• Say: Let's create some data so that we can make a prediction about the probability.
  Have a student fill in an addition table with the correct sums, which represents the rolling of the two number cubes. The table shows the 36 possible outcomes when rolling the two cubes.
  

  Then have a student come to the board and circle all of the odd number sums.

  
• Say: Now let's create some data about multiplication.
  Then have a student come to the board and fill in the correct products in the multiplication table.
  Remind the students that the tables represent all the possible outcomes of rolling the two cubes and adding or multiplying the results. Six possible outcomes times 6 possible outcomes equals 36 total outcomes.

Have another student circle all the odd-number products in the multiplication table.

• Say: Now that we have some data about sums and products from rolling our number cubes, we can make some predictions.
• Ask: Who can answer the original question? Will the probability of rolling a sum that is odd be greater than the probability of rolling a product that is odd?
  Students should compare the circled odd numbers in the tables and conclude that finding an odd sum is more likely.
• Ask: When we roll both cubes and add, how many outcomes are there? (36)
• Ask: How many of those outcomes are odd numbers?
  (18 odd numbers)
• Ask: What is the probability of the sum being an odd number?
  ( = )
• Ask: How many total outcomes are there when we roll two cubes and multiply the numbers? (36)
• Ask: How many of these products are odd? (9)
• Ask: What is the probability that the product will be an odd number? ( = )
• Ask: Compare the probabilities of the two events. Which is more likely, rolling an odd-number sum or rolling an odd-number product? Students should find that rolling an odd-number sum is more likely than rolling an odd-number product. They should point out that > .

  Have students make predictions about outcomes by answering the following questions, using data from this table.