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# 7.10: Map Quest 5

Difficulty Level: At Grade Created by: CK-12

Look at the map and list of facts below. Can you figure out the distances in miles between the cities using a ruler? Can you name the cities using the facts? In this concept we will learn how to read and work with maps.

• Fact 1: Hilton to Time is 20 miles.
• Fact 2: Time to North Shore by way of Hilton is 80 miles.
• Fact 3: Westway to North Shore is 20 miles less than Westway to Raleigh.
• Fact 4: Time to Pepper is 20 miles longer than Pepper to Edmonton.
• Fact 5: Edmonton is 80 miles from Raleigh.

### Guidance

In order to solve the problem above, use the problem solving steps.

• Start by describing what information is given.
• Then, identify what your job is. In these problems, your job will be to figure out where each city is on the map.
• Next, make a plan for how you will solve. In these problems, measure distances with a ruler and use the facts to figure out which city is which.
• Then, solve the problem.
• Finally, check your solution. Verify that the measured distances between the cities work with the facts.

#### Example A

Use your ruler and the key to figure out distances between cities. Use the facts to name the cities.

• Fact 1: Portland to Ellsworth by way of Surrey is 500 miles.
• Fact 2: Surrey is 300 miles from Ellsworth.
• Fact 3: Felton to Dayton is 50 miles less than Felton to Granada.
• Fact 4: Simpson to Dayton round trip is 200 miles.

Solution:

We can use problem solving steps to help.

$& \mathbf{Describe:} && \text{The map shows 7 cities. One is Surrey. The key shows that one inch stands for}\\&&& \text{100 miles. The facts give information about location and distances between cities.}\\& \mathbf{My \ Job:} && \text{Use the facts. Name the cities.}\\& \mathbf{Plan:} && \text{Measure distances in inches. Use the key to figure out actual distances. Use the}\\&&& \text{facts to name the cities.}\\& \mathbf{Solve:} && \text{Fact} \ 2: \ \ \text{B is Ellsworth}\\&&& \text{Fact} \ 1: \ \ \text{A is Portland}\\&&& \text{Fact} \ 3: \ \ \text{D is Felton, E is Dayton, C is Granada}\\&&& \text{Fact} \ 4: \ \ \text{F is Simpson}\\& \mathbf{Check:} && \text{Fact} \ 1: \ \ \text{Portland to Ellsworth by way of Surrey is} \ 5 \ \text{inches or} \ 500 \ \text{miles.}\\&&& \text{Fact} \ 2: \ \ \text{Surrey to Ellsworth is } \ 3 \ \text{inches, or} \ 3 \times 100, \ \text{or} \ 300 \ \text{miles.}\\&&& \text{Fact} \ 3: \ \ \text{Felton to Dayton is} \ 1.5 \ \text{inches, or} \ 1.5 \times 100, \ \text{or} \ 150 \ \text{miles.}\\&&& \qquad \qquad \ \text{Felton to Granada is} \ 2 \ \text{inches or,} \ 2 \ \times 100, \ \text{or} \ 200 \ \text{miles.}\\&&& \qquad \qquad \ 200 - 150 = 50 \ \text{miles}\\&&& \text{Fact} \ 4: \ \ \text{Simpson to Dayton roundtrip is} \ 2 \ \text{inches, or} \ 200 \ \text{miles.}$

#### Example B

Use your ruler and the key to figure out distances between cities. Use the facts to name the cities.

• Fact 1: Regis to Hoosier round trip is 70 miles less than the round trip from Regis to Bandoff.
• Fact 2: Sandford to Tulsa is the same distance as Eckard to Tulsa.
• Fact 3: Eckard to Adams is 35 miles more than Adams to Hoosier.

Solution:

We can use problem solving steps to help.

$& \mathbf{Describe:} && \text{The map shows 7 cities. One is Regis. The key shows that one inch stands for}\\&&& \text{70 miles. The facts give information about location and distances between cities.}\\& \mathbf{My \ Job:} && \text{Use the facts. Name the cities.}\\& \mathbf{Plan:} && \text{Measure distances in inches. Use the key to figure out actual distances. Use the}\\&&& \text{facts to name the cities.}\\& \mathbf{Solve:} && \text{Fact} \ 1: \ \ \text{F is Bandoff and E is Hoosier}\\&&& \text{Fact} \ 2: \ \ \text{B is Tulsa}\\&&& \text{Fact} \ 3: \ \ \text{A is Sanford, C is Eckard, D is Adams}\\& \mathbf{Check:} && \text{Fact} \ 1: \ \ \text{Regis to Hoosier round trip is } \ 5 \ \text{inches or} \ 350 \ \text{miles.}\\&&& \qquad \ \text{Regis to Bandoff round trip is } \ 4 \ \text{inches or} \ 280 \ \text{miles.}\\&&& \text{Fact} \ 2: \ \ \text{Sandford to Tulsa and Eckard to Tulsa are both} \ 1 \ \text{inch, or} \ 1 \times 70, \ \text{or} \ 70 \ \text{miles.}\\&&& \text{Fact} \ 3: \ \ \text{Eckard to Adams is} \ 2.5 \ \text{inches, or} \ 2.5 \times 70, \ \text{or} \ 175 \ \text{miles.}\\&&& \qquad \qquad \ \text{Adams to Hoosier is} \ 2 \ \text{inches or,} \ 2 \ \times 70, \ \text{or} \ 140 \ \text{miles.}\\&&& \qquad \qquad \ 175 - 140 = 35$

#### Concept Problem Revisited

• Fact 1: Hilton to Time is 20 miles.
• Fact 2: Time to North Shore by way of Hilton is 80 miles.
• Fact 3: Westway to North Shore is 20 miles less than Westway to Raleigh.
• Fact 4: Time to Pepper is 20 miles longer than Pepper to Edmonton.
• Fact 5: Edmonton is 80 miles from Raleigh.

We can use problem solving steps to help.

$& \mathbf{Describe:} && \text{The map shows 7 cities. One is Hilton. The key shows that one inch stands for}\\&&& \text{40 miles. The facts give information about location and distances between cities.}\\& \mathbf{My \ Job:} && \text{Use the facts. Name the cities.}\\& \mathbf{Plan:} && \text{Measure distances in inches. Use the key to figure out actual distances. Use the}\\&&& \text{facts to name the cities.}\\& \mathbf{Solve:} && \text{Fact} \ 1: \ \ \text{F is Time}\\&&& \text{Fact} \ 2: \ \ \text{E is North Shore}\\&&& \text{Fact} \ 3: \ \ \text{D is Westway}\\&&& \text{Fact} \ 4: \ \ \text{A is Pepper and B is Edmonton}\\&&& \text{Fact} \ 5: \ \ \text{C is Raleigh}\\& \mathbf{Check:} && \text{Fact} \ 1: \ \ \text{Hilton to Time is} \ \frac{1}{2} \ \text{inch or} \ 20 \ \text{miles.}\\&&& \text{Fact} \ 2: \ \ \text{Time to North Shore by way of Hilton is} \ 2 \ \text{inches, or} \ 2 \times 40, \ \text{or} \ 80 \ \text{miles.}\\&&& \text{Fact} \ 3: \ \ \text{Westway to North Shore is} \ 2 \ \text{inches, or} \ 2 \times 40, \ \text{or} \ 80 \ \text{miles.}\\&&& \qquad \qquad \ \text{Westway to Raleigh is} \ 2 \ \frac{1}{2} \ \text{inches or,} \ 2 \ \frac{1}{2} \times 40, \ \text{or} \ 100 \ \text{miles.}\\&&& \qquad \qquad \ 100 - 80 = 20 \ \text{miles}\\&&& \text{Fact} \ 4: \ \ \text{Time to Pepper is} \ 1 \ \text{inch, or} \ 40 \ \text{miles.}\\&&& \qquad \qquad \ \text{Pepper to Edmonton is} \ \frac{1}{2} \ \text{inch, or} \ 20 \ \text{miles.}\\&&& \qquad \qquad \ 40 - 20 = 20 \ \text{miles}\\&&& \text{Fact} \ \ 5: \ \text{Edmonton to Raleigh is} \ 2 \ \text{inches, or} \ 2 \times 40, \ \text{or} \ 80 \ \text{miles.}$

### Vocabulary

A map is a picture that represents an area of land. A ruler is a device that measures and finds the distance between two points.

### Guided Practice

1. Use your ruler and the key to figure out distances between cities. Use the facts to name the cities.

• Fact 1: Sample to Telegraph to Antonville is 180 miles.
• Fact 2: Sample to Readville round trip is 100 miles.
• Fact 3: Readville is 60 miles from Antonville.
• Fact 4: Diablo to Carlton is 15 miles less than Diablo to Bedford.
• Fact 5: Bedford to Sample to Readville is 60 miles.

2. Use your ruler and the key to figure out distances between cities. Use the facts to name the cities.

• Fact 1: Brickyard to Yerba is 300 miles
• Fact 2: Yerba to Brio is the same distance as Yerba to Tempe.
• Fact 3: Superstition is 30 miles closer to Tempe than to Yerba.
• Fact 4: Brickyard to Danyo is 90 miles.
• Fact 5: Littleton is 30 miles from Danyo.

3. Use your ruler and the key to figure out distances between cities. Use the facts to name the cities.

• Fact 1: Trenton to Storrs is 20 miles more than Storrs to Wentworth.
• Fact 2: Wentworth to Storrs is 20 miles.
• Fact 3: Storrs to Leopold round trip is 120 miles
• Fact 4: New Bertson to Leopold to Carlton is 70 miles.
• Fact 5: Halland to Leopold is 10 miles more than Leopold to Carlton.

1. A is Bedford, B is Sample, C is Readville, D is Antonville, E is Carlton, F is Diablo

2. A is Tempe, B is Superstition, C is Yerba, D is Brio, E is Danyo, F is Littleton

3. A is Wentworth, B is Carlton, C is Leopold, D is Halland, E is New Bertson, F is Trenton

### Practice

1. Use your ruler and the key to figure out distances between cities. Use the facts to name the cities.

• Fact 1: Grinder to Riverwalk to Sienna is 225 miles.
• Fact 2: Sienna to Riverwalk round trip is 270 miles.
• Fact 3: Hartman to Grinder is 180 miles.
• Fact 4: Snake City to Sienna is the same distance as Sienna to Briarwood.
• Fact 5: Ringville to Hartman is 45 miles.

2. Use your ruler and the key to figure out distances between cities. Use the facts to name the cities.

• Fact 1: Calder to Whitton to Ballard is 360 miles.
• Fact 2: Ballard roundtrip to Nicksville is 400 miles.
• Fact 3: Calder to Exeter is 40 miles more than Exeter to Reston.
• Fact 4: Reston to Franklin is 240 miles.
• Fact 5: Nicksville to Franklin is 120 miles.

3. Use your ruler and the key to figure out distances between cities. Use the facts to name the cities.

• Fact 1: Girard to Browning by way of Dallas is 125 miles.
• Fact 2: Girard to Dallas is the same distance as Crowville to Browning.
• Fact 3: Houston to Coventry is 75 miles less than Browning to Girard.
• Fact 4: Coventry to Winston is 100 miles.

4. Use your ruler and the key to figure out distances between cities. Use the facts to name the cities.

• Fact 1: Redwood to Mateo is 75 miles.
• Fact 2: Mateo to Evergreen is the same distance as Evergreen to Longwood.
• Fact 3: Redwood to Berkview is 100 miles.

5. Use your ruler and the key to figure out distances between cities. Use the facts to name the cities.

• Fact 1: Albany to Queens is 180 miles.
• Fact 2: Venice to Albany is 90 miles.
• Fact 3: Albany to Sacrey is 240 miles.
• Fact 4: Sacrey to Denton is the same distance as Albany to Venice.

Jan 18, 2013