what are we going to do? what does dilation mean? dilation means: _______________________ cfu # 1 if...

What are we going to do?

What does dilation mean?Dilation means:

_______________________

_______________________

CFU # 1

If the scale factor is GREATER THAN 1, the new image or figure will be ___________ than the original.

If the scale factor is LESS THAN 1, the new image or figure will be ____________ than the original.

CFU # 2

When creating a Dilation, how does the scale factor’s size affect the size of the new figure?

1 enlargements or reductions in size

Vocabulary

We will use Dilations1 to show Proportional Relationships on a Coordinate Plane.

Learning Objective

Activate Prior Knowledge

NAME:__________________________Thursday, November 20, 2014 ‘A’ Week

to enlarge or reduce the size of an image or object.

larger

smaller

Skill Development/Guided Practice (continued)

What does a dilation do to an image? A dilation __________ _______________________. If my figure is enlarged, I am multiplying by a factor greater than ______, which increases the size of my original.

If my figure is a reduction, I am multiplying by a factor less than ______ (I could also divide), which decreases the size of my original.

CFU

2

1

3

Describe the scale factor used in the comparisons below.Dilations show us enlargements or reductions.

Look at the diagrams shown below: 1

1

enlargesOR reduces the size of it

ORIGINAL NEW

(ORIGINAL) (NEW)

Guided Practice (CLASSWORK) Thursday, 11.20.14

1. Find your original coordinates for the pre-image (the original figure).2. Multiply the factor of dilation by the original coordinates, then plot the points AND graph the new figure.

Dilations show us enlargements or reductions. Follow the directions given below:

DILATION OF 2.5

DILATION OF 4.5

T ( , )Q ( , )N ( , )P ( , )

T’ ( , )Q’ ( , )N’ ( , )P’ ( , ) P ( , )

R ( , )F ( , )H ( , )

Original Figure New Figure

Original Figure New Figure

Name: ____________________________

INTERPRETING YOUR GRAPH: Because the dilation is greater than ___ , your new

image will be ______ than the original, in this case ________ the size of the original.

EXAMPLE:

1. Find the coordinates of the original figure.

2. Multiply by the factor of dilation by the original figure’s coordinates (in this case – multiply by 2.5).

3. Write your new ordered pairs (New Figure).

4. Plot the points and connect each point to create your new figure.

-1 2 x 2.5 -2.5 5

1 2 x 2.5 2.5 5

2 0 x 2.5 5 0-1 -2 x 2.5 -2.5 -5

1larger

2.5 times

1 1 x 4.5 4.5 4.5 0 -1 x 4.5 0 -4.5-1 -1 x 4.5 -4.5 -4.5

-1 0 x 4.5 4.5 0

P’ ( , )R’ ( , )F’ ( , )H’ ( , )

DILATION OF 1.5

I’ ( , )N’ ( , )S’ ( , )U’ ( , )

I ( , )N ( , )S ( , )U ( , )

Guided Practice (Enlargement of a Figure)

DILATION OF 4.5

H ( , )K ( , )W ( , )T ( , )

H’ ( , )K’ ( , )W’ ( , )T’ ( , )

1. Find your original coordinates for the pre-image (the original drawing).2. Multiply the factor of dilation by the original coordinates, then plot the points.

Dilations show us enlargements or reductions.

0 10 01 11 -1

0 4.50 04.5 4.54.5 -4.5

H’

K’

W’

T’

-2 33 32 -2-3 -2

-3 4.54.5 4.5

3 -3

-4.5 -3

I’ N’

S’U’

Original Figure New Figure Original Figure New Figure

Guided Practice (Reduction of a Figure)

1. Find your original coordinates for the pre-image (the original drawing).2. Multiply the factor of dilation by the original coordinates, then plot the points.

Dilations show us enlargements or reductions.

W ( , )I ( , )B ( , )L ( , )

W’ ( , )I’ ( , )B’ ( , )L’ ( , )

S’ ( , )A’ ( , )J’ ( , )T’ ( , )

S ( , )A ( , )J ( , )T ( , )

Original Figure New Figure Original Figure New Figure

0 3-2 2-2 -33 -2

0 1.5-1 1-1 -1.51.5 -1

W’I’

B’L’

4 23 -14 -35 -2

DILATION OF ½ DILATION OF 0.5

2 1 1.5 -0.5 2 -1.5 2.5 -1

S’

A’

J’T’

What did you learn today about dilations / plotting and locating points on a coordinate plane? (Pair-Share) Use and define each of the words from the word bank.

Skill Closure

Summary Closure

Word Bankcoordinatesordered pair

dilationquadrant

pointplot

enlargementreduction

factorscale factor

DILATIONS enlarge or reduce the size of a figure. We can manipulate ordered pairs based on the dilation given.DILATIONS greater than 1 will make a figure larger, while dilations less than one will make a figure smaller.

Ordered Pair

(2, 3)

x and y

Write ordered pairs for the each point shown.Apply the factor of the dilation to the ordered pairs.Identify and plot the new points, then sketch the figure.

Identify the points given on a coordinate plane.

1

23

DILATION OF 0.5M ( , )D ( , )A ( , )W ( , )

-1 5 1 5

4 3

M’

Because the dilation is less than 1, our new image will be smaller than the original, in this case ½ (HALF)

the size of the original image.

Which operations are used in dilations?A. Addition B. SubtractionC. MultiplicationD. Division

CFU

-1 4

M’ ( , )D’ ( , )A’ ( , )W’ ( , )

-0.5 2.5 0.5 2.5

2 1.5 -0.5 2

D’

A’W’

Independent Practice

DILATIONS enlarge or reduce the size of a figure. We can manipulate ordered pairs based on the dilation given.DILATIONS greater than 1 will make a figure larger, while dilations less than one will make a figure smaller. Closure



1

23

DILATION OF 2.5

A ( , )W ( , )H ( , )L ( , )

A’ ( , )W’ ( , )H’ ( , )L’ ( , )

Because the dilation is _______ than 1, our new image will be ________ than the original, in

this case _______ the size of the original.

NAME________________PERIOD _____

11.20.14 HOMEWORK

ORIGINAL FIGURE NEW FIGURE0 22 20 -1

-1 1

0 55 50 -2.5

-2.5 2.5greater

larger2.5 times

A’ W’

H’

L’

Independent Practice

DILATIONS enlarge or reduce the size of a figure. We can manipulate ordered pairs based on the dilation given.DILATIONS greater than 1 will make a figure larger, while dilations less than one will make a figure smaller. Closure



1

23

DILATION OF 1/4

D ( , )R ( , )I ( , )

D’ ( , )R ( , )I’ ( , )

Because the dilation is ________ than 1, our new image will be

________ than the original, in this case _______ the size of the

original.

NAME________________PERIOD _____

11.20.14 HOMEWORK

ORIGINAL FIGURE NEW FIGURE

5 44 -4-3 -1

1.25 1 1 -1-0.75 -0.25

lesssmaller

¼ of

D

R

I

D’

R’

I’

what are we going to do? what does dilation mean? dilation means: _______________________ cfu # 1 if...

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