1. Patterns and Relationships

2. Keywords Divisibility Rules Algebraic expression Numerical coefficient
Algebra tiles
Constant term
Relation
Linear Relation
Unit tile
Variable tile

3. Divisibility Rules 2 ~ if the number is even
3 ~ if the sum of the digits is divisible by 3
4 ~ if the number represented by the last two digits is divisible by 4
5 ~ if the ones digit is 0 or 5

4. Divisibility Rules 6 ~ if the number is divisible by 2 and 3
8 ~ if the number represented by the last three digits is divisible by 8
9 ~ if the sum of the digits is divisible by 9
10 ~ if the ones digit is 0

5. Divisibility Practice
Is 261 divisible by 3?
Is divisible by 5?
Will 8 divide into 782?
Yes No
Yes No
Yes No
Please turn on your speakers to hear if you are correct

6. Algebraic Expressions
Variable ~ a letter such as x , that represents a quantity that can vary
Ex. Below are expressions and their meanings
A number times 9: 9n
14 more than a number: 14 + n or n + 14
36 divided by a number: 36 x

7. Algebraic Expressions
Every item in an expression has its own name
5 is the constant term
3x - 5
x is the variable
3 is the numerical coefficient

8. Evaluating Expressions
Evaluating an algebraic involves replacing the variable with a given value
Ex. 1 Evaluate the expression 3x – 2 by replacing x with 5
Replace x with 5
Use order of operations to simplify

9. Relationships in Patterns
When a variable is related to an expression that contains the variable a relation is created
Ex. John’s Science class goes an a field trip and picks up garbage on the banks of the river. If there are n students in the class and each student picks up 4 bags of garbage, determine the relation that describes the situation. Use the relation to find the number of bags picked up if the class has 17 students
Let n be the number of students in the class
Since each student will pick up 4 bags the relation is 4n
Use the relation 4n and replace the variable n with 7, which is the number of students 4n
4 x 17 68
68 bags of garbage will be picked up

10. Patterns and Relationships in Tables
An input/Output table relates a variable with a relation
The output column values are calculated by
Replacing n with the values in the input column
Input n
Output n + 3 1 4 2 5 3 6 7 8 9 10
n + 3
2 + 3 5
n + 3
6 + 3 9