Understanding Scale Factors and Proportions

The video tutorial covers lesson 8.1 on solving problems involving scale drawings. It explains the concept of scale factors, which are numbers used to multiply the side lengths of a figure to create a proportional scale drawing. The tutorial provides visual examples using triangles and practical examples of scaling lines and figures. It also includes problem-solving exercises involving scale factors and proportions, and discusses real-world applications such as maps and drawings. The lesson concludes with a task for students to write sentences summarizing what they learned.

What is a scale drawing?

• A drawing that is always larger than the original

• A drawing that is always smaller than the original

• A drawing that is proportional to the original

• A drawing that is identical to the original

What is a scale factor?

• A number used to multiply the side lengths of a figure

• A number used to divide the side lengths of a figure

• A number used to subtract from the side lengths of a figure

• A number used to add to the side lengths of a figure

If a triangle with side lengths 1, 1, and 1 is scaled by a factor of 3, what are the new side lengths?

• 4, 4, 4

• 1, 1, 1

• 2, 2, 2

• 3, 3, 3

What happens to the side lengths of a figure when multiplied by a scale factor?

• They become proportional

• They become larger

• They remain the same

• They become smaller

In a 3:1 scale, if the original side length is 3, what is the new side length?

• 6

• 9

• 15

• 12

How do you calculate the new length of a line when scaled by a factor of 3?

• Multiply the original length by 3

• Subtract 3 from the original length

• Divide the original length by 3

• Add 3 to the original length

If a line is originally 3 units long and is scaled by a factor of 3, what is the new length?

• 6 units

• 12 units

• 9 units

• 15 units

What is the scale factor if a length changes from 2 inches to 5 inches?

• 2

• 3

• 2.5

• 1.5

How do you solve for a new side length using proportions?

• Add the scale factor to the original length

• Subtract the scale factor from the original length

• Multiply the original length by the scale factor

• Divide the original length by the scale factor

On a map, if 1 inch equals 5 miles, how far apart are two cities that are 8 inches apart on the map?

• 40 miles

• 50 miles

• 20 miles

• 30 miles