A useful marking guide describes the evidence an answer must show, including valid routes you did not use in your own solution. It also makes a boundary clear: a matching final number does not make contradictory reasoning correct. Writing these rules before marking helps two teachers discuss the same evidence rather than rely on an impression of the response.
This guide builds and tests a small scoring instrument using invented measurement tasks and fictional responses. Its marks and partial-credit decisions are original low-stakes classroom choices. They are not KCSE, KPSEA, KJSEA, KNEC or KICD marking rules. A teacher must check suitability for the intended class and follow any applicable assessment instructions.
Write the task and solve it before allocating credit
Four-mark task: “A cord is 2.4 m long. A piece 65 cm long is cut off, with no other loss. How much cord remains? Show a unit conversion and your subtraction. Give your answer with a unit. You may work in centimetres or metres.”
The intended evidence is a correct conversion, a subtraction representing what remains, an accurate numerical result and an interpretable unit. Long prose, a particular column layout and attractive handwriting are not outcomes. The task deliberately permits either unit so a sound alternative does not become an instruction error.
Solution in centimetres: 2.4 m = 240 cm. Remaining length = 240 − 65 = 175 cm. Check by addition: 175 + 65 = 240 cm.
Solution in metres: 65 cm = 0.65 m. Remaining length = 2.4 − 0.65 = 1.75 m. The two answers agree because 1.75 m = 175 cm. A drawing or partition into 2 m and 40 cm is also valid if it visibly establishes equivalent quantities and the subtraction.
The completed four-mark guide
Each criterion below is worth one mark. The short labels are local conveniences, not official marking codes. Judge the whole response for evidence: a single clear line can establish more than one criterion, and no mark requires copying the wording of the model.
| Criterion | Award 1 mark for | Boundary |
|---|---|---|
| C: conversion | Correctly relating the lengths in a common unit: 2.4 m = 240 cm, or 65 cm = 0.65 m, or equivalent visible evidence. | Do not infer a demonstrated conversion from the final answer alone. A valid labelled drawing may supply it. |
| M: remaining-length model | Subtracting the removed length from the starting length, using quantities presented in the same unit: 240 − 65 or 2.4 − 0.65. | A recognisable subtraction of the learner’s own converted lengths may show this relationship even after a conversion error. Addition, reversing the subtraction, or directly subtracting 65 cm from the bare number 2.4 earns no M mark. |
| A: numerical answer | The correct numerical remainder: 175 when the answer is in centimetres, or 1.75 in metres. If working is present, it must support the result without an unresolved contradiction. | A correct answer without working may earn A. A matching number reached through a visibly invalid equation does not earn A under this guide. |
| U: unit | A length unit attached to the stated remainder and consistent with the calculation’s chosen scale: centimetres/cm or metres/m. | This mark can survive an arithmetic slip. Do not award it for a unit of area or an answer whose scale changes without conversion. For an answer without working, assess the stated value and unit together. |
“175 centimetres” and “1.75 metres” are equivalent final answers. “1 m 75 cm” is also acceptable if supported by a valid route. Units supplied in a labelled answer column can be sufficient; insist on visible meaning, not repeated symbols on every line. The maximum is four marks, however many methods are shown.
Score the four anchor responses
These invented responses are calibration examples, not records of actual learners. Before looking at the scores, ask a colleague to award C, M, A and U separately. Then compare the evidence behind each difference.
| Response | Visible working | C, M, A, U | Total and reason |
|---|---|---|---|
| A: fully correct | 2.4 m = 240 cm; 240 − 65 = 175; 175 cm remains. | 1, 1, 1, 1 | 4/4. All four kinds of evidence are present. |
| B: arithmetic slip | 2.4 m = 240 cm; 240 − 65 = 165; 165 cm remains. | 1, 1, 0, 1 | 3/4. Conversion and model are sound, but the subtraction is inaccurate. The unit still describes the stated remainder on the chosen scale. |
| C: alternative method | 65 cm = 0.65 m; 2.40 − 0.65 = 1.75; 1.75 m remains. | 1, 1, 1, 1 | 4/4. The metres route supplies the same evidence. |
| D: missing requested reasoning | 175 cm. | 0, 0, 1, 1 | 2/4. Correct numerical and unit evidence is present, but conversion and subtraction were requested and are not shown. |
Response B loses only A. Do not subtract another “carelessness” mark after applying the table. Response D does not prove how the answer was obtained; equally, missing working is not evidence of misconduct. Report the specific gap: the two requested steps are absent.
Worked boundary: the right number after the wrong method
Now test this additional invented response: “2.4 m = 240 cm; 240 + 65 = 175; therefore 175 cm.” The conversion is correct, but addition does not model cutting off a piece, and 240 + 65 is 305, not 175. The final number cannot repair either defect.
Under the stated guide, award C = 1, M = 0, A = 0 and U = 1, giving 2/4. The unit mark recognises only the appropriate unit on the chosen scale. It is not credit for the incorrect operation. Do not award the subtraction mark merely because 175 matches the key.
This distinguishes absent evidence from contrary evidence. In response D, there is no demonstrated route to credit, but no shown contradiction invalidates the correct answer evidence. In the added response, the learner explicitly supplies a false derivation. Another classroom guide could define answer credit differently, but its rule would need to be stated and applied consistently; it must still avoid crediting an incorrect method as correct.
Resolve a calibration disagreement by criterion
Suppose two fictional markers give response B scores of 3 and 2. The second marker has withheld both accuracy and unit credit because “165 cm is a wrong answer”. Return to U: it assesses the kind and scale of the unit, not numerical accuracy. B shows a centimetres calculation and a centimetres answer. U is present; A is absent. The agreed score is 3/4.
Record the clarification as: “A numerical subtraction slip removes A only when conversion, subtraction model and unit remain evidenced.” Recheck any responses already marked under the stricter interpretation. Do not change criteria for only the script that triggered the discussion.
A conversion error needs its own review. For example, “2.4 m = 24 cm; 24 − 65 = −41 cm” earns C = 0, M = 1, A = 0 and U = 1 in this illustrative guide. M recognises the correct starting-minus-removed relationship using the learner’s stated common-unit quantities; it does not approve the conversion. C and A are both absent because the conversion and the required numerical remainder are separate assessed evidence. The impossible negative remainder should prompt teaching discussion.
This guide therefore allows limited credit for a surviving relationship but does not carry a conversion error into full numerical-answer credit. That is a declared design choice, not a universal error-carried-forward rule. If your main aim is accurate conversion rather than distinguishing these separate skills, redesign the criteria and the question before use.
A short explanation task needs evidence rules too
Two-mark task: “Parcel X has a measured mass of 300 g. Parcel Y has a measured mass of 450 g. Which parcel has the greater mass? Use the measurements to explain.”
Complete answer: Parcel Y has the greater mass because 450 g is greater than 300 g. It is 150 g heavier. Award 1 mark for identifying Y and 1 for a valid supporting comparison of the supplied masses. The difference is useful but is not required: both “450 g > 300 g” and “150 g more” provide suitable support. Do not demand both comparisons for one evidence mark.
“Y, because 450 g is more than 300 g” earns 2/2. “Y” earns 1/2. “X, because its box looks bigger” earns 0/2: appearance is neither supplied nor a substitute for the stated masses. A correct comparison can be expressed in a short sentence, labelled calculation or inequality. Elaborate vocabulary does not earn extra credit.
Do not award the identification point if the response ultimately selects X, even if it quotes both masses correctly. Quoting data without a valid comparison is not explanation evidence. If the final choice is unclear because the response gives two incompatible conclusions, ask a second marker to review the same stated criteria rather than guessing the learner’s intended choice.
Three practice tasks with solutions
- Apply the guide to a new calculation. A tank contains 3.2 L of water; 850 mL is removed. How much remains? Request conversion, subtraction and a unit, allowing litres or millilitres. Solution: 3.2 L = 3,200 mL; 3,200 − 850 = 2,350 mL. Alternatively, 3.2 − 0.85 = 2.35 L. Both earn C1, M1, A1, U1. A fictional response with the correct conversion and subtraction model but “2,450 mL” earns 3/4 under the same arithmetic-slip rule.
- Detect unsupported answer credit. For that tank problem, a response says “3.2 L = 3,200 mL; 3,200 + 850 = 2,350 mL”. Solution: C1, M0, A0, U1 gives 2/4. Addition would give 4,050 mL, and adding does not represent removal. A printed answer match cannot justify either M or A.
- Accept an equivalent explanation. For the parcels, a response says “Y: X would need another 150 g to match it.” Solution: 2/2. Y is identified and the difference correctly relates the supplied masses. Requiring the exact sentence “450 is greater than 300” would reject valid evidence.
Where professional judgement remains necessary
No short guide anticipates every sound representation. When an unfamiliar method appears, solve it independently, identify what each line establishes, and compare that evidence with the criteria. Add a documented accepted alternative if appropriate, then apply it across all comparable responses. Do not let the first model become the only permitted method.
If handwriting prevents interpretation, distinguish uncertainty from an incorrect mathematical claim. Use the school’s consistent clarification arrangements where appropriate; do not supply hints or invite selective rewriting. If the task itself is ambiguous, repair the assessment process rather than assuming every unexpected answer is a learner error. Small low-stakes scores should inform further evidence gathering, not high-impact decisions about a learner.
Frequently asked questions
Must the learner use my method?
No. Accept a valid method that meets the prompt and establishes the required evidence. Check an unfamiliar route before rejecting it.
Can a correct answer without working earn full marks?
Not on this task, which explicitly requests conversion and subtraction. It earns the numerical and unit marks, while the two reasoning marks remain unsupported.
Does every wrong answer receive zero?
No. Correctly demonstrated conversion, modelling or units can remain creditworthy. Award only the criteria actually evidenced.
Should every later step receive carried-forward credit?
No. Define any dependency and carry-forward rule in advance. This guide preserves relationship and unit evidence but requires the true numerical remainder for A.
What if the final number is right but the working is false?
Withhold credit for the invalid method. Under this guide, the contradicted numerical result also does not earn A; independently valid evidence such as conversion may still count.
Should spelling or handwriting affect these marks?
Only where meaning cannot be interpreted. Presentation and spelling are not separate assessed outcomes in these measurement tasks.
What if two teachers still disagree?
Identify the disputed criterion and evidence, seek a subject colleague’s judgement where needed, and record a consistent resolution. Do not conceal uncertainty by averaging unexplained scores.
Reference for the scoring approach
The historical National Open University of Nigeria measurement and evaluation course, Module 3, Unit 5, discusses preparing scoring guides alongside questions and assessing relevant answer features. It is not a source of current Kenyan marking policy. All criteria, boundaries and sample responses above are original classroom illustrations.
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