Growing patterns

Learning Objectives Identify growing patterns in sequences of numbers and shapes. Describe the term-to-term rule of a growing pattern using words. Extend a growing pattern to find subsequent terms. Represent the rule of an additive growing pattern using an algebraic expression involving 'n' (the term number). Distinguish between additive and multiplicative growing patterns. Apply pattern rules to predict terms far down the sequence. Translate visual growing patterns into numerical sequences. Have you ever noticed how things grow around you, like plants or even your own height? 🌱 What if numbers and shapes could grow too, following a secret rule? In this lesson, you'll become a pattern detective! You'll learn to spot growing patterns, figure out their...

TermDefinitionExample PatternA sequence of numbers, shapes, or objects that repeats or follows a predictable rule.2, 4, 6, 8, ... (adding 2 each time) Growing PatternA pattern where numbers or shapes increase in a predictable way, following a specific rule.1, 3, 5, 7, ... (numbers are increasing) TermEach individual number or item in a pattern or sequence.In the pattern 5, 10, 15, 20, ..., the number '10' is the 2nd term. Term Number (Position)The place or order of a term in a sequence (e.g., 1st, 2nd, 3rd term). We often use the variable 'n' to represent the term number.In the pattern 5, 10, 15, 20, ..., the term '15' is at position n=3. RuleThe mathematical operation(s) that describe how to get from one term to the next, or from the term number to the term...

Identifying Additive Patterns $$ \text{Term}_n - \text{Term}_{n-1} = d $$ (where $d$ is a constant number) To check if a pattern is additive, find the difference between consecutive terms. If the difference ($d$) is always the same, the pattern is additive. To find the next term, add $d$ to the previous term. Identifying Multiplicative Patterns $$ \text{Term}_n \div \text{Term}_{n-1} = r $$ (where $r$ is a constant number, $r \neq 0$) To check if a pattern is multiplicative, find the ratio (by dividing) between consecutive terms. If the ratio ($r$) is always the same, the pattern is multiplicative. To find the next term, multiply the previous term by $r$. Finding the Nth Term (Position-to-Term Rule for Additive Patterns) $$ T_n = d \times n + c $$ (where $T_n$ is the $...