№ 002 · Mathematical literacy · Formulate
Is a travel pass worth it?
Students turn an everyday situation into a mathematical problem, compare two ways of paying and justify a decision.
Material for students
Aliya takes the bus to school
A single ride costs 200 tenge. A monthly pass costs 4,000 tenge and allows unlimited rides for the month. On school days Aliya rides to school and back. There are 22 school days in a month.
In summer Aliya only goes to a club twice a week (there and back).
Illustrative prices.
Questions
Teacher's guide
Skill: translating a real situation into mathematics (formulate), calculating (employ) and taking the result back to the situation (interpret).
Full answer: 1) 22 × 2 × 200 = 8,800 tenge, which is 4,800 tenge more than the pass, so the pass is better. 2) 21 rides: 4,000 ÷ 200 = 20, so at 20 rides both cost the same, and from 21 rides the pass is cheaper. 3) In summer about 4 weeks × 2 × 2 = 16 rides = 3,200 tenge, which is cheaper than the pass; convenience may still affect the decision.
Typical mistake: forgetting the return trip (counting 22 rides) or answering question 2 with “20”: at 20 rides both options cost exactly the same.
In your subject
Economics
Compare mobile phone plans or gym memberships.
Physics
Compare travel time and speed for different kinds of transport.
Computer science
Solve the problem with a spreadsheet or a simple program.
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