Are your students struggling with adding and subtracting decimals? It can seem so straightforward to us teachers, but it is a skill that has many misconceptions to combat. Let’s discuss common misconceptions and tips for teaching decimal addition and subtraction.
CCSS and TEKS
Let’s check out what the standards say about decimal addition and subtraction:
The Common Core State Standards are very specific while the TEKS are pretty vague, so I ran to a 2022 released STAAR test to see how 5.3(K) would be tested.
STAAR Test Question
I can make a couple of observations about what I notice in this problem:
- The decimals are out to the hundredths place.
- Students will need to fill in 0s. One of the addends is only to the tenths place while the other 2 are to the hundredths place.
- There are 3 addends.
- This problem is multi-step and requires both addition and subtraction to solve.
- The problem can be solved by just using the whole numbers and ignoring the decimal portion.
Common Misconceptions
The most common issue you will encounter with decimal addition and subtraction is students lining up the decimals incorrectly. That problem is only exacerbated when there is a whole number with no visible decimal point. Students want to line up numbers at the ones place like they have been doing for years. You will have to fight and correct this practice.
Tips for Adding and Subtracting Decimals
Use Models – The CRA Framework means starting with concrete models (try base ten blocks and rods) to physically engage with the addition and subtraction. You could even use coins to practice the problem below. Then I recommend moving onto 10×10 grids and then lastly, number lines so students can represent what is happening mathematically. As students practice, they can move onto the algorithm.
Decimal Point in a Whole Number – As mentioned above, students have previous knowledge of money and this is your best entry point for students placing the decimal in a whole number. I had an anchor chart in my classroom that was a little cheat for students. If I saw students misplace the decimal (for whatever reason, students want to place the decimal in the number 24 right in the middle and make it 2.4!) I would just point to the anchor chart.
Thank you to Lori on Facebook who said, “If the decimal’s not in sight, put it to the right!” Bless her for this little rhyme that makes this concept sticky!
Use Graph Paper – This visual is on the Maneuvering the Middle handouts, and it is a great way to keep your students’ work neat and organized. As students continue to practice, I would draw an arrow through the decimal points to show that they needed to be lined up. If you don’t use our materials, then I would recommend using (or printing) graph paper.
Estimate First – Similar to decimal multiplication, I teach students to check their work by estimating their answer using the whole numbers only. Not only is this a great way to check if their answer makes sense, but when I was looking at the 2022 STAAR released test, I realized that it reinforces the standard 5.3(A) “estimate to determine solutions to mathematical and real‐world problems involving addition, subtraction, multiplication, or division.”
Practice, Practice, Practice
Maneuvering the Middle has a plethora of activity bundles to help support adding and subtracting decimals:
What tips do you have for teaching adding and subtracting decimals?
