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# Using Sequences and Series to Make Connections

Lesson 11 of 15

## Objective: Students will be able to be involved in a wide variety of challenges in this lesson! From an interesting “act it out” warm up problem – to a hint of Pascal’s Triangle; each activity will challenge the students in the practice standards and extend the content previously learned.

*40 minutes*

#### Warm Up

*15 min*

As the students enter the classroom, be sure to have the PowerPoint displayed with the opening problem slide active. I also provide a half sheet of paper with the problem written on it so that the students don’t have any excuse to get started!

*Randy’s house is one mile from the school. He starts walking to school one day, goes half the distance from home to school and stops. He turns around, heads home, goes half the distance from the point where he turned around and his home, and stops. He turns around, heads toward school, goes half the distance from where he turned around and school, and stops. He turns around, heads towards home, goes half the distance from where he turned around and his home, and stops… this continues for a LONG time! *

1) Stand up and act out the scenario in our classroom. Perform at least 5 turns.

2) Draw on your half sheet of paper the scenario that you just acted out.

3) Compare scenario drawings with 2 people around you.

4) Calculate Randy’s limiting position(s)

A few notes:

- This activity connects nicely to the previous lesson.
- Kinesthetic learners will enjoy acting out the scenario, but all learners can benefit from getting out of their seats and being able to act out the situation.
- It’s mathematical modeling… with people!
- The activity is structured such that the students MUST understand the problem prior to ever being able to attempt an answer – this is so important in mathematics!
- A discussion of possible methods of solution can begin 7-8 minutes after problem roll out. Although not all students will be completely finished with the problem, ALL students at least understand it and are ready talk about the process that they were involved in using.
- Many students will share out how they treated one directional move as positive, and one as negative - - other students may elect to share a different approach. These are GREAT to talk about!

Teacher Behavior:

As the students are working on the Opening Activity, rotate the classroom to check and see how last night’s homework assignment went. (As it states on the PowerPoint Slide, the students should have this out and ready for you to take a look at.) This will give you a picture as to how the second phase of the lesson will go, and what types of questions you can anticipate from the students.

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##### Resources (6)

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- UNIT 1: Culture Building Unit - Welcome to the New Year!
- UNIT 2: Exponential and Logarithmic Functions
- UNIT 3: Sequences and Series
- UNIT 4: Statistics: Something for Everyone
- UNIT 5: Review Lessons
- UNIT 6: Writing Prompts in Mathematics
- UNIT 7: Trig Tidbits
- UNIT 8: Functions, Problem Solving, and 21st Century Skills
- UNIT 9: Polynomials and Problem Solving
- UNIT 10: Probability
- UNIT 11: Imagine This! Imaginary and Complex Numbers
- UNIT 12: Let's Explore Radicals!

- LESSON 1: Introduction to Sequences
- LESSON 2: Arithmetic Sequences and Series
- LESSON 3: Geometric Sequences and Series
- LESSON 4: Sequences and Series Battleship!
- LESSON 5: A Double-Dose of Series Application
- LESSON 6: Mortgages and Geometric Series DAY #1
- LESSON 7: Mortgages and Geometric Series DAY #2
- LESSON 8: Mortgages and Geometric Series DAY #3
- LESSON 9: Mortgages Wrap-up and Additional Scaffolding
- LESSON 10: Investigating Infinite Geometric Series
- LESSON 11: Using Sequences and Series to Make Connections
- LESSON 12: The Binomial Theorem
- LESSON 13: Sequences and Series Partial Unit Review
- LESSON 14: Sequences and Series Partial Unit Review II
- LESSON 15: Unit Test: Sequences and Series