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 becomeCan 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 becomeCan 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 becomeCan 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