## Rate Changes as Trail Becomes Difficult - Section 3: Guided Hike

*Rate Changes as Trail Becomes Difficult*

# Take a Hike in Bryce Canyon National Park: Math Stories

Lesson 6 of 6

## Objective: SWBAT solve for the unknown variable in word stories related to the distance, time or miles per hour traveled while hiking.

**Mini Review: Addition and Subtraction with Regrouping**

**Standard Algorithm and Expanded Form**

I call students to the carpet with their whiteboards and marker and proceed through a brief review examples. This or basic fact practice will be our lesson opener for most of the fourth quarter.

The goal in this mini review is to enrich and solidify the skills of students who have attained mastery and to provide constant extra support for students who have not year reached mastery. In contrast with the rest of my lessons, in this brief section, at this time of the year, I follow a very tight routine.

#### Resources

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*Today we are going to be using multiplication and division to solve some story problems. Before I tell you the topic of the story problems, I’d like you to look at this.* (Show Peekaboo Loop topographic map).

*What is this?* *Think and then discuss with a neighbor.* *Be prepared to be called on to share your thoughts with the class.*

I give students about 30 seconds of quiet think time.

Here is the way one student responded to the question, What Kind of a Map Is This?

Once I've briefly discussed the concept of a hiking map with the students, I give them a brief Explanation of Contour Lines. Finally, I present students with a problem that requires some critical reasoning ,when I ask why a trip on a loop trail that is 3 miles long will never be a 3 mile hike.

Here is how they reasoned through the question, "Why is a hike around Peekaboo more than 3 miles?" Peekaboo loop is the first slide in the presentation (in the next section) that accompanies the word problems.

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#### Guided Hike

*35 min*

In this set of word problems centered around hiking in Bryce Canyon, students are looking at the distance of a hike, the completion time, and then are using division to figure out the imaginary hiker's average speed.

Rate is not a 3rd grade expectation, but in this context, with support, it provides an interesting way to practice division. This presentation should be used in conjunction with the student word problem page.

If you think this is too hard for your students, think again! Here is a student explaining that the rate per hour should decrease with increased difficulty of the climb.

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#### Homework

*1 min*

I ask students to write two division or multiplication problems about a person who walks, hikes or runs at a realistic speed for a realistic distance. Students ready to extend are given the freedom to write this up as they wish. The majority of students needed support - this is what I gave them:

Write math stories about hiking or walking for...

- 1 mile each hour, you pick how long the hike is
- 3 miles in an hour, 4 hours, how far did they go?
- 24 miles total, 2 miles an hour, how many hours

My goal in giving this homework assignment is that they make the attempt, not that they work out complicated rate problems. About half of the class stuck with the one mile/hr examples but to my surprise the rest of them tackled more complex problems in a way that showed the beginning of an understanding at the very least.

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- UNIT 1: 1st Week: Getting to Know Each Other Through Graphs
- UNIT 2: Addition and Subtraction
- UNIT 3: Multiplication
- UNIT 4: Introduction to Basic Division
- UNIT 5: Division in Context
- UNIT 6: Time
- UNIT 7: Rounding
- UNIT 8: Place Value Practice
- UNIT 9: Fractions
- UNIT 10: Math and Me: Nutrition, Health and More
- UNIT 11: Geometry in Architecture
- UNIT 12: Time Cycle 2
- UNIT 13: Patterns in Math
- UNIT 14: Area and Perimeter
- UNIT 15: Solving Mult-Step Word Problems Using the Four Operations
- UNIT 16: Musical Fractions
- UNIT 17: Volcanoes (Data Collection, Graphs, Addition & Subtraction)

- LESSON 1: Fundraiser Finance (Pickles for a Profit)
- LESSON 2: Fundraiser Math: Solving for Individual Item Cost
- LESSON 3: Metro Math
- LESSON 4: A Day in D.C.
- LESSON 5: Sonoran Desert Scenarios: Addition and Subtraction Word Problems
- LESSON 6: Take a Hike in Bryce Canyon National Park: Math Stories