Unpopular opinion: most kids aren’t ready for the standard algorithm when we teach it. Teaching division strategies for upper elementary is about way more than ‘Does McDonald’s Sell Cheeseburgers.’ and in this post I am going to walk you through the exact progression following the concrete-representation-abstract (CRA) model of teaching division to your 4th and 5th grade students.
Students need to have a basic conceptual knowledge of what division actually is, so the algorithm isn’t just a bunch of words. Before you can jump to the steps, they need to know the conceptual understanding. These strategies come after knowing that dividing is putting into equal groups or knowing how many equal groups you can make.
If you teach 4th or 5th grade division, then this is the post for you. The difference between 4th and 5th grade division is mainly that students go from 1-digit to 2-digit divisors. Another thing to note is the CCLS does not have students being introduced to the algorithm until 6th grade, but I know some states teach it as early as 4th so I’ve included it in this post.
Why Students Struggle With Long Division
The struggle with division starts in third grade with fact fluency gaps. Understanding fact families and knowing the relationship between division and multiplication is so important to building division knowledge.
Whichever strategy you’re teaching to divide, there are a lot of steps for students to memorize. If you have a student with an IEP who struggles with multi-step directions, then division might be a struggle for them. Scaffolds or tools are a great resource for you to give them so that they can become used to the steps, but like any tool, it needs to be gradually removed.
Some students rely on their memorization and can’t apply what they are learning to other problems. This hurts them down the line when making connections to different division strategies.
Using the CRA Model to Teach Division
Just a reminder, the CRA approach is concrete, representation, abstract. When solving, students gravitate to one of these methods. In division, concrete can look like using base ten blocks or place value discs and separating into groups or using base ten blocks to show the area model. If students prefer to draw the area model or the place value discs that’s a representation of what’s going on. Finally, if they go right to the partial quotients and follow the steps for it or the algorithm, that’s an abstract approach.
If you’re new to the CRA model, then head over to this post first. In it, I share about the approach to teaching math and helping bridge the gaps.
The Progression of Division Strategies for 4th & 5th Grade Students
Like everything I teach, I always try to think of the CRA model when teaching it. Division is no different. Whichever strategy I am working on with my students I have a concrete, representation, and abstract way of working it out.
Place value and multiples of 10
The first prerequisite for division is understanding place value and multiples of 10. Knowing place value helps with knowing which multiples of 10 to multiply the divisor by. Being able to look at a problem and see how much to multiply the divisor by to get as close as possible to the dividend is a skill that will be useful when it comes to the algorithm and understanding it beforehand will be so helpful to your students.
Going back to the CRA model, students can take a base ten block and model 10 or 100 times a number by grouping that number of base ten pieces. They’ll know a pile of 4 one-hundred flats = 400 and make the connection to 4 x 100 = 400. They can also represent this on the page by drawing the base ten blocks on their page.
Area Model Division
When teaching the area model for division, start with base ten blocks. Students can see the numbers and really get a chance to relate division to multiplication. It’s a tool they know how to use from early elementary years and will give them the hands on approach to dividing with area model.
The representation of this is fairly obvious. Students are drawing the area model out from the base ten blocks they are using. They’re able to create their rectangle by knowing what to separate the dividend by in order to divide.
Lastly, we have the abstract. This one is a little tricky because the entire strategy is really representative of division rather than algorithm, but you can show students the beginnings of partial quotients, which is the next strategy in the progression.
Partial Quotients
You may have heard of partial quotients as “The Big 7” strategy for dividing. Honestly, I have found when teaching division to use the terms that the strategies are actually called work best because when they get to another grade they’ll know what the teacher is talking about.
When thinking about this strategy in the CRA model, this is all abstract. There are no pictures or manipulatives helping them to divide. You might give them a tool to help them with the steps (like this one) or give them a spot to show their side work, but really it’s all abstract.
This strategy is best introduced after students understand what division is and can see the relationship between division and multiplication. This strategy also relies heavily on knowing multiples of 10 and being able to use them to help them.
The Standard Algorithm
Getting to the standard algorithm should be the last part of the division puzzle. Only after they are fluent in understanding the relationship between multiplication and division should the algorithm be taught.
In my personal opinion, this should not be the goal for students. Understanding division and being able to use any strategy they are comfortable with should be the goal.
Anywho, the algorithm is the abstract piece of learning division. It’s all procedure and steps to follow, which can be confusing to someone just starting out with division.
Final Notes
Whichever level of math you’re teaching it’s so important to emphasize conceptual understanding. Using the CRA model to help you plan for your lesson will give all of your students access to the conceptual understanding by letting them use what they are comfortable with to solve.
