Have you ever tried to make a map of something real? To do this successfully, you will need to use a scale and actual measurements.
Use this Concept to learn all about scale dimensions, then you will be able to answer these questions at the end of the Concept.
In the last Concept, you learned how to figure out actual dimensions or distances when you had been given a scale.
Now we are going to look at figuring out the scale given the actual dimensions.
To do this, we work in reverse. To make a map, for instance, we need to “shrink” actual distances down to a smaller size that we can show on a piece of paper. Again, we use the scale. Instead of solving for the actual distance, we solve for the map distance.
Suppose we are making a map of some nearby towns. We know that Trawley City and Oakton are 350 kilometers apart. We are using a scale of 1 cm : 10 km. How far apart do we draw the dots representing Trawley City and Oakton on our map?
We use the scale to write ratios that make a proportion. Then we fill in the information we know. This time we know the actual distance between the two towns, so we put that in and solve for the map distance.
Our answer is 35 cm.
Using our scale, to draw a distance of 350 km on our map, we need to put Trawley City 35 centimeters away from Oakton.
We can figure out the scale using a model and an actual object too.
Jesse wants to build a model of a building. The building is 100 feet tall. If Jesse wants to use a scale of 1” to 25 feet, how tall will his model be?
To solve this proportion we cross multiply.
Now let's practice. Use the scale 1" = 100 miles.
The distance from Kara's home to the family summer house is 150 miles. How many inches is that on the map?
Solution: 1.5 inches
The distance from Kara's home to her Grandmother's home is 2000 miles. How many inches is that on the map?
Solution: 20 inches
If the distance from Mark's home to his Grandmother's is half of Kara's, how many inches is that on the map?
Solution: 10 inches
Here is the original problem once again.
Now that Alex has figured out what he wants the garden to look like, he wants to make a drawing of the plot that is accurate.
What does this mean?
It means that Alex wants to use a scale to draw his design. When you use a scale, you choose a unit of measurement to represent the real thing. For example, if you want to draw a picture of a ship that is 100 feet long, it doesn’t make sense to actually make a drawing 100 feet long. You have to choose a unit of measurement like an inch to help you.
Alex’s decides to use a scale of 1” = 1 ft., but he is having a difficult time.
Keep in mind the measurements he figured out in the last Concept.
First, we start by figuring out the dimensions of the square. Here is our proportion.
Here are the vocabulary words used in this Concept.
a ratio that compares a small size to a larger actual size. One measurement represents another measurement in a scale.
the comparison of two things
a pair of equal ratios, we cross multiply to solve a proportion
Here is one for you to try on your own.
How many feet tall will the model be? Would this scale work for a model?
To figure this out, we first have to look at the scale that Joaquin is using. If Joaquin had chosen 1" = 1 foot then the scale height of the model would be 480 feet. But Joaquin used one - half inch as his scale, so the model will be 240 inches tall.
That means that it will be 20 feet high. This is too big! Joaquin will need to use a smaller scale.
Here are a few videos for review.
James Sousa on Scale Factors
http://teachertube.com/viewVideo.php?video_id=79418&title=PSSA_Grade_7_Math_19_Map_Scale – You will need to register with this website. This is a video about solving a ratio and proportion problem.
Directions: Use the given scale to determine the scale measurement given the actual distance.
Given: Scale 2” = 150 miles
1. How many scale inches would 300 miles be?
2. How many scale inches would 450 miles be?
3. How many scale inches would 75 miles be?
4. How many scale inches would 600 miles be?
5. How many scale inches would 900 miles be?
Directions: Use the given scale to determine the scale measurement for the following dimensions.
Given: Scale 1” = 1 foot
7. What is the scale measurement for a tree that is 1 yard high?
8. What is the scale measurement for a tower that is 36 feet high?
9. How many feet is that?
Directions: Use what you have learned about scale and measurement to answer each of the following questions.
11. Joaquin is building the model of a tower. He is going to use a scale of 1” = 1 foot. How big will his tower be in inches if the actual tower if 480 feet tall?
12. How many feet high will the model be?
13. Is this a realistic scale for this model? Why or why not?
15. What scale would Joaquin need to use if he wanted his model to be 5 feet tall?