Florida B.E.S.T. MA.912.AR.10.2

MathGrades 9–12Solve problems involving sequences and series.

The Standard

Given a mathematical or real-world context, write and solve problems involving geometric sequences.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students represent repeated multiplication in a context with a geometric sequence. They determine the initial value and common ratio, write a rule, and use it to answer questions about later terms.
What Mastery Looks Like: Students choose the correct starting value and common ratio from a context. They write an explicit or recursive rule, calculate requested terms, and explain what the values mean in the situation.
Common Misconceptions: Students may add a constant amount instead of multiplying by a constant ratio. They may confuse the first term with term zero or use the percent rate instead of the growth factor. Negative ratios can also cause sign errors.
How to Assess It: Use this exit ticket: A phone worth $800 loses 15% of its value each year. Write a formula and find its value after four years.

Lesson moves

Give groups 80 counters, have them remove half each round, record five terms, and write an explicit rule.
Ask students to explain why a 12% yearly increase uses a common ratio of 1.12 rather than 0.12.
Play ratio match cards, pairing context cards with sequence lists, recursive rules, and explicit formulas.
Model a car losing 18% of its value yearly, then compare predicted values after three, five, and eight years.

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