Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)



The two properties of addition (commutative and associative) serve as strategies to help students fluently solve problems. Taught strategies such as “Fact Families” and “Making 10” are applications of the commutative and associative properties (respectively). The commutative and associative properties do not hold for subtraction, and this can be easily demonstrated. To make use of these properties in subtractive problems, students can be taught the “think addition” method for subtracting.

Understanding the Standard:

  • Teach the concept of fact families.
  • When adding, students can look for ways to “make 10” in order to make computing sums and differences easier. For example, to add 2+6+4, using the associative property to first add 6+4 allows for the expression to become 2+(6+4) = 2 + 10 = 12.
  • Students do not need to know the specific names of properties, however, practice in using the processes within those properties will benefit their learning in later grade levels. For example, if 8+3=11 is known, then 3+8=11 is also known.

    Questions to Focus Instruction:

    • Can students reason that addition and subtraction are relational, in that there are “families” of facts?
    • Can students employ a variety of strategies to find sums and differences?
    • Can students communicate the reasoning behind the strategies they used in computing sums and differences?
    • Are students able to show with visuals and concrete models the processes in their computation using the properties?


      Prior to: Students are able to demonstrate an understanding that “adding or counting on” involves addition and that “taking away” or “breaking apart” involves subtraction. Students can add and subtract fluently through 10.

      At Grade Level:
      Students will add and subtract fluently showing a variety of methods and strategies in computing the sums or differences. Students demonstrate an understanding that quantities on both sides of the equal sign must be identical.

      Moving Beyond: Building upon their previous mastery, students will employ the properties of addition and subtracting when computing sums and differences through 100, even when regrouping is necessary. Students may look for ways to make numbers other than 10, such as 50 or 100, in larger sums. Go to 3.OA.B.5 to the progression of related skills.

      2Students need not use formal terms for these properties.