Reason with shapes and their attributes

Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.





Students will recognize the "part-whole" relationship in representations of basic fractions such as 1⁄2 and 1⁄4 and be able to match the spoken, written, concrete, and pictorial representations of whole numbers, one- half, and one-fourth. Hexagons (and other easily partitioned shapes) provide a wonderful opportunity to introduce such fractional concepts. Mastery of this skill later prepares them for more sophisticated explorations with fractions.

Understanding the Standard:

    • Manipulatives such as circle fractions provide a wonderful opportunity to introduce the part-whole relationship that exists with fractions. Begin with the whole, half and fourths pieces to allow students to create a basic understanding of this concept. Allow students to explore using the fourths to make halves, and wholes in order to show the equal relationship among the pieces.
    • Allow ample opportunity for students to familiarize themselves with the written words (whole, halves, and fourths) with picture and concrete representations.
    • Introduce real-life examples of the part-whole relationship through such experiences as cutting a pizza, pie, large cookie, or cake into equal shares. The bigger the pieces, the fewer pieces are yielded. However, the more times the circle must be divided, the individual pieces become smaller in size. The same experience should be discovered with other shapes (square, triangle, rectangle, hexagon, etc.).
    • Students should be presented with opportunities to share 5 cookies among 4 people. This leads naturally into the splitting of a shape into fair shares.

      Specific Questions to Focus Instruction:

        • What activities can I provide that will allow for the exploration of wholes, halves, and fourths?
        • How can I provide experiences that will introduce the concept of part-whole relationships in shapes and as they relate to such operations as subtraction?
        • Can my students construct a whole circle using only halves and fourths?
        • Can my students communicate the relationship between the parts as related to the whole circle?
        • Do my students understand that by separating a circle into more pieces, it yields smaller pieces of the whole?
        • Can students divide a rectangle or a circle into 2 or 4 equal shares using playdough, or with pencil and paper?
        • Can my students accurately describe the shares using the words and phrases from the standard?
        • Can my students explain that if someone cuts a cookie into fourths and then ate the whole cookie, they ate 4 pieces of cookie?
        • Can students recognize that dividing a circle into two unequal pieces does not yield halves?
        • Can students cut a shape in half without being given a guide?
        • When looking at a shape divided into equal pieces, can students describe the pieces accurately using language like "halves" and "fourths"?
        • Can students observe that a fourth is half of a half? Can students see that depending on the whole, the same object may be viewed as either a half or a fourth?


          Prior to: Students have a basic knowledge of composing shapes using several of the same size shape.

          At Grade Level:
          Students are able to correctly partition pieces that represent wholes, halves and fourths. Students can create picture representations or drawings that depict these concepts as well. Additionally, students can use appropriate vocabulary to describe the relationship between the pieces and the whole.

          Moving Beyond: Students will identify other fractions, such as thirds or eighths, that represent the relationship between the parts and the whole. See 2.G.A.3 for progression.