Work with sequences and make predictions

Today we will learn about work with sequences and make predictions. Math helps us solve problems and understand the world around us.

Input-output tables show a rule that transforms one set of values (input) into another set (output). To find the rule: look at how output changes as input changes. If adding: output = input + constant (rule: add 7). If multiplying: output = input × constant (rule: multiply by 3). If the pattern is more complex, try subtracting the input from the output, or dividing. Testing the rule: apply it to every row to verify it works for all pairs, not just one. Sequences extend patterns: arithmetic sequences add/subtract a fixed amount each time (5, 10, 15, 20—add 5); geometric sequences multiply/divide by a fixed amount (3, 6, 12, 24—multiply by 2). Identifying patterns and rules develops the algebraic thinking needed for functions and equations.

Let's break this down step by step so it's easy to understand. Follow along with the examples, and don't worry if it takes some practice to get the hang of it!

Remember: Making mistakes is part of learning. If something is tricky, try again, look at the examples, or ask for help.