This flower is made up of yellow hexagons, red trapezoids, and green triangles.
Write sentences to describe the ratios of the shapes that make up this pattern.
How many of each shape would be in two copies of this flower pattern?
2.2
Activity
Here are diagrams representing three mixtures of powdered drink mix and water:
How would the taste of Mixture A compare to the taste of Mixture B?
Use the diagrams to complete each statement:
Mixture B uses cups of water and teaspoons of drink mix.
The ratio of cups of water to teaspoons of drink mix in Mixture B is .
Mixture C uses cups of water and teaspoons of drink mix.
The ratio of cups of water to teaspoons of drink mix in Mixture C is .
How would the taste of Mixture B compare to the taste of Mixture C?
2.3
Activity
A recipe for one batch of cookies calls for 5 cups of flour and 2 teaspoons of vanilla.
Draw a diagram that shows the amount of flour and vanilla needed for two batches of cookies.
How many batches can you make with 15 cups of flour and 6 teaspoons of vanilla? Show the additional batches by adding more ingredients to your diagram.
How much flour and vanilla would you need for 5 batches of cookies?
Whether the ratio of cups of flour to teaspoons of vanilla is , , or , the recipes would make cookies that taste the same. We say that these ratios are equivalent.
Find another ratio of cups of flour to teaspoons of vanilla that is equivalent to these ratios.
How many batches can you make using this new ratio of ingredients?
2.4
Activity
The recipe for Perfect Purple Water says, “Mix 8 ml of blue water with 3 ml of red water.”
Jada mixes 24 ml of blue water with 9 ml of red water. Andre mixes 16 ml of blue water with 9 ml of red water.
Which person will get a color mixture that is the same shade as Perfect Purple Water? Explain or show your reasoning.
Find another combination of blue water and red water that will also result in the same shade as Perfect Purple Water. Explain or show your reasoning.
Student Lesson Summary
A recipe for fizzy juice says, “Mix 5 cups of cranberry juice with 2 cups of soda water.”
To double this recipe, we would use 10 cups of cranberry juice with 4 cups of soda water. To triple this recipe, we would use 15 cups of cranberry juice with 6 cups of soda water.
This diagram shows a single batch of the recipe, a double batch, and a triple batch:
We say that the ratios , , and are equivalent. Even though the amounts of each ingredient within a single, double, or triple batch are not the same, they would make fizzy juice that tastes the same.
When mixing colors, doubling or tripling the amount of each color will create the same shade of the mixed color. In fact, you can always multiply the amount of each color by the same number to create a different amount of the same mixed color.
For example, a batch of dark orange paint uses 4 ml of red paint and 2 ml of yellow paint.
To make two batches of dark orange paint, we can mix 8 ml of red paint with 4 ml of yellow paint.
To make three batches of dark orange paint, we can mix 12 ml of red paint with 6 ml of yellow paint.
Here is a diagram that represents 1, 2, and 3 batches of this recipe.
We say that the ratios , , and are equivalent because they describe the same color mixture in different numbers of batches, and they make the same shade of orange.