Math - 2018-19

K.5 - Fractions

The student will 

  • investigate fractions by representing and solving practical problems involving equal sharing with two sharers.

Adopted: 2016


  • So that I can experience equal sharing to help me develop a deeper learning for later learning of fractions

  • So that by understanding equal sharing I can think about sharing food among friends, dividing up materials and cooking


  • Practical situations with fractions should involve real-life problems in which students themselves determine how to subdivide a whole into equal parts, testing those parts to be sure they are equal, and using those parts to re-create the whole.
  • Fractions can have different meanings: part-whole, division, measurement, ratio, and operator.  The focus of this grade level is to develop the idea of equal sharing (division) and part-whole relationships.  Fraction notation will be introduced in grade two.
  • Young children understand equal sharing problems intuitively because of their experiences sharing objects with siblings, friends, etc.  Consider the following examples:
    • Two children sharing six sandwiches
    • Two children sharing one sandwich
    • Two children sharing four brownies
  • For two children sharing one sandwich, a child might say that each will get half of the sandwich.  For two children sharing four brownies, a child might say they each will get half of the brownies, while another child might say they will get one of the two pieces. 
  • Teachers should use vocabulary such as halves.  Students may name the parts as halves but may also use language such as “one piece out of the two pieces” to describe half.  Students at this level should not be expected to use fraction vocabulary or notation. Informal, integrated experiences with fractions at this level will help students develop a foundation for deeper learning at later grades. Understanding the language of fractions furthers this development.
  • Students should be encouraged to create drawings or use concrete objects or other representations to solve problems.
  • Fraction models at this level should be able to be continuously divided (e.g., cookies, brownies).  It is important to use models that can be continuously divided when there are remainders so those remainders can be cut into as many equal parts as needed.
  • In each fraction model, the fractional parts must be equal shares of a whole.
  • Equal parts may be different shapes but maintain the same value (e.g., a sandwich could be cut in two equal pieces vertically, horizontally, or diagonally to represent halves).
  • The fraction name half tells the number of equal parts in the whole.


The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

  • Share a whole equally with two sharers, when given a practical situation.
  • Represent fair shares concretely or pictorially, when given a practical situation.
  • Describe shares as equal pieces or parts of the whole (e.g., halves), when given a practical situation.

Updated: Aug 22, 2018