A drink recipe says to mix 4 teaspoons of powdered drink mix for every cup of water. Here are two ways to represent multiple batches of this recipe:

A discrete diagram for two quantities labeled "drink mix, in teaspoons" and " water in cups." For the number of teaspoons of drink mix, there are 8 small squares. For the number of cups of water, there are 2 large squares. Two groups of 4 small squares and 1 large square are indicated and one group of 4 small squares and 1 large square is circled.

1. How can we tell that and are equivalent ratios?
2. How are these representations the same? How are these representations different?
3. How many teaspoons of drink mix should be used with 3 cups of water?
4. How many cups of water should be used with 16 teaspoons of drink mix?
5. What numbers should go in the empty boxes on the double number line diagram? What do these numbers mean?

Here is a diagram showing Elena’s recipe for one batch of light blue paint.

1. Complete the double number line diagram to show the amounts of white paint and blue paint in different-sized batches of light blue paint.

   

2. Compare your double number line diagram with your partner. Discuss your thinking. If needed, revise your diagram.

3. How many cups of white paint should Elena mix with 12 tablespoons of blue paint? How many batches would this make?

4. How many tablespoons of blue paint should Elena mix with 6 cups of white paint? How many batches would this make?

5. 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.
6. How do you know that these mixtures would make the same shade of light blue paint?

Andre likes a hot cocoa recipe with 1 cup of milk and 3 tablespoons of cocoa. He poured 1 cup of milk but accidentally added 5 tablespoons of cocoa.

1. How can you fix Andre’s mistake and make his hot cocoa taste like the recipe?

2. Explain how you know your adjustment will make Andre’s hot cocoa taste the same as the one in the recipe.