Front end addition (also called left-to-right addition) is one of the most powerful mental math strategies for teaching addition of 2 or 3-digit numbers. However, many people are confused by why it is important and why it can be more effective than traditional vertical addition.

It can be tough, especially with parents, trying to explain the rationale for using front end addition. This is especially true for those people who believe math strategies should remain how they used to be when they were children. However, this is usually due to being unaware. Once people see it in action, it usually does not take long to convert them to “believers” in the effectiveness of this strategy, as well as other mental math strategies. When I was teaching 3rd and 4th Grade, I had students who could literally solve an equation within seconds using front end addition.

The best part is that this strategy promotes real understanding. In an equation where you use the standard algorithm to solve it, you use a series of steps. This includes adding the ones first, carrying if needed, then adding the tens, carrying if needed, etc.

The standard algorithm does not encourage understanding of place value and number sense. For example, in the equation shown below, students are not encouraged to understand that the number 435 is made up of a 400, 30, and 5. Instead, this number just appears as a 4, a 3, and a 5, and that is how students work with it. They are simply performing the series of steps – adding a column and carrying if needed.

When you use front end addition, or left-to-right addition, students possess real understanding. To use this strategy, you add from left to right. So first you add the hundreds (400+200) to make 600. Then you add the tens (30+70) to make 100. Then you add the ones (5+8) to make 13. Lastly, you add 600+100+13 to make a sum of 713. I realize that this sounds like a lot of work and the illustration below looks confusing. But if you begin doing this, you will find that all of these steps happen in your head in a matter of a few seconds. It is effective, efficient, and it promotes real number sense understanding. This is SO important.

If you’d like resources that include the Front End Addition Strategy, I’ve included a few of my best-sellers below.

The Addition Station is a best-selling resource for teaching addition strategies. You’ll find the front end addition strategy in the upper grades Addition Stations. These Math Stations are self-paced, student-centered stations for the basic math strategies. Students move through the levels at their own pace, ensuring that they are always challenged, and working to their full potential. You’ll find that your students BEG you to do this (not joking)! Find the 1st and 2nd Grade Addition Stations HERE, and the 3rd and 4th Grade Addition Stations HERE.

This mental math strategy unit is designed ONLY for the Front End Addition strategy. Read more about exactly what’s included by clicking HERE or on the image below:

The Front End Addition unit is also included in the Mental Math Addition Collection, which can be found HERE or by clicking on the image below. This collection includes units for six of the most effective mental math strategies.

## 10 Comments

Thanks so much for your post. You answered some questions that I had been searching the web for. 🙂

Do you find that this strategy confuses students as they begin to subtract?

Hi Monica! No, not at all! Using mental math strategies actually improve understanding because students better understand what the numbers really mean. In subtraction, there is a similar strategy called Expanding the Subtrahend. You can see my You Tube video about it here: http://www.youtube.com/watch?v=tI5AXWGqb_w

Have a great evening,

Shelley

I have aced Calculus and Matrix Transformations in college, and been a computer programmer for 30 years, and I feel DUMBER after reading these ridiculous techniques.

If you feel dumber after reading these "ridiculous techniques," you obviously have never taught math to a diverse group of young learners. Congratulations for acing Calculus and Matrix Transformations and for being a computer programmer for 30 years. You are in an infinitesimal percent the world's population. While you are very lucky that math skills come easily to you, they certainly do not for everyone. Most children that I work with need strategies to be explicitly taught to them in order for them to be successful in math. You should be ashamed of yourself for insulting someone who dedicates so much of her free time (and own money, I am sure) providing resources to help CHILDREN.

Thank you for your time and for sharing your techniques. I have been looking for a way that I could use to back up my boys and girls learning from school while using my understanding of maths. What you have provided here works well for me.

we certainly teach this strategy for all 4 operations but we call it the partial products or splitting method. It is a fantastic way for students to break numbers into smaller (or easier) parts mentally and then perform the operation. Love it!

The ancient Greeks used not only front end addition, but front end multiplication. Examples are given in “A Manual of Greek Mathematics” by Sir Thomas L. Heath (Oxford University Press, 1931, still in print from Dover Publications), p. 29-32. I ran into a method of doing front end arithmetic for the first time many years ago in middle school, in the early 1960s, reading the regular math article in “Science and Math Weekly” (SMW) which I got at school while other kids were reading My Weekly Reader, Junior Scholastic, etc. Heath’s book gives some examples from Eutocius’ commentary on Archimedes. The SMW article noted our common method of long division is already front end arithmetic, and Heath gives an example of division from Theon of Alexandria, and even gets into extraction of numerical square root. Yes, students SHOULD reach for their calculators on tests, because the objective is to get a correct answer, and get it quickly; but they should all know HOW to do these operations by hand, or mentally – better to understand what they are doing.

Love your posts! Have a lot of ‘a-ha!’ moments after reading them! Thanks for creating them and sharing them 😁👍