Fractions as parts of shapes

CONCEPTUAL

Mathematics›Fractions|Ages 8—9|ID: mt_idbKDrf9qZ

Partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole

Mastery Evidence

Partition a rectangle into 6 equal-area parts and label each 1/6
Show two different ways to partition a square into 4 equal parts
Given a pre-partitioned shape, write the unit fraction for one part

Assessment Prompt

“If you ask [child] to fold a square piece of paper into 8 equal parts, can they tell you what fraction of the whole square each part represents?”

Prerequisites2

Fractions of a whole
hardAges 8—9
Splitting shapes into equal parts (age 7+)
hardAges 7—8

Show full prerequisite tree

Fractions of a whole hard
Must understand unit fractions to express area parts as 1/b
- Fractions of amounts hard
  Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
  - Finding halves and quarters (age 5+) hard
    Working with 1/4, 2/4, 3/4 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
    Working with fractions 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'
  - Division as equal sharing soft
    Finding fractions of quantities uses equal sharing (division)
    - 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'
  - Fraction Notation hard
    Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
  Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
  Partition into equal shares is prerequisite to understanding unit fractions
  - Decomposing a shape into more equal shares hard
    Understanding equal shares of different shapes requires concept of more shares = smaller
    - 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'
  - Halves & Quarters of Shapes hard
    Extends partitioning from halves/fourths to include thirds
    - 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'
Splitting shapes into equal parts (age 7+) hard
Prior partitioning experience feeds into area-fraction work
- Decomposing a shape into more equal shares hard
  Understanding equal shares of different shapes requires concept of more shares = smaller
  - 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'
- Halves & Quarters of Shapes hard
  Extends partitioning from halves/fourths to include thirds
  - 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'

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