In "Halloween Candy Logic" 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.

• reason as they think about and justify their solution as the only possible correct answer.

• communicate about their thinking by discussing it with classmates, parents, and teachers, as well as by posting their written solution on the message board, and communicating via the message board with other students from around the world.

• make connections between mathematics and the subject of candy, which is inherently interesting to children. In the extension activities, students connect the operation of multiplication to measurement and data collection.

• 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 mathematical content in this challenge:
Solving logic problems such as the one described in the "Halloween Candy Logic" challenge falls under the math content area of data analysis and statistics. In these problems, a logic chart or matrix can provide a clear, visual representation of data. The chart helps students match candy choices to Barney, Danny, Aunty, Uncle Bill, and Gina.

By the process of elimination, students should be able to solve the problem based on only a few clues. Solving logic problems also calls for deductive reasoning, a prerequisite for algebraic thinking.

About the challenge:
Using logical reasoning is a good strategy for solving math problems too. It requires that the children analyze clues for bits and pieces of information, and then use that information in order to solve the challenge. Children can solve the challenge by working individually, in cooperative groups or with family members at home. It is important for children to discuss the reasoning used to arrive at their answers. Older children may wish to make up their own logic problems for the class to solve.

The harder challenge is an example of a problem that can be solved by working backwards, or employing a "time-line" approach.

Hershey® Bar	Snickers®

Extensions:
Data Collection/Surveys - Number
According to the U.S. Census 2000, 41.1 million children, ages 5 to 14 live in the US. A national survey found that 93% of this age group go "trick or treating" on Halloween. An informal survey found that the median amount of candy collected by each "trick or treater" was 68 pieces.*

Using this data, have students survey the class to see how many students went trick or treating. Then, depending on the age of the group, figure out about how many pieces of candy might have been collected by the class by estimating, using a calculator or some other calculation method. (About how much was collected throughout the U.S., on Halloween 2003?)

*From Math in Middle School, Oct 2002.

Data Collection - Sorting
If you live in a place where children collect candy at Halloween, you may find that they have lots left over. A good project might be to see how many ways they can sort their candy into two groups and list these ways.

Examples include:

Estimation and Measurement Activities:

Over 1 million miles of Twizzler® licorice is made in a year! If you placed Twizzler® licorice end to end (no fair stretching!) that's nearly 5 roundtrips from the Earth to the Moon!

• Estimate about how long a Twizzler® "whip" is, in centimeters or inches. (A centimeter is about the width of your little fingernail. An inch is about the distance between the first and second knuckle on your finger.) Which was easier to estimate – in centimeters or inches?

• Measure to see how long one Twizzler® "whip" is, using a centimeter ruler. Based on this measurement, how long would a whole package of Twizzler® candies be if you placed each piece end to end?

• Estimate the weight of a Twizzler® whip in grams. (1 gram is about the weight of paper clip.) Based on this estimate, how much would a bag of Twizzler® whips weight?

• Estimate about how many Skittles® candies will fit into a tablespoon without spilling. Test your estimate.

• Compare the weight of candies. How many Skittles® balance a Starburst®? Which candy weighs the least? The most?

• What is the area of a Starburst® candy? A mini-candy bar?