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Decomposing a shape into more equal shares

CONCEPTUAL
Mathematics›Fractions|Ages 6—7|ID: mt_hyvHv2BCwb

Understand that decomposing a shape into more equal shares creates smaller shares

Mastery Evidence

  • Explain that a quarter of a pizza is smaller than a half of the same pizza
  • Demonstrate that fourths are smaller pieces than halves
  • Compare the size of halves and quarters of the same shape

Assessment Prompt

“If a pizza is shared between 2 people and then the same pizza is shared between 8 people, can [child] explain why each slice is smaller when more people share it?”

Curriculum Standards1 alignment

1.G.3Common Core State Standards for Mathematics
Partition circles and rectangles

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.

G

Prerequisites1

Show full prerequisite tree
  • Halves & Quarters of Shapes hard

    Comparing share sizes requires experience partitioning into halves and quarters

    • Finding halves and quarters (age 5+) hard

      Partitioning into fourths/quarters extends from Y1 understanding of quarters

      • What Is a Half? hard

        Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4

        • Division as equal sharing hard

          Finding a half requires equal sharing into 2 groups — a division concept

          • Subtraction as taking away or separating hard

            Division as equal sharing/grouping requires understanding subtraction as taking away/separating

            • How Many in Total? hard

              Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

              • One-to-one counting hard

                Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

    • What Is a Half? hard

      Partitioning shapes into halves extends from Y1 understanding of halves

      • Division as equal sharing hard

        Finding a half requires equal sharing into 2 groups — a division concept

        • Subtraction as taking away or separating hard

          Division as equal sharing/grouping requires understanding subtraction as taking away/separating

          • How Many in Total? hard

            Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

            • One-to-one counting hard

              Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

Unlocks2