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

This study guide covers Criterion C (Communicating) and Criterion D (Applying mathematics in real-life contexts) in IB MYP Mathematics. It follows the IB MYP Mathematics guide (for use from September 2020 and January 2021, first assessment 2022) and its Year 1, Year 3 and Year 5 objectives and assessment criteria. The guide publishes one descriptor set for each of those three years, so this page works the same way and does not split the content by course level. Use it with the revision notes and the practice questions. The course hub is at MYP Mathematics and the printable list is the MYP Mathematics checklist.

What the two criteria cover

Each criterion is marked out of 8 and sits in one of four bands: 1-2, 3-4, 5-6 and 7-8. Teachers make a best-fit judgment across the strands. The guide says all strands of all four criteria must be assessed at least twice in every MYP year.

Strand	Criterion C: Communicating	Years it applies
i	Mathematical language: notation, symbols, terminology	1, 3, 5
ii	Forms of representation used to present information	1, 3, 5
iii	Moving between forms of representation	3, 5 (not demonstrated in Year 1)
iv	Lines of reasoning	1, 3, 5
v	Logical structure	1, 3, 5

Strand	Criterion D: Applying mathematics in real-life contexts	Years it applies
i	Identify relevant elements of the situation	1, 3, 5
ii	Select appropriate strategies	1, 3, 5
iii	Apply the strategies to reach a solution	1, 3, 5
iv	Accuracy of the solution	1, 3, 5
v	Whether the solution makes sense in context	1, 3, 5

Note that Criterion D has five strands in every year, including Year 1, where strand v asks you to describe whether the solution makes sense.

What changes from Year 1 to Year 5

The guide says the wording of the objectives is “quite similar” across years while the mathematics gets harder. The differences are small but they matter, because they are the words a teacher will use when placing your work.

Strand	Year 1	Year 3	Year 5
C i	oral and written statements	oral and written explanations	oral and written explanations
C iii	not demonstrated	move between forms	move between forms
C iv	coherent reasoning	complete and coherent reasoning	complete, coherent and concise reasoning
D iv	explain the degree of accuracy	explain the degree of accuracy	justify the degree of accuracy
D v	describe whether the solution makes sense	explain whether it makes sense	justify whether it makes sense

The pattern is clear. Year 1 asks you to say what you did. Year 3 asks you to give reasons. Year 5 asks you to give valid reasons backed by evidence, and to keep the writing tight.

Criterion C: communicating

Strand i: mathematical language

This means correct notation, symbols and terminology, in speech and in writing. Typical slips are chaining equals signs across different quantities, writing 2^3 or 4.5E3 instead of 2³ or 4.5 × 10³, and using “times” and “x” without care. The guide’s conventions for on-screen examinations make the point directly: use mathematical notation, not calculator notation, and write subscripts and superscripts correctly.

Strand ii: forms of representation

Choose the form that fits the information: a table for discrete values, a graph for a trend or rate of change, an equation for a rule, a diagram for geometry, a sentence for a conclusion. A form is correct when it is labelled, scaled and titled so a reader needs nothing else.

Strand iii: moving between forms

From Year 3 you are expected to translate. Take a context that arrives as words and show it as a table, a rule and a graph, then read information back from one form into another.

Worked example 1. A water tank holds 40 litres. A pump adds 12 litres each minute. The tank holds at most 250 litres.

1. Table, with t in minutes and V in litres:

t	0	1	2	3	4
V	40	52	64	76	88

2. Rule: the value starts at 40 and rises by 12 each minute, so V = 40 + 12t.
3. Graph: a straight line. The vertical intercept is 40 (the starting volume). The gradient is 12 (litres per minute). The line stops at V = 250.
4. Read back: V = 190 gives 40 + 12t = 190, so t = 150 ÷ 12 = 12.5 minutes.
5. Full tank: 40 + 12t = 250 gives t = 17.5, so the rule only applies for 0 ≤ t ≤ 17.5.

Each form carries the same facts, and the final line states the domain in words and symbols. That final line is what shows you moved between forms with understanding.

Strand iv: lines of reasoning

Reasoning is complete when no needed step is missing, coherent when each step follows from the one before, and concise when nothing unnecessary is included. Year 5 adds concise to the other two.

Worked example 2. Show that the sum of five consecutive integers is always a multiple of 5.

Weak: “1 + 2 + 3 + 4 + 5 = 15. 6 + 7 + 8 + 9 + 10 = 40. Both are multiples of 5, so it works.” This tests two cases. It does not show the result is always true.

Complete, coherent and concise:

Let the integers be n − 2, n − 1, n, n + 1 and n + 2, where n is an integer.
Sum = (n − 2) + (n − 1) + n + (n + 1) + (n + 2) = 5n.
5n is 5 times an integer, so the sum is a multiple of 5.

Three lines, each following from the one before, with the variable defined and the conclusion linked back to the question.

Strand v: logical structure

Present work in an order a reader can follow: the question or aim, the information used, the method, the result, a conclusion. Number steps, label diagrams, and keep each calculation next to the idea it supports.

Criterion D: applying mathematics

The command terms that separate the years

The guide defines the key verbs. Describe means give a detailed account. Explain means give that account and add the reasons or causes. Justify means back an answer or conclusion with sound reasons or evidence. Discuss means weigh up a range of arguments or factors in a balanced way. Each one asks for more than the one before, and each year’s wording tells you which one to expect.

Strands i to iii: identify, select, apply

Identify which facts in the situation matter and which do not. Select a strategy that models the situation. Carry it out to a correct result. A model chosen without checking it fits the situation is a weaker response than one where you say why it fits.

Worked example 3. A rectangular floor measures 4.35 m by 3.8 m. It is to be covered in square tiles of side 0.3 m, bought in boxes of 12. Allow 10% extra for cuts.

Identify: floor area, tile area, a percentage allowance, a box size. The room’s height is not relevant.

Select and apply:

Floor area = 4.35 × 3.8 = 16.53 m²
Tile area  = 0.3 × 0.3  = 0.09 m²
Tiles needed with no waste = 16.53 ÷ 0.09 = 183.67
Add 10%: 183.67 × 1.1 = 202.03 tiles

You cannot buy part of a tile, so round up to 203 tiles. Then 203 ÷ 12 = 16.9, so round up again to 17 boxes, which gives 204 tiles.

Strand iv: the degree of accuracy

The wording by year:

• Year 1 (explain): “The floor is measured to the nearest 0.05 m, so the answer is approximate.”
• Year 3 (explain): add the reason. “Each length could be up to 0.025 m out, so the area is not exact.”
• Year 5 (justify): back it with evidence. Using the smallest and largest lengths the measurements allow, the area lies between 4.325 × 3.775 = 16.33 m² and 4.375 × 3.825 = 16.73 m². That is between about 181 and 186 tiles before the allowance. The spread is only a few tiles, and 203 tiles is well above the top of that range, so the 10% allowance covers both the cuts and the measurement error.

The Year 5 version contains numbers that support the claim. That is the difference between explaining and justifying.

Strand v: does the solution make sense?

Compare the answer with the real situation. In the tiling problem, 17 boxes is sensible because both quantities were rounded up. Rounding down would leave the floor unfinished. A negative tile count, or 202.03 tiles, would not make sense, and saying why shows you checked.

Model validity

The guide notes that extended writing on a modelling task may ask you to judge whether a mathematical model is valid. A model is a rule you use to represent the situation.

Worked example 4. A candle is 24 cm tall and burns down at 1.5 cm per hour. Model: h = 24 − 1.5t, with h in cm and t in hours.

1. Domain: h cannot be negative, so 24 − 1.5t ≥ 0, giving t ≤ 16. The model applies for 0 ≤ t ≤ 16 only.
2. Prediction: after 10 hours, h = 24 − 15 = 9 cm.
3. Test against measurements: at t = 2, 6 and 10 the heights are 21.1, 15.2 and 9.4 cm. The model gives 21, 15 and 9. The gaps are 0.1, 0.2 and 0.4 cm, and they are growing.
4. Interpret: the real burn rate is about (24 − 9.4) ÷ 10 = 1.46 cm per hour, slightly below 1.5.
5. Conclusion: the model is reasonable for a first estimate within the first 10 hours. The growing gap shows the rate is not exactly 1.5. At t = 18 the model gives −3 cm, which is impossible, so it must not be used outside its domain.

A justified conclusion states the evidence (the gaps), the limit (the domain), and the effect on the answer (a small overestimate of the burn rate).

The descriptors in brief

Band	Criterion C in plain words	Criterion D in plain words
1-2	limited language and representation; reasoning hard to follow	some elements identified; limited success reaching a solution
3-4	some correct language; adequate representation; reasoning understood but with gaps	relevant elements identified; a solution reached; sense stated but not always correctly (Year 1), described (Year 3) or discussed (Year 5)
5-6	usually correct; reasoning usually coherent (Year 1), clear but not always coherent or complete (Year 3), complete and coherent (Year 5)	adequate model; valid solution; accuracy described (Years 1, 3) or explained (Year 5); sense stated correctly (Year 1), discussed (Year 3) or explained (Year 5)
7-8	consistently correct; effective moves between forms (Years 3, 5); coherent (Year 1), complete and coherent (Year 3) or complete, coherent and concise (Year 5) reasoning	appropriate model; correct solution; accuracy explained (Years 1, 3) or justified (Year 5); sense described, explained or justified by year

Some strands are marked as not demonstrated in the lower bands. A task that never asks for a strand cannot give you credit for it.

Common errors

• Writing a correct answer with no working, so the reasoning cannot be seen at all.
• Testing two examples and calling it a proof.
• Giving a graph with no axis labels or units.
• Saying “the answer is accurate” without saying why or to what degree.
• Stating “it makes sense” without comparing the number to the situation.
• Extending a model beyond the values where it works.

Next steps

Use the practice questions to try each strand. See also the four criteria in practice and the MYP Mathematics subject guide. Find your gaps with the free 10-minute diagnostics.

Official syllabus

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