Lesson 09: Solving Problems About Proportional Relationships | Unit 2: Introducing Proportional Relationships

Open Ended

For each situation, explain whether you think the relationship is proportional or not. Explain your reasoning. 1. The weight of a stack of standard 8.5x11 copy paper vs. the number of sheets of paper.

Open Ended

For each situation, explain whether you think the relationship is proportional or not. Explain your reasoning. 2. The weight of a stack of different-sized books vs. the number of books in the stack.

Open Ended

Every package of a certain toy also includes 2 batteries. Are the number of toys and number of batteries in a proportional relationship? If so, what are the two constants of proportionality? If not, explain your reasoning.

Multiple Choice

Every package of a certain toy also includes 2 batteries. Use $$t$$ for the number of toys and $$b$$ for the number of batteries to write two equations relating the two variables. Which of the following equations is correct? $$b =$$ $$t =$$

• b = t + 2
• t = 2b
• b = t/2
• b = 2t, t = b/2

Multiple Choice

What is the age difference between Lin and her brother?

• The age differences are 3, 4, 10, and 10.
• 1
• 2
• 5

Open Ended

Is there a proportional relationship between Lin’s age and her brother’s age? Explain your reasoning.

Multiple Select

Select **all** the pieces of information that would tell you $$x$$ and $$y$$ have a proportional relationship.

Let $$y$$ represent the distance in meters between a rock and a turtle's current position and $$x$$ represent the time in minutes the turtle has been moving.

• $$y = 3x$$

• After 4 minutes, the turtle has walked 12 feet away from the rock.

• The turtle walks for a bit, then stops for a minute before walking again.

• The turtle walks away from the rock at a constant rate.

• The turtle starts out walking slowly and speeds up as it gets farther away from the rock.

Open Ended

To make a friendship bracelet, some long strings are lined up. One string is taken and tied in a knot with each of the other strings to create a row of knots. A new string is chosen and knotted with all the other strings to create a second row. This process is repeated until there are enough rows to make a bracelet to fit around a friend's wrist. Are the number of knots proportional to the number of rows? Explain your reasoning.

Multiple Choice

What information do you need to know to write an equation relating two quantities that have a proportional relationship?

• The average of the two quantities and their maximum value.
• The total of both quantities and their individual values.
• The constant of proportionality and the relationship between the two quantities.
• The difference between the two quantities and their minimum value.

Multiple Choice

Consider the problem: A water bucket is being filled with water from a water faucet at a constant rate. When will the bucket be full? What information would you need to be able to solve the problem?

• The color of the bucket and the temperature of the water.
• The time of day when the faucet is turned on.
• The weight of the bucket when empty.
• You need the volume of the bucket and the filling rate of the faucet.