OML Search

Illustrative Mathematics Unit 6.2, Lesson 3: Recipes

Related Topics:
Math Worksheets




Learn more about recipes as a real-life application of ratios, and about how ratios are represented. After trying the questions, click on the buttons to view answers and explanations in text or video.

Return to the list of Illustrative Math lessons


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 hexagons, trapezoids, and triangles arranged to represent a flower. The figure contains 6 yellow hexagons, 2 red trapezoids, and 9 green triangles.

1. Write sentences to describe the ratios of the shapes that make up this pattern.

2. 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 figure of three diagrams, labeled 'A', 'B', and 'C', each contain white and blue squares. Diagram A has 4 white squares and 1 blue square. Diagram B has 4 white squares and 1 blue square. Diagram C has 8 white squares and 2 blue squares. There is a legend labeled 'key' where 1 white square represents 1 teaspoon salt and 1 blue square represents 1 cup water.

1. How would the taste of Mixture A compare to the taste of Mixture B?

2. Use the diagrams to complete each statement:

a. 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 ________.

3. How would the taste of Mixture B compare to the taste of Mixture C?

  • See Possible Answers

    1. Mixture A would taste the same as Mixture B. The ratios of drink mix to water are the same in both.

    2. a. Mixture B uses 1 cup of water and 4 teaspoons of drink mix. The ratio of cups of water to teaspoons of drink mix in Mixture B is 1:4.
    Mixture C uses 2 cups of water and 8 teaspoons of drink mix. The ratio of cups of water to teaspoons of drink mix in Mixture C is 2:8, which is the same as 1:4.

    3. Mixture B would taste the same as Mixture C. Mixture C uses more water and more drink mix, but the ratio of water to drink mix is the same.


Sports drinks use sodium (better known as salt) to help people replenish electrolytes. Here are the nutrition labels of two sports drinks.

Nutrition labels for two drinks. The first reads: serving size 8 fl oz (240 mL), serving per container 4, amounts per serving: calories 50, total fat 0 g 0% of daily value, sodium 110 mg 5%, potassium 30 mg 1%, total carbohydrate 14 g 5%, sugars 14 g, protein 0 g. % daily values are based on a 2,000 calorie diet. The second label reads: serving size 12 fl oz (355 mL), serving per container 2.5, amounts per serving: calories 80, total fat 0 g 0% of daily value, sodium 150 mg 6%, potassium 35 mg 1%, total carbohydrate 21 g 7%, sugars 20 g, protein 0 g. % daily values are based on a 2,000 calorie diet.

1. Which of these drinks is saltier? Explain how you know.

2. 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?

  • Hints

    Look at the sodium content per serving. The second drink has more sodium per serving, but it also has larger servings. How much sodium is there for every fluid ounce/mL of a serving?

  • See Possible Answers

    1. The first drink is saltier. As a ratio, the first drink has 110 ÷ 8 = 13.75 mg sodium for every fluid ounce, while the second drink has 150 ÷ 12 = 12.5 mg sodium for every fluid ounce.

    2. Use a lower ratio of sodium to water, e.g. 11 mg sodium for every fluid ounce of water.




3.3 - Batches of Cookies

A recipe for one batch of cookies calls for 5 cups of flour and 2 teaspoons of vanilla.

1. Draw a diagram that shows the amount of flour and vanilla needed for two batches of cookies.

2. How many batches can you make with 15 cups of flour and 6 teaspoons of vanilla? Indicate the additional batches by adding more ingredients to your diagram.

3. How much flour and vanilla would you need for 5 batches of cookies?

4. 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.
a. Find another ratio of cups of flour to teaspoons of vanilla that is equivalent to these ratios.
b. How many batches can you make using this new ratio of ingredients?

  • See Possible Answers

    1.
    A discrete diagram of squares that represent cups of flour and teaspoons of vanilla. There are 10 white squares to represent cups of flour and 4 smaller yellow squares to represent teaspoons of vanilla, representing ingredients for 2 batches of cookies.

    2. 15 = 5 cups of flour × 3
    6 = 2 teaspoons of vanilla × 3
    With 15 cups of flour and 6 teaspoons of vanilla, you could make 3 batches of cookies:
    A discrete diagram of squares that represent cups of flour and teaspoons of vanilla. There are 15 white squares to represent cups of flour and 6 smaller yellow squares to represent teaspoons of vanilla, representing ingredients for 3 batches of cookies.

    3. 5 cups of flour × 5 = 25
    2 teaspoons of vanilla × 5 = 10
    You would need 25 cups of flour and 10 teaspoons of vanilla to make 5 batches of cookies.

    4. a. 30:12
    b. You could make 6 batches of cookies with this ratio of ingredients.


Lesson 3 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:

A discrete diagram of red and white squares. 1 red square represents 1 cup of cranberry juice and 1 white square represents 1 cup of soda water. 1 batch contains 5 red squares and 2 white squares. There are 3 batches in the picture.

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.



Practice Problems

1. A recipe for 1 batch of spice mix says, "Combine 3 teaspoons of mustard seeds, 5 teaspoons of chili powder, and 1 teaspoon of salt." How many batches are represented by the diagram? Explain or show your reasoning.

A discrete diagram for three quanties labeled 'mustard seeds, in teaspoons', 'chili powder, in teaspoons', and 'salt, in teaspoons'. The data are as follows:  mustard seeds, 9 squares.  chili powder, 15 squares.  salt, 3 squares.

  • Answers

    There are 3 batches in the diagram:

    A discrete diagram for three quanties labeled 'mustard seeds, in teaspoons', 'chili powder, in teaspoons', and 'salt, in teaspoons'. The data are as follows:  mustard seeds, 9 squares.  chili powder, 15 squares.  salt, 3 squares. These squares have been divided into 3 batches.

    Dividing any one of the quantities seen here by the number of teaspoons of an ingredient per batch will give this answer.

    9 squares of mustard seeds ÷ 3 teaspoons of mustard seeds per batch = 3 batches
    15 ÷ 5 teaspoons of chili powder per batch = 3 batches
    3 ÷ 1 teaspoon of salt per batch = 3 batches


2. Priya makes chocolate milk by mixing 2 cups of milk and 5 tablespoons of cocoa powder. Draw a diagram that clearly represents two batches of her chocolate milk.

  • See Possible Answers

    A diagram with 4 white squares representing cups of milk and 10 brown squares representing teaspoons of cocoa powder. 1 batch is 2 white squares and 5 brown squares.

    Two batches of chocolate milk would have 4 cups of milk and 10 tablespoons of cocoa powder.


3. In a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1.
a. Find two more ratios of cups of sparkling water to cups of juice concentrate that would make a mixture that tastes the same as this recipe.
b. Describe another mixture of sparkling water and grape juice that would taste different than this recipe.

  • See Possible Answers

    a. You can make equivalent fractions by multiplying both numbers in the ratio by the same multiplier.
    Equivalent ratios for 3:1 include 6:2 (3 × 2 : 1 × 2) and 9:3 (3 × 3 : 1 × 3).

    b. A non-equivalent ratio would taste different, e.g. 3:2 sparkling water to juice concentrate.


4. Write the missing number under each tick mark on the number line.

A number line with tick marks. From left to right, the tick marks are labeled 18, blank, 30, blank, 42.

  • Answers

    A number line with tick marks. From left to right, the tick marks are labeled 18, 24, 30, 36, 42.

    The missing numbers are 24 and 36. This number line shows skip-counting by 6, or multiples of 6.


5. At the kennel, there are 6 dogs for every 5 cats.

a. The ratio of dogs to cats is ______ to ______.
b. The ratio of cats to dogs is ______ to ______.
c. For every ______ dogs there are ______ cats.
d. The ratio of cats to dogs is ______ : ______.

  • Answers

    a. The ratio of dogs to cats is 6 to 5.
    b. The ratio of cats to dogs is 5 to 6.
    c. For every 6 dogs there are 5 cats.
    d. The ratio of cats to dogs is 5 : 6.


6. Elena has 80 unit cubes. What is the volume of the largest cube she can build with them?

  • Answers

    The largest perfect cube which is less than 80 is 43 = 64. (The next largest is 53 = 125, which is greater than 80.)


5. Fill in the blanks to make each equation true.

a. 3 · 13 = ______
b. 10 · 110 = ______
c. 19 · 119 = ______
d. a · 1a = ______ (As long as a does not equal 0.)
e. 5 · ______ = 1
f. 17 · ______ = 1
g. b · ______ = 1

  • Answers

    a. 3 · 13 = 1
    b. 10 · 110 = 1
    c. 19 · 119 = 1
    d. a · 1a = 1 (As long as a does not equal 0.)
    e. 5 · 15 = 1
    f. 17 · 117 = 1
    g. b · 1b = 1



The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


OML Search


We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.