Relationships in patterns Lesson 1.4

Patterns Patterns can help determine how to solve an expression. How does each term relate to the term number? Term Number 1 2 3 4 Term 6 9 12

Ms. Kim’s class says they will pick up a total of 10 MORE pieces of garbage than Mr. Jeff’s class. Here are the numbers of garbage picked up by different numbers of students. Number of students 2 4 6 8 10 12 Pieces of garbage picked up by Ms. Kim’s class 22 34 46 58 70 82 Pieces of garbage picked up by Mr. Jeff’s class 24 36 48 60 72

Number of pieces of garbage picked up by Mr. Jeff’s class The expression Number of pieces of garbage picked up by Ms. Kim’s class Number of pieces of garbage picked up by Mr. Jeff’s class 10

An explanation... Let n represent the number of students who picked up garbage in Mr. Jeff’s class. Then, the number of pieces of garbage for Mr. Jeff’s class is 6n The number of pieces of garbage for Ms. Kim’s class is 10 + 6n. The number of pieces of garbage is related to the number of students.

Why is the expression 6n + 10? Where did the 6 come from? What is the pattern with the number of pieces in Mr. Jeff’s class? What is the number or students increasing by? So, how did we get the 6?

Flashback to grade 6... Input Output 1 2 3 4

Another example... Mr. Omar is having a party. The cost to rent the room is $50. The cost of the food is $3 per person. A) Write a relation for the cost of the party in dollars. B) How much will a party cost for 10 people? For 15 people? C) How does the relation change if the cost of the food doubles? How much would a party for 10 people cost?

A) 50 + 3n B) i) 50 + (3 x 10) ii) 50 + (3 x 15) =50 + 30 =50 + 45 =$80 =$95 C) 50 + 6n =50 + (6 x 10) =50 + 60 =$110

The cost of renting the room NEVER changes The cost of renting the room NEVER changes. That means the cost of renting the room is __________________. This does not change regardless of how many people attend the party. The cost of the food is the ______________. The cost of the party will change depending how many people come to the party.

Homework Textbook: Page 23-24 #1,3,4,6,7 Workbook: Lesson 1.4