Creating+Rich+Problems

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.

<span style="font-family: Comic Sans MS,cursive;">**How do I assess student work?**
 * <span style="font-family: Comic Sans MS,cursive;">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.)
 * <span style="font-family: Comic Sans MS,cursive;">Use a rubric:
 * <span style="font-family: Comic Sans MS,cursive;">0. No understanding evident.
 * <span style="font-family: Comic Sans MS,cursive;">1. Made an attempt but shows limited understanding.
 * <span style="font-family: Comic Sans MS,cursive;">2. Acceptable but incomplete.
 * <span style="font-family: Comic Sans MS,cursive;">3. Demonstrates clear understanding.
 * <span style="font-family: Comic Sans MS,cursive;">4. Goes beyond expectations.

<span style="font-family: Comic Sans MS,cursive;">__**Open Ended Questions**__ <span style="font-family: Comic Sans MS,cursive;">Examples: **//<span style="font-family: Comic Sans MS,cursive;">1. Traditional Closed Question: //** <span style="font-family: Comic Sans MS,cursive;">Multiply 7 x 8 **//<span style="font-family: Comic Sans MS,cursive;">Made into a Closed Real problem. //** <span style="font-family: Comic Sans MS,cursive;">I went to the zoo yesterday and saw 7 cages with 8 birds in each. <span style="font-family: Comic Sans MS,cursive;">How many birds were there in total? <span style="font-family: Comic Sans MS,cursive;">//**Made into an Open Problem.**// <span style="font-family: Comic Sans MS,cursive;">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).

**//<span style="font-family: Comic Sans MS,cursive;">2. Traditional Closed Question: //**

<span style="font-family: Comic Sans MS,cursive;">Divide 2 into 24 **//<span style="font-family: Comic Sans MS,cursive;">Made into a Closed Real problem. //** <span style="font-family: Comic Sans MS,cursive;">I want to share $24 equally between two people. How much money do they each get? ?  <span style="font-family: Comic Sans MS,cursive;">//**Made into an Open Problem.**// <span style="font-family: Comic Sans MS,cursive;">I want to share $24 equally among my friends. How much does each person receive?

**//<span style="font-family: Comic Sans MS,cursive;">3. Traditional Closed Question: //** <span style="font-family: Comic Sans MS,cursive;">Subtract 35 from 64 <span style="font-family: Comic Sans MS,cursive;">//**Made into a Real Problem.**// <span style="font-family: Comic Sans MS,cursive;">I had 64 eggs and 35 of them hatched. How many have not hatched yet? <span style="font-family: Comic Sans MS,cursive;">//**Made into an Open Problem.**// <span style="font-family: Comic Sans MS,cursive;">I had 64 eggs and some of them hatched. How many may not have hatched yet if just over half have hatched?

**//<span style="font-family: Comic Sans MS,cursive;">4. Traditional Closed Question: //** <span style="font-family: Comic Sans MS,cursive;">What is ½ of 12 <span style="font-family: Comic Sans MS,cursive;">//**Made into a Real Problem.**// <span style="font-family: Comic Sans MS,cursive;">I have 12 jellybeans and half are red. How many are red?? <span style="font-family: Comic Sans MS,cursive;">//**Made into an Open Problem.**// <span style="font-family: Comic Sans MS,cursive;">Half of my jellybeans are red. Draw a picture of my jellybeans.

Bruce Williams. CreatingRealMathematicians.com ||