Name: ______

Lesson 23-Use Scale Drawings to Solve Problems(pages 204-211)

*(Need centimeter grid paper for lesson)

Objective: To interpret scales and scale factors, construct scale drawings, compute real-world distance from a scale drawing, and use scale drawings to solve problems.

Review: You have used a variety of methods to find the unknown quantity in a proportional relationship including multiplicative reasoning, unit rates, and cross products.

  1. Words to Know:

Scale drawing:A smaller or larger representation of an actual figure on paper.

Scale: The ratio of a length in a scale drawing to the corresponding length in the actual figure.

  • Can show the relationship between measurements in different units.

Scale factor: The ratio of the lengths of corresponding sides of a scale and its original figure.

  • Must show the relationship between measurements in the same units.
  1. Solving problems about scale drawings:

Here are three ways to find the actual length of Fran’s room using methods learned earlier this year.

Method 1: Use cross products

Think: what are you comparing (using words)

B. Method 2: Use the scale factor to find the unknown length

There are two possible scale factors for any scale drawing.

  • The ratio of length in the scale drawing : the corresponding length in the actual figure
  • The ratio of the length in the actual figure : to the corresponding length in the scale drawing

The two possible scale factors for this problem are:

This scale factor means each length in the scale drawing is of the corresponding length in Fran’s room.

This scale factor means that each length in Fran’s room is 48 times the

corresponding length in the scale drawing.

Note: The two scale factors are always reciprocals of each other.

You can use either scale factor to find the unknown length but in this example, we can use 48 because the known length is in the scale drawing.

Multiply 3 inches (the length in the scale drawing) by 48 (the scale factor), to find the length of

Fran’s room in inches.

Now convert the total number of inches into feet.

Method 3: Use another relationship present in scale drawings

The ratio of any two lengths in the scale drawing is equal to the ratio of the corresponding lengths in the actual figure.

  1. Reproducing a scale drawing at a different scale

Method 1: Use multiplicative comparisons to find the unknown quantity.

Step 1:Find the length of the rectangle in your scale drawing.

Let= the length of the rectangle in your scale drawing

Write a proportion using the scale of your drawing for the first ratio.

Step 2: Find the width of the rectangle in your scale drawing using the same method.

Step 3: Using your centimeter grid paper, make the scale drawing. Draw a rectangle that is 3 cm by 2 cm and label the sides using the length and width of the actual play space. Make sure you include the scale.

  1. Comparing the scale factor for length to the scale factor for area

Step 1: Find a scale factor for the length.

In the example, we will choose to use the ratio of the lengths on the card to the ratio of the lengths on the scale drawing.

Using the two lengthsUsing the two widths

length on card width of card

length in drawingwidth of drawing

=

Either way the scale factor is ______.

Step 2 : Find the scale factor for the areas.

Area of card:Area of scale drawing:Scale factor:

Area of card 180cm2

Area of scale drawing 20 cm2

The scale factor for the areas is ______

9 is 3 • 3 or 3 squared (32)saz

The scale factor for the areas is the ______of the scale factor for the lengths.

This is true for any scale drawing.

Guided Practice – page 208

Independent Practice – pages 209 - 211