IB MYP Mathematics: Criteria C and D by year: communicating and applying mathematics (MYP Mathematics) – Revision Notes

These revision notes condense Criterion C (Communicating) and Criterion D (Applying mathematics in real-life contexts) from the IB MYP Mathematics guide (for use from September 2020 and January 2021, first assessment 2022), using the Year 1, Year 3 and Year 5 criteria. For full explanations and worked examples, read the study guide first, then test yourself with the practice questions. The course hub is MYP Mathematics and the printable list is the MYP Mathematics checklist. The free 10-minute diagnostics help you pick what to revise.

The criteria at a glance

• Each criterion has a maximum of 8, in four bands: 1-2, 3-4, 5-6, 7-8.
• Teachers use best fit across the strands.
• Every strand of every criterion is assessed at least twice in each MYP year.
• The guide says Criterion C is often assessed on constructed responses and reports, alongside B or D.
• Criterion D is often assessed through modelling or curve-fitting tasks in authentic contexts.

Criterion C strands

Strand	Skill	What earns the top band
i	Language	consistently correct notation, symbols, terminology
ii	Representation	forms chosen to suit the information and used correctly
iii	Moving between forms	effective moves (Years 3 and 5 only)
iv	Reasoning	Year 1 coherent; Year 3 complete and coherent; Year 5 complete, coherent and concise
v	Structure	work consistently organised in a logical order

Year 1 does not demonstrate strand iii at any band.

Criterion D strands

Strand	Skill	Year 1	Year 3	Year 5
i	Identify elements	identify	identify	identify
ii	Select strategies	select	select	select
iii	Apply strategies	apply	apply	apply
iv	Accuracy	explain	explain	justify
v	Makes sense	describe	explain	justify

Strands i to iii do not change in wording across years. The mathematics you apply gets harder.

Command terms (paraphrased from the guide)

Term	Meaning	Use it to
Describe	detailed account of a situation or process	say what happened or what the answer looks like
Explain	account including reasons or causes	say why
Justify	valid reasons or evidence supporting a conclusion	give reasons plus numbers or facts as evidence
Discuss	balanced review of several arguments or factors	weigh both sides, then conclude
Show	give the steps of a calculation or derivation	display every step
Verify	provide evidence that validates a result	substitute or check independently

Notation reminders

These come from the guide’s conventions for on-screen examinations, and they are good habits in every task.

• Write mathematical notation, not calculator notation. For example 4.5 × 10³, not 4.5E3.
• Use superscripts and subscripts correctly: m², x₁.
• Unless told otherwise, give final answers to three significant figures.
• Estimate by rounding. Truncating does not count as estimating.
• Use the equals sign only between quantities that are equal. Do not chain unrelated results.

Method: communicating a solution

1. State what you are finding and define any variable with units.
2. Choose a representation that fits the information.
3. Show one idea per line, in order.
4. Write the result with units and the right rounding.
5. Finish with a sentence that answers the original question.
6. Check that someone else could follow it without asking you anything.

Method: applying mathematics

1. List the relevant facts. Cross out irrelevant ones (identify).
2. Choose a model and say why it fits (select).
3. Carry it out accurately (apply).
4. State the degree of accuracy and its cause (explain), then add evidence such as a range or an error size (justify).
5. Compare the answer with the real situation: size, units, whole numbers, limits (makes sense).

Moving between forms: reminder

For a rule such as C = 18 + 22m: table rows give 40, 62, 84 for m = 1, 2, 3 after adding 18 to each 22m. The graph is a line with intercept 18 and gradient 22. In words, “18 to join and 22 each month”. Reading back from the graph, C = 260 gives 22m = 242, so m = 11. Always check that each form agrees with the others.

Model validity checklist

• State the domain where the model works.
• Test it against at least two data points. Record the gaps.
• Say whether the gaps are growing, shrinking or random.
• Name one thing the model leaves out.
• Do not predict outside the domain, or say clearly that the prediction is unreliable.

Reminder. A savings model B = 800 × 1.04ⁿ gives B = 1012.26 after 6 years, rounded to the nearest penny. It assumes the 4% rate never changes. If the bank changes the rate, the model is no longer valid.

Band ladder, in short

Band	Criterion C	Criterion D
1-2	limited language and forms; reasoning hard to follow	some elements found; limited success
3-4	some correct language; adequate forms; reasoning understandable	relevant elements; a solution reached; sense stated but not always correctly (Year 1), described (Year 3) or discussed (Year 5)
5-6	usually correct; some success moving between forms (Year 3) or usually moving (Year 5)	adequate model; valid solution; accuracy described (Years 1, 3) or explained (Year 5)
7-8	consistent; effective moves; reasoning complete and coherent	model chosen well; correct solution; accuracy explained (Years 1, 3) or justified (Year 5); sense described (Year 1), explained (Year 3) or justified (Year 5)

In the lowest bands several strands read “not demonstrated at this level”. That means those strands are not credited there.

Worked reminders

Rewrite a messy solution. A response reads: “3(x + 4) = 2x + 19 → 3x + 12 = 2x + 19 → x = 7 = 33 = 33”. The arrows and chained equals mix an equation with a check.

Better:

Solve 3(x + 4) = 2x + 19.
Expand: 3x + 12 = 2x + 19
Subtract 2x: x + 12 = 19
Subtract 12: x = 7
Check: left side 3(7 + 4) = 33, right side 2(7) + 19 = 33.

One accuracy statement, three years. For a bike-hire cost of £17.00 worked from times rounded to the nearest half hour:

• Year 1 (explain): the time was rounded, so the cost is approximate.
• Year 3 (explain): rounding to the nearest half hour could change the time by 15 minutes, so the cost could differ.
• Year 5 (justify): with a rate of £3 an hour, a 15 minute change moves the cost by £0.75, so the true cost lies within about £0.75 of £17.00, which is fine for budgeting.

Must-know distinctions

Pair	Difference
complete vs coherent	complete has no missing steps; coherent has steps in a logical order
coherent vs concise	concise means no unnecessary material
explain vs justify	explain gives reasons; justify gives reasons backed by evidence
describe vs explain	describe says what; explain says why
accuracy vs sense	accuracy concerns precision of the number; sense concerns fit to the situation
example vs proof	examples test; a general argument covers every case

Quick self-test

1. In which year is strand iii of Criterion C not demonstrated?
2. Which two strands of Criterion D use “justify” in Year 5?
3. Rewrite 3.6E-2 in mathematical notation.
4. Why is checking 1 + 2 + 3 + 4 + 5 = 15 a weak argument that five consecutive integers always sum to a multiple of 5?
5. A candle model h = 24 − 1.5t has h in cm. For what values of t is it valid?
6. A floor needs 202.03 tiles. How many do you buy, and why?
7. Which command term asks for evidence in support of a conclusion?
8. A balance is modelled by B = 800 × 1.04ⁿ. Find B after 10 years, to the nearest penny.
9. Name the three adjectives that describe Year 5 reasoning at the top band.
10. Give one reason a linear model might fail outside the range of the data.

Answers

1. Year 1 (it is not demonstrated at any band).
2. Strands iv (accuracy) and v (makes sense).
3. 3.6 × 10⁻².
4. It tests one case, so it does not show the result holds for all integers. A general argument using n − 2, n − 1, n, n + 1, n + 2 gives 5n.
5. 0 ≤ t ≤ 16, because 24 − 1.5t ≥ 0 gives t ≤ 16.
6. 203 tiles. You cannot buy part of a tile, so round up.
7. Justify.
8. 800 × 1.04¹⁰ = 1184.20, so £1184.20.
9. Complete, coherent and concise.
10. The real situation may curve, level off or hit a physical limit, such as a negative height.

Where marks are usually lost

• Reasoning that shows only one or two examples and then claims a general rule.
• Chained equals signs such as 4 × 5 = 20 + 3 = 23.
• Graphs without labelled axes, units or a scale.
• Answers with no units or with rounding that does not suit the situation.
• Explaining accuracy with “it is approximate” and nothing more.
• Using “it makes sense” without comparing the answer with the context.
• Predicting beyond the domain of a model.
• Long, repeated working in Year 5, when a short complete argument is asked for.
• Starting with the calculation and leaving the question unstated, so the structure is hard to follow.

Official syllabus

IB Middle Years Programme Mathematics guide (for use from September 2020/January 2021), first assessment 2022, published by the International Baccalaureate Organization. These notes paraphrase the Criterion C and D objectives and the Year 1, Year 3 and Year 5 criteria.