A unit rate shows the relationship between a quantity and one unit of another quantity.
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1 Learning Objective We will compute unit rates. CFU What are we going to do? What does compute mean? Compute means. Vocabular y calculate 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.. Vanessa ran 4 miles this morning in 32 minutes. Find her average time, in minutes, for every mile. miles 4 minutes 32 minutes per mile 2. Edgar downloaded a 0-megabyte video in 5 seconds. What was the downloading rate in megabytes per second? megabytes 0 seconds 5 megabytes per second
2 Concept Development The coordinate plane is a flat surface made by the intersection 2 of two perpendicular 3 number lines. An ordered pair describes 4 the location of a point on the coordinate plane using x- and y-coordinates. s on the Coordinate Plane the vertical number line. y-axis Animated X is the point s distance along the x-axis. (4, 5) Y is the point s distance along the y-axis The origin is where the x-axis and y-axis intersect. T x-axis the horizontal number line. CFU 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. Vocabular y 2 crossing (synonym) 3 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. Determine 5 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 (, ) CFU 2 How did I/you determine the x-coordinate? How did I/you determine the y-coordinate?. Point A (, ) H D E 2. Point B (, ) 3. Point C (, ) 4. Point D (, ) 5. Point E (, ) A F 6. Point F (, ) 7. Point G (, ) B 8. Point H (, ) G C Vocabular y 5 figure out
4 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. 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. CFU 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?. Point A ( 3, 0 ) 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 ) Label Point with Appropriate Letter
5 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. Write this ratio in three different ways below: : to 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: Create a Vertical Table below 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?
6 Concept Development A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. To generate 2 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 s (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 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 )
7 Concept Development A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Proportional Relationship From Tables / s into a Graph ORDERED PAIRS (Black Keys, White Keys) Fill in your ordered pairs (5, 7) Plot the ordered (x,y) pairs to the right Connect points with a straight line. Connect to (0,0) Number of White Keys (y) Number of Black Keys (x)
8 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 Plot and locate points on a coordinate plane. 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 ) Read the ordered pair aloud. Point is at the point (, ) (Problem 2) Plot and label the point at the correct coordinates.. Point A (, ) 2. Point B ( 3, 8 ) 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? Summary Closure What did you learn today about plotting and locating points on a coordinate plane? (Pair-Share) Use words from the word bank. C A Word Bank coordinates ordered pair axis origin point plot
9 . Create s for each (x, y) pair. 2. Graph the ordered pairs on graph to the right. 3. Connect the points with a line.
10 Periodic Independent Review Practice (continued) Plot and locate the points. LABEL:. Point A (, ) A 2. Point B (, ) D 3. Point C (, ) 4. Point D (, ) B PLOT: 5. Point E ( 9, 5 ) 6. Point F ( 5, 6 ) 7. Point G (, 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). The coordinates of point B are (6, 4). Yes Yes No No A B C 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
11 Independent Pract ice (HOMEW ORK 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. 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 (, ). Point A (, ) 2. Point B (, ) A F 3. Point C (, ) 4. Point D (, ) D 5. Point E (, ) 6. Point F (, ) 7. Point G (, ) 8. Point H (, ) E C H B G
12 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. 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.. Point A ( 8, ) 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 ) Origin (0,0)
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