Monday, January 28, 2013

Strategies for Adding and Subtracting Decimals

By Cassandra Hatfield, RME Assessment Coordinator

Why is it that many kids struggle when adding and subtracting decimals? After working as a math specialist in elementary schools, I have some theories about why students that I taught in middle school often struggled with this concept.

When an elementary student is asked to solve 36 + 4, some strategies I have seen include:
Counting On
Making 10
The US Standard Algorithm
How would a child’s strategy change if we asked them to solve 3.6 + 0.4? The truth is, it should not:
  • Counting on: If the student understands that tenths increase just as the ones place increases, they can still do this strategy.
  • Making 1: Have you ever thought to relate making 10 with whole numbers to making 1 with tenths? Or making 100 with whole numbers and making 1 with hundredths? Consider teaching a lesson comparing the ways to make 10 with the ways to make 1 using tenths and the ways to make 100 using hundredths, or even tenths and hundredths. This will support students in solving with mental math instead of the standard algorithm.
  • The standard algorithm: Let’s be truthful, when solving the whole number problem 36 + 4 with the standard algorithm, would you “line up the decimals?” Technically, yes. However, you weren't aware because the decimal was not visible. If students are taught to add whole numbers with the standard algorithm by “lining up the place values,” we can teach the same principal as it applies with decimals. The standard algorithm was invented to create an efficient uniform way of computing. The common theme in using the standard algorithm in addition and subtraction is that the place values are lined up. This ensures that the computation is accurate. This same principle applies when students add 3.6 + 0.4 - without a deep understanding of place value many students misplace the decimal point.
  • In early elementary, students practice counting around the class or by multiples of whole numbers. Have you ever thought about counting around the class by increments of decimals?

Assessing Decimal Addition and Subtraction
In Teaching Elementary and Middle School Mathematics (2013), a suggested activity for formative assessment is to ask students to compute the sum of a problem involving different numbers of decimals places.
For Example:
75.35 + 4.7 + 0.671
For this assessment, interview students estimating the sum and then computing the exact answer. The goal of this assessment is to record “whether they are showing evidence of having an understanding of decimal concepts and the role of the decimal point. Note whether students get the correct sum by using a rule they learned in an earlier grade but have difficulty with their explanations. Rather than continue to focus on how to add or subtract decimals, struggling students should shift their attention to basic decimal concepts.”

Summing It All Up
If we place more value on mental math strategies, as well as lining up the place values when computing with the standard algorithm,  students may develop a deeper understanding for the skill.

Van de Walle, J. A., Karp, K. S., Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally. Upper Saddle River, NJ: Pearson Education, Inc.


  1. Thinking about the "value of the place" seems to be the way that we need to pose to our students. Knowing conceptually that adding parts of a number to parts or whole of another number. Students must be able to connect the numbers to the visual of the meaning.

  2. love this. It really explains further to the public about knowing how to add/subtract decimals


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