Algebra 3 Lesson Plan: Sequence and Series by Melanie Carter

By the end of this lesson, students will be able to:

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1. Define and distinguish between arithmetic and geometric sequences
2. Write arithmetic and geometric sequences both recursively and explicitly
3. Translate between recursive and explicit forms of sequences
4. Apply sequence models to real-world situations

Standard Alignment

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This lesson aligns with A3.FN.7: Write and use arithmetic and geometric sequences recursively and explicitly to model situations, translating between the two forms.

Essential Question

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How can we use sequences to model and predict patterns in real-world situations?

Guided Practice: Translating Between Forms

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In small groups, students will practice translating between recursive and explicit forms of both arithmetic and geometric sequences. Use Padlet to share and discuss solutions.

Independent Practice: Sequence Identification

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Students will individually identify whether given sequences are arithmetic, geometric, or neither, and write them in both recursive and explicit forms.

Real-World Application

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Students will research and present real-world examples of arithmetic and geometric sequences (e.g., population growth, compound interest). They'll create Padlet posts to share their findings with the class.

Differentiation: Remediation

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For students needing additional support, provide a step-by-step guide for identifying and writing sequences.

Differentiation: Extension

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Challenge advanced students to explore and present on more complex sequences, such as Fibonacci or Lucas sequences.

Summative Assessment: Sequence Quiz

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End-of-lesson quiz covering identification of sequence types, writing sequences in recursive and explicit forms, and translating between forms.

Reflection Discussion

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Guide a whole-class discussion on the importance of sequences in modeling real-world situations. Ask students to share examples they found most interesting or surprising.

Exit Ticket: Key Takeaways

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Students will submit a Padlet post answering: 1) What's the main difference between arithmetic and geometric sequences? 2) How can translating between recursive and explicit forms be useful?

Sequence Practice Worksheet

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Complete a worksheet with various sequence problems, including writing sequences in both forms and translating between them.

Real-World Sequence Project

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Research and create a presentation on a real-world application of either an arithmetic or geometric sequence. Include the sequence in both recursive and explicit forms.

Online Sequence Game

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Play an online game to reinforce understanding of arithmetic and geometric sequences.

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Explicit formula for sequences

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Geometric Sequence and Series