Compare fractions by benchmark, by common numerator, by common denominator, or by distance from one.
RAT.COMPARE_FRACTIONS“I can order fractions and explain my reasoning without always finding a common denominator.”
Order 5/8, 3/5, 7/12, and 4/7 and justify at least two comparisons by reasoning rather than computation.
| Course | Unit | Depth | Role | Checkpoint |
|---|---|---|---|---|
| Grade 3 | Unit fractions | intro | introduce | ✓ |
Nothing in the atlas depends on this yet.
Equal-length bars split into halves, thirds, fourths… stacked for direct comparison.
Equivalence is seen before it is computed.
engine: stacked segmented bars with snap comparison
A measured line for locating, comparing, ordering, and jumping between numbers.
One representation carries whole numbers, fractions, integers, and irrationals.
engine: axis scene + tick generator + hop actor
Scene archetype: fraction_bar
RAT.CMP.BIGGER_DENOMSays 1/8 > 1/3 because 8 > 3.
Repair: Cut the same strip into 3 and into 8 and compare one piece each.
One row per instructional system. Rows marked cluster carry authored treatment for this family of topics; rows marked template are derived from the system’s general pattern and are not topic-specific research. Confidence is recorded on every row.
Fractions are defined from the unit fraction: 1/b is one part of a whole split into b equal parts, and a/b is a copies of it. The number line is required from Grade 3 precisely so that a fraction is understood as a number rather than a shaded picture.
Fractions are introduced with fraction bars and immediately linked to the bar model, so the same rectangle used for whole-number word problems now carries fractional parts. Equivalence is seen on a wall of stacked bars before it is generated by multiplication.
Fractions arrive with the language of parts and shares embedded in problems from the start ("two fifths of the pupils"), so a fraction is met as an operator on a quantity as much as a number. Comparison is argued structurally rather than by converting everything to decimals.
Fractions appear as notation to be manipulated from Level D onward, beginning with reducing and converting between improper and mixed forms. Meaning is not addressed; the learner acquires the rules by graded repetition and then applies them.
The unit fraction is established through a lesson in which the class must agree what the whole is, since the same piece is one half of one thing and one quarter of another. The tape diagram then makes the whole explicit in every subsequent problem.
Fractions are defined, the rules for equivalence and reduction are stated, and practice sets drill them, with fraction circles used illustratively rather than as a reasoning tool. The topic recurs in mixed review long after the unit ends.
Fraction circles and skittles let a child physically divide a whole and name the parts, with the insets making it obvious when parts are unequal. Equivalence is discovered by fitting pieces together rather than by a rule.
Fractions are approached as an extension of the number system with questions about density and ordering that graded curricula skip, and comparison problems are chosen so that finding a common denominator is the slow route.
Fractions are built with fraction walls and bar models across Years 2-6, with a strong emphasis on fractions of a set as well as of a shape, and on placing fractions on a number line. Variation exercises hold the whole constant while the partition changes.
Units build from partitioning tasks to locating fractions on a number line, with equivalence argued from partitioned diagrams before any generating rule appears. Comparison strategies are elicited and compared rather than prescribed.