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Lesson 8

1. Lesson 8

1.1. Explore

Mathematics 20-2 M6 Lesson 8

Module 6: Proportional Reasoning

 
Explore
 

The process of moving involves a lot of “making sure things fit.”

 

This is a photo of a house in a box.

Comstock/Thinkstock

Akuti has decided to decorate one of the walls in her new room with a mural. The wall is 11 ft long by 8 ft high. Akuti wants the mural to be centred on the wall and has decided to make it a similar rectangle to the wall with a scale factor of 1:2.

 

Try This 1
 

Use the interactive animation Drawing a Mural to help Akuti determine the area and placement of the mural on her bedroom wall.

 

 

This is a screenshot for Drawing a Mural.

 

Did You Know?


Murals can be found all over Alberta. Some towns like Trochu, Three Hills, and High River have murals painted on the outside of buildings. The artists need to ensure that the images on the murals are proportional. Can you find other examples of murals in your community?

 

This photo is of a mural on the outside of a building in Alberta.

© Travel Alberta



The strategy Akuti used to determine the area of her mural is only one way of solving the problem. Equations can also be used to solve for the unknown area.



textbook

Read “Example 1: Reasoning about scale factor and area” on pages 476 and 477 of the textbook. Jasmine and Hank used different strategies to determine the actual area. As you read over the example, think about why the value of k is greater than 1 in Jasmine’s solution but less than 1 in Hank’s solution.

 

The relationship between area and scale factor of two similar objects can also be used to determine dimensions.

 

Read “Example 2: Reasoning about scale factor and area to determine dimensions” on pages 477 and 478 of the textbook. As you look at Rani’s solution, consider the following questions:

  • How did Rani know that the rectangles were similar?
  • Why did Rani need to determine the square root of k2?
Self-Check 1


textbook
  1. Complete “Your Turn” on page 478 of your textbook. Answer

  2. Complete “Practising” questions 6, 7, 9, 10, and 15 on pages 480 and 481 of your textbook. For question 15, the measurements of the rectangle are 2.6 cm by 0.75 cm. Answer

  3. If you want a challenge, try “Extending” questions 18 and 19 on page 482 of your textbook. Answer