Unit 2, Lesson 6
Introducing Double Number Line Diagrams
Grade 6
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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.
Here is a diagram showing Elena’s recipe for one batch of light blue paint.
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?
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.
Explain how you know your adjustment will make Andre’s hot cocoa taste the same as the one in the recipe.
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 . Multiplying both ingredients by the same number creates equivalent ratios.
This double number line shows that the ratio is equivalent to . If you mix 20 cups of cranberry juice with 8 cups of soda water, it makes 4 times as much fizzy juice that tastes the same as the original recipe.
A double number line diagram uses a pair of parallel number lines to represent equivalent ratios. There is one number line for each quantity in the ratio. The tick marks for equivalent ratios line up.
This double number line diagram shows that and are equivalent ratios.