**The Answer is: 7**

**METHOD 1:**

*Strategy: Use the definition of a week.*In 45 consecutive days there are 6 weeks and 3 days. Each of the 6 weeks contains one Monday. In order to have the greatest number of Mondays, one of the 3 days left must also be a Monday.

**The greatest number of Mondays that can occur in 45 consecutive days is 7**.

**METHOD 2:**

*Strategy: Start at 1 and count by sevens.*Suppose day 1 is a Monday. Mondays will occur on days 1, 8, 15, 22, 29, 36, 43. The next Monday would be after day 45. The greatest number of Mondays in 45 consecutive days is 7.