Chapter 2 · Measurement and Problem Solving
2.11Numerical Problem-Solving Strategies and the Solution Map
10 min · two checks
Predict
What belongs on a solution map before any arithmetic?
The idea
- Draw a solution map for a multistep problem.
- Apply Observe, Plan, Compute, Check in order.
A solution map is a one-line sketch of the unit path. For “what is the mass of 2.50 L of a liquid whose density is 0.880 g/mL?” the map is liters → milliliters → grams, with factors 1000 mL / 1 L and 0.880 g / 1 mL. Drawing it stops you from multiplying by density when you needed to divide, because the units will not land on grams if the factor is upside down.
The same four beats work for almost every numerical section after this one. Observe the givens and the wanted unit. Plan the map. Compute left to right with cancellations visible. Check significant figures and whether the size is sane. When a later chapter feels new, it is often this chapter wearing a chemistry costume: moles, gases, and solutions are unit conversions with extra equalities.
Keep these
- Map the units before you calculate.
- Observe, Plan, Compute, Check — in that order.
- Most later numerical work is a longer conversion chain.
Worked path
Milk has a density of about 1.03 g/mL. Find the mass, in kilograms, of 1.75 L.
Observe
Map: L → mL → g → kg.