# Creating Open Problems. Bruce Williams

Open Ended Questions

Why are they important?

Open ended questions allow access to the question by all students.

Students self differentiate by using numbers they feel comfortable with.

They demonstrate the level of student understanding.

They require more than remembering facts.

Student learning is developed by undertaking thinking activities.

There is more than one correct solution, and always more than one way to solve the problem.

How do I create “good” questions?

Work Backwards from the answer to a closed question. I.e Give the answer and ask for the question.

Modifying a Closed Question by leaving out at least one number. (see below)

How do I use open questions in my classroom?

Pose the question and ensure all students understand the question. Do not prompt of hint at the solution or appropriate strategies. Make the students think for themselves.

Allow students time to work on the problem. aAsk them to draw a picture.

Share student strategies and solutions. Remember the strategies are more important than the solution.

The teacher pulls all the pieces together into a tidy bundle.

How do I assess student work?

Use the student responses to inform your teaching. What areas do I need to give students more exposure to? (Not what do I need to tell them.)

Use a rubric:

0. No understanding evident.

1. Made an attempt but shows limited understanding.

2. Acceptable but incomplete.

3. Demonstrates clear understanding.

4. Goes beyond expectations.

Open Ended Questions

Examples:

1. Traditional Closed Question:

Multiply 7 x 8

Made into a Closed Real problem.

I went to the zoo yesterday and saw 7 cages with 8 birds in each.

How many birds were there in total?

Made into an Open Problem.

I went to the zoo yesterday and saw cages with birds. There were 8 birds in each cage. How many birds might there have been in total? (Extension: Draw a picture showing your answer).

2. Traditional Closed Question:

Divide 2 into 24

Made into a Closed Real problem.

I want to share $24 equally between two people. How much money do they each get? ?

Made into an Open Problem.

I want to share $24 equally among my friends. How much does each person receive?

3. Traditional Closed Question:

Subtract 35 from 64

Made into a Real Problem.

I had 64 eggs and 35 of them hatched. How many have not hatched yet?

Made into an Open Problem.

I had 64 eggs and some of them hatched. How many may not have hatched yet if just over half have hatched?

4. Traditional Closed Question:

What is ½ of 12

Made into a Real Problem.

I have 12 jellybeans and half are red. How many are red??

Made into an Open Problem.

Half of my jellybeans are red. Draw a picture of my jellybeans.

Bruce Williams. CreatingRealMathematicians.com