Math: Deductive Reasoning Assignment
1. Examine the relationship below:
1 + 2 + 3 = 6 3 · 2 = 6
5 + 6 + 7 = 18 3 · 6 = 18
10 + 11 + 12 = 33 3 · 11 = 33
a) Give another example that shows the same pattern.
b) Describe the pattern.
c) Danielle makes the following conjecture: When you add three consecutive numbers, your answer is always a multiple of 3. Use deductive reasoning to prove that Danielle's conjecture is true for all integers.
2. Sandra found this number trick on Internet. Think about the date of your birthday.
-Take the number for the month of your birthday. (For example, April = 4, December = 12)
-Multiply the number by 5
-Add 3
-Multiply by 4
-Add 5
-Multiply by 5
-Add the day of your birthday
-Subtract 85
-Write your answer
a) State your birth date and determine the answer. Show each step of the process.
b) Let m represent the number for the month of your birthday and d represent the day. Prove how this trick works using deductive reasoning.