Part-Whole Fraction Reasoning
A fraction names equal parts of a whole that equals one; from a part you can find the whole, the remaining fraction, or a fraction of a number. Learners partition equally, see a fraction as a count of unit fractions, and recover the whole from a given part. This part-whole model is the foundation of all fraction operations.
grade 3–6 GeometryFractionsOperations Draw a DiagramCreate a Physical Representation
Progression (13)
g4 1. A fraction is a count of unit fractions Fractions
g3 2. Fractions require equal partitioning of the whole FractionsGeometry
g3 3. The whole is one; find the remaining fraction Fractions
g3 4. Recover the whole from a fractional part FractionsOperations
g3 5. Split a whole into proper-fraction portions FractionsOperations
g5 6. Sum fractional parts of a whole Fractions
g5 7. Fraction of a quantity by multiplying Fractions
g5 8. Map length equals real distance times scale FractionsMeasurement & data
g5 9. Whole as 1: find remaining fraction Fractions
g5 10. Find the whole from a fractional part Fractions
g5 11. Bouncing ball: repeated fraction-ratio heights Fractions
g5 12. A fraction of a quantity equals whole times fraction Fractions
g6 13. Get the whole from a fractional part Number systemRatiosExpressions
Bridges to competition (2)
Reasoning problems that extend this idea toward competition:
Name shaded part as a fraction Other
Shade a fraction of a shape Other