What are we going to do? What does compute mean? Compute means __________. CFU 1 calculate...

What are we going to do?

What does compute mean?Compute means __________.

CFU

1 calculate

Vocabulary

We will compute1 unit rates.

Learning Objective

Activate Prior KnowledgeA unit rate shows the relationship between a quantity and one unit of another quantity.

miles 4

32minutes

1. Vanessa ran 4 miles this morning in 32 minutes. Find her average time, in minutes, for every 1 mile.

2. Edgar downloaded a 10-megabyte video in 5 seconds. What was the downloading rate in megabytes per second?

megabytes 10

5seconds

144 =

324 = 8

8 minutes per mile

155 =

105 = 2

2 megabytes per second

Use the ratio table to find the unit rate.

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 TB (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

Concept Development

“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?

CFU

1

2

Skill Development/Guided PracticeThe 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

Skill Development/Guided Practice (continued)

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


Plot and label the point at the correct coordinates.


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

3

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

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.

Concept Development

A ratio is a relationship between two quantities.• A ratio can be written with words or

numbers.

On a piano, there are five black keys for every seven white keys.

57 5:7 5 to 7

Write this ratio in three different ways below:

black keys 5 10 30 35

white keys 7 21 28 35

Fill in the table below to make equivalent ratios:

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?

black keys white keys

Create a Vertical Table below

5 71415 20 25

42 4910 14( , )

If there are 5 black keys then there are 7 white keys.

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


black keys 5 10 15 20 25 30 35

white keys 7 14 21 28 35 42 49

Equivalent Ratios

× 2

× 2

Explain why the ratios

are equivalent ratios.

In your own words, what is a proportional relationship?A proportional relationship ___________.

CFU

57

2535

and

On a piano, the ratio of black keys to white keys is 5 to 7.

× 3

× 3

× 4

× 4



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.

black keys 5 10 15 20 25 30 35

white keys 7 14 21 28 35 42 49

Equivalent Ratios× 2× 3× 4Proportional Relationship From Tables

Creating Ordered Pairs (x,y) From TablesIn 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)

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 ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )

Explain what the values in an ordered pair (x,y) tell you in this problem.

What does x describe?

What does y describe?

When x and y are written as an ordered pair (x,y) what do the letters describe together?

CFU

Concept Development

A proportional relationship is a set of equivalent ratios.Equivalent ratios have equal values using different numbers.

black keys 5 10 15 20 25 30 35

white keys 7 14 21 28 35 42 49

Proportional Relationship From Tables / Ordered Pairs into a Graph

ORDERED PAIRS (Black Keys, White Keys) Fill in your ordered pairs

(5 , 7) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )

Num

ber

of

Whit

e K

eys

(y)Plot the first 3

ordered (x,y) pairsto the right

Connect points witha straight line.

Does the line touch at the Origin (0,0)?

Number of Black Keys (x)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

242322212019181716151413121110 9 8 7 6 5 4 3 2 1

10 14

15 21

20 28

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

Skill Closure

Access Common Core

Summary Closure

Word Bank

coordinatesordered pair

axisoriginpointplot



(Problem 1) Read the ordered pair aloud. “Point ___ is at the point (__, __)” (Problem 2) Plot and label the point at the correct coordinates.


23


1. Point A ( ___, ___ )6 7

2. Point B ( 3, 8 )

B

A

Alicia thinks that the coordinates of point C on the coordinate plane are (6, 4). Do you agree with her? Why or why not?

C

Ordered Pair

(2, 3)

x and y

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 )( , ) ( , )

( , )( , ) ( , )

A

B

C

Periodic Review 1

1. Point A ( ___, ___ )

2. Point B ( ___, ___ )

3. Point C ( ___, ___ )

4. Point D ( ___, ___ )

5. Point E ( 9, 5 )

6. Point F ( 5, 6 )

7. Point G ( 1, 9 )

8. Point H ( 7, 8 )

5 9

6 5

9 1

8 7

E

D

F

G

H

Which of the following sentences is true about the points plotted on the graph?

The coordinates of point A are (3, 5).

The coordinates of point B are (6, 4).

The distance of point C from the y-axis is 8.

The distance of point B from the x-axis is 4.

Yes No

Yes No

Yes No

Yes No

AB

C

Plot and locate the points.

Ordered Pair

(2, 3)

x and y

Independent Practice (continued)

Independent Practice



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


23


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 9

9 2

6 3

4 6

2 4

5 8

7 0

8 5

Ordered Pair

(2, 3)

x and y

Independent Practice (continued)



Plot and label the point at the correct coordinates.


23


1. Point A ( 8, 1 )

2. Point B ( 2, 7 )

3. Point C ( 7, 2 )

4. Point D ( 7, 7 )

5. Point E ( 6, 4 )

6. Point F ( 0, 9 )

7. Point G ( 5, 3 )

8. Point H ( 3, 6 )C

D

E

F

G

H

A

B

Ordered Pair

(2, 3)

x and y

Origin(0,0)

What are we going to do? What does compute mean? Compute means __________. CFU 1 calculate...

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