Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.


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Unpacking the Standard: 2.G.A.3
Student Friendly Learning Target: 2.G.A.3


Students will recognize the "part-whole" relationship in whole pieces and their fractional parts. Students should describe and partition a whole into two halves, three thirds, etc. within the shapes of circles and rectangles and refer to these pieces with that language. At this grade level, students should not be using the formal symbols of “½”, “1/3”, and “¼”.

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, thirds, and fourths pieces 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 make partitions of circles and rectangles write the words (whole, halves, thirds, and fourths) with each picture and concrete representations.
    • Introduce real-life examples of the part-whole relationship through such experiences as cutting a pizza, pie or large cookie cake. 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.
    • Students should compare their ways of partitioning shapes, and then ask whose half (or third, etc.) is bigger.  

      Questions to Focus Instruction:


        • Can my students recognize that a whole circle that already existed before partitioning is still there, as 2 halves, 3 thirds, or 4 fourths?
        • Do my students understand that by separating a circle into more pieces, it yields smaller pieces of the whole?
        • Can students use grid paper to divide a shape into equal pieces that are not the same in shape?
        • Can students compare a fourth, a third, and a half and place them in order of size?
        • Can students partition circles and rectangles into a given number of equal shares, and use the correct vocabulary to describe their actions?



          Prior to: Students are able to correctly identify 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. See 1.G.A.3.

          At Grade Level:
          Students will identify wholes, halves, thirds, and fourths as fractions of rectangles and circles that represent the relationship between the parts and the whole.

          Moving Beyond:
          Students will express a section of a whole shape as 1/2, 1/3, or 1.4. Further, they will identify equivalent fractions and compare fractional pieces with one another. See 3.G.A.2 for progression.