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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.

Answers:

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.

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Difficulty Level:

At Grade

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Date Created:

Jan 18, 2013

Last Modified:

May 27, 2014
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