In "The Camping Trip" challenge, students have opportunities to employ all five process standards. They will problem solve as they decide on a strategy for solving a problem where the answer is not immediately obvious. They reason as they think about and justify their solution. They should have opportunities to communicate about their solution by discussing it with classmates, parents, and teachers. Children will be able to make connections between mathematical concepts (patterns, number, estimation, data, and measurement) in order to solve the problem and do the extension activities. Finally, all students will have opportunities to create and use representations (drawings, charts, words, equations, manipulatives, etc.) to provide a record of their efforts to understand the mathematics of this challenge and make their understanding available to others.

About the mathematics involved in this challenge:
Where there is pattern, there is algebra. Recognizing obvious patterns allows children to make generalizations about what is coming next. In this problem, children must connect their knowledge of simple repeating patterns, odd and even numbers and ordinality. Some students may be able to generalize that every odd numbered child will be tickled by the first ghost and even that every other odd numbered child will be tickled by both ghosts. Recognizing these patterns will allow children to continue the pattern to answer questions such as "If there were 50 scouts in the line, would the 47th scout be tickled once, twice, or not at all." (Since 47 is an odd number, it is a given that it will be tickled at least once.)

About the challenge:
While children may choose to solve this problem using several strategies (Act Out, Use Models, Draw a Picture), I would like to focus on drawing a picture as an appropriate strategy for this problem. It is often said that a picture is worth a thousand words, and it can be true in problem solving. Drawing can help students visualize the problem so that seemingly complex problems can become easy to solve because it helps children focus on the essential elements of the situation. Drawing can also be an entry point into writing about mathematics. Perhaps because "Draw a Picture" is one of the first strategies taught to young mathematicians, some people view this strategy as rather low level. It is true that the strategy's efficiency fades as children grow older and their ability to work in the abstract increases. However there will always be problems that become clearer when a picture or diagram is used. In fact many college math professors advise their students to try drawing a picture before proceeding to any other strategy! It is important to explain that these pictures do not need to be detailed or even realistic. A circle can represent a child. In fact adding lots of detail to pictures tends to draw students' attention away from the mathematics in the problem. When demonstrating "Draw A Picture" be sure to keep the drawing simple in order to keep the children's focus on the problem.

Modifications of the Problem:
Modifications can usually be made by allowing younger learners to use physical models and illustrations to help understand the situation. Very young children can solve the problem if it is modified so that there is just one ghost doing the tickling. To make the problem more challenging for older learners, make it more complex. For instance, add a third ghost tickling in a different pattern or add more scouts to the line. Ask more difficult questions about the situation, such as "Would the 26th scout be tickled once, twice or never?" "Can you discover a way to accurately predict the number of bites for a scout in any place in the line?"

Extensions of the Problem:
"Ouch!"
"Ouch!" is a group game that is fun to play and helps children discover number patterns and multiples. The class or group gets into a circle and determines a pattern, such as "even numbers." Start counting off around the circle, and when it is your turn, if you are an even number, you must say "ouch!" and sit down. Continue around the circle until only one child is left standing. (Other patterns might be every fifth number, numbers that end in zero, prime numbers, etc. depending on the level of the class.)

Problem Solving

Recipe for Camp Fire S'Mores

Serves 1

1 marshmallow (slightly toasted over campfire)
1 square from a Hershey's ™milk chocolate bar
2 square graham crackers.

Put the chocolate square on top of the toasted marshmallow.
Put the toasted marshmallow between the graham crackers to make a sandwich.
Enjoy!

If you are making up the shopping list, and you plan for each of the 12 boy scouts to have 2 S'Mores after their hike, how many of each ingredient would you put on the list?

______graham crackers
______marshmallows
______chocolate bars*

*this is a challenge because you need to know how many individual squares are contained in each Hershey's bar. (12)