1. Problem Solving Strategies Algebra/Use a Variable Look for a Pattern Make a List Solve a Simpler Problem

2. Using Algebra/Variables How to use this strategy: Look for a pattern that can be described in words and/or a general formula Finding Patterns: Look at the sequences of numbers Look at input/output table for rule Start with simpler case first Use finite differences

3. Using Algebra/Variables When to use this strategy: The phrase �any number� is used There is a list of numbers that can be generated from the problem There is an input/output that can be described as a rule A large number of cases are involved

4. Example 1 Determine the sum of the first 50 odd counting numbers. Step 1: odd counting numbers are 1, 3, 5, 7, 9 � and so on. I am adding together the first 50 of these odd numbers starting with 1+3+5� Step 2: The plan will be to start with simpler problems and look for a pattern in the smaller/simpler sums

5. Example 1 Step 3: Use an input/output table to keep track of the simpler sums and look for a pattern. Input-how many odd #�s am I adding? Output-what is the sum? Do you see the pattern?

6. Example 1 The pattern that related the input to the output is: Sum of n number of odd numbers is n x n (the sum of the first 3 odd numbers was 3 x 3) So the sum of the first 50 0dd numbers is 50 x 50, or 2500 Step 4: Look back and verify answer

7. Example 1 Imagine each odd number represented by tiles in the following shapes (note the number of tiles used represents the odd number, show below are 1, 3 and 5)