Lesson 2: Practice Problems

Problem 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.

Problem 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.

  1. 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.

  2. Describe another mixture of sparkling water and grape juice that would taste different than this recipe.

Problem 3

Here is a diagram showing a mixture of red paint and green paint needed for 1 batch of a particular shade of brown.

Add to the diagram so that it shows 3 batches of the same shade of brown paint.

A discrete diagram for two quantities labeled "red paint, in cups" and "green paint, in cups". The data are as follows: red paint, 2 squares. green paint, 3 squares.

Problem 4

To make 1 batch of sky blue paint, Clare mixes 2 cups of blue paint with 1 gallon of white paint.

  1. Explain how Clare can make 2 batches of sky blue paint.

  2. Explain how to make a mixture that is a darker shade of blue than the sky blue.

  3. Explain how to make a mixture that is a lighter shade of blue than the sky blue.

Problem 5

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

A number line with 7 tick marks with the first tick mark labeled 0, the third is labeled 6, and the 6th is labeled 15

Problem 6 From Unit 1 Lesson 4

Find the area of the parallelogram. Show your reasoning.

A parallelogram in a grid. The parallelogram has two vertical sides that are 3 units tall and two sides that rise 4 units over 7 units across.