Non-routine problem solving (Grade 6)
What Grade 6 tests
Grade 6 non-routine problems mix rates, proportional reasoning, and integer arithmetic. A rate problem is safe if you write the units: km/h, L/min, pages/day. Cancelling units tells you whether to multiply or divide.
Core rules
- Rate: rate = amount ÷ time. Rearranged, amount = rate × time and time = amount ÷ rate.
- Average speed: total distance ÷ total time. It is not the average of the two speeds when the times differ.
- Work rates add: if one pipe fills a tank in 6 h, its rate is 1/6 tank per hour; a second pipe at 1/4 tank per hour gives a combined rate of 1/6 + 1/4 = 5/12, so the time is 12/5 = 2.4 h.
- Proportional scaling: multiply or divide both quantities by the same number; set up a ratio table rather than guessing.
Worked example
A car travels 240 km at 60 km/h and returns along the same road at 40 km/h. Find the average speed for the whole trip. Outward time = 240 ÷ 60 = 4 h. Return time = 240 ÷ 40 = 6 h. Total distance = 480 km; total time = 10 h. Average speed = 480 ÷ 10 = 48 km/h. The trap answer is (60 + 40) ÷ 2 = 50 km/h, which is wrong because the car spends more time at the slower speed. Answer: 48 km/h.
Traps
- Averaging speeds instead of using total distance and total time.
- Mixing minutes and hours in one calculation.
- Forgetting the return trip doubles the distance.
- Rounding a rate too early and carrying the error into the final answer.