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Map Quest - Reason Proportionally

Teacher Notes

Map Quest presents maps showing cities and connections between them. Students use the key and reason proportionally to determine distances in miles, then use the facts to identify the cities. All keys show numbers of miles per inch, and all distances on maps are whole numbers of inches.

Solutions

Map Quest 1

A is Bakersville

B is Dayton

C is Akron

D is Zucker

Map Quest 2

A is Medford

B is Dayton

C is Alta

D is Gerard

E is Waban

Map Quest 3

A is Stanton

B is Recker

C is Higley

D is Power City

E is Salt City

Map Quest 4

A is Wood Hill

B is Post

C is Dryville

D is Cave Creek

E is Spider City

Use your ruler and the key.

Figure out distances in miles between cities.

Then use the facts to name the cities.

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.

A is __________

B is __________

C is __________

D is __________

&\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 Mesa}\!\\&&& \text{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, so} \ B\!\\&&& \text{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.}

Map Quest 1 - Reason Proportionally

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 __________

Map Quest 2 - Reason Proportionally

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 __________

Map Quest 3 - Reason Proportionally

Use your ruler and the key.

Figure out distances in miles between cities.

Then use the facts to name the cities.

Facts:

  1. Baseline to Stanton is 60 miles
  2. Baseline to Stanton to Recker is 180 miles.
  3. Baseline 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 __________

Map Quest 4 - Reason Proportionally

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 15 miles from Fanta.
  2. Wood Hill to Post is 30 miles.
  3. Spider City to Cave Creek to Post is 30 miles.
  4. Dryville is 15 miles from Post and 45 miles from Wood Hill.

A is __________

B is __________

C is __________

D is __________

E is __________

Extras for Experts: Map Quest 1 – Reason Proportionally

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 __________

Extras for Experts: Map Quest 2 – Reason Proportionally

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 __________

Extras for Experts: Map Quest 3 – Reason Proportionally

Use your ruler and the key.

Figure out distances in miles between cities.

Then use the facts to name the cities.

Facts:

  1. Sutton to Fenton is 100 miles more than Sutton 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.

A is __________

B is __________

C is __________

D is __________

E is __________

Extras for Experts: Map Quest 4 – Reason Proportionally

Use your ruler and the key.

Figure out distances in miles between cities.

Then use the facts to name the cities.

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. Culter to Menton is twice the distance of Menton to Reston.

A is __________

B is __________

C is __________

D is __________

E is __________

Extras for Experts: Map Quest

Solutions

Extra for Experts: Map Quest 1

A is Lorraine

B is Fernville

C is Alton

D is Loon Creek

E is Culver City

Extra for Experts: Map Quest 2

A is Santa Casa

B is Taco

C is Mentos

D is Albion

E is Felton

Extra for Experts: Map Quest 3

A is Fenton

B is Waban

C is Newton

D is Malden

E is Briars

Extra for Experts: Map Quest 4

A is Trenton

B is Brazelton

C is Culver

D is Florence

E is Menton

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CK.MAT.ENG.SE.1.Algebra-Explorations-K-7.6.16

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