The Student May Not Be the Problem
A student completes every row of a table correctly.
They identify the pattern.
They write the general rule.
The mathematics is accurate.
Then the Criterion B result comes back at Level 3–4.
It is tempting to conclude that the student needs harder mathematics.
Sometimes the real problem was written into the task before the student ever saw it.
If every step was prescribed, the student never had to choose a mathematical technique. If the prompt only asked for a pattern, the student never had to verify it. If the final instruction said “state the rule,” there was no opportunity to justify why the rule should continue to work.
The ceiling may be in the assessment.
That is the central idea behind a recent Koncepts discussion on MYP Mathematics Criterion B: Investigating Patterns.
The IB itself makes the design issue unusually clear. Guidance quoted in IB research states:
“A task that does not allow students to select a problem-solving technique is too guided.”
For students in MYP Year 3 and above, overly guided investigations can limit the evidence students are able to demonstrate for Criterion B.
Read the supporting IB research
That changes the way Criterion B tasks should be designed.
What Does MYP Math Criterion B Actually Assess?
MYP Mathematics uses four assessment criteria:
- Criterion A: Knowing and understanding
- Criterion B: Investigating patterns
- Criterion C: Communicating
- Criterion D: Applying mathematics in real life contexts
Each criterion has a maximum achievement level of 8.
For a broader explanation of how the four MYP criteria and achievement levels connect to the final grade, read MYP Grading: Criteria A–D & 1–7 Scale.
The IB describes Criterion B as an opportunity for students to work through mathematical investigations and develop as inquirers, thinkers and problem solvers.
View the official MYP Mathematics subject brief
For Year 5, Criterion B broadly asks students to:
- Select and apply mathematical problem solving techniques to discover complex patterns
- Describe patterns as general rules consistent with their findings
- Prove, or verify and justify, those general rules
This distinction matters because Criterion B is not simply about spotting a pattern.
A student who notices that a sequence increases by three has identified a pattern.
A student who develops a general expression has generalised it.
A student who tests the expression against further cases has verified it.
A student who explains mathematically why the relationship must continue to hold has moved into justification or proof.
These are different levels of mathematical thinking.
Why Many Criterion B Tasks Stop at Level 3–4
Consider a common classroom investigation:
Complete the table for (n = 3, 4, 5, 6) using the method shown. Identify the pattern and state a general rule.
There is nothing inherently wrong with this activity.
It may be useful during teaching.
The problem appears when it becomes the complete Criterion B assessment.
The student has already been told:
- Which cases to investigate
- Which method to use
- How to organise the results
- What kind of answer to produce
Very little investigation remains.
The student is applying a procedure and reporting a relationship.
That creates useful evidence, but it provides limited opportunity to demonstrate independent method selection, verification, justification or proof.
Criterion B task design should therefore not begin with:
Is this mathematics difficult enough?
A better question is:
What mathematical decisions does the student actually have to make?
The Shift From Level 3–4 to Level 7–8
The biggest difference is not always the topic.
It is the intellectual responsibility given to the learner.
Compare these two versions.
Version 1
Use the diagonal counting method shown to complete the table for polygons with 3 to 8 sides. State the pattern.
The teacher has selected the method.
The teacher has selected the cases.
The student follows the procedure and reports the result.
Now consider:
Version 2
Investigate the number of diagonals in an (n)-sided polygon. Choose a mathematical method to develop a general rule. Verify your rule for several cases and justify why it works for any (n).
The mathematical topic has barely changed.
The student's role has changed completely.
They now need to choose, generalise, test and justify.
That creates much stronger opportunities for higher Criterion B achievement.
Wording Alone Does Not Create a Level 7–8 Task
A small wording change can remove a major ceiling.
Changing:
Use this method.
to:
Choose a suitable method.
gives the student more responsibility.
Changing:
State your rule.
to:
Verify and justify your rule.
creates space for deeper reasoning.
But adding the word justify to the end of a weak task does not automatically make it suitable for Level 7–8.
The mathematics itself must support the demand.
Students need a pattern rich enough to investigate.
There must be something meaningful to generalise.
There needs to be enough freedom for students to select a technique.
The rule must be testable.
There must also be a mathematical reason behind the relationship that students can explain.
A phrase can open the door.
The task still needs somewhere for that door to lead.
Verification and Justification Are Not the Same Thing
This distinction is central to strong Criterion B work.
Suppose a student discovers the formula:
$$ D=\frac{n(n-3)}{2} $$
for the number of diagonals in an (n)-sided polygon.
They test (n=5).
The formula gives 5.
They draw a pentagon and count 5 diagonals.
They then test (n=6).
The formula gives 9.
Their diagram also contains 9 diagonals.
The student has provided useful verification.
They have shown that the rule works for additional cases.
But those examples do not prove that it works for every polygon.
For justification, the student could reason that every one of the (n) vertices connects to (n-3) non-adjacent vertices.
That initially gives:
$$ n(n-3) $$
But every diagonal has now been counted twice, once from each endpoint.
Therefore the number of unique diagonals must be:
$$ D=\frac{n(n-3)}{2} $$
Now the student is explaining why the relationship exists.
That is different from simply checking that it works.
Students need repeated experience with this distinction before it appears in a summative assessment or eAssessment.
Five Prompt Changes That Improve Criterion B Tasks
Teachers do not always need completely new investigations.
Many existing tasks can be opened up.
1. From Given Method to Method Choice
Instead of:
Use the table method to find the pattern.
Try:
Choose a suitable method to investigate the pattern.
The learner now has responsibility for selecting the approach.
2. From Continue to Generalise
Instead of:
Find the next three terms.
Try:
Develop a general rule for the (n)th term.
Continuing a sequence demonstrates recognition.
Generalising requires the student to describe the mathematical relationship.
3. From Check to Verify
Instead of:
Check your answer for (n=8).
Try:
Verify your rule using several cases that were not used to create it.
Testing now becomes part of the mathematical argument.
4. From Verify to Justify
Instead of:
Show that your formula works for three examples.
Try:
Justify why the general rule should hold for all valid values.
The learner must move beyond numerical examples.
5. From Procedure to Investigation
Instead of giving five numbered steps that determine the entire route, provide enough structure for students to begin while leaving genuine mathematical choices inside the investigation.
Removing excessive scaffolding does not mean removing all support.
Students still need a clear entry point.
The aim is to support access without making every mathematical decision for them.
A Criterion B Task Needs a Complexity Floor
Method choice is only one part of strong Criterion B design.
A task can allow students to choose a technique while still producing mathematics that is too simple to sustain deeper investigation.
Before using a task summatively, ask:
- Is there a meaningful pattern to discover?
- Can the relationship be expressed as a general rule?
- Does the task allow more than one sensible approach?
- Can students test the rule against new cases?
- Is there something mathematically meaningful to justify?
- Can students explain why the pattern exists rather than simply report that it exists?
- Does the highest achievement require correct mathematical findings?
If several answers are no, adding “justify your answer” at the end will not fix the assessment.
Why This Matters for MYP eAssessment
Criterion B becomes especially visible in MYP Mathematics eAssessment.
The official MYP Mathematics subject brief explains that the on-screen examination includes an Investigating patterns task assessing Criteria B and C.
View the official MYP Mathematics subject brief
This means Criterion B is not a skill students should encounter only shortly before an examination.
Students need regular experience:
- Investigating unfamiliar relationships
- Selecting their own approaches
- Looking for patterns
- Developing general rules
- Testing those rules
- Explaining mathematical reasoning
- Justifying why relationships hold
A learner who spends several years completing heavily scaffolded investigations may become very good at following mathematical steps.
Then an assessment removes those steps.
The resulting difficulty may not be a content problem.
The student may simply have had too little practice making mathematical decisions independently.
Good eAssessment preparation therefore begins much earlier than exam season.
It begins with better everyday Criterion B tasks.
A Quick Criterion B Task Audit
Before assigning your next investigation, hide the rubric and read only the task instructions.
Ask these questions.
Method
Does the student choose a mathematical technique, or have I already chosen it?
Pattern
Is the learner discovering a meaningful relationship?
Generalisation
Does the task require a general rule rather than several correct examples?
Verification
Must students test their rule beyond the examples used to create it?
Justification
Do students need to explain why the relationship holds?
Proof
Where appropriate, can students construct a convincing mathematical proof?
Accuracy
Does high achievement depend on mathematically correct findings?
Communication
Does the task also create enough space for students to communicate their reasoning clearly?
If the task cannot produce evidence for one of these areas, a detailed rubric cannot create that evidence afterwards.
Design the Task Before You Design the Rubric
A beautifully written 1–8 rubric cannot rescue an assessment that never allows students to demonstrate the upper descriptors.
Task design and rubric design need to happen together.
For a practical walkthrough of building criterion-tagged MYP questions, read IB MYP Assessment Generator: Build Criterion-Tagged Questions with the Right Command Terms.
The Koncepts MYP Assessment Generator allows teachers to create assessments around a selected subject, MYP context and assessment criterion, then review the associated questions, rubric and markscheme before assigning them.
Teachers can also use the Koncepts MYP Rubric Generator to create task-specific descriptors across achievement levels 1–8.
For the complete assessment-to-rubric workflow, see the IB MYP Assessment Generator & Rubric Maker Guide.
The teacher still needs to ask the most important question:
Does the task actually give students an opportunity to demonstrate what the upper descriptors require?
A rubric can describe Level 7–8 beautifully.
The task has to make Level 7–8 possible.
The Ceiling Is Often Written Before the Student Begins
Criterion B is not simply asking students to notice patterns.
It is asking them to investigate mathematics.
That means choosing.
Testing.
Generalising.
Verifying.
Justifying.
And where appropriate, proving.
A student cannot demonstrate independent method selection when every method has already been selected for them.
They cannot justify a general rule if the assessment ends with “state the pattern.”
They cannot become comfortable with independent mathematical investigation if every classroom task has the route already marked.
The solution is not automatically harder mathematics.
It is better assessment design.
Give students enough structure to enter the investigation.
Then give them enough space to make mathematical decisions of their own.
That is where Criterion B moves from completing a pattern worksheet to genuinely investigating patterns.
