Transcript ORDERED PAIRS

Learning Objective
CFU
We will compute1 unit rates.
What are we going to do?
What does compute mean?
Compute means __________.
Vocabulary
1
Activate Prior Knowledge
calculate
A unit rate shows the relationship between a quantity and one unit of another quantity.
Use the ratio table to find the unit rate.
1. Vanessa ran 4 miles this morning in 32 minutes.
Find her average time, in minutes, for every 1 mile.
miles
minutes
4
32
4
32
4=
1
4=
8
8 minutes per mile
2. Edgar downloaded a 10-megabyte video in 5 seconds.
What was the downloading rate in megabytes per second?
megabytes
seconds
10
5
10
5=
2
2 megabytes per second
5
5=
1
Concept Development
Ordered Pair
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.
(2, 3)
x and y
Ordered Pairs on the Coordinate Plane
y-axis
– the vertical number line.
10
Animated
CFU
T
On your whiteboard, write an
example of an ordered pair.
Which number is the xcoordinate? Which is the ycoordinate? How do you know?
Which of the following is the
ordered pair that identifies the
location of the point T?
9
8
“X is the point’s distance along
the x-axis.”
7
6
5
A T
B (7, 9)
5
(4,
4 5)
4
In your own words, what is an
ordered pair?
“An ordered pair is ______.”
“Y is the point’s distance
along the y-axis.”
3
2
1
Vocabulary
1
2
3
4
5
6
7
8
9
10
The origin is where the x-axis and y-axis intersect.
x-axis – the horizontal
number line.
2
crossing (synonym)
crossing at a 90 degree angle
4 shows (synonym)
3
Skill Development/Guided Practice
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.
Plot and locate points on a coordinate plane.
1 Determine5 the x-coordinate of the point. (write) Hint: The distance along the x-axis.
2 Determine the y-coordinate of the point. (write) Hint: The distance along the y-axis.
3 Read the ordered pair aloud. “Point ___ is at the point (__, __)”
H
2 ___
6 )
1. Point A ( ___,
Ordered Pair
(2, 3)
x and y
CFU
1 How did I/you determine the
x-coordinate?
2 How did I/you determine the
y-coordinate?
E
D
2. Point B ( ___,
3 ___
3 )
3. Point C ( ___,
6 ___
1 )
2 ___
9 )
4. Point D ( ___,
F
A
5. Point E ( ___,
9 ___
10 )
6. Point F ( ___,
7 ___
6 )
B
7. Point G ( ___,
2 ___
0 )
8. Point H ( ___,
0 ___
10 )
C
G
Vocabulary
5
figure out
Skill Development/Guided Practice (continued)
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.
Plot and locate points on a coordinate plane.
1 Determine the x-coordinate of the point. (write) Hint: The distance along the x-axis.
2 Determine the y-coordinate of the point. (write) Hint: The distance along the y-axis.
3 Plot and label the point at the correct coordinates.
Ordered Pair
(2, 3)
x and y
CFU
1 How did I/you determine the
x-coordinate?
2 How did I/you determine the
y-coordinate?
3 How did I/you plot and label
the point?
A
1. Point A ( 3, 10 )
D
2. Point B ( 2, 7 )
G
3. Point C ( 4, 6 )
B
C
4. Point D ( 5, 9 )
5. Point E ( 0, 5 )
E
6. Point F ( 7, 0 )
7. Point G ( 8, 8 )
H
8. Point H ( 4, 3 )
F
Concept Development
On a piano, there are five black
keys for every seven white keys.
A ratio is a relationship between two quantities.
• A ratio can be written with words or numbers.
Write this ratio in three
different ways below:
5
5:7
5 to 7
7
A proportional relationship is a set of equivalent ratios.
Equivalent ratios have equal values using different numbers.
• To generate an equivalent ratio, multiply or divide each quantity in a ratio by the same number.
• Multiplying or dividing by the same number does NOT change the ratio.
Fill in the table below to make equivalent ratios:
14
15 20 25
42 49
The number of black keys should remain
proportional to the number of white keys.
How can you tell if they remain proportional?
Information in Tables can be used horizontally
or vertically. Which style works best for you?
Create a Vertical Table below
(
10
,
)
14
Concept Development
A proportional relationship is a set of equivalent ratios.
Equivalent ratios have equal values using different numbers.
• To generate2 an equivalent ratio, multiply or divide each quantity in
a ratio by the same number.
• Multiplying or dividing by the same number does NOT change the ratio.
Proportional Relationship
On a piano, the ratio of
to
is
CFU
5
25
Explain why the ratios 7 and 35
are equivalent ratios.
to .
In your own words, what is a
proportional relationship?
A proportional relationship
___________.
Equivalent Ratios
If Ifthere
thereare
are
thenthere
thereare
are
then
. .
Concept Development
A proportional relationship is a set of equivalent ratios.
Equivalent ratios have equal values using different numbers.
• To generate2 an equivalent ratio, multiply or divide each quantity in
a ratio by the same number.
• Multiplying or dividing by the same number does NOT change the ratio.
Proportional Relationship From Tables
Equivalent Ratios
CFU
Explain what the values in an
ordered pair (x,y) tell you in
this problem.
What does x describe?
Creating Ordered Pairs (x,y) From Tables
In this case, Black Keys are first, so the are going to be (X) and
White Keys are second, so they are going to be (Y)
What does y describe?
When x and y are written as an
ordered pair (x,y) what do the
letters describe together?
There are seven pairings of black keys : white keys.
Write the ordered pairs below as (Black Keys, White Keys)
ORDERED PAIRS (Black Keys, White Keys)
The first ordered pair has been filled in for you.
(5,7)( , )( , )( , )( , )( , )( , )
Concept Development
A proportional relationship is a set of equivalent ratios.
Equivalent ratios have equal values using different numbers.
Proportional Relationship From Tables / Ordered Pairs into a Graph
ORDERED PAIRS
(Black Keys, White Keys)
(5 , 7) Plot the first 3
ordered (x,y) pairs
10
14
( , )
to the right
(15 , 21)
(20 , 28) Connect points with
( , ) a straight line.
( , ) Does the line touch at
( , ) the Origin (0,0)?
Number of White Keys (y)
Fill in your ordered pairs
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Number of Black Keys (x)
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.
Skill Closure
Ordered Pair
(2, 3)
x and y
Plot and locate points on a coordinate plane.
1 Determine the x-coordinate of the point. (write) Hint: The distance along the x-axis.
2 Determine the y-coordinate of the point. (write) Hint: The distance along the y-axis.
3 (Problem 1) Read the ordered pair aloud. “Point ___ is at the point (__, __)”
(Problem 2) Plot and label the point at the correct coordinates.
6 ___
7 )
1. Point A ( ___,
2. Point B ( 3, 8 )
B
Access Common Core
Alicia thinks that the coordinates of point C
on the coordinate plane are (6, 4). Do you
agree with her? Why or why not?
A
C
Summary Closure
What did you learn today about plotting and locating points on a coordinate plane? (Pair-Share)
Use words from the word bank.
Word Bank
coordinates
ordered pair
axis
origin
point
plot
1. Create Ordered Pairs for each (x , y) pair.
2. Graph the ordered pairs on graph to the right.
3. Connect the points with a line.
(6 ,10 )
( , )
( , )
( , )
( , )
( , )
Periodic Review
1
Independent
Practice
(continued)
Ordered Pair
Plot and locate the points.
5 ___
9 )
1. Point A ( ___,
(2, 3)
G
x and y
A
2. Point B ( ___,
6 ___
5 )
H
3. Point C ( ___,
9 ___
1 )
8 ___
7 )
4. Point D ( ___,
5. Point E ( 9, 5 )
D
F
B
E
6. Point F ( 5, 6 )
7. Point G ( 1, 9 )
8. Point H ( 7, 8 )
C
Which of the following sentences is true about the points plotted on the graph?
The coordinates of point A are (3, 5).
Yes
No
B
A
The coordinates of point B are (6, 4).
Yes
No
The distance of point C from the y-axis is 8.
Yes
No
The distance of point B from the x-axis is 4.
Yes
No
C
Independent Practice
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.
Plot and locate points on a coordinate plane.
1 Determine the x-coordinate of the point. (write) Hint: The distance along the x-axis.
2 Determine the y-coordinate of the point. (write) Hint: The distance along the y-axis.
3 Read the ordered pair aloud. “Point ___ is at the point (__, __)”
2 ___
9 )
1. Point A ( ___,
A
2. Point B ( ___,
9 ___
2 )
F
3. Point C ( ___,
6 ___
3 )
4 ___
6 )
4. Point D ( ___,
D
H
5. Point E ( ___,
2 ___
4 )
6. Point F ( ___,
5 ___
8 )
7. Point G ( ___,
7 ___
0 )
E
C
B
8. Point H ( ___,
8 ___
5 )
G
Ordered Pair
(2, 3)
x and y
Independent Practice (continued)
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.
Plot and locate points on a coordinate plane.
1 Determine the x-coordinate of the point. (write) Hint: The distance along the x-axis.
2 Determine the y-coordinate of the point. (write) Hint: The distance along the y-axis.
3 Plot and label the point at the correct coordinates.
1. Point A ( 8, 1 )
F
2. Point B ( 2, 7 )
3. Point C ( 7, 2 )
B
D
H
4. Point D ( 7, 7 )
5. Point E ( 6, 4 )
E
6. Point F ( 0, 9 )
G
7. Point G ( 5, 3 )
C
8. Point H ( 3, 6 )
A
Origin
(0,0)
Ordered Pair
(2, 3)
x and y