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 students should be exposed to before standard algorithm. 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. So many of these strategies pair nicely together and connect really well to the standard algorithm. The goal is not for students to master every strategy. Rather, the goal is for students to conceptually understand how dividing large numbers works and to find a strategy that works best for them.
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
Starting off with base 10 blocks, 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.
It can be super helpful to provide real life problems when working through each of these strategies. Use these division word problems as you guide students through modeling each division problem. Each of these problems are the same type of division problem (splitting into groups). There are also open problems. These work great for differentiating your small groups or letting students choose what numbers to use for the problems.
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 split the hundreds blocks into equal groups of whatever number we are dividing by. 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 is in each group, is part of our answer. So if each group we make has 200, we place 200 at the top as part of our quotient, and so on.
I created these slides (Dividing with Base 10 Blocks) to help guide students through building different division problems inside the place value chart. Students will need their own copy of the division place value chart and base-10 blocks. By the end of the slides students will be drawing the blocks instead of using real base-10 blocks. We will talk about this in the next section.
Base 10 Block Pictures in Place Value Chart
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…..we talk about how sometimes…adults are a little 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 usually ends up being the most used strategy in my classroom!
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 quotient strategies.
You can download all the division resources in one place right here.