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 2–4 MDNBTOA Convert to AlgebraIdentify Subproblems
Progression (8)
2-2 1. Find two lengths from sum and difference 2.MD.B.5
3-1 2. Reduce to one unknown to solve 3.OA.D.83.NBT.A.23.OA.A.4
3-1 3. Reduce relations to a single-unknown equation 3.OA.D.83.OA.A.3
3-2 4. Find a rectangle side via one unknown 3.MD.D.83.OA.A.4
3-2 5. Set up one-unknown equation for capacities 3.MD.A.23.OA.D.8
3-2 6. Combine sum and difference of two weights 3.MD.A.23.OA.D.8
4-1 7. Set up an equation with one unknown angle 4.MD.C.7
4-2 8. Eliminate to find two decimals from sum and difference 5.NBT.B.7