Compare Rates with Tables and Graphs Teachers, be sure to read the notes section of every slide for additional information. (Common Core Standard 6.RP.3a)

In our previous lesson we learned about unit rates In our previous lesson we learned about unit rates. Remember, when a rate is expressed as a quantity of 1, they are called unit rates. Before we get started on our lesson, let’s take a look at how rates can be used in a real-world scenario.

Does anyone know what kind of animal this is? It’s a Cheetah!

The cheetah is the fastest land animal in the world.

More facts… The cheetah's slender, long-legged body is built for speed. Cheetahs are tan in color with black spots all over their bodies. They can also be distinguished from other big cats by their smaller size, spotted coats, small heads and ears and distinctive "tear stripes" that stretch from the corner of the eye to the side of the nose. Cheetahs height ranges from 2 ½ to 3 feet. Weight is between 110-140 pounds. Lifespan: 10 - 12 years. Tear stripes

Trivia Question 1. Name two countries where Cheetahs can be found. Africa and a small portion of Iran. 2. Can cheetahs roar? Unlike other big cats, cheetahs cannot roar. However, they can purr on both inhale and exhale, like domestic cats!

How fast can a cheetah travel? You will often work with unit rates when dealing with distances and time. Reading Problem Assuming that a cheetah is running at a constant speed, the table below represents the number of miles he can travel over a period of time. How can we use our knowledge of unit rates to complete the table and find out how fast the cheetah can travel per hour? To find missing “y” values in a table, start by determining the unit rate. Teachers, once you find the unit rate, show them where it goes in the table. A cheetah can travel 75 miles in 1 hour. Then use the unit rate to fill in the missing “y” values. 75 • 2 = 150 75 • 4 = 300 Unit Rate = 𝒚 𝒙 = 𝟐𝟐𝟓 𝟑 = 75

Are the ratios in the table “equivalent” and how can you tell? Yes they are! Each ratio is equivalent because they have the same unit rate! 75 Hours (x) Miles (y) Unit Rate 1 75 75/1 = 75 2 150 150/2 = 75 3 225 225/3 = 75 4 300 300/4 = 75 5 375 375/5 = 75

Plot the data from your table onto the graph provided. Hours (x) Miles (y) 1 75 2 150 3 225 4 300 5 375 You should point out where the unit rate shows up in the table and on the graph.

I’m going to let you figure it out! Which is faster… a Sail Fish or the Frigate Bird? I’m going to let you figure it out!

Hours (x) Miles (y) 1 2 136 3 4 5 Hours (x) Miles (y) 1 2 3 4 380 5 Task Find the missing values of each table. Plot the points. Which animal is faster? Hours (x) Miles (y) 1 2 136 3 4 5 Hours (x) Miles (y) 1 2 3 4 380 5 Give the students a few minutes to complete the problem. Then review the answer given on slide 13.

How many of you think the Sail Fish is faster? Who thinks the Frigate Bird is faster? Sail Fish Frigate Bird Wait for student responses then proceed to the next slide for the answer.

Let’s review the answer Find the missing values of each table. Plot the points. Which animal is faster? Hours (x) Miles (y) 1 68 2 136 3 204 4 272 5 340 Hours (x) Miles (y) 1 95 2 190 3 285 4 380 5 475 Ensure that the students know how to set up the ratio: unit rate = y/x. Ensure that the students know how to use the unit rate to find the missing “y” values: y = unit rate • x Point out where unit rate appears on the table and in the graph.

The steeper the line, the more miles traveled per hour. Can you tell which has the greatest unit rate by just looking at the two lines? Yes! The steeper the line, the more miles traveled per hour. In other words, the steepest line has the greatest unit rate. The steeper the line, the more miles traveled per hour! So, the steepest line has the greatest unit rate. You should also point out where the unit rates show up on the graph.

Closure Today, We learned to find missing values in a table. We plotted the pair of values from the table onto to a coordinate plane. We compared ratios in tables. We also learned… You can find the unit rate from a table by dividing your y value by the x value. You can then use the unit rate to find other missing values in the table.

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