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How to Open Up Word Problems (and promote digital literacy, too!)

by Heidi Schuler-Jones

In today’s classroom, we know that it is not enough to simply teach math content and skills. Students also need to develop facility with technology tools. Using a traditional word problem as a starting point, here are some ideas for doing so.

First, think about ways to ‘open up’ a word problem:

1. Limit the information provided to students and instead have them find information based on their own interests.
2. Allow students to make choices on figures, when possible, or recommend a range of choices.
3. Instead of having one answer, provide a way for students to evaluate the information they gathered, organize and make meaning of the information, and communicate the reasoning behind the choices they made using a variety of methods, visuals, and models.
4. Differentiate the same problem for multilevel classrooms by providing conditions for the types of numbers to use. For example, using less-friendly numbers for more advanced students or more friendly and common numbers for less advanced students. Other options: provide more or less information, offer more or less decisions, provide more or less steps (each of these can provide a push for more advanced students or support for those needing greater assistance).

Next, consider where digital literacy tools might be appropriate and useful.

Suggested digital literacy tools can extend beyond the basic calculator functions. Encourage students to use more advanced functions on their smart phone calculator apps and/or to become familiar with spreadsheet and graphing functions found in programs like Microsoft Excel, Google Sheets, and Desmos.

Now, let’s apply these tips to ‘open up’ a traditional workbook problem into opportunities for deeper, more active learning.

Traditional workbook problem:
John is interested in buying a used car for $15,000. He puts down 25% with the rest to be paid over a 5-year period. If his monthly payments are $197, how much will he pay altogether for the car?

Steps to Open Up Word Problems	Closed (traditional) word problem	Opened-up word problem
Limit the information provided to students and instead have them find information based on their own interests.	John is interested in buying a used car for $15,000.	Check out the prices of vehicles at two different dealerships in the area. Decide on a vehicle that might suit your needs.
Allow students to make choices on figures, when possible, or recommend a range of choices.	He puts down 25% with the rest to be paid over a 5-year period.	Decide the amount you want to put down and the number of years you want to finance the vehicle. Decide the maximum monthly payment you can afford.
Instead of having one answer, provide a way for students to evaluate the information they gathered, organize and make meaning of the information, and communicate the reasoning behind the choices they made using a variety of methods, visuals, and models.	If his monthly payments are $197, how much will he pay altogether for the car?	Create a graph and/or in-out table to show the cost of the vehicle over the years that you have financed it for and be prepared to explain your choices.
Differentiate the same problem for multilevel classrooms by providing conditions for the types of numbers to use. For example, using less-friendly numbers for more advanced students or more friendly and common numbers for less advanced students. Other options: provide more or less information, offer more or less decisions, provide more or less steps (each of these can provide a push for more advanced students or support for those needing greater assistance).		Conditions for more advanced students: Estimate a reasonable answer first. Use two different down payment percents with a non-repeating fraction or decimal in each. Compare two different car deals on a trend graph. Conditions for less advanced students: Estimate a reasonable answer first. Use one of the following benchmark percents for the down payment: 10%, 15%, or 25%. Use the provided in-out table below to track the cost of the vehicle after the down payment (Year 0) and for each of the next 5 years.
Suggested digital literacy tools can extend beyond the basic calculator functions. Encourage students to use more advanced functions on their smart phone calculator apps and/or to become familiar with spreadsheet and graphing functions found in programs like Microsoft Excel, Google Sheets, and Desmos.	Calculator Smart phone (calculator	Calculator Smart phone (calculator) Amortization calculator or app Web search Spreadsheets and graphs    *   Excel    *  Google Sheets    *  Desmos

Another way to open-up traditional problems is to remove the question completely and simply ask, “What do you notice?” and “What do you wonder?” Using our example above, the word problem would thus shorten to simply:

John is interested in buying a used car for $15,000. He puts down 25% with the rest to be paid over a 5-year period.

Students spend a minute jotting down the things they notice and wonder and then share these observations with a partner or the whole class. It generates critical thinking and reasoning about what information is needed before attempting to plug into a formula or calculating numbers that may not be relevant. It’s quite common for students to come up with the actual question themselves but in their own words, which helps to make sense of the problem. It also gives them practice developing test-like questions themselves based on their own understanding of the problem and the choices they make.

From those noticings/wonderings, students can follow the steps to open-up word problems as shown in the table above. Watch this video to learn more about this strategy: Ever Wonder What They’d Notice?: Annie Fetter

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