Quest Ladder
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Quest Ladder / Numbers and equations
Numbers, equations and grids
Three formats for answers that are values rather than words, and the settings that decide how exact a learner must be.
Right to three decimal places is a decision, not a default.
The three formats
| Format | The answer is |
|---|---|
| Numeric input | A number, optionally with units. |
| Equation input | An expression or equation, judged on what it means rather than how it is typed. |
| Matrix / grid | A grid of values. Rows and Columns each run 2 to 8, defaulting to 3. |
All three pair naturally with changing values: the same question generates with different numbers every time, and the marking follows automatically because the correct answer is computed rather than typed.
How close is close enough
A numeric answer almost never wants an exact string comparison — 0.333, 0.3333 and 1/3 are the same understanding typed three ways. The answer policy handles this.
- Numeric tolerance with Tolerance type set to Absolute accepts anything within a fixed distance. Right for a measurement.
- Percentage accepts anything within a proportion of the true value. Right when the magnitude varies between generated versions, which it usually does.
- Acceptable range — minimum and maximum accept a band outright, for questions with a genuine spread of defensible answers.
- Default tolerance in Extra settings sets the starting value for questions generated from this type.
Percentage tolerance is the right default for a parametric type. An absolute tolerance of 0.5 is generous on an answer near 3 and meaningless on one near 30,000, and a generated question can produce both.
Units
Require units in Extra settings decides whether a bare number is accepted. Turning it on makes the unit part of the answer, which is the whole point in physics and chemistry and an irritation in pure arithmetic.
When units matter, use the Value with unit or Quantity with unit parameter type for the changing values as well, so the generated question and its computed answer agree about what the number is measuring.
Equivalent forms
Equation input is the one that surprises people. Set Evaluation mode to Symbolic / algebraic equivalence and 2x+4, 4+2x and 2(x+2) are all accepted, because the engine compares the mathematics rather than the characters.
Equivalent forms in Extra settings, 0 to 6 with a default of 2, tells the generator how many alternative arrangements to prepare. Use it when you want a learner to be able to stop at any reasonable point rather than reach one canonical form.
If you genuinely need one specific arrangement — a question about factorising — turn equivalence off and say so in the stem, or the learner who answers correctly in the wrong form will be marked wrong without knowing why.
Grids
A matrix grid marks cell by cell, each a slot on the correct answer step with its own marks. Split evenly divides the total across them, and Marking mode decides whether a single wrong cell costs the whole question.
All-or-nothing on a 3×3 grid asks for nine correct cells for any credit. Weighted is almost always the better teaching instrument, and the per-cell marks are what the class report reads when it tells you which cell the class gets wrong.