterals.
6. Formative Assessment: Students will individually sort shapes and categorize them on a tree map according to type.
7. Culminating Activity: Students will create their own triangle, quadrilateral, and pentagon using marshmallows and toothpicks.

What was that? Did I just say toothpicks? As in small, sharp projectiles made of wood? Okay, so this is where the second guessing comes in. Have I lost my freaking mind?!!! Let's just list the ways this could go oh-so-wrong...

1. They could poke themselves in the eye and be blinded for life.
2. They might jab themselves and end up with MRSA or some other horrid affliction.
3. They might accidentally swallow one and pierce their internal organs.
4. They could pretty easily use the marshmallows and toothpicks to build a giant phallic symbol.
5. I could be sued and/or lose my license for most of the above happenings.

So what should I do? Use the toothpicks! I mean, what's an effective lesson without a little danger, right? I have exactly 26 hours to change my mind and then I have to hit "submit" and send my lesson on its way. So, if anyone objects to this plan of mine, speak now or forever hold your peace.