Gathering Info, Using Tech

The introduction to the problem in Act I intentionally leaves out information necessary to solve the problem. This requires students to figure out the information they will need for themselves. Making this determination is a crucial, though often neglected, part of the problem solving process that requires students to think critically about the problem at hand. Having students figure out the information they need to know makes this problem even more realistic, because people in the real world are rarely given a problem along with three needed values and a formula.

After giving students an opportunity to think through what the problem asks and what they need to answer it, students should come up with the following ideas:

  • In order to find which fruit makes the cheapest snack, we need to know which type of fruit is cheaper per piece.
  • Needed information:
    • Price per pound of each type of fruit
    • Weight of an individual apple and pear, respectively

Knowing in advance that this information will be required to solve the problem, Act II is ready upon student request.

We now have a clear idea of what we need to find and the information with which to find it. Next comes choosing appropriate technological tools to solve the problem. While a variety of approaches could be used to solve this problem, we will analyze a solution in which a student utilizes a spreadsheet.

The weight of each piece of fruit is given in ounces, but the price of the fruit is given per pound. Using a spreadsheet, we will organize our information by putting the weight in ounces of a given piece of fruit in the first column, converting the weight in ounces to the weight in pounds in the second column, with the unit price per apple and pear in the third and fourth columns, respectively, as shown below.

unit-price-spreadsheet

The above data was created in Numbers with the following steps:

  1. To enter the weight of fruit in ounces in column B, enter 1 in B2. In B3, enter this formula: B2+1 and fill this formula down to cell B17.
  2. To calculate the weight of fruit in pounds, we must divide the number of ounces in column B by 16 ounces. Enter this formula into C2: B2/16. Fill this formula down column C.
  3. To calculate the price per apple, we must multiply $2.49/lb times the weight of fruit in column C. Enter this formula into D2: 2.49*C2. Fill this formula down column D.
  4. Repeat step 2 in column E, using this formula: 2.99*C2.

It should be noted that the cells in columns D and E were formatted with a currency format so that the values were rounded to the nearest hundredth with a dollar sign. View the above steps in the pictures below:

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Next, we use the information organized in the spreadsheet to find that a 4 oz. pear costs $0.75 while a 6 oz. apple costs $0.93.

unit-price-of-fruit-highlighted

Creating a data chart that includes various weights for the fruit provides students with the opportunity for further analysis. For example, students can observe that the unit prices of the fruit are the same when an apple weighs 6 oz. and a pear weighs 5 0z., or when an apple weighs 12 oz. and a pear weighs 10 oz. (although that is big fruit).

From this, we conclude that the pears make a more cost-effective snack, and the students are rewarded with a video in Act III that verifies their conclusion by showing the respective checkout totals for purchasing three apples and three pears.

But like any great story, this problem has a sequel! Continue to the next page for more.

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