IB MYP Mathematics: Criteria A and B by year (MYP Mathematics) – Revision Notes

Quick recall for Criterion A (knowing and understanding) and Criterion B (investigating patterns) in the IB Middle Years Programme Mathematics guide, first assessment 2022, covering the Year 1, 3 and 5 descriptor sets. For full explanations and worked examples, read the study guide. Test yourself with the practice questions. Wider resources: the subject hub, the printable checklist and the free 10-minute diagnostics. The guide has no tiers, and standard and extended mathematics are judged on the same criteria.

The basics

Fact	Detail
Criteria in the subject	A, B, C, D, equally weighted
Maximum per criterion	8
Levels	0, then 1-2, 3-4, 5-6, 7-8
Band labels	limited, adequate, substantial, excellent
Judgement	best fit across the strands
Years with published descriptors	1, 3 and 5

A level of 0 means no band descriptor is reached. Schools must assess every strand of every criterion twice or more per programme year.

Criterion A: strands and bands

Strands, in the same words every year:

• i select suitable mathematics
• ii apply it successfully
• iii solve correctly in a variety of contexts

Band	Problems	Situations
1-2	simple	familiar
3-4	more complex	familiar
5-6	challenging	familiar
7-8	challenging	familiar and unfamiliar

Remember: the strand wording for Criterion A does not change between Years 1, 3 and 5. Only the mathematics you meet changes.

Method for a Criterion A problem

1. Read the context and name the branch of mathematics (number, models, space, data).
2. Say in one line why the method fits (“right-angled triangle, so Pythagoras”).
3. Carry out the method and show each step.
4. Check the answer against the context: units, rounding direction, reasonableness.

Worked reminder: unit rate

12 notebooks cost 31.20. Find the cost of 20.

31.20 ÷ 12 = 2.60 each, and 2.60 × 20 = 52.00. Check: 20 is 5/3 of 12, and 31.20 × 5/3 = 52.00.

Worked reminder: Criterion A with a model

A sapling 40 cm tall grows 6% taller each month. In which month is it first taller than 100 cm? Repeated percentage growth is exponential: 40 × 1.06^t > 100, so 1.06^t > 2.5 and t > ln 2.5 ÷ ln 1.06 = 15.73 (or test whole values, since logarithms are extended content). Check: t = 15 gives 95.9 cm and t = 16 gives 101.6 cm. The answer is 16 months.

What changes from Year 1 to Year 5

Feature	Year 1	Year 3	Year 5
Criterion A wording	fixed	same	same
Typical Criterion A content	ratios, area, simple equations	area and volume, forming equations, rules for sequences	Pythagoras, trigonometry, quadratics, exponential functions (logarithms in extended)
Criterion B pattern type	recognise a pattern	discover complex patterns	complex patterns, general rules
Criterion B top evidence	verify on other examples	verify and justify	prove, or verify and justify
Guided task cap	6	4	4

The content row is a typical illustration drawn from the guide’s framework, which describes its topics as examples; schools choose what to teach.

Criterion B: strands by year

Strand	Year 1	Year 3	Year 5
i	apply techniques to recognise patterns	select and apply techniques to discover complex patterns	select and apply techniques to discover complex patterns
ii	relationships or general rules that fit the findings	relationships and/or general rules	general rules
iii	verify that the pattern works for other examples	verify and justify relationships and/or rules	prove, or verify and justify, general rules

Bands at a glance

Band	What you show
1-2	simple patterns with teacher support; predictions consistent with the pattern; strand iii not demonstrated
3-4	techniques applied without support; Years 3 and 5 on simple patterns, Year 1 on patterns in general; suggest a rule or how it works; strand iii not demonstrated
5-6	Years 3 and 5: choose and use techniques on complex patterns; Year 1: apply techniques to recognise patterns; rule consistent with findings; verify
7-8	as 5-6, with correct findings (Year 1 also selects the techniques); verify and justify (Year 5: prove, or verify and justify)

Caps to remember

Situation	Maximum level
Fully guided task, Years 1 and 2	6
Fully guided task, Year 3 and up	4
Rule consistent with incorrect findings, Year 3 and up (rule of equivalent complexity)	6

Simple versus complex (guide’s Year 5 examples, non-exhaustive)

Simple	Complex
linear	other quadratics
ax²	cubic, quartic
ax² + c	exponential
	rational f(x)/g(x)

Key distinctions

Pair	Difference
Verify and justify	Verify = test on further cases. Justify = explain why it must work.
Justify and prove	Prove = a general algebraic or structural argument that covers every case.
Consistent and correct	Consistent = the rule fits your data. Correct = your data are right.
Predict and generalise	A prediction names one value (the 20th term). A general rule works for any n.
Guided and open	If the task names the technique, the Criterion B ceiling drops.

Investigation method in steps

1. Table. Build 5 to 6 cases from a diagram or calculation.
2. Differences. First differences constant: linear. Second differences constant: quadratic. Ratios constant: exponential.
3. Conjecture. State it in words, then with n.
4. Test on a case you did not use to build the rule.
5. Justify from the structure of the problem, or prove algebraically.

Worked reminder: linear rule

Pattern: 7, 11, 15, 19. Differences are 4, so the rule starts 4n. For n = 1, 4 + 3 = 7, so u = 4n + 3. The 10th term is 43. Check against the pattern by taking n = 5: 23, which continues 19, 23.

Worked reminder: quadratic rule

Pattern: 4, 10, 18, 28, 40. First differences 6, 8, 10, 12; second differences are 2, so the rule starts n². Subtracting n² leaves 3, 6, 9, 12, 15, which is 3n. So u = n² + 3n = n(n + 3). The 7th term is 70.

Worked reminder: exponential rule

Pattern: 3, 6, 12, 24. Ratio is 2 each time, so u = 3 × 2^(n − 1). Test n = 5: 3 × 16 = 48, which is double 24. Total of first n terms: 3(2^n − 1). For n = 5 this is 93, and 3 + 6 + 12 + 24 + 48 = 93.

Worked reminder: proof

Claim: the product of two consecutive integers is always even. Take n and n + 1. If n is even, the product n(n + 1) has an even factor. If n is odd, then n + 1 is even, so again the product is even. Both cases are covered, so the claim holds for every integer n.

Quick self-test

1. A student picks suitable methods for challenging problems in familiar contexts but is unsure in unfamiliar ones. Which Criterion A band fits best?
2. Are the Criterion A descriptors worded differently in Year 1 and Year 5?
3. What is the highest Criterion B level for a fully guided Year 3 task?
4. What is the highest Criterion B level for a fully guided Year 1 task?
5. Find the rule and the 10th term for 5, 9, 13, 17.
6. Find the rule and the 7th term for 4, 10, 18, 28, 40.
7. Which bands of Criterion B include strand iii?
8. State the difference between the Year 5 strand iii wording at bands 5-6 and 7-8.
9. A Year 5 student writes a rule that fits their (wrong) data. What is the highest level, and what condition applies?
10. For 3, 6, 12, 24, what is the sum of the first 5 terms?

Answers

1. 5-6.
2. No. The wording is the same; the problems you face change.
5. Differences are 4, so u = 4n + 1. The 10th term is 41.
6. u = n(n + 3), and the 7th term is 70.
7. 5-6 and 7-8. It is not demonstrated in bands 1-2 or 3-4.
8. At 5-6 you verify the validity of the rules. At 7-8 you prove them, or verify and justify.
9. 6, provided the rule is of equivalent complexity to a correct one.
10. 3(2^5 − 1) = 93.

Where marks are usually lost

• Describing a pattern as “going up by 4” without writing a rule in n.
• Giving a rule from two data points, with no further case to test it.
• Calling a check of a few cases a “proof” in Year 5.
• Skipping the table, so there is no evidence of how the rule was found.
• Writing a rule that fits your data but never checking that the data themselves are right.
• Naming the method but not applying it, or applying it without saying why it fits.
• Rounding a “how many whole” answer down when the question needs the first value that exceeds a limit.
• Treating a familiar-looking problem as unfamiliar and over-complicating it, or the reverse.
• Following a task’s instructions step by step in an investigation, which limits the level available for choosing techniques.

Official syllabus

International Baccalaureate Organization, Middle Years Programme Mathematics guide, from 2020, first assessment 2022. Criterion A and Criterion B for Years 1, 3 and 5 are paraphrased from this guide.