Scale Word Problems Scaffolded Worksheet
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Date:
Grade Level Scaffold
Scale Word Problems
Step-by-Step Guide & Scaffolded Practice
Toolbox
How Scale Works & Reference Conversion Guide
Visual Scale Bar (Example)
1 in
2 in
3 in
4 in
0 mi 50 mi 100 mi 150 mi 200 mi
3 Simple Steps to Solve
- Underline the scale ratio (drawing vs. real).
- Build a table and skip count or multiply.
- Match the target number & write your answer.
Fraction Tip: \(\frac{1}{2}\) = Half of 1 whole | \(\frac{1}{4}\) = One quarter (half of \(\frac{1}{2}\))
Worked Example Study this before you begin!
Problem: A map scale is 1 inch = 40 miles. How many inches equal 120 miles?
Step 1: Write Scale
1 inch = 40 miles
Step 2: Skip Count (Table)
<table class="w-full text-center mt-1 border border-black font-semibold"><tbody><tr class="bg-zinc-200 border-b border-black"><td class="p-0.5">Inches</td><td class="p-0.5">1</td><td class="p-0.5">2</td><td class="p-0.5 bg-zinc-300 font-black">3</td></tr><tr><td class="p-0.5">Miles</td><td class="p-0.5">40</td><td class="p-0.5">80</td><td class="p-0.5 bg-zinc-300 font-black">120</td></tr></tbody></table>
Step 3: Answer
120 miles = 3 inches
Problem 1
Map Scale
A map has a scale of 1 centimeter = 50 miles. The actual distance between New York City and Washington, D.C., is 225 miles. What is the distance, in centimeters, between the two cities on the map?
Step 1: Fill in the Skip-Counting Chart
| Centimeters | Actual Miles |
|---|
| 1 cm | 50 miles |
| 2 cm | 100 miles |
| 3 cm | 150 miles |
| 4 cm | 200 miles |
| 0.5 cm (\(\frac{1}{2}\) cm) | 25 miles |
Step 2: Add up the pieces to make 225 miles:
200 miles + 25 miles = 225 miles
4 cm + 0.5 cm = cm
Final Answer:
Distance on map:
centimeters
Scale Word Problems (Scaffolded Edition) Page 1 of 4
Guided Practice
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Problem 2
Skip Counting / Multiples
The scale says that 1 inch : 350 miles. How many inches is 1,750 miles?
Step 1: Complete the Miles Ladder
Keep adding 350 until you reach 1,750:
| Inches | Miles |
|---|
| 1 in | 350 mi |
| 2 in | 700 mi |
| 3 in | 1,050 mi |
| 4 in | 1,400 mi |
| 5 in | ________ mi |
Step 2: Division Check (Optional)
You can also divide total miles by the scale unit:
\(1,750 \div 350 = \) ______
Final Answer:
1,750 miles =
inches
Problem 3
Fractions Helper
The scale of a drawing is \(\frac{1}{2}\) inch : 6 feet. A distance measures \(1\frac{1}{2}\) inches. What is the distance in feet?
Step 1: Break Down \(1\frac{1}{2}\) Inches
How many \(\frac{1}{2}\)-inch blocks make \(1\frac{1}{2}\) inches?
Block 1: \(\frac{1}{2}\) inch = 6 feet
Block 2: \(\frac{1}{2}\) inch = 6 feet
Block 3: \(\frac{1}{2}\) inch = 6 feet
\(\frac{1}{2} + \frac{1}{2} + \frac{1}{2} = 1\frac{1}{2}\) inches total
Step 2: Add the Feet Together
Add 6 feet for each \(\frac{1}{2}\) inch:
6 ft + 6 ft + 6 ft = _____ ft
Final Answer:
The distance is
feet
Scale Word Problems (Scaffolded Edition) Page 2 of 4
Guided Practice
Name:
Problem 4
Blueprint Scale
The scale on a blueprint of a home is 1 inch : 4 feet. The actual length of the family room is 26 feet. What is the blueprint length?
Step 1: Skip Count by 4s
Count up to get as close to 26 as possible:
1 in = 4 ft
4 in = 16 ft
2 in = 8 ft
5 in = 20 ft
3 in = 12 ft
6 in = 24 ft
Remaining feet: 26 ft - 24 ft = 2 ft
Since 4 ft = 1 in, then 2 ft = 0.5 in (\(\frac{1}{2}\) in)
Step 2: Combine Whole & Half
Add your 6 inches and your half inch:
6 inches + 0.5 inches = ______ inches
You can write your answer as a decimal or fraction (\(6\frac{1}{2}\)).
Final Answer:
Blueprint length:
inches
Problem 5
Friendly Benchmarks
On the map it says for every 2 inches is 35 miles. How many inches would 420 miles be?
Step 1: Friendly Jump Milestones
Use easy 10s and doubles:
| Inches | Miles | How we got it |
|---|
| 2 in | 35 mi | Given scale |
| 4 in | 70 mi | Double the 2 in |
| 20 in | 350 mi | 10 times the 2 in |
| 24 in | 420 mi | 350 mi + 70 mi |
Step 2: Division Check
Find how many 35-mile chunks are in 420 miles:
\(420 \div 35 = 12\text{ jumps}\)
Each jump is 2 inches:
\(12 \times 2\text{ inches} = \) ______
Final Answer:
420 miles =
inches
Scale Word Problems (Scaffolded Edition) Page 3 of 4
Final Practice Questions
Name:
Problem 6
Quarter-Inch Scale
The scale on a map is \(\frac{1}{4}\) in : 18 miles. The state capital is 252 miles from the border. How far is the state capital from the border on the map?
Step 1: Jumps of 18 miles
Divide 252 miles by 18 to find the number of \(\frac{1}{4}\) inches:
\(252 \div 18 = 14\text{ quarter-inches}\)
Step 2: Change to whole inches
4 quarters = 1 in | 14 quarters = \(3\frac{2}{4}\) in = \(3\frac{1}{2}\) in
Answer:
inches
Problem 7
Centimeter Scale
A map has a scale of 1 centimeter = 15 miles. The actual distance between Rochester and New York City is 330 miles. What is the distance, in centimeters, between the two cities on the map?
Step 1: Benchmark Helper
10 cm = 150 miles
20 cm = 300 miles
2 cm = 30 miles
Step 2: Add to reach 330 miles
300 mi + 30 mi = 330 mi
20 cm + 2 cm = ______ cm
Answer:
centimeters
Problem 8
Multiplication Pattern
The scale on the map is 1 inch : 120 miles. How many miles would it be for 4 inches?
Step 1: Count by 120s for each inch
<table class="w-full text-center border border-black font-bold bg-white"><tbody><tr class="bg-zinc-200 border-b border-black"><td class="p-0.5 border-r border-black">1 in</td><td class="p-0.5 border-r border-black">2 in</td><td class="p-0.5 border-r border-black">3 in</td><td class="p-0.5 bg-zinc-100">4 in</td></tr><tr><td class="p-0.5 border-r border-black">120 mi</td><td class="p-0.5 border-r border-black">240 mi</td><td class="p-0.5 border-r border-black">360 mi</td><td class="p-0.5 bg-zinc-100">______</td></tr></tbody></table>
Step 2: Multiply
\(4 \times 120 = \) ______ miles
Answer:
miles
Scale Word Problems (Scaffolded Edition) Page 4 of 4
