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The Common Core – Operations & Algebraic Thinking

by Early Math Counts

The 2nd section of the Kindergarten Mathematics Core is called “Operations & Algebraic Thinking” which sounds daunting, to say the least.  However, once you actually read the content, you will see that it is only focused on Adding and Subtracting (not really sure why they don’t just say that.)

Understand addition, and understand subtraction.

  • CCSS.Math.Content.K.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
  • CCSS.Math.Content.K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
  • CCSS.Math.Content.K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
  • CCSS.Math.Content.K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
  • CCSS.Math.Content.K.OA.A.5 Fluently add and subtract within 5.

1 Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)


I appreciate the authors’ intent in this standard as they have clearly limited the learning outcomes for kindergarten-aged children by specifically restricting the range of numbers that children should be able to compute to and from.  Keeping it within a manageable range recognizes the complexity of the standard and manages expectations of children.

In the early childhood world, we explore this algebraic thinking (simple addition and subtraction) through songs and finger plays (5 Little Ducks Went Out One Day, 5 Green and Speckled Frogs, Way up High in the Apple Tree) using our fingers as visual cues to help children see one less duck or frog by folding our fingers down.  Usually, children still need to count the fingers that are still out as they are not quite able to “take away” yet. “Taking away” requires that children can go backward – but remember, many young children have simply memorized the numbers in order but reversing the order is very hard to do.

Simple addition using objects should be introduced during play.  If children are playing with blocks and they need “1 more”, be sure to verbalize that, reinforcing the vocabulary and the concept that “1 more” is “adding 1” to the set.  Keep it simple with numbers under 5.  If you find that you have children who are grasping this fairly well, broaden the number range to 10.

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