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Operations & Algebraic Thinking


Kindergarten students are introduced to addition and subtraction with small numbers, and they work toward fluency with these operations for numbers within 5.


Kindergarten students develop their understanding of addition and subtraction by making sense of word problems. Students experience a variety of addition situations that involve putting together and adding to and a variety of subtraction situations that involve taking apart and taking from.


Students use objects (such as two-color counters, clothespins on hangers, connecting cubes, 5-frames, and stickers), fingers, mental images, sounds, drawings, verbal explanations and acting out the situation to represent these operations.


Word problems with real-life applications provide students with a context to develop their understanding of addition and subtraction. Kindergarten students learn that addition is putting together and adding to and subtraction is taking apart and taking from. Kindergartners use objects or math drawings (with simple shapes such as circles) to model word problems.

The end of kindergarten expectations include the following:


  • Representing addition and subtraction using a variety of objects, sounds, and behaviors such as clapping or acting out situations

  • In the context of word problems, add and subtract within 10

  • Decompose numbers less than ten into pairs in more than one way (e.g. 5 = 2 + 3 and 5 = 4 + 1)

  • For any number less than ten, find the number that makes 10 when added to the given number

  • Fluently add and subtract within 5

Vocabulary List:


Here is a list of important vocabulary words, from the California Mathematics Frameworks, that children can learn to use correctly by the end of their kindergarten year.


  • Bigger

  • Smaller

  • Add

  • Subtract

  • Take away

  • Addition

  • Subtraction

  • Adding

  • Subtracting

  • Make 10

  • All together

  • Equals

  • The same as

  • In all

  • Total

  • Amount left

What it looks like:


How can you tell if a child understands these concepts? Here are some examples of children demonstrating an understanding of operations and algebraic thinking at this grade level:


  • A child expresses understanding that adding more blocks to his pile results in a bigger pile

  • A child adds 4 red blocks to 3 green blocks and recognizes that she now has 7 blocks altogether


California Early Math Project