##
* *Reflection: Perseverance
Make it More - Section 2: Put it into Action

This reflection is about perseverance; both mine and my students! I thought this set of story problems were fairly straightforward and selected them because they covered a range of earlier concepts from working with formulas to writing a quadratic equation. What I found as my students worked on these at their seats and then presented them to the class on the front board was that some the problems were more complicated than I'd assumed.

The three different problems solved on my board show the range of thinking and ability in my class. The students doing Problem #3 set up the equation nicely and persevered to get the final cubic equation. What was really interesting was when a classmate asked how they got from the cubic equation to h=1 and they replied "We graphed it in our calculator and got the zero." This made me grin because it's just the kind of strategic use of tools I hope to develop in my students.

The students doing Problem #9 drew a nice diagram to help them set up the equation, but forgot to use common units for time until another student watching them caught their mistake and told them. They persevered to rework the equation using 53/60 and found an answer that made sense.

The students doing Problem #4 really struggled at first with what to do with all the variables until a classmate suggested they cancel out all the parts that were the same for both balloons. There was some interesting discussion about whether that was okay mathematically, until the student making the suggestion reminded them that they cancel things out all the time in fractions which is what the factor really comes from.

Overall, this lesson gave my students an opportunity to work collaboratively and to stick to the problems even when the going got tough.

# Make it More

Lesson 2 of 10

## Objective: SWBAT apply complicated equations in one variable.

## Big Idea: More storytelling, only this time your students get to read the stories and figure out the answers.

*55 minutes*

#### Set the Stage

*10 min*

I begin this lesson with a story problem on the board that can be modeled by an exponential function instead of linear or quadratic. This builds on the previous lesson, giving my students a chance to solidify their understanding of algebraic models.

*In 1980 wind turbines in Europe generated about 5 gigawatt-hours of energy. Over the next 15 years the amount of energy generated increased by about 59% per year. Approximately what year did the energy generated top 80 gigawatt-hours.*

I ask my students to figure out the answer in any way they choose and to be ready to share their answer and math. **(MP1, MP4) **While they're working I walk around offering encouragement and redirection as necessary. When everyone is done I ask for volunteers to put their work and answers on the board. I have my students review the board and check the equations/answers for themselves to see which if any seem to work. I talk about what I do if none of the answers are correct in my video. Usually at least one student recognizes that an annual percentage increase means an exponential equation and has written a fairly good solution. I write the word "exponential" next to that problem then ask about any other functions we've looked at this year and serve as scribe to write them down. When everyone has had a chance to make suggestions, I tell my students they will be working with a variety of functions today.

#### Resources

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#### Put it into Action

*40 min*

*You will need copies of the Story Problems for this section of the lesson.* For this part of the lesson I tell my students they will be working in teams to attack and solve real-world problems. I explain that they will be responsible for setting up the equations, finding answers to the questions asked, and checking their solutions for reasonableness. I suggest that there might be some easy questions and some that will be more challenging, but assure my students that they can solve them all. I tell them today they will work with their back-partner but that they must each write out their own work for each problem. For those who complain about duplicating each other's work, I advise them to try the problems separately first, then compare their work so it will be different. **(MP1, MP2, MP4) **I distribute the Story Problems and while my students are working I walk around offering encouragement and redirection as necessary.

After about 30 minutes or when everyone is done, I randomly select teams to post their equation and solution for a problem on the board. My board fits three to four students at a time, so it doesn't take long to get all the problems posted. I then ask my students to compare their work to what is posted and offer any questions or comments. **(MP3) **This gives everyone a chance to check their work and to see several different ways to solve the problems.

#### Resources

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#### Wrap it Up

*5 min*

To close this lesson I ask my students to reflect silently for a moment about one problem that was solved in a way they found particularly interesting or that they didn't expect and be ready to discuss it with the class. After a minute or so, I randomly select a student to share his/her thoughts, reminding my students that this is not a time for critiquing, but rather an opportunity to hear alternative thinking. I continue until everyone has an chance to share, then make my own observations about what they've just said, summarizing any patterns I heard.

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- UNIT 1: First Week!
- UNIT 2: Algebraic Arithmetic
- UNIT 3: Algebraic Structure
- UNIT 4: Complex Numbers
- UNIT 5: Creating Algebraically
- UNIT 6: Algebraic Reasoning
- UNIT 7: Building Functions
- UNIT 8: Interpreting Functions
- UNIT 9: Intro to Trig
- UNIT 10: Trigonometric Functions
- UNIT 11: Statistics
- UNIT 12: Probability
- UNIT 13: Semester 2 Review
- UNIT 14: Games
- UNIT 15: Semester 1 Review

- LESSON 1: Make It
- LESSON 2: Make it More
- LESSON 3: Double Trouble
- LESSON 4: Going Graphic
- LESSON 5: Out of Bounds
- LESSON 6: Limiting Your Options
- LESSON 7: Does it Work?
- LESSON 8: Twist It
- LESSON 9: Creating Algebraically Review Stations
- LESSON 10: Creating Algebraically; Assessment