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# Arithmetic Sequences Day 2 and Quiz

Lesson 3 of 19

## Objective: SWBAT find the explicit formula for an arithmetic sequence.

## Big Idea: Students can use the structure of a sequence to construct a formula that will allow them to find any term.

*40 minutes*

#### Opening

*5 min*

Students will individually analyze the Given Sequence and formula to determine if the formula correctly describes the pattern in the sequence. Students will need to use quantitative reasoning (MP2) along with their knowledge of algebra to offer a rationale for why they think the formula is correct or incorrect. I will ask students to use a non_verbal cue (thumbs up/down) to get a poll of student thinking. Then, students will be able to process their thinking out with a partner.

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#### Cooperative Analysis

*10 min*

The opening activity for this lesson serves two purposes. First, to allow students to practice working with arithmetic sequences. The second is to allow students to practice analyzing a sequence to determine if it follows a pattern described by an equation.

The students will pursue this second purpose through **cooperative peer assessment**. Each student will receive another student's ticket out from the previous lesson ( see Photo Nov 14, 9 13 50 PM.jpg). They will analyze the student's work to determine if the written formula is correct (MP3). Once students have had a chance to analyze the work, they will give the student feedback on how to improve it.

In order for me to keep track, students papers are marked with either a plus (incorrect) or a check mark (correct). As the students work I will circulate throughout the room and answer questions students have about their interpretations of the relationship between the equation and the pattern.

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#### Formative Assessment

*25 min*

The front side of this arithmetic_sequences_quiz incorporates questions that spiral back to content from an earlier unit. The back of the quiz serves as a formative assessment for student's understanding of sequences.

The quiz asks students to provide justifications for their answers (MP3). I intend the justification prompts to enable students to make their thinking more visible. This will allow me to gain better insight into the students' understandings and misunderstandings. If the quiz is successful, I will gain a deeper perspective from which to teach during the rest of the unit.

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- LESSON 1: Patio Problem: Sequences and Functions
- LESSON 2: Arithmetic Sequences
- LESSON 3: Arithmetic Sequences Day 2 and Quiz
- LESSON 4: Arithmetic Sequences Day 3
- LESSON 5: Arithmetic Sequences: Growing Dots
- LESSON 6: Graphing Linear Functions Using Tables
- LESSON 7: Linear Functions
- LESSON 8: Discrete and Continuous Functions
- LESSON 9: Rate of Change
- LESSON 10: Slope as a Rate of Change - Day 1 of 2
- LESSON 11: Slope as a Rate of Change - Day 2 of 2
- LESSON 12: Graphing Linear Functions Using Intercepts
- LESSON 13: Graphing Linear Functions Using Slope Intercept Form
- LESSON 14: Comparing Graphs of Linear Functions Using Dynamic Algebra
- LESSON 15: Using Linear Functions for Modeling
- LESSON 16: Writing the Equation for a Linear Function (Day 1 of 2)
- LESSON 17: Writing the Equation of A Linear Function (Day 2 of 2)
- LESSON 18: Graph Linear Equations Practice
- LESSON 19: Solving Two Variable Inequalities Part 2