By Jane M. Wilburne, Posted September 15, 2014 –   

An interesting problem that I have used with elementary school students, classroom teachers, and preservice teachers involves opportunities to engage in various problem-solving strategies. The most important step in this problem is Understanding the problem. It offers students the chance to reason and think critically about what the problem is asking them to find and the meaning of the problem. The problem can be adapted in context and quantity to meet the needs of students from primary grades to upper middle level grades.

A fast food restaurant sells chicken nuggets in packs of 4 and 7. What is the largest number of nuggets you cannot buy? How do you know this is the largest number you cannot buy?

The word cannot is the key term in the problem. In many situations where I have presented this problem, students are confused by the meaning of the problem. I usually have to start them off by asking them if they could buy only 1 nugget (no), 2 nuggets (no), 3 nuggets (no), 4 nuggets (yes: 1 pack of 4), 5 or 6 nuggets (no), 7 nuggets (yes: 1 pack of 7), 8 nuggets (yes: 2 packs of 4 nuggets), and so on.

In most cases, students make a list of consecutive numbers and try different addition combinations of 4 and 7 to see if they can make the number of nuggets. Some students use colored chips to represent the packs of nuggets. For example, red chips represent packs of 4 nuggets, blue chips represent packs of 7 nuggets. Two red chips and one blue chip would represent 4 + 4 + 7 = 15 nuggets. Students get lots of practice adding combinations of multiples of 4 and multiples of 7 because addition can be used to solve the problem. Students in primary grades can engage in a similar problem with smaller numbers of nuggets in each package.

Try the problem and see what you get. Then try to create another problem using a different context and different numbers. For example, what is the largest number of pencils you could not purchase if pencils came in packages of 5 and 8? Do you see any patterns with respect to the solution and what types of numbers work best in the context of the problem?

Jane M. Wilburne is an associate professor of mathematics education at Penn State Harrisburg. She teaches content and methods courses for both elementary and secondary mathematics teachers as well as graduate mathematics education courses. She is a co-author of Cowboys Count, Monkeys Measure, and Princesses Problem Solve: Building Early Math Skills Through Storybooks (Brookes Publishing 2011) and has published numerous manuscripts in Teaching Children Mathematics, among other journals. Jane began serving as a member of the Teaching Children Mathematics Editorial Panel in May 2014, and her term will continue through April 2017.

Archived Comments

Love the mcnugget task! I use it in my elementary education problem solving class. Interesting fact -- the original task used the original numbers McDonalds sold nuggets in when they were first introduced: 6, 9 and 20.
Posted by: AndrewT_47214 at 9/17/2014 7:26 PM