Patterns and Relationships

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

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

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

Divisibility Practice Is 261 divisible by 3? Is 12345 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

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

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

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

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

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