Exploring Equivalent Ratios with Double Number Lines

This video tutorial introduces the concept of equivalent ratios and focuses on using the double number line method to find them. The teacher explains that equivalent ratios maintain the same relationship by multiplying or dividing each part of the ratio by the same number. The tutorial includes three examples: making fizzy juice with cranberry juice and soda water, selling Gatorade and chips, and washing cars. Each example demonstrates how to set up and use a double number line to solve ratio problems, emphasizing the importance of keeping tick marks aligned and consistent.

What is the purpose of using the double number line method in finding equivalent ratios?

• To visually compare different quantities

• To add and subtract values directly

• To calculate the percentage differences

• To determine the weight of each item

What is the fundamental principle to maintain when finding equivalent ratios?

• Convert ratios to percentages

• Always use even numbers

• Multiply or divide both parts of the ratio by the same number

• Divide by the highest common factor

If the ratio of cranberry juice to soda water is 5:2, how many cups of soda water are needed for 10 cups of cranberry juice?

• 8 cups

• 6 cups

• 4 cups

• 2 cups

How do you align the number lines when setting them up for comparison?

• Align them based on the highest value

• Ensure each line has different intervals

• Use different colors for each line

• Make sure the tick marks on each line are directly opposite each other

In the cranberry juice to soda water example, how many cups of soda water are required for 20 cups of cranberry juice?

• 8 cups

• 5 cups

• 12 cups

• 10 cups

What is the correct method to extend the number lines if needed?

• Restart from zero

• Only extend the top line

• Add random intervals

• Continue with the same counting pattern

For the Gatorade to chips ratio problem, how many bags of chips correspond to 24 bottles of Gatorade?

• 32 bags

• 36 bags

• 30 bags

• 28 bags

What is the ratio of Gatorade to chips in the corner store example?

• 2:3

• 1:1

• 3:4

• 4:3

In the car washing problem, if you wash 8 cars, how many cars does your friend wash?

• 10 cars

• 12 cars

• 14 cars

• 16 cars

If the ratio of cars washed by you to your friend is 2:3, how many cars does your friend wash when you wash 6 cars?

• 7 cars

• 10 cars

• 8 cars

• 9 cars