Designing quality open- ended
tasks in mathematics
Louise Hodgson
May 2012
Characteristics of good questions
 Require more than remembering a fact or
reproducing a skill,
 Students can learn from answering the
questions; teachers can learn about the
students,
 May be several acceptable answers.
Sullivan and Lilburn 2004
Why open ended questions?
•They engage all children in mathematics
learning.
•Enable a wide range of student responses.
•Enable students to participate more actively in
lessons and express their Ideas more
frequently.
•Enable teachers opportunity to rove and probe
student mathematical thinking.
Characteristics of good
teachers
•They plan less
•The lesson is predominately about
interacting with the students.
•Peter Sullivan 2008
Making questions open ended
Method 1: Working backwards
 Indentify a mathematical topic or
concept.
 Think of a closed question and write
down the answer.
 Make up a new question that
includes (or addresses) the answer.
Method 1: Working backwards
How many chairs are in the room?
(4)
can become ….
I counted something in our room. There
were exactly four. What might I have
counted?
Method 1: Working backwards
Round this decimal to one decimal place:
5.7347
can become ….
A number has been rounded off to 5.8.
What might the number be?
Method 1: Working backwards
Find the difference between 6 and 1
can become ….
Method 1: Working backwards
The difference between two
numbers is 5. What might the two
numbers be?
Making questions open ended
Method 2: Adapting a standard
question
 Indentify a mathematical topic or
concept.
 Think of a standard question
 Adapt it to make an open ended
question.
Method 2: Adapting a standard
question
What is the time shown on this clock?
Can become…
My friend was sitting in class and she
looked up at the clock. What time
might it have shown? Show this time
on a clock
Method 2: Adapting a standard
question
731 – 256 =
Can become…
Arrange the digits so that the
difference is between 100 and 200.
Method 2: Adapting a standard
question
Ten birds were in a tree. Six flew away.
How many were left?
Can become…
Method 2: Adapting a standard
question
Ten birds were in a tree. Some flew
away. How many flew away and
how many were left in the tree?
Now have a go yourselves!
In the number 35, what does
the 3 mean?
.
Some important considerations
•The mathematical focus
•The clarity of the task/
question
•That it is open ended
Building open ended tasks into a
lesson
It is important to plan two further
questions/ prompts:
•For those children who are unable to start
working (enabling prompts).
•For those children who finish quickly
(extending prompts).
High quality response
Examples of evidence of a high quality response includes those
that:
•Are systematic (e.g. may record responses in a table or
pattern).
•If the solutions are finite, all solutions are found.
•If patterns can be found, then they are evident in the response.
•Where a student has challenged themselves and shown
complex examples which satisfy the constraints.
•Make connections to other content areas.
Discuss the tasks and adaptions.
Consider the following:
1. What is the maths focus of the
closed task?
2. Does the new tasks have the same
mathematical focus?
3. Is the new task clear in its wording?
4. Is the new task actually open
ended?
Lesson structure
Key components:
•Open ended tasks which allow all students
accessibility,
•Explicit pedagogies,
•Enabling prompts for those children who are
experiencing difficulty,
•Additional task or question to extend those
children who complete the original task.
References
Sullivan, P., & Lilburn, P. (2004). Open – ended
maths activities. Melbourne, Victoria: Oxford.
Sullivan, P., Zevenbergen, R., & Mousley, J.
(2006). Teacher actions to maximize
mathematics learning opportunities in
heterogeneous classrooms. International Journal
for Science and Mathematics Teaching. 4, 117143
louise.hodgson@catholic.tas.edu.au