This document discusses designing quality open-ended tasks in mathematics. It provides two methods for creating open-ended questions: working backwards from a closed question and adapting a standard question. Good open-ended tasks engage all students, allow for diverse responses, and enable teachers to interact with and understand students' mathematical thinking. When planning open-ended tasks, teachers should consider the mathematical focus, clarity of the task, and include enabling and extending prompts. High quality student responses systematically consider all possible solutions and make connections across mathematical concepts.

1. Designing quality open- endedDesigning quality open- ended
tasks in mathematicstasks in mathematics
Louise HodgsonLouise Hodgson
May 2012May 2012

2. Characteristics of good questionsCharacteristics of good questions
Require more than remembering a fact orRequire more than remembering a fact or
reproducing a skill,reproducing a skill,
Students can learn from answering theStudents can learn from answering the
questions; teachers can learn about thequestions; teachers can learn about the
students,students,
May be several acceptable answers.May be several acceptable answers.
Sullivan and Lilburn 2004Sullivan and Lilburn 2004

3. Why open ended questions?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.

4. Characteristics of good
teachers
•They plan less
•The lesson is predominately about
interacting with the students.
•Peter Sullivan 2008

5. Making questions open endedMaking questions open ended
Method 1: Working backwardsMethod 1: Working backwards
Indentify a mathematical topic orIndentify a mathematical topic or
concept.concept.
Think of a closed question and writeThink of a closed question and write
down the answer.down the answer.
Make up a new question thatMake up a new question that
includes (or addresses) the answer.includes (or addresses) the answer.

6. Method 1: Working backwardsMethod 1: Working backwards
How many chairs are in the room?How many chairs are in the room?
(4)(4)
can become ….can become ….
I counted something in our room. ThereI counted something in our room. There
were exactly four. What might I havewere exactly four. What might I have
counted?counted?

7. Method 1: Working backwardsMethod 1: Working backwards
Round this decimal to one decimal place:Round this decimal to one decimal place:
5.73475.7347
can become ….can become ….
A number has been rounded off to 5.8.A number has been rounded off to 5.8.
What might the number be?What might the number be?

8. Method 1: Working backwardsMethod 1: Working backwards
Find the difference between 6 and 1Find the difference between 6 and 1
can become ….can become ….

9. Method 1: Working backwardsMethod 1: Working backwards
The difference between twoThe difference between two
numbers is 5. What might the twonumbers is 5. What might the two
numbers be?numbers be?

10. Making questions open endedMaking questions open ended
Method 2: Adapting aMethod 2: Adapting a
standard questionstandard question
Indentify a mathematical topic orIndentify a mathematical topic or
concept.concept.
Think of a standard questionThink of a standard question
Adapt it to make an open endedAdapt it to make an open ended
question.question.

11. Method 2: Adapting a standardMethod 2: Adapting a standard
questionquestion
What is the time shown on this clock?What is the time shown on this clock?
Can become…Can become…
My friend was sitting in class and sheMy friend was sitting in class and she
looked up at the clock. What timelooked up at the clock. What time
might it have shown? Show this timemight it have shown? Show this time
on a clockon a clock

12. Method 2: Adapting a standardMethod 2: Adapting a standard
questionquestion
731 – 256 =731 – 256 =
Can become…Can become…
Arrange the digits so that theArrange the digits so that the
difference is between 100 and 200.difference is between 100 and 200.

13. Method 2: Adapting a standardMethod 2: Adapting a standard
questionquestion
Ten birds were in a tree. Six flew away.Ten birds were in a tree. Six flew away.
How many were left?How many were left?
Can become…Can become…

14. Method 2: Adapting a standardMethod 2: Adapting a standard
questionquestion
Ten birds were in a tree. Some flewTen birds were in a tree. Some flew
away. How many flew away andaway. How many flew away and
how many were left in the tree?how many were left in the tree?

15. In the number 35, what does
the 3 mean?
.
Now have a go yourselves!Now have a go yourselves!

16. Some important considerationsSome important considerations
•The mathematical focus
•The clarity of the task/
question
•That it is open ended

17. Building open ended tasks into aBuilding open ended tasks into a
lessonlesson
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).

18. High quality responseHigh 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.

19. Discuss the tasks and adaptions.Discuss the tasks and adaptions.
Consider the following: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?

20. Lesson structureLesson 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.

21. ReferencesReferences
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, 117-
143
louise.hodgson@catholic.tas.edu.au