Ahhhhh long division! The bane of many of our existence…only kind of kidding. But on a serious note…teaching division can be some pretty rough times. BUT it doesn’t have to be that way! Many state standards now require teachers to teach wayyyy more than just the standard algorithm for long division because they want students to really build conceptual understanding instead of just memorizing steps! Common Core standards don’t even teach the standard algorithm until 6th grade! Let’s walk through several long division strategies.
I teach in Texas, and we teach the standard algorithm in 4th, but there are many strategies that are suppose to be taught prior to that. Originally, I, like many other teachers, did not love this change. Mostly because…that’s not how I was taught! My first two years teaching 4th, I honestly skimmed over or completely skipped some of the lessons leading up to the standard algorithm. This was mostly due to the fact that I didn’t understand those other strategies…because I did not have the strong conceptual understanding needed to use those strategies. I made it my goal my third year teaching to really research and understand those other strategies…and along my way I found many more! I learned soooo much and was really won over to the idea of my students conceptually understanding division instead of just memorizing the steps of the algorithm.
Because there are so many division strategies, I’ve decided to break this post into two parts. In this post, we will cover the progression from base 10 blocks to the standard algorithm. In part 2 of long division strategies, we will go over two partial product strategies and I will also include a bonus strategy that I just learned about that I know you’re going to love! So many of these strategies pair nicely together and connect really well to the standard algorithm.
These first few strategies transition using the CRA model. CRA stands for concrete, representational (pictures), and abstract. We move from base 10 blocks (concrete), to drawing the blocks(representational), and then finally just to using the numbers and their values (abstract).
Base 10 Blocks
So I always started out with using actual base 10 blocks…even when I wasn’t a very good teacher, I at least did this! Ha! Just not as in depth or for as long as I should have. We simply count out the total number we need, draw circles on the table for our groups, then evenly split up the blocks. This provides ample opportunity to talk about the need to trade out a hundred for 10 tens and a tens for ten ones.
Base 10 Blocks in Place Value Chart
Next, still using our base 10 blocks, we move on to organizing these blocks into a division place value chart. We write our divisor on the outside. Starting in the hundreds place, we try to make groups of whatever number we are dividing by, as shown in the example below. Whatever blocks are left and cannot be grouped, move to the next place value. We again have to practice exchanging hundreds for tens and tens for ones. We always talk about how hundreds aren’t allowed in the tens club! However many groups we make, is part of our answer. So if we are able to make 2 groups of hundreds, we place 200 at the top as part of our quotient, and so on.
Base 10 Block Pictures in Place Value Chart
We then discuss how sometimes the numbers are too large to get base 10 blocks out, or sometimes those may not be available, like during a test. So we move on to using the same strategy, but instead of using concrete base 10 blocks we move on to drawing the base 10 blocks. This would be the representational stage of the CRA model. Just like with our real base 10 blocks we place the total in the place value chart and then circle groups according to whatever we are dividing by. Click the link to download this free long division place value mat to laminate and reuse.
Place Value Chart with Values
The next part is one of my faves! So many lightbulbs and “ohhhh” moments! We completely take away the base 10 blocks and instead, write the value of each digit in the number into the place value boxes. So 534 would split into 500, 30, and 4…expanded notation whoop whoop! The picture below better shows how this connects directly to the step before. We also use the same language as when we had the pictures and blocks. Instead of saying how many times will 4 go into 5, we say how many groups of 4 can we make with 500. We continue this language the whole way through.
Place Value Chart with Digits
Then…..drumroll please…..I tell the kids that I’m feeling kind of lazy, so instead of writing the entire value of the number in each place value, I’m only going to write the digit. But it’s okay, because since it’s in the hundreds place, I still know what it’s really worth. At this point, this strategy matches the standard algorithm beautifully! Just instead of bringing each digit down, you are bringing them across the place value chart. This is my absolute favorite way to divide!
One of my favorite things to do is place these strategies side by side with the same problem and have students compare and contrast. They make so many amazing connections!
Stay tuned for the next long division strategies post where we will discuss a couple partial product strategies and a new to me strategy that you’re going to love!
Want to watch these strategies in action??? Check out this video!
Click the link below to grab the division maze