Non-routine problem solving (Grade 7)
What Grade 7 tests
Grade 7 problems usually require a translation step: words to an equation, a diagram to an angle equation, or a counting problem to cases. Once the equation is written, solve it systematically and check whether the answer makes sense in the original story.
Core rules
- Define the variable explicitly: "Let s be the son's age now" is safer than "Let x be the answer."
- Translate in order: "is" becomes =, "more than" becomes +, "times as old" becomes multiplication.
- Solve systems by substitution or elimination. Substitution is faster when one equation already isolates a variable.
- Angle facts: straight line 180°, triangle 180°, vertically opposite angles equal. Label every angle you can before writing an equation.
- Counting with cases: split by a condition (for example, first digit cannot be zero), count each case, then add.
Worked example
A father is 4 times as old as his son. In 12 years, he will be twice as old. Find the son's age now. Let the son's age be s. The father is 4s. In 12 years: 4s + 12 = 2(s + 12). Expand: 4s + 12 = 2s + 24. Subtract 2s: 2s + 12 = 24, so 2s = 12 and s = 6. Check: son 6, father 24; in 12 years, 18 and 36, and 36 = 2 × 18. Answer: 6 years old.
Traps
- Adding 12 to only one side of the age comparison.
- Solving for the father when the question asks for the son.
- Dropping a case in a counting problem because it "looks unusual."
- Assuming a diagram is to scale when it is not.