# Party Time

In the problem Party Time, students use mathematical concepts of logic, reasoning, and counting methods. The mathematical topics that underlie this problem are knowledge of logic, deductive reasoning, counting principles/strategies, and a variety of mathematical representations such as tree diagrams, Venn diagrams, tables, charts, and matrices.In each level, students must make sense of the problem and persevere in solving it (MP.1). Each problem is divided into five levels of difficulty, Level A through Level E, to allow access and scaffolding for students into different aspects of the problem and to stretch students to go deeper into mathematical complexity.

PRE-K
In this task, students act out a problem and use manipulatives to determine the number of guests invited to a party through examination of set invites—guests inviting other sets of guests.

LEVEL A
In this level, students determine the number of guests invited to a party through examination of set invites, with guests inviting other sets of guests.

This level has students use multiplication within 100 to solve a word problem by using drawings and/or equations to represent the problem (3.OA.A.3).

LEVEL B
In this level, students are asked to determine the number of girls at the party with short red hair, given a number of logic clues. The students need to partition a whole using simple fractional amounts (1/2 and 1/4). The students apply logical reasoning to determine the possible number of red-headed girls at the party.

This level has students solve a word problem involving multiplication of a fraction by a whole number by using a visual model to represent the problem (4.NF.B.4c).

LEVEL C
In this level, students are presented with a set of clues regarding the guests’ names, costumes, and time of arrival at the party. The students are asked to match each of the partygoers to their names, costumes, and arrival times.

This level does not directly align to any standards. This problem could be used to promote logical thinking for middle or high school students. Students can organize the given information in a table and use deductive reasoning to arrive at the solution.

LEVEL D
In this level, the students are asked to determine when a game is fair for both players. Students justify their findings and explain when the game is fair.

This level has students find the sample space for pulling two tiles out of a bag containing tiles of two different colors without replacement (S-CP.A.1). Students use combinations to determine the sample spaces for possible games (S-CP.B.9). Students use the multiplication counting principle and interpret the result to determine if the game is fair (S-CP.B.8). Students interpret the results from their analysis and their understanding of conditional probability to determine how many chips of each color should be added to the bag so that the game is fair for each player playing it.

LEVEL E
In this level, students are asked to solve a complex logic puzzle involving handshakes among a group of people. Students must defend their solution and explain how they solved the puzzle.

This level does not directly align to any standards. This problem could be used to promote logical thinking for middle or high school students. Students can organize the given information using a diagram or table and use inductive reasoning to arrive at the solution and generalize the pattern.

PROBLEM OF THE MONTH