Primary Standards:

MAFS.2.G.1.3 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.

Content Knowledge:

Although the formal study of fractions does not begin until 3rd grade, 1st and 2nd graders work to develop foundational understanding about fractions as they engage in geometry investigations.  As they partition circles, squares, and rectangles and discuss what they see, they begin to internalize some of the language of fractions, e.g. half of, fourths, etc.

In 1st grade, students partitioned shapes into halves and fourths, in 2nd grade students will extend this to partitioning circles and rectangles into thirds.  2nd graders will also extend their knowledge of investigations and discoveries to conclude that as a shape is decomposed into more parts, the parts become smaller and smaller, equal shares don’t always look the same, and two halves, three thirds, and four fourths make a whole. Students should explore circles and rectangles partitioned in multiple ways to recognize that equal shares may be different shapes within the same whole.

GCG 1 – Learning Goal: As a mathematician, I can partition circles and rectangles into halves and fourths and name the parts

  • Step 1: Partition circles and rectangles into two equal parts. Use the vocabulary of half, halves, half of and two of to name the parts
  • Step 2: Partition circles and rectangles into four equal parts. Use the vocabulary of fourth, quarter, fourth of, quarter of, and four of to name the parts

GCG 2 – Learning Goal: As a mathematician, I can partition circles and rectangles into halves, thirds, and fourths and name the parts

  • Step 1: Partition circles and rectangles into three equal parts. Use the vocabulary of third, thirds, third of, and three of to name the parts
  • Step 2: Count by halves, thirds, and fourths to name parts and wholes
  • Step 3: Decompose circles and rectangles into halves, thirds, and fourths.  Compose wholes using parts

GCG 3 – Learning Goal: As a mathematician, I can create equal shares that are different shapes

  • Step 1: Partition rectangles in different ways so that the equal parts are different shapes
  • Step 2: Prove that different shaped halves, thirds, or fourths are the same size
  • Step 3: Solve problems about sharing wholes equally