{"id":534,"date":"2018-10-15T12:39:14","date_gmt":"2018-10-15T16:39:14","guid":{"rendered":"https:\/\/adultnumeracyatterc.wordpress.com\/?p=534"},"modified":"2018-10-15T12:39:14","modified_gmt":"2018-10-15T16:39:14","slug":"making-the-most-of-word-problems","status":"publish","type":"post","link":"https:\/\/www.terc.edu\/adultnumeracycenter\/making-the-most-of-word-problems\/","title":{"rendered":"Making the Most of Word Problems"},"content":{"rendered":"

by Sarah Lonberg-Lew<\/p>\n

\"The<\/p>\n

Whether they\u2019re called word problems, story problems, or problems in context, they usually amount to the same thing \u2013 a short story about a character who for some reason needs to know how long it will take to do a task or how much it will cost to go on ten rides at the fair. Why do our students need to know how to answer these questions?<\/p>\n

The clearest reason seems to be that they will have to do so on the high school equivalency test that is standing between them and their next step, be it college or career. To that end, it makes sense to teach students a strategy for finding the answer quickly and with a minimum of fuss.<\/p>\n

As a result, many teachers choose to have students memorize a mini-dictionary of key words:<\/p>\n

more<\/span> = add<\/h5>\n
less<\/span> = subtract<\/h5>\n
of<\/span> = multiply<\/h5>\n
each<\/span> = divide<\/h5>\n

\u2026 and the list goes on.<\/p>\n

There are two problems with this approach. The first, and relatively minor problem, is that it doesn\u2019t actually work.<\/p>\n

The word \u201cmore\u201d can indicate subtraction as easily as addition in a word problem, for example:<\/p>\n

\n

Jack has five more<\/u> apples than Jill. Jack has eight apples. How many does Jill have?<\/em><\/span><\/p>\n<\/blockquote>\n

The word “each\u201d can mean multiply as easily as it can mean divide. Contrast the following problems:<\/p>\n

\n

Suzy gave five apples to each<\/u> of her four friends. How many apples did she give out?<\/em><\/span><\/p>\n

Suzy had twenty apples and gave the same amount to each of her four friends.\u00a0<\/em>How many did apples did each<\/u> friend get?<\/em><\/span><\/p>\n<\/blockquote>\n

Test makers know the key word dictionary, too and will likely present students with problems for which these key word shortcuts don’t work. This is not because they are trying to trick our students or make them fail, but because the purpose of word problems is not to assess how well the students have memorized the key words. It is to assess their ability to reason.<\/p>\n

And this brings me to the second and much bigger problem with this approach: it wastes our students\u2019 time and deprives them of the opportunity to learn something valuable. Using key words to solve tidy word problems may help them score some points on the test, but that\u2019s where its (already questionable) usefulness ends. It\u2019s a shame to invest so much time and energy on such a short-sighted goal. Instead we can choose to capitalize on the need to learn to solve word problems as an opportunity to develop confidence and skill with mathematical reasoning and critical thinking.<\/p>\n

One good way to push students to reason about word problems instead of trying to find the answer as quickly as possible is to remove the question and maybe even some necessary information from the problem. For example:<\/p>\n

Jack and Jill went apple picking. The orchard charges $8 per person for admission. A half-peck bag costs $10 and a one-peck bag costs $18. <\/em><\/p><\/blockquote>\n

Think of all the questions your students could ask and answer with this simple scenario, like:<\/p>\n