CHAPTER 3_ Math In The Modern World.pptx

Problem Solving and Reasoning

1. CHAPTER 3 : PROBLEM SOLVING AND REASONING (CONTINUATION) PREPARED BY: JOHN LUIS M. BANTOLINO, LPT

2. PROBLEM SOLVING WITH PATTERN Pattern analysis is a critical 21st century skill. Finding a pattern is a strategy in which students look for patterns in the data in order to solve the problem. In here, students look for items or numbers that are repeated or a series of events that repeat. CHAPTER 3: PROBLEM SOLVING AND REASONING (CONTINUATION) PREPARED BY: JOHN LUIS M. BANTOLINO, LPT

3. SEQUENCE An ordered list of numbers such as 5, 14, 27, 44, 65,… is called a sequence . The numbers in a sequence that are separated by commas are the terms of the sequence. In the above sequence, 5 is the first term, 14 is the second term, 27 is the third term, 44 is the fourth term, and 65 is the fifth term. The three dots “…” indicate that the sequence continues beyond 65, which is the last written term. It is customary to use the subscript notation to designate the nth term of a sequence .   CHAPTER 3: PROBLEM SOLVING AND REASONING (CONTINUATION) PREPARED BY: JOHN LUIS M. BANTOLINO, LPT

4. DIFFERENCE TABLE When we examine a sequence, it is natural to ask questions like “What is the next term?” and “What formula or rule can be used to generate the terms?”. To answer these questions, we often construct a difference table , which shows the differences between successive terms of the sequence. CHAPTER 3: PROBLEM SOLVING AND REASONING (CONTINUATION) PREPARED BY: JOHN LUIS M. BANTOLINO, LPT

5. DIFFERENCE TABLE Example 1: Difference table of the sequence 2, 5, 8, 11, 14, … Sequence: 2 5 8 11 14 First differences: 3 3 3 3 CHAPTER 3: PROBLEM SOLVING AND REASONING (CONTINUATION) PREPARED BY: JOHN LUIS M. BANTOLINO, LPT

6. DIFFERENCE TABLE Example 2: Difference table of the sequence 5, 14, 27, 44, 65, … Sequence: 5 14 27 44 65 First differences: 9 13 17 21 Second differences: 4 4 4 CHAPTER 3: PROBLEM SOLVING AND REASONING (CONTINUATION) PREPARED BY: JOHN LUIS M. BANTOLINO, LPT