Lesson 3
Recipes
Let’s explore how ratios affect the way a recipe tastes.
3.1: Flower Pattern
This flower is made up of yellow hexagons, red trapezoids, and green triangles.
![A figure that contains 6 yellow hexagons, 2 red trapezoids, and 9 green triangles.](https://cms-im.s3.amazonaws.com/5bkUwdtYhzJpkRu2szUjikco?response-content-disposition=inline%3B%20filename%3D%226-6.2.A.PP_Image_5.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.A.PP_Image_5.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000047Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8428681e707693e289279a8e1cd90985901aed1cb29d78354effee6509c6dc4f)
- 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?
3.2: Powdered Drink Mix
Here are diagrams representing three mixtures of powdered drink mix and water:
![A discrete diagram for three quantities.](https://cms-im.s3.amazonaws.com/JbHRvR7Bfit4Grx1Q5JtHigx?response-content-disposition=inline%3B%20filename%3D%226-6.2.B1_Image_3.2.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.B1_Image_3.2.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000047Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f831f9974b6d67af40f7b22d094a9ac042e71798876107bbbffda6730dcf01be)
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How would the taste of Mixture A compare to the taste of Mixture B?
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Use the diagrams to complete each statement:
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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 ________.
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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 ________.
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- How would the taste of Mixture B compare to the taste of Mixture C?
Sports drinks use sodium (better known as salt) to help people replenish electrolytes. Here are the nutrition labels of two sports drinks.
![Two nutrition Labels. Drink A. Drink B.](https://cms-im.s3.amazonaws.com/KnUzqBoxPmqse4kW7TxmoYbY?response-content-disposition=inline%3B%20filename%3D%226-6.2.B3.Extension.01.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.B3.Extension.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000047Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f9f530eefebd86560b24c474d3ea37c11a478f3cd69ca3b010b84f2055dd0f80)
- Which of these drinks is saltier? Explain how you know.
- If you wanted to make sure a sports drink was less salty than both of the ones given, what ratio of sodium to water would you use?
3.3: Batches of Cookies
A recipe for one batch of cookies calls for 5 cups of flour and 2 teaspoons of vanilla.
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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?
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Whether the ratio of cups of flour to teaspoons of vanilla is \(5:2\), \(10:4\), or \(15:6\), the recipes would make cookies that taste the same. We call these equivalent ratios.
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Find another ratio of cups of flour to teaspoons of vanilla that is equivalent to these ratios.
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How many batches can you make using this new ratio of ingredients?
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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:
![Equivalent ratios of a recipe for fizzy juice.](https://cms-im.s3.amazonaws.com/pAc6mUN2vNQxtE5MGRDpXNfN?response-content-disposition=inline%3B%20filename%3D%226-6.2.B1_Image_6.1.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.B1_Image_6.1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000047Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=14b782d7795763a90ef7fbcf332b6fffe8f13fc29082c6ed3d25f6ba0681d7a0)
We say that the ratios \(5 : 2\), \(10 : 4\), and \(15 : 6\) 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.