Do Now Monday, December 16, 2013

Do Now Monday, December 16, 2013

James, Ken, Chris, and Jessie ordered a pizza from Lucia’s Italian Restaurant. They pizzas only come in one size and are in the shape of a square. James already had a burger a couple hours before and is

not very hungry. James thinks that he can eat 10% of the pizza. Ken is very hungry and says he could eat half of the pizza. Chris thinks he will eat ¼ of the pizza, and Jessie says he is going to order a salad instead of eating pizza. If the friends eat the portions they have predicted, what percent of the pizza

will be left over? Justify your thinking using the 10x10 grid above.

James

Ken

What are we going to learn?

What does dilation mean?Dilation means ____________

_________________________.

CFU

Students, you already know how to plot points onto a number line. Now, we will use that skill to identify figures on coordinate planes.

Make Connection

Identify each of the four quadrants. Describe what relationship exists between their ordered pairs (x , y).

1 enlargements or reductions in size

Vocabulary

We will use Dilations3 to show Proportional Relationships on a Coordinate Plane.

Learning Objective

Activate Prior Knowledge

QUADRANT

NAME:__________________________Monday, December 16, 2013 ‘B’ Week

1QUADRANT

QUADRANT QUADRANT

2

3 4

( + , + )

enlarging or reducing size.

( - , + )

( - , - ) ( + , - )

1 2 3 4 5 6 7 8 9 10

2

10

4

5

6

7

8

9

3

1

x-axis

y-axis

The coordinate plane is a flat surface made by the intersection2 of two perpendicular3 number lines. An ordered pair describes4 the location of a point on the coordinate plane using x- and y-coordinates.

On your whiteboard, write an example of an ordered pair.Which number is the x-coordinate? Which is the y-coordinate? How do you know? Which of the following is the ordered pair that identifies the location of the point T?

A (9, 7)B (7, 9)In your own words, what is an ordered pair? “An ordered pair is ______.”

CFU

Ordered Pairs on the Coordinate Plane

2 crossing (synonym) 3 crossing at a 90 degree angle4 shows (synonym)

Vocabulary

Activating Prior Knowlegdge (Continued)

“X is the point’s distance along the x-axis.”

“Y is the point’s distance along the y-axis.”

– the horizontal number line.

– the vertical number line.

The origin is where the x-axis and y-axis intersect.

(4, 5)54

“Y is the point’s distance along the y-axis.”

“X is the point’s distance along the x-axis.”

T

Animated

Ordered Pair

(2, 3)

x and y

Determine5 the x-coordinate of the point. (write) Hint: The distance along the x-axis.

Determine the y-coordinate of the point. (write) Hint: The distance along the y-axis.

Read the ordered pair aloud. “Point ___ is at the point (__, __)”

Plot and locate points on a coordinate plane.1

23

How did I/you determine the x-coordinate?

How did I/you determine the y-coordinate?

When the x-coordinate and the y-coordinate are put together, they form an_____________.

CFU

1

2

Skill DevelopmentThe coordinate plane is a flat surface made by the intersection of two perpendicular number lines. An ordered pair describes the location of a point on the coordinate plane using x- and y-coordinates.

A

B

C

D

E

F

G

H

1. Point A ( ___, ___ )

2. Point B ( ___, ___ )

3. Point C ( ___, ___ )

4. Point D ( ___, ___ )

5. Point E ( ___, ___ )

6. Point F ( ___, ___ )

7. Point G ( ___, ___ )

8. Point H ( ___, ___ )

2 6

3 3

6 1

2 9

9 10

7 6

2 0

0 10

5 figure out

Vocabulary

Ordered Pair

(2, 3)

x and y

3

Move Left / Right on x-axis.

Move Up / Down on y-axis.

ordered pair

Skill Development/Guided Practice (continued)

Determine the x-coordinate of the point. (write) Hint: The distance along the x-axis.

Determine the y-coordinate of the point. (write) Hint: The distance along the y-axis.

Plot and label the point at the correct coordinates.

Plot and locate points on a coordinate plane.1

23

How did I/you determine the x-coordinate?

How did I/you determine the y-coordinate?

How did I/you plot and label the point?

CFU

1

2

The coordinate plane is a flat surface made by the intersection of two perpendicular number lines. An ordered pair describes the location of a point on the coordinate plane using x- and y-coordinates.

Ordered Pair

(2, 3)

x and y

1. Point A ( 3, 10 )

2. Point B ( 2, 7 )

3. Point C ( 4, 6 )

4. Point D ( 5, 9 )

5. Point E ( 0, 5 )

6. Point F ( 7, 0 )

7. Point G ( 8, 8 )

8. Point H ( 4, 3 )

C

D

E

F

G

H

A

B

3


How did I/you determine which figure is the original?

What does a dilation show? 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

4

Determine which figure is the original.Determine which figure is the enlargement or reduction.

Dilations show us enlargements or reductions.

For the following example, the blue figure is a DILATION (enlargement or reduction) of the red figure.

ORIGINAL:DILATION (NEW IMAGE):

ORIGINAL:DILATION (NEW IMAGE):

REDBLUE

REDBLUE

“The original RED figure has gone through a reduction to become the BLUE figure. The RED figure measured 9 x 9, the BLUE figure measures 3 x 3. What factor did the RED figure multiply or divide by?

“The original RED figure has gone through a reduction to become the BLUE figure. The RED figure measured 9 x 9, the BLUE figure measures 3 x 3. What factor did the RED figure multiply or divide by?Divide by 3. Multiply by 2

1

1

Relevance (Continued)

T. Alice is at the theater. She would like to go to the gas station. Write directions for her.

S. Felix is at the hardware store. He would like to go to the bank. Write directions for him.

1st 2nd 3rd 4th 5th 6th

2nd

6th

3rd

4th

5th

1st

Bank

Gas Station

Hardware Store

Theater

Application

Alice should go RIGHT (travel EAST) 1 block, then turn LEFT (travel NORTH) 4 blocks

How did I/you determine what the question is asking?How did I/you determine the math concept required?How did I/you determine the relevant information?How did I/you solve and interpret the problem?How did I/you check the reasonableness of the answer?

CFU

2

1

3

4

5

Felix should go RIGHT (travel EAST) 1 block, then turn LEFT (travel NORTH) 2 blocks

Ordered Pair

(2, 3)

x and y

DILATION OF 0.5

I’ ( , )N’ ( , )S’ ( , )U’ ( , )

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


DILATION OF 3

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. Ex.) A will become A’.

Dilations show us enlargements or reductions.

0 10 01 11 -1

0 30 03 33 -3

H’

K’

W’

T’

-2 33 32 -2-3 -2

-1 1.51.5 1.5

1 -1

-1.5 -1

I’ N’

S’U’

Plotting and locating points on a coordinate plane will help you understand information in real life.

1

Does anyone else have another reason why it is relevant to plot and locate points on a coordinate plane? (Pair-Share)

How can a visual example make it easier to see the true changes in a DILATION? (Pair-Share)

CFU

Relevance We have talked about similar figures during the past week. We know that similar figures are not congruent, but have sides that maintain a common ratio. A DILATION describes the relationship between two similar figures as a reduction or enlargement in size. The relationship can be easily

modeled on a coordinate plane using x- and y-coordinates.

Dilations allow us to see enlargements or reductions visually.

2

Information in real life is often presented in graphs on a coordinate plane.

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

Skill Closure

Summary Closure

Word Bank

coordinatesordered pair

dilationquadrant

pointplot

enlargementreduction

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 0.5Y ( , )R ( , )T ( , )

Y’ ( , )R’ ( , )T’ ( , )

-2 3 2 1

-1 -2

-1 1.5 1 0.5

-0.5 -1Y’

R’

T’

Because the dilation is less than 1, our new image will

be smaller than the original, in this case ½ the

size of the original.

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 0.5

M ( , )K ( , )H ( , )Q ( , )

M’ ( , )K’ ( , )H’ ( , )Q’ ( , )

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

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

original.

NAME________________PERIOD _____

12.16.13 HOMEWORK

ORIGINAL FIGURE NEW FIGURE

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

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 _____

12.16.13 HOMEWORK

ORIGINAL FIGURE NEW FIGURE

Documents

Do Now Monday, December 16, 2013