How to Teach Adding and Subtracting Decimals
In 6th grade, my math students have typically come to me knowing the ‘rules’ for adding and subtracting decimals.
However, when the number of digits in the numbers they’re adding or subtracting aren’t the same, they don’t necessarily line the numbers up the way they need to…even though they ‘know’ the rules. Why is this?
I believe it’s because they really don’t understand the point of ‘lining up the decimal points.’
My belief is reinforced by student comments I collected one year as we began our decimal operations unit.
I asked my 6th grade math students to solve 35.2 + 7.489 and then explain why their answer made sense. These are a few of their responses:
- “0.11009 makes sense because I tried my best and if I remember correctly, addition problems you don’t need to line the decimals together”
- “0.7838 makes sense because when I added I knew that it doesn’t matter how it’s lined up”
- “7.841 makes sense because with adding you only have to add the decimals on the top. Then you add and finally add the decimal back in.”
- “79.41 makes sense because you do it just like an addition problem (that’s how I remember it anyway)”
- “42.689 – this makes sense to me because this is how I learned it. You do simple addition, but line up the decimal points”
- “42.689 makes sense because I used what my fifth grade teacher taught me, line up decimals, add zeros so everything is lined up and then solve.”
- “42.689 – I don’t know how it makes sense, but it’s how I learned to do it.”
Of the 120 students in my classes, only 8 said the answer made sense because “35 + 7 is 42” or because “I estimated” or “when we’re doing addition, we know we end up with a bigger number.”
I don’t want to assume that students who didn’t write this didn’t think about those things at all, but to the majority of students, their answers “made sense” when they followed the rules – even if they didn’t remember the rules correctly.
What’s the Point?
Lining up the decimal points helps us line up the place values so that place values are added with or subtracted from ‘like’ place values.
If students don’t understand the point of lining up the decimal points when adding and subtracting decimals, then somehow they’ve missed the idea of place value.
And what do we do if they numbers don’t even HAVE a decimal point?? (Some students get pretty lost when that happens.)
Start With Estimating When Adding or Subtracting Decimals
- Identify the whole numbers in the problem and add them together (or subtract), to get an estimate. If necessary, students should circle the whole numbers.
- Line up the whole numbers according to their place value (ones place with ones place, tens with tens). If the whole numbers are lined up correctly, the decimals will automatically be lined up (and if students have a problem like 50 – 9.625, lining up the 0 and 9 in the ones places will put the decimal points in the correct place.
- Add a decimal point if needed (for whole numbers) and annex zeros so the decimal part of the numbers have the same place values.
- Complete the operation.
- Compare the answer to the estimate to see if the answer is close.
Tools for Teaching Decimal Addition and Subtraction
I include this in my unit notes and practice, and I also use math wheels for note-taking.
The math wheels break the processes into steps and allow room for examples and practice. They also give students a chance to color-code, doodle, color, and add memory triggers to their notes. Then they can keep them in the notebooks all year for reference.
A couple practice decimal activities:
There are a couple free decimal activities found in the blog posts linked below that I’ve used to give my students some additional decimal operations practice.
Decimal Operations Problem Solving
Decimal Practice with Number Puzzles
What are your tried and true methods for how to teach adding and subtracting decimals?
Resources to Practice Adding and Subtracting Decimals: