We know it is important to ask more open ended questions in math but we can't always find the right ones for the topic we are teaching. So how does one go about creating this type of question.
One way is to give the answer and ask students to find all possible combinations which give the answer. An example would be "Find as many ways to find an area of 48 square feet." There are multiple possibilities.
Another way of creating open ended is to select two different answers to the same question, one right, one wrong or two incorrect answers and ask the students to explain why the answer they selected is wrong. Then they should correct it.
Find math problems to the real world and relate the information to something they know such as providing restaurant menus and a school menu. Have the students find the cost of the same meal from a restaurant. You could ask students to discuss math they see on the way home from school. Their answer might include a sale for books so they are 50% off or others they see.
Ask students to write down everything they know about a topic before beginning the unit and at the end. This way they only have to share what they know. In addition, it is good to have students include vocabulary words they know. One could even go so far as to have students brainstorm their ideas.
Take textbook questions and adjust them so students have to explain their thinking. Rather than have students round 23 to either 20 or 30, ask them to explain when you want to round to 20 or when its better to round to 30.
Have students create a problem based on the information given such as the answer is 18 and the problem must include subtraction. The student might write 36-18 while another student might come up with 18 - 0. Both questions are correct.
Think about these things as you create the questions:
1. Does it focus on essential concepts?
2. Does it lead to other questions?
3. Does it tap real world situations?
4. Does it allow students to work together to find solutions?
5. Does it allow for multiple pathways or multiple solutions?
Have fun creating your own open ended questions. Let me know what you think.