Turning Textbook Questions Into Open Ended Questions.

Textbooks are so nice but most of the time, the questions found in each section are closed ended because they have just one answer which is either correct or not.  It is important to learn to take the questions out of the textbook to rewrite them into open ended questions so as to inspire mathematical thinking and conversation. 

Furthermore, students get used to the idea that all questions have one answer when in reality that might not be true.  For instance, if you are buying new cabinets for your kitchen, the cost is often dependent of the type of wood used, the type of cabinets, and size.  

So to change textbook questions into open ended questions, there are a couple of different ways to do it but there are some things to keep in mind.  One needs to identify a mathematical topic or concept to address.  Think about how to express the question so that it has several possible answers rather than just one.

One way to accomplish this is to take look at the question such as "What is the perimeter of a rectangle that is 13 inches long and 8 inches wide" and find the answer - 42 inches.  Rephrase the question " Construct two rectangles with a perimeter of 42 inches.  This question has more than one answer which makes it a better question.  

Other strategies one can use to convert open problems or questions into open questions include turning the question around by asking the student to suggest ways to get the answer instead of finding the answer.  Ask the student to identify similarities and differences such as in "How are 85 and 90 similar?" "How are they different?"  This question might lead to a student saying they are similar because they are multiples of 5 but they are different because one is a multiple of 10 while the other is not.

Ask students to explain something such as "6 is a factor of two different numbers.  What else might be true about two numbers?" This could lead to something like "If 6 is a factor of two different numbers, the two numbers are also divisible by 2 and 3."  Have students create a sentence such as "Create a sentence that includes the numbers 5 and 8 with the words "more" and "and"?".  You might end up with a response of " The product of three and four is more than 10."  Include soft words such as almost or nearly such as "You multiply two numbers together and the product is almost 600.  What might those two numbers be?"

If you are want to rewrite word problems to make them more open ended, there are six different things one can do to make it open ended.  The original problem from the book read " How many nickels are in 55 cents.  The first thing is to remove all restrictions so it reads "How many coins does it take to make 55 cents?  Students have a choice of which coins they will use to answer the question.  Second is to remove the known so you might say "I have a closed handful of nickels, how many do I have?"  This requires students to estimate a reasonable number of coins.  

Third way is to swap the known with the unknown and remove the restriction so instead of saying nickels, write the question so it is more general "I have 5 coins, 3 are the same, how much do I have?".  Again students have a variety of choices from pennies to nickels to dimes, to quarters or even half dollars and dollar coins.  Fourth, one needs to remove the known and the restriction and change the unknown such as I have 5 coins, how much money do I have?"  Finally change the known, unknown, and restriction such as "What is the shortest or longest line that could be made with 5 coins?" or "I have some coins in my hand, how much money might I have?"

It doesn't take much to change the closed question into an open ended question. Let me know what you think, I'd love to hear.  Have a great day.