How I shape IB DP Math so it lands on exam day

Week 6, Term 1 with my DP Year 1 SL group, we’d reached optimisation. A gorgeous-looking task had students find the maximum area of a fenced rectangle, but the mark scheme rewarded a single numeric answer with no communication. It was on-topic but missed the IB fit: no command term like “hence,” no justification of assumptions, no explicit place for a derivative test, and zero mention of technology-allowed checks.

What I look for now is structure that mirrors Paper 1 vs Paper 2 habits, space to state and test assumptions, and prompts to show reasoning. HL tweaks often mean pushing to parameterise or generalise. SL needs clarity and correct use of GDC without outsourcing the thinking. I keep a shortlist of community-built tasks in ClassPods so Monday-me can grab something that asks students to communicate, not just compute.

It’s mildly annoying how many glossy resources ignore IB command terms. “Prove” shows up where “show that” would do, or “calculate” where “determine” is a better cue for method + reason. The mismatch trains the wrong habits, and untraining takes weeks.

Last Thursday with Year 13 HL, I flashed a probability set on the board and asked, “Where are the command terms?” Crickets. Great reminder: if students can’t find them, the resource probably isn’t using IB language cleanly. My rapid checks take two minutes and save me hours of reteaching.

First, command terms: do items really use “state,” “hence,” “justify,” “comment” appropriately—or are they generic? Second, technology: does the set label which parts are technology-allowed and expect GDC screens or regression outputs as evidence? Third, structure: are parts scaffolded a→b→c with marks for method and communication, not just final answers? Fourth, communication: is there a prompt to define variables, state assumptions, and interpret in context?

I’ll often spin up a draft set that meets those checks and then tune difficulty for SL or HL extensions. If you want to see how I prototype a lesson pack with those filters baked in, you can spin one up in ClassPods and inspect the prompts against your scheme of work before teaching it.

Monday, Week 3, DP Year 1 SL, my class mixed up “stationary point” with “maximum” on a past-paper style warm-up. I re-routed into a structured lesson that matches how they’ll be examined, using a named worked example I’ve leaned on for years: The Apple Crate Optimization.

Objective: Determine dimensions of an open-top box, cut from a 30 cm by 20 cm sheet, that maximises volume; justify the nature of the stationary point; interpret results in context with technology-allowed checks.

• Starter (7 min): Two quick “state/identify” items on stationary points from a graph. No calculators.
• Main worked example (15 min): The Apple Crate Optimization. Define x, form V(x), domain, differentiate, solve V’(x)=0, second derivative test. I model full sentences for assumptions and units.
• Guided practice (12 min): Pairs tackle a similar sheet-metal problem; GDC allowed to verify max.
• Formative check (8 min): One “hence determine” twist: change sheet size and predict effect before calculating.
• Plenary (5 min): “Comment” prompt: Is the model reasonable? What real constraints did we ignore?

I keep the pack and mark scheme in ClassPods so I can duplicate it for HL with an extra parameterisation extension and a CAS cross-check section.

Two Fridays ago, Year 12 SL nailed the calculus but lost marks on explanation. I stopped blaming “careless writing” and started handing out a tiny rubric stapled to their practice papers. It trains the communication the IB actually awards.

Use this as-is tomorrow:

• Definitions and notation (2 marks): Variables defined, correct units, appropriate symbols. 2=all precise; 1=minor slips; 0=unclear/missing.
• Method visibility (2 marks): Steps shown and justified (e.g., derivative rules named). 2=clear chain; 1=some gaps; 0=opaque leap to answer.
• Use of technology (1 mark): GDC/CAS use indicated and interpreted (e.g., “GDC regression r=0.87 suggests…”). 1=present and sensible; 0=missing/misused.
• Reasoning and interpretation (2 marks): “Hence/therefore” statements connect results to context. 2=coherent; 1=limited; 0=none.
• Accuracy (1 mark): Final answer correct with units/significant figures appropriate to context.

I paste this mini-grid into any practice pack and require students to self-mark before I do. I also keep a copy ready in ClassPods so it travels with the task, not just the lesson plan.

On Wednesday, my Year 13 HL/SL combined group had three EAL students and two who were out last week on a trip. We slowed the opener and used sentence stems on the board: “We define … as …,” “Hence we … because …,” “Using GDC we verify ….” That tiny scaffold keeps bilingual students inside the mathematical register while still moving.

For pacing, I run HL/SL splits mid-lesson: SL finishes with the second derivative test while HL pushes to a parameterised version or a domain nuance. Absent students get a recorded worked example and a short retrieval quiz the next day. For revision, I spiral the same structure across units: command-term hunt, worked example, exam-style pair task, short plenary “comment.”

If you’re coordinating across a department, it helps to agree on which parts are technology-allowed and what communication looks like in each unit. If you need to check whether your department plan fits your budget this term, the plan details are here and easy to share: ClassPods pricing.