Understanding Rates and Ratios

This lesson covers the concept of constant rates, expanding from specific rates like speed to general rates. It includes examples such as lawn mowing and water flow, demonstrating how to calculate and graph these rates. The lesson also provides exercises on typing, painting, and walking rates, encouraging students to apply the concepts learned.

What is a rate in mathematical terms?

• A difference between two values

• A sum of two quantities

• A ratio of two different measurements

• A comparison of two numbers with the same units

Which of the following is an example of a rate?

• 3 cups of sugar

• 60 miles per hour

• 10 dollars

• 5 apples to 3 oranges

If Pauline mows 35 square feet in 2.5 minutes, how much can she mow in 10 minutes?

• 100 square feet

• 70 square feet

• 140 square feet

• 35 square feet

What equation represents the area Pauline can mow in T minutes?

• Y = 10T

• Y = 2.5T

• Y = 35T

• Y = 14T

What is the difference between average rate and constant rate?

• Average rate is used for non-time related measurements

• Constant rate is only used for speed

• Average rate is always higher than constant rate

• Average rate changes over time, constant rate does not

In Example 2, what is the rate of water flow from the faucet?

• 3.5 gallons per minute

• 5 gallons per minute

• 10.5 gallons per minute

• 7 gallons per minute

How many pages can Juan type in 20 minutes if he types at a constant rate of one page every 3.5 minutes?

• 6 pages

• 5.7 pages

• 4.5 pages

• 5 pages

If Emily paints at a rate of 32 square feet in 5 minutes, how much can she paint in 2 minutes?

• 8 square feet

• 12.8 square feet

• 10 square feet

• 15 square feet

Joseph walks at a constant speed of 0.5 miles in 6 minutes. How far can he walk in 60 minutes?

• 4 miles

• 6 miles

• 3 miles

• 5 miles

What is the purpose of using graphs in constant rate problems?

• To make calculations more complex

• To visually interpret data and relationships

• To increase the difficulty of problems

• To avoid using equations