Open-ended math questions are problems that are able to be solved in more than one way. Students are required to explain their thinking when answering open-ended question. This method lets a teacher know whether her students grasp the reasoning behind basic math skills -- or simply mastered a formula. Often these questions take the form of a word problem whereby students provide a written response that contains the answer and process used to find that answer. Once students determine what the question is asking, there are multiple strategies to choose from that will help answer the question.
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Making a table is a way to solve math problems with a lot of information. A basic table is made by creating a t-chart or two-column graph to record the information from the problem. For example, a toilet paper company is able to make 16 rolls of toilet paper in 15 minutes. How many rolls of toilet paper will the company make in two hours? To solve this problem, make a table with 15 minute intervals in the left column and the number of toilet paper rolls in the right column. There are 120 minutes in an hour, so there will be eight rows on the chart. Fill in the values to learn that the company will make 128 rolls of toilet paper in two hours (or 120 minutes).Find a Pattern
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Questions that ask students "what is the next number in the sequence?" or "which number will come fifth?" frequently require students to identify a pattern. For example, find the next three numbers in the sequence 2, 5, 8, 11. Students will identify that three is added to each number to get the next number and complete the pattern with the numbers 14, 17 and 20.
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A problem that requires working backwards contains the end result of the problem. For example, Sarah spent $30 dollars during her shopping trip and left the mall with $18 in her wallet. How much money did she begin with? Working backwards, students will create the equation x - 30 = 18 and solve it to figure out that Sarah had $48 at the beginning of her shopping trip. While this is a simple problem, problems that require students to work backwards are found at multiple levels of mathematics.
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Drawing a picture helps to solve many open-ended math questions. Questions related to measurement, geometry and probability are best answered with this strategy. For example, if a question asks what the probability is of drawing three green marbles out of a bag that contains three green marbles, five red marbles and six blue marbles, a student might choose to draw a picture of the marbles and cross out three green marbles to visualize the problem.
