"Which Would You Rather?" Open Ended Questions.

It is important to incorporate open ended questions in math that encourage math-based conversations and helps students learn to justify their thinking used to support their thinking.  The best thing about an open ended question is that there is no one answer.  These types of questions encourages higher level thinking to solve problems.  In addition, open ended questions allow students to see that it is possible to use different ways to solve the problems and can produce more than one answer.

By having students open ended questions, they gain confidence in themselves because struggling students can use basic skills to find an answer while more advanced abilities can use different skills to find an answer and both are correct.  If the problems are written well, they easily become engaged. Furthermore, open ended questions encourage students to utilize creativity to solve the chosen problems.

In addition, student responses to the problems can be used by the teacher to assess their level of understanding and ability.  Open ended problems provide informal assessment but the teacher can see the thinking used to solve it, the methods used to solve it, and their understanding of the situation overall.  

The last thing about using open ended math problems is they can be used as warm-up or bell ringer problems, independent, small groups, or even whole class.  When introducing the use of open ended problems, it is important to model the process which can be done as a whole class activity.  Another time, students can work in pairs or small groups to find an answer to the problem and share the answer with the teacher via a video or google classroom.  

I read about the “Which would you rather” activity in one of Matt Miller’s blogs.  I wondered how I could use it in my math class because math is a bit different.  I found a site which provides  “Which would you rather?” Activities to help get started.  There are quite a few already created to start you off.

The selection offered at this site has quite a few ready to use questions for grades K to 12, enough for several months if you do one a week.  Each “Which would you rather” possibility are very open ended. The answer may depend on what you prefer, while others make the person think about the differences based on the situation.

One has students decide which possibility would you rather?  The situation is that you and two friends want pizza for lunch.  If you buy one pie and get a 10% discount, buy two pizzas and get 20 % off, and buy three pizzas to get 30% off.  Would you prefer Option A where each of you buys an individual pizza or option B where one of you buys three pizza on one check and you split the cost with the others.  

It is nice to have a separate worksheet for students to fill out as they work through the question.  The worksheet should have a way for them to say they prefer option ? Rather than option ? because.  There should also be a place for them to show their work and what things did they consider as they began the problem.

There are other types of open ended questions that I’ll cover another time.  This is something I could easily send home for students to work on because there are no correct answers they can find on the internet and they can’t do it via some app like photo math.  Let me know what you think, I’d love to hear.  Have a great day.

Writing Open Ended Questions

Ask students

We hear so much about integrating open ended questions in class but have you ever wondered
why?  What advantages are there to using open ended questions?  What is the best way to use them in class?

One great thing about open ended questions is there is not one correct answer.  Most textbooks are filled with problems designed to have only one possible solution. These problems are designed to be solved using a specific process.  Unfortunately, real life problems are not always as neatly solved as those in the textbooks.

In addition, these types of problems can be solved by students of different abilities with a differing level of knowledge.  These are perfect for differentiating the lessons to meet the needs of all students. These problems encourage student thinking and decision making. Textbook problems do not encourage students to develope their mathematical thinking.

The last thing these types of problems do is to help students develop their reasoning and communication abilities. The justification for the method chosen when working textbook problems is they use the method taught in the section. The reason for knowing the answer is it was in the back of the book.

The great thing about textbooks is they can provide problems which can be rewritten into open ended questions with a bit of adjustment.  First step is to start with the answer while throwing out the actual problem.  Instead of asking what 1/2 of 12 is, begin with the answer of 6.


Then create a question asking students to design a problem that gives produces that answer. So you could say 6 is a fraction of a number - what is that number and what is the fraction?

In addition there are a few other ways to create open ended questions for students.  One way is to ask students to compare and contrast numbers, shapes, graphs, probability, or measurements.  This requires more than something like 95 and 100 are different because one has 2 digits and the other has 3 digits.

Another way is to have students explain how something such as 5 is a factor of two numbers, what might be true for the two numbers? Or you could write a statement using soft words like almost or close such as two numbers multiplied together is almost 600?

Finally, have students make up sentences using numbers and mathematical words such as 8, 5, less, and. This allows for more than one answer.

If you have students who are not good at expressing their thoughts or using a more in depth explanation, these are some good ways to start students on their paths.  Let me know what you think, I would love to hear.

Creating Open Ended Questions

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. 

Writing Open Ended Questions

  Yesterday, I talked about visible thinking.  One of the suggestions was to use questions that had no one right answer so students had to explain their thinking.  Unfortunately, it is not always easy to find questions that meet the criteria so its important to know how to change questions from having only one answer to a more open ended one or create your own questions.

Lets first look at taking specific questions found in the textbook and turning them into more open ended questions.

  Take a process question such as "Calculate 47 x 25" and rewrite it to read "Calculate 47 x 25 in two different ways.". Or take a question like "I have a quarter, a dime, and three nickles in my pocket, how much do I have?" and change it to "I have 5 coins in my pocket, how much might they be worth?"."

Instead of finding the volume of a rectangular prism measuring 2.1 by 8.2 by 3.4 and rewrite it so the student is asked to create a word problem where you need to find the volume of a rectangular prism in order to solve it.  You could also rewrite it to require students to find all the possible dimensions of a rectangular prism with a volume of 120 m^3.


Next lets look at techniques for creating open ended questions.

1.  Think of Jeopardy where the answer is given and the contestant provides the question but in this case there is more than one answer.  An example might be "Area of 30 square feet" which gives four possible questions such as "What is a rectangle that is 3 by 10, or 2 by 15, or 1 by 30 or 4 by 5".  This will be a student's first thought but it also allows for questions like "What is a triangle with a height of 10 feet and a base of 6 feet."

2. Use examples that have wrong answers and have the students decide where the mistake is and how to correct it.  It might be a question like "George thinks 24 + 37 equals 51 but Jill says its 511.  Who is correct?  Explain your answer."  In this case both answer are wrong so they have to explain that.  It could also be a question involving one person seeing five rectangles in a design while the other person sees three rectangles and two squares.  The student has to help settle the disagreement.

3. Get menu's or price lists from real world places and have students calculate things like "How much would a school lunch cost if it were bought at this restaurant?" Get a news paper and ask students to speculate on the relationship between the space articles and ads take up on a page.

4. Use the Tell Me All technique which simply asks students to write down what they know on a topic such as fractions, roots, factoring, etc.

Tomorrow we'll look at creating good "Which one does not belong?" questions.  Let me know what you think.