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# 6.7: Map Quest 4

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? Can you name the cities using the facts? In this concept we will learn how to read and work with maps.

Facts:

1. Woodstock to Toledo is 40 miles.
2. Mesa to Kent is 80 miles.
3. Rocky Creek to Mesa round trip is 40 miles.
4. Mesa to Toledo is the same distance as Woodstock to Kent.

### 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. Figure out distances in miles between cities. Then use the facts to name the cities.

Facts:

1. Bakersville to Zucker is 100 miles.
2. Zucker to Saugus is 75 miles.
3. Saugus is halfway between Bakersville and Dayton.
4. Akron is 50 miles from Saugus.

A is __________

B is __________

C is __________

D is __________

Solution:

We can use problem solving steps to help.

\begin{align*}&\mathbf{Describe:} && \text{The map shows} \ 4 \ \text{cities,} \ A, B, C \ \text{and} \ D.\!\\ &&& \text{The key shows that 1 inch stands for} \ 25 \ \text{miles.}\!\\ &&& \text{Facts give information about distances between cities.}\!\\ & \mathbf{My \ Job:} && \text{Use the facts. Name the cities.}\!\\ & \mathbf{Plan:} && \text{Measure distances in inches between cities.}\!\\ &&& \text{Use the key to figure out distances in miles.}\!\\ &&& \text{Decide which clue to use first.}\!\\ & \mathbf{Solve:} && \text{Use Fact} \ 2. \ \text{Zucker to Saugus is} \ 75 \ \text{miles means} \ 3 \ \text{inches.} \ D \ \text{is} \ 3 \ \text{inches from}\!\\ &&& \text{Saugus so} \ D \ \text{is Zucker.}\!\\ &&& \text{Use Fact} \ 1: \text{Bakersville to Zucker is} \ 100 \ \text{miles, so} \ A \ \text{is Bakersville.}\!\\ &&& \text{Use Fact} \ 4: \text{Akron is 50 miles from Saugus.} \ C \ \text{is} \ 2 \ \text{inches and} \ \text{so C is Akron.}\!\\ &&& \text{Use Fact} \ 3: \text{Saugus is halfway between Bakersville and Dayton.} \ A \!\\ &&&\text{is Bakersville so} \ B \ \text{must be Dayton.}\!\\ & \mathbf{Check:} && \text{Fact} \ 1, \ \text{Bakersville to Zucker is} \ 4 \ \text{inches, and} \ 4 \times 25 = 100 \ \text{miles.}\!\\ &&& \text{Fact} \ 2, \ \text{Zucker to Saugus is} \ 3 \ \text{inches, and} \ 3 \times 25 = 75 \ \text{miles.}\!\\ &&& \text{Fact} \ 3, \ \text{Bakersville to Saugus and Dayton to Saugus are each} \ 1 \ \text{inch, or} \ 25 \ \text{miles.} \!\\ &&& \text{Fact} \ 4, \text{Akron is} \ 2 \ \text{inches or} \ 2 \times 25 = 50 \ \text{miles from Saugus.}\end{align*}

#### Example B

Use your ruler and the key. Figure out distances in miles between cities. Then use the facts to name the cities.

Facts:

1. Gentry to Dayton to Alta is 200 miles.
2. Medford is 50 miles from Dayton.
3. Waban is 50 miles from Gerard.
4. Medford to Gerard is 150 miles.

A is __________

B is __________

C is __________

D is __________

E is __________

Solution:

We can use problem solving steps to help.

\begin{align*}&\mathbf{Describe:} && \text{The map shows} \ 5 \ \text{cities,} \ A, B, C, D \ \text{and} \ E.\!\\ &&& \text{The key shows that 1 inch stands for} \ 50 \ \text{miles.}\!\\ &&& \text{Facts give information about distances between cities.}\!\\ & \mathbf{My \ Job:} && \text{Use the facts. Name the cities.}\!\\ & \mathbf{Plan:} && \text{Measure distances in inches between cities.}\!\\ &&& \text{Use the key to figure out distances in miles.}\!\\ &&& \text{Decide which clue to use first.}\!\\ & \mathbf{Solve:} && \text{Use Fact} \ 1. \ \text{Gentry to Dayton to Alta is} \ 200 \ \text{miles means} \ 4 \ \text{inches.} \!\\ &&& \ C \ \text{is} \ 4 \ \text{inches from Gentry} \ \text{so} \ C \ \text{is Alta and} \ B \ \text{is Dayton.}\!\\ &&& \text{Use Fact} \ 2: 50 \ \text{miles is} \ 1 \ \text{inches, so} \ A \ \text{is Medford.}\!\\ &&& \text{Use Fact} \ 4: D \ \text{to} \ A \ \text{is} \ 3 \ \text{inches so} \ D \text{is Gerard and E must be Waban.} \!\\ &&& \text{Use Fact} \ 3 \ \text{to check:} \ E \ \text{to} \ D \ \text{is} \ 1 \ \text{inches or} \ 50 \ \text{miles.}\!\\ & \mathbf{Check:} && \text{Fact} \ 1, \ \text{Gentry to Dayton to Alta is} \ 4 \ \text{inches, and} \ 4 \times 50 = 200 \ \text{miles.}\!\\ &&& \text{Fact} \ 2, \ \text{Medford to Dayton is} \ 1 \ \text{inches, and} \ 1 \times 50 = 50 \ \text{miles.}\!\\ &&& \text{Fact} \ 3, \ \text{Waban to Gerard is} \ 1 \ \text{inch, and} \ 1 \times 50 = 50 \ \text{miles.}\!\\ &&& \text{Fact} \ 4, \ \text{Medford to Gerard is} \ 3 \ \text{inches or} \ 3 \times 50 = 150 \ \text{miles.}\end{align*}

#### Example C

Use your ruler and the key. Figure out distances in miles between cities. Then use the facts to name the cities.

Facts:

1. Buschre to Stanton is 60 miles
2. Buschre to Stanton to Recker is 180 miles.
3. Buschre to Salt City to Power City is 120 miles.
4. Higley is 60 miles from Recker.

A is __________

B is __________

C is __________

D is __________

E is __________

Solution:

We can use problem solving steps to help.

\begin{align*}&\mathbf{Describe:} && \text{The map shows} \ 5 \ \text{cities,} \ A, B, C, D \ \text{and} \ E.\!\\ &&& \text{The key shows that 1 inch stands for} \ 60 \ \text{miles.}\!\\ &&& \text{Facts give information about distances between cities.}\!\\ & \mathbf{My \ Job:} && \text{Use the facts. Name the cities.}\!\\ & \mathbf{Plan:} && \text{Measure distances in inches between cities.}\!\\ &&& \text{Use the key to figure out distances in miles.}\!\\ &&& \text{Decide which clue to use first.}\!\\ & \mathbf{Solve:} && \text{Use Fact} \ 3. \ \text{Buschre to Salt City to Power City is } \ 120 \ \text{miles means} \ 2 \ \text{inches.} \!\\ &&&\ D \ \text{is} \ 2 \ \text{inches from Buschre} \ \text{so} \ D \ \text{is Power City and } \ E \ \text{is Salt City}.\!\\ &&& \text{Use Fact} \ 1: 60 \ \text{miles is} \ 1 \ \text{inch, so} \ A \ \text{is Stanton.}\!\\ &&& \text{Use Fact} \ 2: B \ \text{to Buschre is} \ 3 \ \text{inches so} \ B \text{must be Recker and} \ C \ \text{must be Higley.}\!\\ &&& \text{Use Fact} \ 4 \ \text{to check:} \ C \ \text{to} \ B \ \text{is} \ 1 \ \text{inch or} \ 60 \ \text{miles.}\!\\ & \mathbf{Check:} && \text{Fact} \ 1, \ \text{Buschre to Stanton is} \ 1 \ \text{inch, and} \ 1 \times 60=60 \ \text{miles.}\!\\ &&& \text{Fact} \ 2, \ \text{Buschre to Stanton to Recker is } \ 3 \ \text{inches, and} \ 3 \times 60 = 180 \ \text{miles.}\!\\ &&& \text{Fact} \ 3, \ \text{Buschre to Salt City to Power City is} \ 2 \ \text{inches, and} \ 2 \times 60 = 120 \ \text{miles.}\!\\ &&& \text{Fact} \ 4, \ \text{Higley to Recker is} \ 1 \ \text{inch or} \ 1 \times 60 = 60 \ \text{miles.}\end{align*}

#### Concept Problem Revisited

Facts:

1. Woodstock to Toledo is 40 miles.
2. Mesa to Kent is 80 miles.
3. Rocky Creek to Mesa round trip is 40 miles.
4. Mesa to Toledo is the same distance as Woodstock to Kent.

We can use problem solving steps to help.

\begin{align*}&\mathbf{Describe:} && \text{The map shows} \ 4 \ \text{cities,} \ A, B, C \ \text{and} \ D.\!\\ &&& \text{The key shows that 1 inch stands for} \ 20 \ \text{miles.}\!\\ &&& \text{Facts give information about distances between cities.}\!\\ & \mathbf{My \ Job:} && \text{Use the facts. Name the cities.}\!\\ & \mathbf{Plan:} && \text{Measure distances in inches between cities.}\!\\ &&& \text{Use the key to figure out distances in miles.}\!\\ &&& \text{Decide which clue to use first.}\!\\ & \mathbf{Solve:} && \text{Use Fact} \ 3. \ \text{Round trip of} \ 40 \ \text{miles means} \ 2 \ \text{inches.} \ D \ \text{is} \ 1 \ \text{inch from}\!\\ &&& \text{Mesa so roundtrip is} \ 2 \ \text{inches.} \ D \ \text{is Rocky Creek.}\!\\ &&& \text{Use Fact} \ 2: 80 \ \text{miles is} \ 4 \ \text{inches, so} \ A \ \text{is Kent.}\!\\ &&& \text{Use Fact} \ 4: B \ \text{to} \ A \ \text{is} \ 3 \ \text{inches and} \ C \ \text{to Mesa is} \ 3 \ \text{inches.} \ A \ \text{is Kent,}\!\\ &&& \text{so B is Woodstock and} \ C \ \text{must be Toledo.}\!\\ &&& \text{Use Fact} \ 1 \ \text{to check:} \ B \ \text{to} \ C \ \text{is} \ 2 \ \text{inches or} \ 40 \ \text{miles.}\!\\ & \mathbf{Check:} && \text{Fact} \ 1, \ \text{Woodstock to Toledo is} \ 2 \ \text{inches, and} \ 2 \times 20 = 40 \ \text{miles.}\!\\ &&& \text{Fact} \ 2, \ \text{Mesa to Kent is} \ 4 \ \text{inches, and} \ 4 \times 20 = 80 \ \text{miles.}\!\\ &&& \text{Fact} \ 3, \ \text{Rocky Creek to Mesa is} \ 1 \ \text{inch, or} \ 2 \ \text{inches round trip, and} \!\\ &&& \ 2 \times 20 =40 \ \text{miles.}\!\\ &&& \text{Fact} \ 4, \text{Mesa to Toledo is} \ 3 \ \text{inches or} \ 3 \times 20 = 60 \ \text{miles and Kent to}\!\\ &&& \text{Woodstock is} \ 3 \ \text{inches or} \ 3 \times 20 = 60 \ \text{miles.}\end{align*}

### 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. Figure out distances in miles between cities. Then use the facts to name the cities.

Facts:

1. Wood Hill and Spider City are both 50 miles from Fanta.
2. Wood Hill to Post is 100 miles.
3. Spider City to Cave Creek to Post is 100 miles.
4. Dryville is 50 miles from Post and 150 miles from Wood Hill.

A is __________

B is __________

C is __________

D is __________

E is __________

2. Use your ruler and the key. Figure out distances in miles between cities. Then use the facts to name the cities.

Facts:

1. Bayside to Culver City is 10 miles.
2. Lorraine is 40 miles from Bayside.
3. Culver City to Loon Creek to Alton is 30 miles.
4. Fernville is 50 miles from Bayside.

A is __________

B is __________

C is __________

D is __________

E is __________

1. A is Wood Hill, B is Post, C is Dryville, D is Cave Creek, E is Spider City

2. A is Lorraine, B is Fernville, C is Alton, D is Loon Creek, E is Culver City

### Practice

For each problem, use your ruler and the key. Figure out distances in miles between cities. Then use the facts to name the cities.

1.

Facts:

1. Satton to Fenton is 100 miles more than Satton to Briars.
2. Briars to Newton is the same distance as Newton to Waban.
3. Waban to Newton round trip is 400 miles.
4. Newton to Malden round trip is 200 miles.

2.

Facts:

1. Reston to Florence to Culver to Brazelton is 250 miles.
2. Brazelton is 50 miles from Reston.
3. Trenton to Brazelton is 150 miles.
4. Culver to Menton is twice the distance of Menton to Reston.

3. Use your ruler and the key. Figure out distances in miles between cities. Then use the facts to name the cities.

Facts:

1. Albion to Riverside is 40 miles.
2. Felton is 120 miles from Riverside and 40 miles from Mentos.
3. Taco to Mentos to Albion is 200 miles.
4. Santa Casa is 40 miles from Taco.

A is __________

B is __________

C is __________

D is __________

E is __________

4. Use your ruler and the key. Figure out distances in miles between cities. Then use the facts to name the cities.

Facts:

1. Pontero to Bard is the same distance as Pontero to Fessler to Bradley.
2. Pontero to Fessler is 60 miles.
3. Bard to Petersburg is the same distance as Bard to Gilton.
4. Gilton to Petersburg is 120 miles.

A is __________

B is __________

C is __________

D is __________

E is __________

5. Use your ruler and the key. Figure out distances in miles between cities. Then use the facts to name the cities.

Facts:

1. Bellview to Press is the same distance as Bellview to Tapestry Falls.
2. Spiketon to Bellview is 50 miles.
3. Tapestry Falls to Tinseltown is 50 miles.
4. Tapestry Falls to Tinseltown to Paradise is 100 miles.

A is __________

B is __________

C is __________

D is __________

E is __________

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