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* *Reflection: Problem-based Approaches
Mission Impossible: Roll Out - Section 1: Roll Out Entry Document and Pairs

Why save dessert for last?

I have had a great deal of success in my classroom in regards to teaching problem solving thanks to an approach shared with me by a fellow teacher.

Rather than saving “story problems” for the end of the unit, as was the case when most of us were in high school, I like to front-load my units with these problems and then teach the skills needed to dive into them mathematically. Aside from creating a hook for the unit, and a reason to learn the skills, this also provides the students with a more authentic experience. In the real world, they will likely be faced with a problem and then asked to identify and learn the skills needed to solve the problem – not visa-versa. With this said, why save the “dessert” story problems for the end of the unit when they can be better enjoyed right at the start, when the students appetite is hungry for knowledge!

*Why save dessert for last?!*

*Problem-based Approaches: Why save dessert for last?!*

# Mission Impossible: Roll Out

Lesson 1 of 11

## Objective: SWBAT represent the flights of two military aircraft visually (diagrams) and algebraically (expressions and equations). SWBAT collaborate and problem solve effectively.

See strategies folder video narrative for Know/N2K protocol. This important process is vital for teaching complex problem solving skills! After allowing all partners to construct their own Knows/N2K’s, create a class generated list to be certain that everyone is on the same page.

Contracts: If you feel collaboration might become an issue in your class, or you simply would like to make sure that you promote and teach good collaboration skills in your classroom, you may wish to have the students write contracts. These contracts written by the students explicitly state group expectations and responsibilities. Including clauses for attendance and homework completion can add an element of peer accountability that is hard to beat!

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#### Circulate the Rubric

*5 min*

Circulate the rubric to see what N2K’s can be crossed off by reading it. If logistical N2K’s remain, answer appropriate ones as needed. HOWEVER, DO NOT ANSWER N2K’s THAT ARISE FROM THE MATHEMATICS IN THE PROBLEM! This takes away from the challenge of the problem that is meant to be an introduction for the students when it comes to problem solving and mathematical modeling. (MP1, MP4)

I like to use the rubric because is keeps the students accountable for really understanding the problem, and demonstrating this understanding to me through a wide variety of learning outcomes (MP1).

A few things to look for in this problem:

- The students must research the flight speeds of the two aircraft. There will be unique approaches and answers!
- Watch for students in an "unproductive struggle" - we want for them to wrestle with the complexity of the problem, without being totally stuck in the mud.

#### Resources

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#### Homework and Work Time

*15 min*

Today has been about the problem solving process. As an introduction to the mathematics, and to determine my students' proficiency I assign Homework Workshop #1 due the next day. I encourage the students to continue the Mission Impossible problem until they hit a stopping point (???) for the day. Many students will be drawing diagrams or looking up the speed of the aircraft online – a necessary component to solving the problem!

The homework assignment is meant to see just how comfortable students are with problem solving, and what processes they use for attacking a problem. I am looking for examples of higher level of thinking. It is likely they will have questions on the following day. I emphasize the problem solving and thinking PROCESS, not the answers. For example, question 3 does not include enough information to completely solve the problem.

**Note**: *It is important NOT to provide the students with the speed of the aircraft, even if they ask. When my students come to me saying they need more information to solve the problem (or we list it as a class N2K) I reply with a question of my own: ***Where can you find this information?*** I students to know that problems often do not have all the details provided. This develops MP1 and MP5 skills by encouraging students to consult reliable sources and/or learn about elements of the problem needed support the mathematical problem solving. Possible sources for aricraft speed are: Wikipedia, consulting family members in the Air Force, contacting a local Air Base. If your students are unaccustomed to doing this kind of research you might need to explain (likely more than once) that it is okay for answers to vary. This creates a great platform for discussion at the end of the problem! (MP3)*

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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: Mission Impossible: Roll Out
- LESSON 2: Mission Impossible: Day #2
- LESSON 3: Mission Impossible: Mission Complete!
- LESSON 4: Mission Possible - 5 Scenarios in 5 Days: Day #1
- LESSON 5: Mission Possible - 5 Scenarios in 5 Days: Day #2
- LESSON 6: Mission Possible - 5 Scenarios in 5 Days: Day #3
- LESSON 7: Mission Possible - 5 Scenarios in 5 Days: Day #4
- LESSON 8: Mission Possible - 5 Scenarios in 5 Days: Day #5
- LESSON 9: Mission Possible - 5 Scenarios in 5 Days: Business Meetings!
- LESSON 10: Problem Solving Assessment
- LESSON 11: A Confidence Builder! Problem Solving and Reflection