Florida B.E.S.T. MA.912.AR.10.3

MathGrades 9–12Solve problems involving sequences and series.

The Standard

Recognize and apply the formula for the sum of a finite arithmetic series to solve mathematical and real-world problems.

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

Teacher's field guide

What Students Need to Do: Students recognize term lists that change by a constant amount and distinguish the list from its total. They identify needed values and use Sₙ = n(a₁ + aₙ)/2 to calculate the sum.
What Mastery Looks Like: A student can identify the first term, last term, and number of terms from a pattern or context. They calculate the total accurately and explain what it represents.
Common Misconceptions: Students may confuse a sequence with the sum of its terms. They may use the common difference as the number of terms, miscount terms, or apply a geometric rule.
How to Assess It: Exit ticket: A theater has 18 seats in row 1 and 4 more seats in each following row. How many seats are in 15 rows? Show your formula values.

Lesson moves

Build six tile rows containing 3, 5, 7, 9, 11, and 13 tiles, then verify the total with the formula.
Compare 4 + 7 + 10 + ... + 31 with its reversed form, then explain why pairing terms helps find the total.
Match cards showing arithmetic patterns, formula values, and totals, then check each set with a calculator.
Calculate the total saved over 12 weeks when weekly deposits begin at $10 and increase by $5 each week.

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