Math 1 · Unit 9 · Lesson 5
Building Sequences from the Real World
Turn a story, a table, or a picture pattern into a sequence and use it. First decide the type: equal differences means arithmetic, equal ratios means geometric. Then write the rule and answer the question. Pizza toppings, an orchard, a stack of cups, and splitting bacteria, plus the simple and compound interest balances from Unit 8. Always ask what n counts and whether the counting starts at 0 or at 1, because the story decides.
The big idea
A real situation becomes a sequence in three moves. Decide the type with the equal-steps check: equal differences means arithmetic, equal ratios means geometric, and adding gives arithmetic while multiplying gives geometric. Write the rule, the start plus d times the number of steps, or the start times r to the number of steps, and say what n counts. Then answer the question, putting in n for a far term, or setting the rule equal to a value (or building a table) to find which term reaches it. The story decides where the counting starts: if the first input is 1 there are n minus 1 steps, and if it is 0 there are n steps and the start is the y-intercept itself. Simplifying an arithmetic rule can uncover a real meaning for the zeroth term, like the price of a plain pizza. The yearly balances from Unit 8 fit the same pattern: simple interest is arithmetic and compound interest is geometric.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with the three moves, the four situations worked, the where-does-n-start question, and the orchard by elimination. Plus a worksheet with an answer key and a short lesson plan.
Where this goes next
NC Math 1 standards in this lesson: NC.M1.F-BF.1a (build linear and exponential functions, including sequences, from a description, a table, or two points), NC.M1.F-BF.2 (use explicit and recursive forms to model situations), NC.M1.F-LE.1 (linear or exponential from equal steps).