Evaluate variable expressions for number sequences

Learning Objectives Define a variable and a variable expression. Identify the rule (the variable expression) that creates a number sequence. Substitute a given number for a variable in an expression. Use simple order of operations (multiplication/division before addition/subtraction) to evaluate an expression. Generate terms in a number sequence using a given variable expression. Complete a simple input-output table based on a variable expression. Ever wonder how a robot knows what to do next? 🤖 It follows a rule, just like we will with number patterns! In this lesson, you will become a pattern detective! We will learn about special math codes called 'variable expressions' that create number sequences. Understanding these codes will help you predict what number c...

TermDefinitionExample VariableA letter or symbol that stands for a number that can change or is unknown.In the expression `n + 5`, the letter `n` is the variable. Variable ExpressionA math phrase that includes at least one variable, numbers, and operation signs.`8 * y` is a variable expression. It means 8 times some number `y`. Number SequenceAn ordered list of numbers that follow a specific rule or pattern.5, 10, 15, 20, ... is a number sequence where each number is 5 more than the last. RuleThe instruction that tells you how to create the number sequence. It's often written as a variable expression.For the sequence 3, 4, 5, 6, ..., the rule could be `n + 2`, where `n` is the position of the term (1, 2, 3, 4...). SubstituteTo replace the variable in an expression with a specific num...

Additive Rule n + c Use this when a constant number `c` is added to the term's position `n` to find the value. For example, if the rule is `n + 5`, the first term (n=1) is 1+5=6, the second term (n=2) is 2+5=7, and so on. Multiplicative Rule c * n Use this when the term's position `n` is multiplied by a constant number `c`. If the rule is `4 * n`, the sequence is 4, 8, 12, 16... Two-Step Rule (c * n) + d Use this for more complex patterns. First, you multiply the term's position `n` by a number `c`, and then you add another number `d`. Always multiply before you add.