Lesson 6Introducing Double Number Line Diagrams
Learning Goal
Let’s use number lines to represent equivalent ratios.
Learning Targets
I can label a double number line diagram to represent batches of a recipe or color mixture.
When I have a double number line that represents a situation, I can explain what it means.
Lesson Terms
- double number line diagram
Warm Up: Number Talk: Adjusting Another Factor
Problem 1
Find the value of each product mentally.
Activity 1: Drink Mix on a Double Number Line
Problem 1
The other day, we made drink mixtures by mixing 4 teaspoons of powdered drink mix for every cup of water. Here are two ways to represent multiple batches of this recipe:
How can we tell that
and are equivalent ratios? How are these representations the same? How are these representations different?
How many teaspoons of drink mix should be used with 3 cups of water?
How many cups of water should be used with 16 teaspoons of drink mix?
What numbers should go in the empty boxes on the double number line diagram? What do these numbers mean?
Are you ready for more?
Problem 1
Recall that a perfect square is a number of objects that can be arranged into a square. For example, 9 is a perfect square because 9 objects can be arranged into 3 rows of 3. 16 is also a perfect square, because 16 objects can be arranged into 4 rows of 4. In contrast, 12 is not a perfect square because you can’t arrange 12 objects into a square.
How many whole numbers starting with 1 and ending with 100 are perfect squares?
What about whole numbers starting with 1 and ending with 1,000?
Activity 2: Blue Paint on a Double Number Line
Problem 1
Here is a diagram showing Elena’s recipe for light blue paint.
Complete the double number line diagram to show the amounts of white paint and blue paint in different-sized batches of light blue paint.
Compare your double number line diagram with your partner. Discuss your thinking. If needed, revise your diagram.
How many cups of white paint should Elena mix with 12 tablespoons of blue paint? How many batches would this make?
How many tablespoons of blue paint should Elena mix with 6 cups of white paint? How many batches would this make?
Use your double number line diagram to find another amount of white paint and blue paint that would make the same shade of light blue paint.
How do you know that these mixtures would make the same shade of light blue paint?
Lesson Summary
You can use a double number line diagram to find many equivalent ratios. For example, a recipe for fizzy juice says, “Mix 5 cups of cranberry juice with 2 cups of soda water.” The ratio of cranberry juice to soda water is
This double number line shows that the ratio