## The Exercise Problem.doc - Section 2: Investigation

# The Exercise Plan (Day 2 of 2)

Lesson 5 of 13

## Objective: SWBAT use equations and inequalities to model a situation and solve for unknown values.

#### Open

*3 min*

At the start of class today students rejoin their groups from the previous lesson. I will have them congregate next to their chart paper (either on the wall or at their desks). Students should discuss where they left off, as well as any new ideas that students may have come up with since class ended.

Once students have had a chance to rejoin their conversation from yesterday, I will explain to them that they will be investigating this situation in a more formal way today. I say, "You will be be given more constraints today. And, you will be asked to use some specific strategies."

My goal is for the students to build on the informal, intuitive work that they did yesterday. My experience is that the experience gained during yesterday's lesson allows students to be more successful today. Since they have already grappled with the content in this lesson, they are in a better position to model the problem and construct a solution.

#### Resources

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#### Investigation

*27 min*

The Exercise Problem investigation will require students to see how adding different restrictions to the exercise plan can affect the possible outcomes or options. At this point, students will be in one of two situations:

**Situation 1**: The team of students has already determined a solution that will require Jack to exercise for less than one hour and still burn 500 calories per day. If this is the case, the students will investigate how changing the amount of time can effect the type of workout that Jack needs to do. Students will also apply inequalities to a mixed exercise/diet program.

**Situation 2**: The team of students has not been able to determine a solution. In this case, the remaining questions will guide students to finding an appropriate solution in a more guided way. Students will also apply inequalities to mixed exercise/diet program. Students will also apply inequalities to mixed exercise/diet program. Students will also apply inequalities to mixed exercise/diet program.

In either case, students will be looking at smaller portions of the problem at hand and investigating them more deeply.

- MP1: The questions will require that students think through the problems
- MP3: Students will also need to construct viable solutions to each of the prompts
- MP4: There are three places where students are going to need to take a quantitative situation and generalize it by writing it as a function. This will help students to model the problem in a more general way

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#### Closure

*10 min*

For today's Ticket out the Door students will apply what they have learned over the last two days to reflect on their own goals and experiences. Today's Ticket Out asks students to write an exercise plan for either themselves or a close friend. They should:

- Determine a goal: amount of pounds to lose each week.
- Choose an exercise routine: Here students will need to estimate how fast they can walk/run and how long they will exercise for. How much time will they walk/run?
- Consider if they will include a dieting aspect to their plan.

**Note**: If students are heavier than 205 pounds they can try to determine a relative pattern in the numbers or can use this approximation for calories burned from Runner's World magazine:

- Approximate Calories burned by walking per hour: 1.8 x Body weight in pounds
- Approximate Calories burned by running per hour 4.2 x Body weightin pounds

Here's a link to Runner's World's Calories Burned Calculator:

http://www.runnersworld.com/tools/calories-burned-calculator

#### Resources

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- LESSON 1: Creating Equations to Solve Problems
- LESSON 2: More Solving Problems with Equations
- LESSON 3: Creating Inequalities to Solve Problems
- LESSON 4: The Exercise Plan (Day 1 of 2)
- LESSON 5: The Exercise Plan (Day 2 of 2)
- LESSON 6: Solving Literal Equations
- LESSON 7: Literal Inequalities
- LESSON 8: Rewriting Formulas
- LESSON 9: Printing Presses: Solving more difficult Linear Equations
- LESSON 10: The Groupon Question: Solving Two Variable Equations
- LESSON 11: More with Solving Two Variable Equations
- LESSON 12: Solving Two Variable Inequalities
- LESSON 13: Modeling with Two Variable Equations and Inequalties