The Six-Week Remedial Budget
Mr. V, PGT Mathematics, is asked to plan a six-week remedial programme for Class X. The school has 240 students in Class X. A diagnostic test shows 35% are below the baseline in mathematics. School policy caps a remedial group at 20 students. The programme will run 2 hours per day, 5 days a week, for 6 weeks. The principal has sanctioned ₹1,20,000 for the entire programme, which must cover teacher honorarium at ₹400 per teacher-hour and printed material at ₹15 per participating student. Rooms are available free. Mr. V proposes one teacher per group and wants every identified student to attend all sessions. A colleague suggests reducing the programme to 5 weeks to save money. Mr. V must check whether the plan is feasible within the budget and, if not, propose a defensible alternative.
1. Calculate the number of groups, total teacher-hours, honorarium, material cost, and total cost. Is the proposal within budget?
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Identified students: 35% of 240 = 0.35 × 240 = 84. With a cap of 20 per group, the minimum number of groups is ceil(84 ÷ 20) = 5. (Four groups of 20 and one group of 4, or a balanced five-group split, still requires five teachers.) Teacher-hours per group: 2 hours/day × 5 days/week × 6 weeks = 60 hours. Total teacher-hours: 5 × 60 = 300. Honorarium: 300 × ₹400 = ₹1,20,000. Material: 84 × ₹15 = ₹1,260. Total cost: ₹1,21,260. The proposal exceeds the sanctioned amount by ₹1,260, so it is not feasible as stated. The shortfall is small-about 1.05% of the budget-but it is real. Note that the binding cost is teacher-hours, not material; changing the group sizes within the cap does not reduce the number of groups unless the total falls to 80 or fewer.
2. Evaluate the colleague’s suggestion to reduce the programme to 5 weeks. What is saved, and what is the pedagogical cost?
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At 5 weeks, teacher-hours per group = 2 × 5 × 5 = 50; total = 5 × 50 = 250. Honorarium = 250 × ₹400 = ₹1,00,000. Material remains ₹1,260. Total = ₹1,01,260, which is ₹18,740 below the sanctioned budget and ₹20,000 cheaper than the original plan. The saving comes entirely from cutting 10 instructional hours per group-a 16.7% reduction. The pedagogical cost is that students with baseline deficits lose time for practice, diagnosis, and retesting. Cutting a week may be defensible if the diagnostic shows only mild gaps, but Mr. V has no evidence that five weeks are sufficient. A better decision is to compare the size of the shortfall (₹1,260) with the cost of lost instruction. Requesting a small contingency or using reusable material is less harmful than removing a full week for a 1% budget gap.
3. Propose a revised plan that stays within ₹1,20,000 and preserves the 6-week duration and the 20-student cap. Show the numbers.
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Option A, preferred: keep the six-week, two-hour plan and request ₹1,260 from the school contingency or PTA. The plan then costs ₹1,21,260, of which ₹1,20,000 is the sanctioned honorarium plus material and ₹1,260 is a small top-up. If no top-up is allowed, use Option B: reduce each daily session from 2 hours to 1 hour 50 minutes (11/6 hours). Teacher-hours per group = (11/6) × 5 × 6 = 55; total = 5 × 55 = 275. Honorarium = 275 × ₹400 = ₹1,10,000. Material = ₹1,260. Total = ₹1,11,260, within budget with ₹8,740 to spare. Instruction falls by 5 hours per group (8.3%), less than the 10-hour loss from cutting a week. Option C: keep 2 hours but use reusable laminated worksheets, reducing material to about ₹300, and request only ₹300–₹960 as a top-up. The key is to state the trade-off explicitly and not pretend that a five-week programme is equivalent to six weeks.