Open-Ended Math Problems: Sample Problems and Solution Strategies

Because open-ended math problems require a different type of thinking than most math drills in class, some students enjoy them more. Not many topics in math allow for creativity like open-ended problems do. Practice some at home by using the sample problems and solution strategies below.

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Why Are Open-Ended Math Problems Important?

Open-ended math problems are any problems that can be solved more than one way. Some even have multiple correct answers. These types of questions require logical thinking; frequent practice will help your child develop and refine this skill.

Most math tests that your child will take in school have open-ended math problems. On these tests, teachers usually give partial credit if the student got the wrong answer but showed work. So, when your child practices at home, make sure she shows all the work she did to solve the problem.

In addition, practicing open-ended problems can help your child do better on multiple-choice tests. If your child can solve a problem without even looking at the list of potential answers, he or she will probably get through the test more quickly and will be less distracted by misleading answer choices.

Open-Ended Problems and Solutions

1. Your neighbor offers to pay you in one of two ways before you mow her lawn. Option one is to receive $25 right now. Option two is to be paid $5 an hour. What option would you choose and why?

For problems like this, your child should calculate both options. Depending on how large the neighbor's lawn is, it may be more cost beneficial to be paid by the hour; however, if the yard is very small and it only takes an hour to finish, then you'd receive $5 instead of $25.

2. Bob wants to make five cherry pies for each of his friends. One pie requires two and a half cans of cherries. At the store, there are two brands of canned cherries on sale. Brand one is $3 a can, but brand two is buy one for $5 and get one free. Which is the better deal?

Like the previous problem, the most important strategy is to explore all the options available. However, you must begin by figuring out how many cans of cherries Bob will need in all. Because 5 x 2.5 = 12.5, he will need 13 cans total.

Now, move on to figure out which is the better deal. Try brand one first: 13 x 3 = 39. Because brand two offers buy one get one free, you only have to calculate how much seven cans would cost: 5 x 7 = 35.

Point out non-mathematical things to consider as well. For instance, with brand two, Bob would receive an extra can of cherries, because he's paying for seven cans and gets one free for each can he buys.
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