Scaling Lesson

Unit 1 Review

Today we will review all we have learned in Unit 1 to prepare for our scale model project.

Multiple Choice

How confident do you feel when answering questions about scale copies, corresponding parts, scale factor, scales and scale drawings?

• I feel confident on all questions.

• I feel confident on most questions.

• I feel confident on very few questions.

• I do not feel confident at all.

Our Group Goals

• To feel more confident when answering questions about scale copies, corresponding parts, and scale factor.

• To ask clarifying questions, in hopes to improve understanding before our project.

• To be able to independently answer a question about scale copies, scale factor, or scale drawings correctly.

Defining Scale Copies

A scaled copy is a copy of an figure where every length in the original figure is multiplied by the same number.

For example, the two rectangles on the left are scale copies because every length when going from X to Y is multiplied by 3.

Multiple Select

Which of the following are ways we can tell if a figure IS NOT a scale copy?

• The angles on the inside of the shapes do not match.

• The shape looks distorted compared to the original.

• All sides are multiplied by the same number to get the scale copy.

• All of the above.

• None of the above.

Non-Scaled Copy

Let's talk as a group about why the picture of the bird on the right is not a scaled copy of the original on the right.

Defining Corresponding Parts

The word corresponding parts refers to parts that match between two scaled figures. You can identify corresponding angles, corresponding sides, corresponding points, or corresponding line sedments.

Open Ended

Name a corresponding part in the picture that is not highlighted in red. Write it in a complete sentence. For example, "Line segment/side JK corresponds to line segment/side RS."

Corresponding Distances

Look at the photo on the right and discuss as a group what the corresponding distances/lengths are in the photos. Why is it important to know what the corresponding distances/lengths are?

Defining Scale Factor

Scale Factor is the number which all sides in the original figure are multiplied to get to the scale copy.

What is our scale factor in this figure we looked at on the last slide if your original is the smaller triangle?

Multiple Choice

For example, if the original side length is 5, and the corresponding side length is 25, the scale factor is...

• 5

• 1/5

• 20

Defining Reciprocal

Dividing by a number does not give you the scale factor. However,the reciprocal of the number you divided by does. For example, if your shape is dividing the corresponding sides by 12, the reciprocal of 12 is 1/12, Meaning your scale factor is 1/12.

Question: Here is an unlabeled polygon, along with its scaled copies Polygons A–D. For each copy, determine the scale factor. Explain how you know.

Scale and Scale Drawings

The Scale is the ratio of the length in a drawing (or model) to the length on the real thing.

A Scale Drawing is a drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount (called the scale). 

Open Ended

This is a map of Malta, a scale drawing of Malta. Identify the scale.

Big Four Bridge

• This is an image of the Big Four Bridge in downtown Louisville aka the Walking Bridge

• The total length for the walking bridge and its ramps is 770 m.

• At its tallest point it is 167 m tall.

Open Ended

If we were to make a scale drawing of the Big Four Bridge using a scale of 1 cm to 10 m, what would the length and the height of the scale drawing be?

Check

• What is the scale we are using?

• What operation do we need to do to calculate the sides of the scale drawing?

• Apply it to our problem..

• 770/10 = 77 cm

• 167/10 = 16.7

Multiple Choice

If we were to change our scale to 1 cm is to 20 m, how would this affect our scale drawing.

• It would increase in size.

• It would decrease in size.

• It would stay the same size.

Multiple Choice

How confident do you feel when answering questions about scale copies, corresponding parts, and scale factor?

• I feel confident on all questions.

• I feel confident on most questions.

• I feel confident on very few questions.

• I do not feel confident at all.

Pool Problem: HW

The question:

Here is a scale drawing of a swimming pool where 1 cm represents 1 m.

How long and how wide is the actual swimming pool?

First Step

• First we need to measure the length and width of the scale drawing.

• What is the length of the scale drawing?

• What is the width of the scale drawing?

• Length = 10 cm Width = 5 cm

2nd & 3rd Steps

• Now we need to look at our scale and change the mesurements to the size of the real life pool.

• What is our scale?

• What operation do we use?

• The measurements are the same because the scale is 1 cm to 1 m, we just change the answer to m.

• Answer: Length = 10 m Width = 5 m

Pool Problem Pt. 2

The question: Make a scale drawing of the swimming pool where 1 cm represents 2 m.

What changed in the problem?

Work it out...

• We have a new scale, 1 cm is to 2 m.

• What operation is occuring?

• Apply it to the pool measurements:

• 10/2 = 5 cm is the length

• 5/2 = 2.5 cm is the width

• Now draw your scale drawing.

Answer

Your scale drawing should look like this.