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# End of Unit Differentiated Problem Set

Lesson 19 of 21

## Objective: This lesson is designed to allow the students to grapple with applications of logarithmic and exponential functions. The 5 different problems that are presented each provide a unique challenge for the students. Creativity is also encouraged during the share out portion as the students explain their problem and approach to their peers.

*47 minutes*

#### Problem Roll out

*15 min*

**Pre Class Prep: **

1) Cut problem entry documents into ½ sheets of paper

2) Fold the problems into an envelope and tape them to the white board

3) Pair the students into like ability partners

As the students enter, have your list of partners ready to tell them who they are working with. (As always, tell the students to be professional when receiving the news!) Once both partners have arrived to class, instruct the students to come to the white board and select a problem. The only groups who do not get to randomly select their problem are the high-ability groups. This differentiation is provided to push these students in the “crime scene” problem. As these particular students enter, I simply hand them their challenging problem. Do not post any “crime scene” problems on the whiteboard.

After all envelopes are out, the students will have any one of 5 different problems: *Chef’s Delight, Seismologist, Oceanographer, Crime Scene, and Scientist. *

Now the students are ready to read their half sheet with their partner and begin their KNOW’s and N2K’s for their specific problem. This usually takes anywhere from 5-10 minutes and helps promote good problem solving strategy.

**Please see the KNOW’s/N2K’s Video in the strategies folder**

After completing the KNOW’s/N2K’s, I have every pair of students who has the same problem meet to go over their lists. Around the room, there will be 5 different meetings going on that correspond to the 5 different problems that were rolled out. While this is going on, I rotate the room and listen in on student conversations. The students always want answers to their N2K’s right away, but for the time being I am intentional about answering their questions with questions of my own. Although this frustrates the students, it ensures that they have completely read the problem.

** **

**Resources**: Entry Documents, KNOW’s/N2K’s Video (Strategies Folder)

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#### Work Time!

*20 min*

Allow the students time to work! DO NOT just give them steps or tell them if their answer is correct!

**Crime Scene: **Students may struggle initially and feel as though the problem has “2 unknowns” - however, they will eventually figure out to use the two times that they are given to find the cooling constant, k, for the dead body. Then, they will be able to re-solve the problem for t to find out how long the body has been dead. It is a great process for them to use… Don’t spoil it by telling them what to do!

**Chef’s Delight: **I have had students in the past actually cook food at night and record temperatures as it cools to find the cooling constant. They love this! You can even talk to this group about how different foods heat up at different rates in the microwave. Many motivated groups will be anxious will experiment at home with the mathematics! It makes for a fun discussion on the following day.

**Seismologist: **This was a fun one for my kids because Indiana just had a small earthquake! Even though it was a big deal, they will find that is was TINY in comparison to those that happen in other areas of the world!

**Resources**: none

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The end of the unit has arrived! I circulate the test review sheet at the end of class so that the students have a couple of days to look it over prior to asking questions in class. If your students are not accustomed to collaboratively working on problems in class, you may wish to hold onto the review sheet for one more day – otherwise the students may “check out” of their collaborative team and focus on the review sheet. My students can handle receiving the review because they know the level of expectation AND because they will receive a small collaboration/work ethic grade for the problems that they are working on… looking over the review sheet is something that is to be saved for their own time outside of class! Usually, by the end of class most students are finding a solution to their problem. As this is going on, I encourage them to formulate a plan for presenting their problem to other groups on the following day.

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**Resources**: Unit Test Study Guide

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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 Exponential Functions - Rational Exponents
- LESSON 2: Real Number Exponents
- LESSON 3: A Conceptual Introduction to Exponential Functions: Collaboration, Questioning, and Financial Advice!
- LESSON 4: Discovering Solutions to Exponential Equations
- LESSON 5: An "Exponentially" Rewarding Battle!
- LESSON 6: Productive Struggle - A Pre-Spring Break Challenge of Exponential Functions
- LESSON 7: Compositions, Inverses & Role Play: Extending Concepts to Exponential Functions
- LESSON 8: Exponential Functions and Logarithms - Connecting the Dots
- LESSON 9: Exponentials and Logarithms: LOUD and CLEAR!
- LESSON 10: A Wrap on Logarithmic dB's and An Extension to Logarithmic Properties
- LESSON 11: Classroom Journey: Exponential and Logarithmic Properties
- LESSON 12: Laws of Logarithms and Real Applications
- LESSON 13: Calculator Boot-Camp and Solving Exponential Equations
- LESSON 14: Logs, Loans, and Life Lessons!
- LESSON 15: "Demystifying e" Day #1
- LESSON 16: Logs, Loans, and Life Lessons Collaboration Day!
- LESSON 17: FInal Discussion - "Demystifying e" PLUS Skills Practice with Logarithms
- LESSON 18: Elephant Tracks!
- LESSON 19: End of Unit Differentiated Problem Set
- LESSON 20: Differentiated Problem Share Out - Unit Review
- LESSON 21: Unit Review