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GA Milestones Math Grade 3 study materials
GA Milestones Math Grade 3 study resources

GA Milestones Math Grade 3: Primary fractions as equal parts and numbers

GA Milestones Math Grade 3 · Work through your exam, one topic at a time.

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Primary fractions as equal parts and numbers

Fractions

Fractions

These elementary fraction foundations develop understanding of fractions as equal parts of a whole and as numbers on a number line. Practise unit fractions, partitioning shapes, writing fractions, representing fractions on number lines, equivalent fractions with models, comparing fractions with the same numerator or the same denominator, and expressing whole numbers as fractions.

Core rules and concepts

  • A fraction such as 3/4 means 3 equal parts out of 4 equal parts in the whole. The denominator tells how many equal parts; the numerator tells how many parts are selected.
  • Equal parts matter: a shape split into 4 parts that are not equal does not show fourths.
  • On a number line from 0 to 1, the denominator tells how many equal intervals to make. For fourths, mark 0/4, 1/4, 2/4, 3/4, 4/4 = 1.
  • Equivalent fractions name the same point or same amount: 1/2 = 2/4 = 4/8 when the models show equal-sized wholes.
  • When denominators are the same, compare numerators: 3/8 < 5/8 because 3 same-size parts is fewer than 5 same-size parts.
  • When numerators are the same, compare denominators: 2/3 > 2/5 because thirds are larger than fifths, so 2 thirds is more than 2 fifths.
  • A whole number can be written as a fraction: 1 = 3/3 = 4/4; 2 = 6/3 = 8/4.

Worked example

Compare 2/3 and 2/5. Both fractions have numerator 2, so the numerators are equal. The denominators tell the size of the parts: thirds are larger than fifths because the same whole is split into fewer pieces. Two large thirds cover more than two smaller fifths. Therefore 2/3 > 2/5. A number-line check places 2/3 closer to 1 than 2/5, which is less than 1/2.

Traps that cost marks

  • Comparing denominators as if a larger denominator means a larger fraction. 1/8 is smaller than 1/3.
  • Counting tick marks rather than equal intervals on a number line. With a correctly divided unit, 2/4 is the second fourth-mark and equals one half.
  • Treating 4/4 as 0 or as 4; it equals 1.
  • Using unequal partitions to justify equivalence.
  • Writing the numerator and denominator in the wrong order when the model shows selected parts over total equal parts.