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:

  

Classroom: 2015-16

It's the start of another school year! The classrooms at my school underwent some major renovations over the summer... new walls, new ceilings, and new workrooms. Instead of getting in a week early to set up, we had to wait for final inspection just three days before the kids showed up. Here is what my room looked like when I arrived for pre-planning...

And here is is today...

I'm pretty happy with how it looks considering I threw it together in three days! I switched from desks to tables this year. We'll see how that goes. I thought it would be better for labs, group work, and sharing manipulatives. I've got a class full of TALKERS though.... sigh.

Ten On Ten

Hey ya'll, I'm linking up with Rachael at the Classroom Game Nook for her new Ten On Ten linky. 

That stands for 10 pictures on the 10th of the month. Frankly, I suck when it comes to taking pictures. I think I'm doing great if I take 10 pictures a year. This is going to be a challenge for me...

What? You mean that's only 8 pictures? Oh Rachael, can we make this the "Eight On Ten" Linky, please? 

5 Back-To-School Tips For Teachers

1. Plan dinners for the first week back at school. - Okay, so that's kind of obvious, I know. But here's the real tip... Come up with five easy meals (Sunday through Thursday) that will also be great for leftovers the next day. Then you also have lunch for the entire first week! Getting up early for school is traumatic enough after a summer's worth of sleeping in. Having to make lunch too just adds to the pain. One of my favorite leftover meals is King Ranch Chicken. It's probably not the healthiest thing in the world but it is EASY and delicious (plus my kids like it and it's cheap.... BONUS). Here's the recipe I use: King Ranch Chicken. To make it even faster and easier, I cheat and buy a rotisserie chicken from the deli (shh...don't tell anyone).


2. Put together your school "emergency kit". - What? Like for fire drills? No, that's not what I'm talking about. I keep a small tote bag in my closet full of little things I might need: aspirin, safety pins, deodorant (yeah, it's HOT down here in Florida!), mascara, mouthwash (for those really long days like Open House night), an extra house key, extra sunglasses, Tide-To-Go stain remover, and the all-important emergency chocolate bar. I usually have a pair of flip-flops in there too for when my shoes start to hurt or when I stay after school for awhile.


3. Take a trip to Walmart. - Okay, I'm the first to admit announce that I hate Walmart. I seriously detest the place. In fact, I will happily pay 20% more just to shop somewhere else. However, there is one time I will venture into the depths of Hell-mart... back to school time. Here's why: When the kids bring in 80 packs of those super cheap pencils or several dozen paper pocket folders without prongs, Walmart will let you exchange them without a receipt (as long as they aren't Office Depot brand or something). Now, if you're anything like me, you will end up with an entire shopping cart full of unwanted supplies. So, I strongly suggest that you either call ahead or better yet, go in and talk to the manager while wearing your school badge in a prominent spot. Explain the dilemma of receiving so many unwanted supplies and how it would be so beneficial to your students to be able to exchange them for things they actually need. I've never been turned down.


4. Use your phone in class. - No, do not text your husband ten times to say how you wish summer had been just a month or two longer. You know how easy it is to get off schedule the first few days of school? How many times have you been deep in discussion about reporting vs. tattling only to discover that special area started 10 minutes ago? It happens! So before the first day of school, set your phone to alert you to those transition times.


5. Create new student bags. - One of the most disruptive things to an otherwise smooth school day is a new student coming in. Not that I don't like new students, but if I'm not prepared, my day goes completely off track. A good way to keep things rolling is to prepare a bunch of "new student bags". These include all of the essentials that I normally give students during the first couple days of school: homework folder, supply list, parent letter, student info sheet, folders for reading and math, desk tag, etc. When the new student arrives, I pull out a bag and everything is there. What a lifesaver!

So those are my 5 best back-to-school tips for teachers! Don't forget to stop by my TpT store for the BIG HUGE Back To School Sale on Monday and Tuesday. Everything will be 28% off including:

Don't forget to grab this freebie for all of those kids who speeeeeed through their work...

Enjoy!

Christmas In July!

Christmas is my favorite time of year but it's oh so far away! Luckily, you can enjoy a little bit of the holiday season right here in the middle of July. I've joined in with a group of awesome TpT sellers to bring you an extra special (HUGE) sale on July 13th and 14th. Everyone participating will have four of their best sellers or bundles marked down up to 60% off PLUS there will be a ton of flash freebies available only during the sale!!

To find all of the resources included in the sale, hop on over to TpT and type #Christmasinjuly into the search bar.

Here are the items I've chosen for my sale:

My freebie will be one of my awesome (if I do say so myself) interactive comprehension booklets:

But remember, these will only be available July 13th and 14th. Be sure to also visit some of these other sellers who will also have incredible Christmas In July sales going on:

An InLinkz Link-up