Inference is the mental process of reaching a conclusion based on specific evidence. In math, inference questions come in the form of word problems or statistical analysis. The students must take the data they have available to them to determine an outcome. Activities for inferences should focus on the process of making an inference and developing strong reasoning skills to support the inferences they have made.

## Traffic Jam

Traffic Jam, from the Math Forum website, is a problem involving two groups of people, one moving to the right and the other moving to the left. There is only one open space between the two groups to move. The students must determine how to maneuver the people to the opposite side in the fewest moves possible. This game can be repeated with multiple scenarios such as two people and three spaces and six people with seven spaces. Have the students play multiple games with varying amounts of people, keeping track of the minimum number of moves for each scenario. What can they infer about the number of moves required to complete any of the boards from the patterns that have been created ?

## Logical

The Council Bluffs Community School District offers the word problem "Tug of War" which pits grandmas, football players and a dog against one another in tug of war matches. There are a series of match ups that occur, such as five grandmas versus four football players, which end in a draw. After the students read through all the match ups and results, they are given another match to decide who will win. The students must use the information from the previous results to infer who the winner will be and why this result will occur.

## Candy

Provide the class with a bag of M&Ms or Skittles that have multiple-colored pieces of candy. Each student should count the number of each color present in the bag. The students will then create a chart listing all the combinations present in the bag. The students must use this information to infer what is the most probable color combination of candies if they were provided another bag of candy. This will provide students a chance to analyze data, such as calculating averages and means to make inferences about a hypothetical bag of candy. There is no correct answer to this question as the color distribution is random.

## Hermits

From the Office for Mathematics, Science, and Technology Education, University of Illinois website the problem of infectious hermits works on students' inference skills. An island has six hermits and an infectious disease. One of the hermits is immune. The first hermit gets sick and visits another hermit on the island. The next day the visited hermit visits another hermit on the island. Each hermit gets sick except when the immune hermit is visited, the disease dies out. The students must determine the average number of hermits that get the disease. Change the number of hermits on the island and see if those averages change. What can the students infer if X number of hermits lived on the island?

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