Using open tasks

Open tasks are suitable for a wide range of students. If the tasks are well designed, they can be simplified if necessary so that every student can make a start. They are also suitable for high achievers because the tasks have potential for extension.

Open tasks make excellent assessment tools for content knowledge, problem-solving and reasoning. Teachers can use prompts to see what students understand and are capable of doing.

• Can you see any patterns? So what might the rule (or general case) be?
• Have you got all of the possibilities? How do you know?
• What strategy are you using and why does it work?
• You have not included any … yet. (e.g. big numbers, fractions, negative numbers, composite functions)

To write an open task, base it on a standard one but alter it to expect more than one answer. The resulting task should have many possible correct answers. Open tasks are easy to create for all year levels using this strategy and can be used in all areas of the curriculum.

Here is an example.

Billiard balls.
Source: James Barker/Freedigitalphotos.net

• Some billiard balls are arranged in the shape of an equilateral triangle, with 5 rows and 15 balls. It would also be possible to have a very small triangle with 2 rows and 3 balls. What are some other possible combinations of rows and balls?
• List as many combinations of rows and balls as you can.
• Explain how you worked out your largest example.

For older students extend the problem to triangular and rectangular prisms.