Work Backwards to Recover a Start Value
Given the end state of a chain of operations (or a calculation done wrongly), invert each step in reverse order to recover the original number or position. It begins with undoing simple add/subtract or skip-counts, then reversing a wrong product, undoing geometric moves, and unwinding multi-step decimal and fraction operations. Inversion is the universal 'the result was...' strategy.
grade 2–4 GeometryMeasurement & dataBase-ten numbersFractionsOperations Work BackwardsConvert to Algebra
Progression (9)
g4 1. Skip-count backward to the start Base-ten numbers
g3 2. Recover the unknown, then recompute Operations
g2 3. Undo more/less to find original length Measurement & data
g3 4. Reverse the operations to find the start Operations
g3 5. Recover the original number from a wrong product Operations
g4 6. Reverse the moves to recover original Geometry
g4 7. Undo a wrong fraction operation to recover the start Fractions
g5 8. Reverse decimal operations to recover the start Base-ten numbers
g5 9. Undo a wrong decimal operation to recover the start Base-ten numbers
Bridges to competition (7)
Reasoning problems that extend this idea toward competition:
Work backwards from the result Logic
Fraction word problems via backward reasoning Other
Work backwards in fraction word problems Other
Measure a target in fewest pourings Optimization
Measure a target with unmarked jugs Logic
Find the unknown by working backwards Logic
Recover the starting number Number arrangement