Convert map distance to actual distance.
01 · DISCOVER
Before you begin
Enter your name and school email to save your learning. You’ll explore Proportional Relationships in Tables and then practice 12 questions with feedback.
Success criteria
- I can explain the main math idea in my own words.
- I can use a model, calculation, or example to solve a related problem.
- I can check my answers and explain why a solution makes sense.
Essential question: How can we use scale drawings & maps to solve problems?
02 · LEARN & EXPLORE
Why learn this?
A map scale shows 1 centimeter represents 5 kilometers.
Use the lesson to solve practical comparisons and make predictions.
Represent large spaces on manageable plans.
Build accurate enlargements and reductions.
03 · LEARN & EXPLORE
The mathematical idea
A scale drawing preserves a constant ratio between a distance on a drawing and the real distance.
04 · LEARN & EXPLORE
Build the language of proportional reasoning.
Use these terms as you explain your thinking.
A ratio comparing drawing length with actual length.
A proportional representation of an object.
The multiplier between corresponding lengths.
Lengths in matching positions.
A smaller proportional copy.
A larger proportional copy.
05 · LEARN & EXPLORE
Explore matching values
Study the quantities and explain what stays constant.
| Input | Output |
|---|---|
| 1 | 5 |
| 2 | 10 |
| 4 | 20 |
Explore the math visually
1input units
2input units
3input units
4input units
Compare one unit with multiple units. Identify the multiplier and explain what remains constant.
Find the model or map measurement.
Apply the stated conversion factor.
Convert and report the correct units.
06 · LEARN & EXPLORE
Identify
Find the model or map measurement.
1Notice what quantities, values, or representations are given.
2Use Identify to describe the multiplicative relationship—not only what changed.
3Check that the reasoning works for every value and that the units make sense.
Start with this foundation.
Find the model or map measurement.
drawing07 · LEARN & EXPLORE
Multiply
Apply the stated conversion factor.
1Notice what quantities, values, or representations are given.
2Use Multiply to describe the multiplicative relationship—not only what changed.
3Check that the reasoning works for every value and that the units make sense.
Build on the first idea.
Apply the stated conversion factor.
scale08 · LEARN & EXPLORE
Label
Convert and report the correct units.
1Notice what quantities, values, or representations are given.
2Use Label to describe the multiplicative relationship—not only what changed.
3Check that the reasoning works for every value and that the units make sense.
Connect everything with the final idea.
Convert and report the correct units.
units09 · LEARN & EXPLORE
Step-by-step worked example
A map scale shows 1 centimeter represents 5 kilometers.
- Identify scale: 1 cm : 5 km.
- Find map length: 4 cm.
- Multiply: 4 × 5 = 20 km.
- Label both units and check the scale.
| Input | Output |
|---|---|
| 1 | 5 |
| 2 | 10 |
| 4 | 20 |
10 · LEARN & EXPLORE
Choose the steps; use a hint if needed.
The next three problems remove some of the support. Identify what is known, select the right strategy, calculate carefully, and check the units or representation.
11 · LEARN & EXPLORE
Now complete the work independently.
Complete six questions without following a worked model. Hints remain available when you truly need them, and feedback will explain every answer.
Interactive practice tip: Use a quick sketch, table, or graph to test each answer. After selecting an answer, read the explanation and revisit your model if necessary.
12 · LEARN & EXPLORE
Reflect and submit
Explain the strategy in your own words. How could this mathematical idea help you outside school? Check your units and answer.
INDEPENDENT PRACTICE · 1 OF 12
1 cm on a map equals 4 km. What is 6 cm?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 2 OF 12
A model uses scale 1:10. A 3 cm length represents?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 3 OF 12
5 inches on a blueprint represents 25 feet. Feet per inch?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 4 OF 12
12 km in reality at 1 cm:3 km scale is how many cm?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 5 OF 12
A 2 m actual length is shown as 10 cm. Scale in cm?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 6 OF 12
If a drawing doubles in size, its matching lengths should?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 7 OF 12
On a map, 1 inch represents 12 miles. What do 3.5 inches represent?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Multiply 3.5 by 12.
INDEPENDENT PRACTICE · 8 OF 12
A 30-foot wall is 5 inches on a plan. What is the scale?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Divide actual feet by plan inches.
INDEPENDENT PRACTICE · 9 OF 12
A model uses scale 1:20. A part is 8 cm on the model. Actual length?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Multiply model length by 20.
INDEPENDENT PRACTICE · 10 OF 12
Why must all corresponding lengths use the same scale factor?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Think about what makes the copy accurate.
INDEPENDENT PRACTICE · 11 OF 12
An actual 18-meter length is shown using scale 1 cm = 3 m. Drawing length?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Divide actual meters by 3 meters per centimeter.
INDEPENDENT PRACTICE · 12 OF 12
A map says 1 cm = 5 km. What does 3 cm represent?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Return to the vocabulary and three main ideas if needed.
RESULTS · REFLECT
Your Learning Pathway Results
Check your work and submit your first-attempt score to your teacher.