Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.




Students should represent the concepts of addition and subtraction by using visual images, making sounds to represent objects (such as with rhythm sticks), expressing situations verbally, or acting out situations in order to create a real-world model of an arithmetic fact.

Understanding the Standard:

  • Early learners need a wide assortment of visual cues to help them make the connection between the abstract concept of addition and the concrete result. This can be accomplished by providing them with situations where objects are added to an existing set or two separate sets are combined.
  • Further, students need hands-on practice and visual cues for subtraction by taking from a set or taking a set apart.
  • Establishing the meanings of the vocabulary words “addition” and “subtraction” is critical.
  • The use of manipulatives and technologies is very useful at this age: hands-on activities make such an abstract concept more concrete in nature. For this standard, students will benefit from the opportunity to put manipulatives together or take sets of manipulatives apart.
  • Situations that involve real-life encounters or everyday objects will help students to engage in the learning process.
  • Teachers need to provide opportunities for students to model with verbal and visual cues, such as drawings and the acting out of these situations.
  • Teachers should represent a situation with an expression or equation after it has been modeled with manipulatives, a drawing, or a situation. This will help students make the connection between real-world objects and the more abstract symbolic representation.

Questions to Focus Instruction:

  • Are students able to draw or create a visual representation of an addition or subtraction problem?
  • Do students understand that addition means that something is added to a set or that individual sets are combined and the quantity has increased in value?
  • Do students understand that subtraction means that something is taken away from a set, or that the set is taken apart, and that the quantity in the set has decreased?


Prior to:
Students are able to combine objects together or take objects away from a set even without understanding that they are adding and subtracting.

At Grade Level: Students can assign a numerical value to a group of sorted objects. Students can represent addition and subtraction by putting objects together and taking them apart.

Moving Beyond:
Students will be read a mathematical word problem and can determine what operation(s) should be used by making sense of a given situation and deciding whether putting together, adding to, taking from, etc.will solve the problem.

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