Find Two Unknowns from Sum and Difference
When two unknowns are tied by their sum and their difference (or one relation expressing one in terms of the other), rewrite everything in a single unknown and solve. The structure recurs across lengths, weights, capacities, decimals, rectangle sides, and angles. Reducing to one unknown is the gateway to algebraic thinking.
grade 2–6 Measurement & dataBase-ten numbersOperations Convert to AlgebraIdentify Subproblems
Progression (13)
g2 1. Find two lengths from sum and difference Measurement & data
g3 2. Reduce to one unknown to solve OperationsBase-ten numbers
g3 3. Reduce relations to a single-unknown equation Operations
g3 4. Find a rectangle side via one unknown Measurement & dataOperations
g3 5. Set up one-unknown equation for capacities Measurement & dataOperations
g3 6. Combine sum and difference of two weights Measurement & dataOperations
g4 7. Set up an equation with one unknown angle Measurement & data
g5 8. Eliminate to find two decimals from sum and difference Base-ten numbers
g6 9. A balanced scale means both sides are equal Expressions
g8 10. Add or subtract equations to eliminate unknowns Expressions
g4 11. Same numerator: smaller denominator is larger Fractions
g6 12. Write it as an equation with a single unknown ExpressionsNumber system
g7 13. Name both unknowns and write two equations Expressions
Bridges to competition (2)
Reasoning problems that extend this idea toward competition:
Deduce weights from several balances Logic
Find each digit from sum and difference Number arrangement