IB MYP Mathematics: Key concepts in MYP mathematics: form, logic and relationships (MYP Mathematics) – Revision Notes

These notes condense the key concepts section of the IB Middle Years Programme Mathematics guide (for use from September 2020 or January 2021, first assessment 2022). The section applies to the guide’s mathematics and extended mathematics courses alike. If a point is unclear, the study guide explains it in more depth.

Then test yourself with the practice questions, check coverage on the printable checklist, use the MYP Mathematics hub to find other topics, and try the free diagnostics to find weak spots.

The 16 key concepts (Table 1)

Aesthetics	Change	Communication	Communities
Connections	Creativity	Culture	Development
Form	Global interactions	Identity	Logic
Perspective	Relationships	Systems	Time, place and space

Mathematics contributes form, logic and relationships. The rest come from other subjects but still appear in maths units.

Memory hook for the three: Form is about what something is, Logic is about why a conclusion holds, Relationships are about how quantities connect.

The three mathematics key concepts

Key concept	General MYP meaning	Meaning in MYP mathematics
Form	Shape and underlying structure: organisation, essential nature, outward appearance	Structure and shape are distinguished by properties; also the aesthetic side of constructs
Logic	Reasoning method and principles for building arguments and reaching conclusions	Deciding things about numbers, shapes and variables, and explaining why conclusions are valid
Relationships	Links among objects, properties, ideas and people; changes in them bring consequences	Connections between quantities, properties or concepts, written as models, rules or statements; exploring patterns

Do not confuse MYP logic with symbolic logic. The guide keeps them separate.

Form: method in steps

1. List the properties you are told or can measure: sides, angles, parallel pairs, diagonals.
2. Test each against the definition of the candidate form.
3. Name the most specific form that all the properties support.
4. State which properties you used.

Reminder. A triangle has sides 5, 12 and 13. Check 5² + 12² = 25 + 144 = 169 = 13². The converse of Pythagoras’ theorem applies, so the triangle is right-angled. The form is decided by a property, not a drawing.

Logic: method in steps

1. State the claim clearly.
2. Test it on several values, including awkward ones such as 0 or negatives if allowed. A counterexample ends the claim.
3. If no counterexample appears, write the general case with letters.
4. Simplify to the required form and state the conclusion.

Reminder. Claim: the sum of two consecutive even numbers is never a multiple of 4. Write them as 2n and 2n + 2. Sum = 4n + 2. Since 4n is a multiple of 4, the sum leaves remainder 2. The claim is true for every whole n. Tests: 2 + 4 = 6, 4 + 6 = 10, 6 + 8 = 14.

Relationships: method in steps

1. Identify the two quantities that change together.
2. Build a table of values.
3. Find the constant change or the repeated feature.
4. Write the rule and check it against the table.
5. Use it to predict, then say where it is valid.

Reminder. The rule y = 2x + 3 gives y = 17 when x = 7. If y = 45, then 2x = 42 and x = 21.

Glossary terms to use precisely

Term	Short meaning
Justification	Valid reasons that explain why a rule works
Lines of reasoning	Steps that follow on from one another
Proof	Logical steps leading to a required result
Test	Try a rule on different values
Valid	A solution that makes sense in the setting of the problem
Forms of mathematical representation	Words, formulae, tables, charts, graphs, diagrams, models
Pattern	The order, regularity or predictability in a system

Must-know distinction: a test checks examples; a proof or justification covers every case.

Related concepts (Table 2)

Approximation, change, equivalence, generalization, models, patterns, quantity, representation, simplification, space, systems, validity.

Related concepts are tied to mathematics itself. Key concepts are broader. Teachers may also choose other related concepts, including from other subjects.

Global contexts

Identities and relationships; orientation in space and time; personal and cultural expression; scientific and technical innovation; globalization and sustainability; fairness and development. The guide notes that many maths inquiries lean towards scientific and technical innovation and encourages variety.

Statements of inquiry (Table 3)

A statement of inquiry has three parts: key concept, related concepts, global context. The guide’s seven examples pair as follows.

Key concept	Possible study
Form (twice)	Volume; transformations
Logic (twice)	Parallel lines and transversals; projectile motion
Relationships (three times)	Quadratic functions; exponentials and logarithms; line of best fit

Check: 2 + 2 + 3 = 7 examples.

Typical wording pattern: “[Key concept idea] helps us [do something] in [global context idea].”

Worked reminder: building your own statement

Unit: similar triangles and scale drawings.

1. Choose the key concept: form, because similar triangles share the same shape (equal angles) while size changes.
2. Choose related concepts: space and quantity, since lengths and ratios are compared.
3. Choose a global context: orientation in space and time, since maps and plans represent places.
4. Write one sentence: “The form of a shape stays the same under enlargement, so scale drawings let us describe space accurately.”

Check the sentence contains a big idea, not just a topic name such as “similar triangles”.

Sorting key and related concepts

Item	Key concept (Table 1)?	Related concept (Table 2)?
Logic	Yes	No
Validity	No	Yes
Patterns	No	Yes
Change	Yes	Yes (it appears in both lists)
Systems	Yes	Yes (it appears in both lists)
Relationships	Yes	No

Inquiry questions (Table 4)

Type	Job	Check
Factual	Remembering facts and topics	Can be looked up or calculated
Conceptual	Analysing big ideas	Explains an idea that applies widely
Debatable	Evaluating perspectives, developing theories	No single right answer; argue with evidence

Sorting practice on one statement. Statement: “Models help us make decisions about shared resources.”

• Factual: What is the rule for a straight-line model with gradient 4 and intercept 10?
• Conceptual: What makes a model a good representation of a situation?
• Debatable: Can a model ever be too simple to trust?

Notice how the questions move from one correct answer, to an idea that applies widely, to a judgement that needs evidence.

Reminders of factual answers: gradients of perpendicular lines multiply to −1; area scales by k² and volume by k³ for scale factor k; independent events satisfy P(A and B) = P(A) × P(B).

Links to other subjects’ key concepts

Branch	Key concepts from other subjects (with example topics)
Numerical and abstract reasoning	Change, communication, connections, development, identity, systems (e.g. sets: identity and systems)
Thinking with models	Aesthetics, change, connections, systems, time, place and space (e.g. functions: systems; graphs: aesthetics)
Spatial reasoning	Aesthetics, change, communities, creativity, identity, perspective, time, place and space (e.g. angle properties: communities)
Reasoning with data	Communication, communities, connections, development, global interactions, systems (e.g. samples: communities)

Quick self-test

1. How many key concepts are in Table 1, and which three come from mathematics?
2. A line has gradient 3/4. What is the gradient of a line perpendicular to it?
3. A solid is enlarged by scale factor 5. By what factor do its surface area and volume increase?
4. The rule is 6n − 1. Find the term when n = 20.
5. Write the sum of two consecutive even numbers in terms of n and show it leaves remainder 2 when divided by 4.
6. Classify: “Why can approximation be useful?”
7. Classify: “What is the sum of the interior angles of a triangle?”
8. A box holds 5 green and 3 yellow cubes. Two are taken one after another and not put back. Find P(both green).
9. Name the key concept from other subjects that the guide links with prime numbers.
10. Explain, in one sentence, the difference between testing a rule and justifying it.

Answers

1. 16 key concepts. Form, logic and relationships.
2. −4/3, because (3/4) × (−4/3) = −1.
3. Area by 5² = 25; volume by 5³ = 125.
4. 6 × 20 − 1 = 119.
5. 2n + (2n + 2) = 4n + 2, and 4n is a multiple of 4, so the remainder is 2.
6. Conceptual.
7. Factual (it has a definite answer, 180°).
8. 5/8 × 4/7 = 20/56 = 5/14.
9. Development (also linked with number sequences).
10. Testing checks that a rule works for some values; justifying explains with a general argument why it works for all.

Where marks are usually lost

• Naming a related concept, such as patterns, when the question asks for a key concept.
• Saying “form” means appearance only and leaving out properties.
• Listing tested examples and calling them a proof.
• Writing a statement of inquiry with no global context, or one that names a topic but no big idea.
• Mixing up the question types, especially calling a calculable question conceptual.
• Forgetting that area scales by k² and volume by k³.
• Giving a rule without saying where it is valid.
• Dropping units or the context when interpreting an answer.

Show each step in a clear line of reasoning and use mathematical language precisely.

Official syllabus

IB Middle Years Programme Mathematics guide (for use from September 2020 or January 2021), first assessment 2022, published by the International Baccalaureate Organization.