##
* *Reflection: Coherence
Mortgages Wrap-up and Additional Scaffolding - Section 2: Independent Work Time – Additional Scaffolding on Problem Solving with Series

*Trouble Problems for Students.MOV*

*Mortgages Wrap-up and Additional Scaffolding*

# Mortgages Wrap-up and Additional Scaffolding

Lesson 9 of 15

## Objective: Students will be able to reflect on their mortgage payment calculation activity and independently work through additional problem solving applications surrounding arithmetic and geometric series.

## Big Idea: A time of reflection over an in-depth mathematical investigation - coupled with additional practice and skill building.

*45 minutes*

Now that we have wrapped up the mortgages activity, it is time to put the students through some additional practice dealing with series applications. Attached you will find a worksheet that I use for this. I ask the students to work INDEPENDENTLY on this worksheet until they are stuck. Once they are stuck, I have established a protocol for receiving support. This format really challenges students to make sense of problems and persevere in solving them (MP1). See below:

- Designate 3-4 areas of the room as “help space” – this space should have enough elbow room to work with 3-4 students at a time.
- Students will report to one of these areas of the classroom when they need help.
- The first student at the help space will write the problem # that they are working on
- I use easels and it works really well! Be creative and use what you can, however.
- As other students arrive who are also stuck they are able to collaborate with each other to see what pieces they are confused about.
- The role of the teacher is to be patient and wait until 3-4 students are all at a dead end at one of the help stations before going over and offering support.
- Once the student has resolved their issue they must leave the help station and return to their seat to work independently.

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#### Closure

*2 min*

To close class I direct the student’s attention to #8 and the final two challenge problems. Many times, kids are intimidated by the final problems of the worksheet, especially if they seem abstract and “disconnected” from the more structured problems. I like to have the students quickly fill in the final box of the triangular numbers diagram so that they feel like they have at least gotten the problem rolling. I then clarify what the questions are asking them to do, and give a little history on Plutarch, who is mentioned in Challenge Problem #2. Hopefully, this “de-intimidates” the kids and they are able to view the challenge problem as something that really can be conquered!

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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