Model, solve, interpret
A contextual answer is complete only when the equations match the situation, the pair is solved, and the values make sense with units.
Learning goals
- Model age, cost, number and digit conditions.
- Choose and execute an efficient solution method.
- Interpret and validate the contextual answer.
Concept lesson
Four modelling checks
Define variables and units; translate each condition; keep meanings fixed; reread each equation in words.
Choose the shortest reliable method
Use substitution for an isolated variable; elimination for matching or easily matched coefficients; graphing when specifically requested or interpretation is central.
Context validation
Substitute into both original conditions, attach units and reject impossible values such as negative object counts, invalid digits or ages that contradict time conditions.
Model a two-digit number
Let x be tens digit and y units digit. The number is 10x+y and its reversal 10y+x. Translate the stated sum and reversal relation into two equations.
Solve an age model
For present ages x and y, apply every past or future shift to both people before forming equations; then use the method producing the fewest fractions.
Interpret the ordered pair
After solving a cost problem, write a sentence with rupees per item, substitute into both purchase totals and check non-negativity.
Reject an algebraically valid but impossible result
If a model for numbers of notes yields -3 notes of one denomination, identify whether the algebra, model or supplied conditions must be reconsidered and explain why the contextual answer is invalid.
Application answer structure
Define variables, form two labelled equations, solve with visible steps, and finish with a contextual sentence and check.
Exit ticket
A shop sells 3 notebooks and 2 pens for 94 rupees, and 2 notebooks and 5 pens for 106 rupees. Define variables, form and solve the pair, then validate both prices in context.