# We will compute1 unit rates

## Presentation on theme: "We will compute1 unit rates"— Presentation transcript:

4 32 10 5 We will compute1 unit rates. 1 8 2 1
Learning Objective What are we going to do? What does compute mean? Compute means __________. CFU We will compute1 unit rates. 1 calculate Vocabulary Activate Prior Knowledge 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 4 32 minutes 4 = 1 8 minutes per mile 32 4 = 8 2. Edgar downloaded a 10-megabyte video in 5 seconds. What was the downloading rate in megabytes per second? megabytes 10 5 seconds 10 5 = 2 2 megabytes per second 5 = 1

y-axis x-axis (2, 3) x and y Ordered Pairs on the Coordinate Plane
Concept Development Ordered Pair (2, 3) x and y 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. Ordered Pairs on the Coordinate Plane y-axis – the vertical number line. Animated 2 10 4 5 6 7 8 9 3 1 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 T B (7, 9) In your own words, what is an ordered pair? “An ordered pair is ______.” CFU T “X is the point’s distance along the x-axis.” “X is the point’s distance along the x-axis.” (4, 5) 4 5 “Y is the point’s distance along the y-axis.” “Y is the point’s distance along the y-axis.” 2 crossing (synonym) 3 crossing at a 90 degree angle 4 shows (synonym) Vocabulary x-axis – the horizontal number line. 1 2 3 4 5 6 7 8 9 10 The origin is where the x-axis and y-axis intersect.

Skill Development/Guided Practice
Ordered Pair (2, 3) x and y 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. 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 2 3 How did I/you determine the x-coordinate? How did I/you determine the y-coordinate? CFU 1 2 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 10 5 figure out Vocabulary

Skill Development/Guided Practice (continued)
Ordered Pair (2, 3) x and y 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. 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 2 3 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 A 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 ) D G B C E H 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 7 5:7 5 to 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. Create a Vertical Table below Fill in the table below to make equivalent ratios: black keys white keys black keys 5 10 30 35 white keys 7 21 28 15 20 25 ( , ) 5 7 14 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?

On a piano, the ratio of black keys to white keys is 5 to 7.
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 Explain why the ratios are equivalent ratios. In your own words, what is a proportional relationship? A proportional relationship ___________. CFU 5 7 25 35 and On a piano, the ratio of black keys to white keys is 5 to 7. × 4 × 3 × 2 Equivalent Ratios black keys 5 10 15 20 25 30 35 white keys 7 14 21 28 42 49 × 4 × 3 × 2 If there are 20 black keys then there are 28 white keys. If there are 15 black keys then there are 21 white keys. If there are 10 black keys then there are 14 white keys. 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 From Tables × 4 × 3 × 2 Equivalent Ratios 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 black keys 5 10 15 20 25 30 35 white keys 7 14 21 28 42 49 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) 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 ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )

(5 , 7) ( , ) Plot the first 3 ordered (x,y) pairs to the right 10 14
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 black keys 5 10 15 20 25 30 35 white keys 7 14 21 28 42 49 ORDERED PAIRS (Black Keys, White Keys) Fill in your ordered pairs (5 , 7) ( , ) 24 23 22 21 20 Plot the first 3 ordered (x,y) pairs to the right Connect points with a straight line. Does the line touch at the Origin (0,0)? 19 18 17 16 15 14 Number of White Keys (y) 13 12 11 10 9 8 7 6 5 4 3 2 1 Number of Black Keys (x)

(2, 3) x and y coordinates ordered pair axis origin point plot
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. Word Bank Skill Closure 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. (Problem 1) Read the ordered pair aloud. “Point ___ is at the point (__, __)” (Problem 2) Plot and label the point at the correct coordinates. Plot and locate points on a coordinate plane. 1 2 3 1. Point A ( ___, ___ ) 6 7 2. Point B ( 3, 8 ) B Access Common Core A C Alicia thinks that the coordinates of point C on the coordinate plane are (6, 4). Do you agree with her? Why or why not? Word Bank coordinates ordered pair axis origin point plot Summary Closure What did you learn today about plotting and locating points on a coordinate plane? (Pair-Share) Use words from the word bank.

( , ) (6 ,10 ) ( , ) Create Ordered Pairs for each (x , y) pair.
Graph the ordered pairs on graph to the right. Connect the points with a line. ( , ) (6 ,10 ) ( , )

(2, 3) x and y Ordered Pair Plot and locate the points. 5 9 6 5 9 1 8
Periodic Review 1 Independent Practice (continued) Ordered Pair (2, 3) x and y A B C Plot and locate the points. 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 G 6 5 H 9 1 D 8 7 F E A B C 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 Distractor Analysis Correct Incorrect. Student mistaken (6, 4) for (4, 6) Correct. Incorrect. Student mistaken distance to the y-axis for distance to the x-axis.

Independent Practice Ordered Pair (2, 3) x and y 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. 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. Read the ordered pair aloud. “Point ___ is at the point (__, __)” Plot and locate points on a coordinate plane. 1 2 3 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 8 5

Independent Practice (continued)
Ordered Pair (2, 3) x and y 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. 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 2 3 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 ) F B D H E G C A Origin (0,0)