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# Finding Distances on Maps

Lesson 4 of 12

## Objective: SWBAT solve map scale problems using a double number line

## Big Idea: Remember planning trips before Mapquest or Google Maps? Students find distances using rulers and map scales.

*45 minutes*

#### Introduction

*10 min*

I will start by asking my students how would they or their parents plan a long distance trip? I am sure most will respond that they will use the computer. Then, how do you think people planned trips before the tools on the internet were so readily available? How did people calculate distances and routes on a map? Hopefully this pulls a lot of prior knowledge from students about how to read and interpret maps. I really don't know how much experience my current group of students will have had with "analog" map reading.

I will then walk my students through the example problem. Several students will need help using their rulers to measure distances. Some students will think they should start at the number one and measure from there. While it is possible to accurately measure from any point, I will encourage them to start from 0!

The rest of the problem is to focus on the proportional relationship represented by a map scale.

#### Resources

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#### Guided Problem Solving

*10 min*

This next problem is similar to the example problem but students now measure in inches. To keep things simple, I will have students measure to the nearest half inch. Again I will need to be on the lookout for students who are measuring on the metric side of the ruler.

Students must then explain how they know that the found measurement is equivalent to the given scale. This is **MP3**. It also addresses one of the essential questions of the unit: 1) How can proportional relationships be identified?

#### Resources

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#### Independent Problem Solving

*20 min*

Now the students are on their own with their partners to solve the next set of problems. There are several things to look out for here. Each problem asks students to complete their number line using a specific increment. I'll make sure students are doing this correctly. On problem 1, students are asked to identify two possible unit rates from the given scale. Some students may treat this as identical and say 5 to 1. Here I may say, "If 1 cm equals 5 miles will 1 mile be represented by a length less than or greater than 1 cm?". It may help to use the double number line as a visual reference.

The final problem requires students to actually identify the scale given the length of 2 miles. The last two problems require students to solve rate problems involving distance to time.

#### Resources

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#### Exit Ticket

*5 min*

Before going into the exit ticket, we will summarize the lesson by discussing the map scale and how we represented equivalent ratios on the double number line. Then students will take the exit ticket.

This exit ticket will be worth 4 points. A score of at least 3 correct answers will be considered as a sign of success.

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- LESSON 1: Proportional Relationships of Whole Numbers
- LESSON 2: Proportional Relationships With Decimals
- LESSON 3: Proportional Relationships With Fractions
- LESSON 4: Finding Distances on Maps
- LESSON 5: Scaling a Recipe
- LESSON 6: Determine Equivalent Ratios - Scale Factor Between Ratios
- LESSON 7: Determine Equivalent Ratios - Scale Factor Between Terms
- LESSON 8: Determine The Graph of a Proportional Relationship
- LESSON 9: Determine Equivalent Ratios - Common Unit Rate
- LESSON 10: Writing The Constant of Proportionality Equation
- LESSON 11: Writing Equations for Proportional Relationships
- LESSON 12: The Distance Formula