Modelling Situations with Formulae and Graphs
Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations
What a learner can do afterwards
- Translate a word problem or real-world situation into an algebraic expression or formula
- Construct a table of values from an algebraic rule
- Plot the corresponding graph and interpret it in the context of the problem
1 · Read
A formula is a short rule written with letters and numbers. It lets you turn a real situation into maths you can calculate. If one quantity depends on another, like cost depending on distance, you can write that link as a formula.
A taxi charges £2 just to start the ride, plus £1.50 for every mile you travel. Let m stand for the number of miles. The total cost is c = 2 + 1.5m. Check it for 4 miles: c = 2 + 1.5 × 4 = 8, so the ride costs £8.
To draw the graph, plot each pair of numbers as a point: miles across, cost up. The points form a straight line because the cost rises by the same £1.50 each time. Where the line crosses the cost axis shows the starting fee, and how steep it is shows the price per mile.
A word problem becomes a formula, the formula becomes a table, and the table becomes a graph you can read.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.