Question

unit 2, lesson 3
lesson 3 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.

mustard seeds (tsp)
chili powder (tsp)
salt (tsp)

1. 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.
2. 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.

Explanation:

Step1: Analyze number of ingredients per batch for spice - mix

For the spice - mix, 1 batch requires 3 teaspoons of mustard seeds, 5 teaspoons of chili powder, and 1 teaspoon of salt.

Step2: Count ingredients in the diagram

In the diagram, there are 9 teaspoons of mustard seeds, 15 teaspoons of chili powder, and 3 teaspoons of salt.

Step3: Calculate number of batches

For mustard seeds: $\frac{9}{3}=3$. For chili powder: $\frac{15}{5}=3$. For salt: $\frac{3}{1}=3$. Since the number of batches calculated from each ingredient is 3, the number of batches represented by the diagram is 3.

Step4: Diagram for chocolate - milk (description)

For Priya's chocolate - milk, 1 batch has 2 cups of milk and 5 tablespoons of cocoa powder. For 2 batches, we would draw 2 groups of 2 cups of milk (represented by some symbol, e.g., circles) and 2 groups of 5 tablespoons of cocoa powder (represented by another symbol, e.g., squares).

Step5: Find equivalent ratios for fizzy grape juice

The ratio of sparkling water to grape juice concentrate is 3:1. Equivalent ratios are found by multiplying both parts of the ratio by the same non - zero number. So, 6:2 (multiply by 2) and 9:3 (multiply by 3) are two more ratios that would make a mixture that tastes the same.

Step6: Describe a different - tasting mixture

A ratio of 4:1 of sparkling water to grape juice concentrate would be a mixture that tastes different than the 3:1 ratio.

Answer:

1. 3 batches.
2. Draw 4 circles to represent 4 cups of milk (2 batches of 2 cups each) and 10 squares to represent 10 tablespoons of cocoa powder (2 batches of 5 tablespoons each).
3. a. 6:2, 9:3

b. A ratio of 4:1 of sparkling water to grape juice concentrate.