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.
Rewritten readings were written for this dataset.
2 · Watch
Take it off screen
Where it sits
Learn first
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
20 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.