Word Problems — Distance, Rate, Time

d = rt is elementary's bridge from arithmetic to algebra. One equation, three variables — solve for any. Indirect aim: algebraic problem setup, unit awareness, preparation for physics.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Word Problems
• Level: Ages 8-10

Objectives

• Apply the formula d = r × t
• Solve for any one variable given the other two
• Handle unit conversions (km/h, m/s)
• Set up and solve real-world motion problems

Materials

• Problem slips
• Formula chart (d = rt, r = d/t, t = d/r)
• Calculator
• Real maps and schedules

Instructions

1. Present: a car drives 60 km/h for 2 hours — distance? d = 60 × 2 = 120 km. 2. Present: 300 km in 4 hours — rate? r = 300/4 = 75 km/h. 3. Present: 150 km at 50 km/h — time? t = 150/50 = 3 h. 4. Unit conversion: 60 km/h = 60000 m/3600 s ≈ 16.7 m/s. 5. Round-trip problems. 6. Two cars meeting. 7. Real schedule: compute travel time between cities. 8. File solutions.

Educator tip

The formula triangle (d on top, r and t below) is a mnemonic. Cover the unknown variable to get the formula.

Assessment

Observe formula setup, unit handling, and multi-step problem solving.

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