A useful MYP Criterion D application task gives students a decision that mathematics can improve. The context needs enough detail to support a model, enough choice to reveal students' thinking, and a reason to ask whether the answer will work in practice.

Refill Ready is an original task for MYP Years 4-5. A school is hiring extra water-refill stations for sports day. Students must choose a combination that can serve the expected demand within a budget, test changes in participation and explain the limits of their recommendation.

The free pack includes a student task, a worked solution, task-specific marking guidance and a constructed sample response with teacher annotations. It is designed for classroom practice and for the department conversation that follows: what distinguishes a correct calculation from a convincing application of mathematics?

Download the free Criterion D application pack

Student task: three pages with the context, data, modelling prompts and working space.
Teacher guide: seven pages with answers, sensitivity checks, marking guidance, an annotated sample and moderation prompts.

Download the complete pack - 10-page PDF

Free for classroom copying and internal department sharing. All event data and prices are fictional. The sample is a constructed teaching example, not an actual student submission or an IB-scored exemplar.

What should a Criterion D task make visible?

The IB mathematics subject brief describes Criterion D as applying mathematics in real-life contexts: students transfer knowledge, use appropriate strategies, reach conclusions and reflect on their results. The IB assessment overview explains the role of tasks designed and marked by classroom teachers.

For this task, the evidence is visible in the connections students make. They must translate attendance into demand, distinguish an outlet from a station, deal with whole refills and whole hire units, and judge a result against both capacity and cost. Their evaluation should then explain which assumptions could change the decision.

The teacher guide offers five evidence lenses: relevant context, mathematical strategy, application, degree of accuracy and sense in context. These are our planning prompts, not a reproduced official rubric. Use the applicable descriptors in your school's current licensed mathematics guide for assessment judgments.

The context: extra refill stations for sports day

The school expects 600 attendees. Existing drinking-water points remain available; the proposed hire adds capacity during a 40-minute lunch window. The baseline estimate is that 60% of attendees use the extra stations, each filling one 500 mL bottle once. Students must also test 45% and 75% participation.

Each outlet is usable for 85% of the window. The remaining time allows for interruptions, separately from the handling time already included in a full refill cycle. The order has a single $30 delivery charge; water costs $0.004 per litre. The total budget is $400, and attendees bring their own bottles.

Fictional equipment data supplied to students
Equipment	Station A	Station B
Hire per station	$95	$150
Independent outlets	1	2, operating simultaneously
Four full-cycle trial times	16, 18, 19, 19 seconds	22, 23, 25, 26 seconds per outlet
Mean cycle time	18 seconds	24 seconds per outlet

A cycle includes positioning the bottle, filling it and moving away. In the baseline model, students treat the mean as a fixed cycle time and assume demand can be shared between outlets. There are enough hire units available, and the stated prices include all other charges. These are modelling assumptions, rather than claims about a real supplier or a school's drinking-water requirements.

The student task: make a recommendation

Recommend which stations the school should hire for the expected demand. Show that the combination provides enough complete refills within the budget, and establish why no cheaper combination works. Test both alternative participation scenarios. Justify your rounding and accuracy, evaluate the model's usefulness, and explain what the school should check before booking.

Students can choose a table, algebra, a graph or a spreadsheet. The student sheet asks them to identify quantities and assumptions before presenting a comparison. It does not supply the finished model or prescribe an enumeration table.

The final product is a short report to the events coordinator, with mathematical working attached. A hire list without reasoning gives the teacher little evidence of how the decision was reached. A long report without a valid comparison has the same problem.

Worked solution: establish capacity before comparing prices

The following sections contain the answers. At expected participation, demand is 600 × 0.60 = 360 refills. Each bottle holds 0.5 L, so the water volume is 180 L.

Each outlet has 40 × 60 × 0.85 = 2,040 usable seconds. Station A therefore completes 113 refills: 2,040 ÷ 18 = 113.33…, but the unfinished part of a refill cannot be counted. Each B outlet completes 85 refills, so a B station supplies 170.

Let a and b represent non-negative whole numbers of A and B stations. A suitable baseline model is:

Capacity: 113a + 170b ≥ 360.
Total cost: 95a + 150b + 30 + 0.004(180) ≤ 400.

Delivery and the modelled water volume cost the same for every hire combination serving this demand. Students can therefore compare hire costs first, then check the full total.

Four baseline options: 4 A stations provide 452 refills for $410.72; 2 A and 1 B provide 396 for $370.72; 1 A and 2 B provide 453 for $425.72; 3 B provide 510 for $480.72. Only the second option is within the $400 budget. — For each B count, compare the smallest A count that meets demand. This gives a systematic search rather than a collection of convenient examples.

With no B stations, four A stations are needed. With one B, two A are needed. With two B, one A is still needed because 340 refills are insufficient. Three B stations already cost $450 in hire, so additional B stations cannot produce a cheaper result.

The least-cost baseline choice is 2 A and 1 B. It supplies 396 refills for $370.72, leaving $29.28 in the budget. Its 36 extra refills are 10% of baseline demand. That capacity margin does not establish a probability of success or a waiting time.

Changed demand should change the decision

The sensitivity check gives students a reason to revisit their model rather than append a general sentence about limitations.

Cheapest sufficient hire in each participation scenario
Participation	Demand	Cheapest hire	Capacity	Full cost
45%	270	1 A + 1 B	283	$275.54
60%	360	2 A + 1 B	396	$370.72
75%	450	4 A	452	$410.90

At 75% use, the original recommendation is 54 refills short. The cheapest sufficient hire exceeds the budget by $10.90. Students should state that no hire combination meets both constraints at this demand. They should not describe four A stations as an affordable recommendation under the unchanged budget.

The teacher guide establishes that the largest capacity affordable within $400 is 396 refills. This corresponds to 66% participation. The school could investigate a larger budget or a longer, staggered refill window, but any altered plan needs a fresh calculation.

What does a justification of accuracy look like?

“I rounded to two decimal places” says how a result is displayed. A useful explanation connects precision and uncertainty to the context: incomplete refill cycles cannot be pooled across outlets; stations must be hired in whole numbers; money is reported to cents; and the participation estimate and four timing trials are limited evidence about future use.

A numerical check makes the discussion stronger. If every A cycle takes 19 seconds and every B cycle takes 26 seconds, using the slowest recorded trials, capacities become 107 for A and 156 for B. The chosen plan then serves 2(107) + 156 = 370 refills. It still covers expected demand in this scenario, but the margin has fallen from 36 to 10.

This is a stress check, not a statistical confidence interval. Four observations do not establish that no later refill will be slower. Similarly, even enough total capacity across 40 minutes cannot guarantee short queues if most people arrive together or distribute unevenly between outlets.

A sample response teachers can discuss together

The guide includes a complete constructed report with annotations beside the context, strategy, calculation, sensitivity and evaluation evidence. Its recommendation is conditional:

I would provisionally choose 2 A and 1 B for expected demand. The model does not tell us how long any person waits: everyone might arrive in the first few minutes, outlets might be used unevenly, and refills may be slower. Before booking, I would time a longer trial and record arrivals across lunch to test the 85% allowance and whether demand can be shared.

First page of the constructed Refill Ready report, with teacher annotations beside the context, capacity model, systematic comparison and baseline recommendation — The annotated response continues with changed demand, justified accuracy and a practical evaluation in the teacher guide.

A contrasting extract gives the correct baseline figures but claims that two decimal places establish accuracy and that capacity alone proves the plan works. Ask colleagues to identify what this extract demonstrates and what evidence is still missing. Avoid assigning a guaranteed achievement level from one paragraph.

Use the marking guidance without turning it into a checklist

Read the complete response before making a best-fit judgment against the applicable descriptors. Look for the connections between the model, its application and its interpretation. A correct optimum with an unsupported evaluation differs from a response that explains how uncertain inputs affect the recommendation.

For a short moderation meeting, record the proposed level, evidence locations, support given, why an adjacent judgment fits less well and one next step. Accept equivalent strategies when the reasoning is visible. A spreadsheet with unexplained outputs does not establish a model simply because the numbers match.

Useful feedback can be specific: “How can you rule out every cheaper combination?”, “Which input is uncertain, and what changes when you test it?” or “What would you measure to find out whether the queue assumption is reasonable?” These prompts help students develop the decision rather than just decorate the report.

Share it, teach it, then adapt it

Use the student PDF separately from the answers. The complete pack is free to copy for classes and share internally with a department. Public worked answers make it particularly useful for formative assessment, planning and moderation. For later summative use, change the data or constraints, solve the revised task fully and review the clarification before releasing it.

Download Refill Ready: the complete Criterion D application pack

For a complementary assessment resource, try our MYP Criterion B investigation: Crossing Paths. For the wider framework, read MYP Mathematics Criteria A, B, C and D explained. For year-group planning, explore the Year 4 and Year 5 curriculum resources.

Original task, fictional data, diagrams, marking guidance and constructed response: Full Marks Education. This is not an IB-issued or endorsed assessment. Consult your current licensed IB mathematics guide for the applicable descriptors.

MYP Criterion D Application Task: Free Pack and Marking Guide