Lessons 4-7 Homework: Peck

Scale Factor Homework 9/28/20

This will be a guided homework assignment. It is due by 10/5/2020. If you need help please reach out by either calling/texting me, emailing me, or sending me a message in Google Classroom.

Scaled Relationships

In lesson 4, we discussed the relationships between corresponding parts and using those to identify scaled vs. not scaled copies.

For example...

we know these rectangles are scaled copies because all of the angles are the same and all sides of the smaller rectangle are multiplied by the same scale factor of 3 to get the corresponding side lengths on the bigger rectangle.

This is shown here:

6 x 3 = 18 and 4 x 3 = 12

Multiple Select

Now it's your turn: Select all the statements that must be true for any scaled copy of polygon P.

• The side lengths are all whole numbers.

• The angle measures are all whole numbers.

• The scale copy has exactly 1 right angle.

• If the scale factor between polygon P and the scale copy is 1/5, then each side length of polygon P is multiplied by 1/5 to get the corresponding side length of the scale copy.

• If the scale factor is 2, each angle in P is multiplied by 2 to get the corresponding angle in Q.

Open Ended

Are the 2 birds scaled copies of each other? Explain how you know.

Scaled Copies & Patterns

In lesson 5, we saw patterns that existed for different scale factors.

For example...

when we look at the 3 sets of figures, each set shows a different pattern in scale factors.

Beyonce: If the copy is smaller, the scale factor is less than 1.

Avatar: If the copy is larger, the scale factor is greater than 1.

Skateboard: If the copy is the exact same, the scale factor is exactly 1.

Multiple Select

Now it's your turn: Rectangles P, Q, R, and S are scaled copies of one another. Identify which of the following pairs have a scale factor less than 1.

• from P to Q

• from R to P

• from Q to S

• from S to P

• from P to S

Open Ended

Are two squares with the same side lengths scaled copies of one another? Explain your reasoning.

Scale Drawings

In lesson 7, you explored the use of scales for scale drawings.

For example...

this map is a scale drawing. The scale shows that 1 cm on the map represents 30 miles on land.

This means that if the distance between Amarillo and Oklahoma City on the scale drawing is 8.5 cm, the distance between the cities in real life is 255 miles. This is because 8.5 x 30 = 255.

Multiple Choice

Now it's your turn: A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building. What are the dimensions of this rectangular room in the actual building?

• 9 feet long and 16.5 feet wide

• 19.25 inches long and 30.25 inches long

• 30 inches long and 16.5 inches wide

• 30 feet long and 55 feet wide