Proportional Relationships- Day 5

Two Equations for Each Relationship

Lesson 5

Objective:

Today I will use the vocabulary “reciprocal” to explain related proportional relationships so that I can write two equations to represent a proportional relationship. I know I am successful when I can complete Cool Down 5 to earn a 4.

Missing Figures

Here are the second and fourth figures in a pattern.

Open Ended

What do you think the first and third figures in the pattern look like?

Open Ended

Describe the 10th figure in the pattern.

Meters and Centimeters

There are 100 centimeters (cm) in every meter (m).

Open Ended

0.94 m =?? cm

Open Ended

1.67 m =?? cm

Open Ended

57.24 m =?? cm

Open Ended

250 cm = ?? m

Open Ended

78.2 cm = ?? m

Open Ended

123.9 cm = ?? m

Open Ended

For the first table, find the constant of proportionality. (x)

Open Ended

For the second table, find the constant of proportionality. (y)

Open Ended

What is the relationship between these constants of proportionality?

Open Ended

For each table, write an equation for the proportional relationship. Let x represent a length measured in meters and y represent the same length measured in centimeters.

Filling a Water Cooler

It took Priya 5 minutes to fill a cooler with 8 gallons of water from a faucet that was flowing at a steady rate. Let w be the number of gallons of water in the cooler after t minutes.

Multiple Select

Which of the following equations represent the relationship between w and t? Select all that apply.

• w=1.6t

• w=0.625t

• t=1.6w

• t=0.625w

Open Ended

What does 1.6 tell you about the situation?

Open Ended

What does 0.625 tell you about the situation?

Open Ended

Priya changed the rate at which water flowed through the faucet. Write an equation that represents the relationship of w and t when it takes 3 minutes to fill the cooler with 1 gallon of water.

Open Ended

Was the cooler filling faster before or after Priya changed the rate of water flow? Explain how you know.

Feeding Shrimp

At an aquarium, a shrimp is fed 15 gram of food each feeding and is fed 3 times each day. 

Open Ended

How much food does a shrimp get fed in one day?

Open Ended

Complete the table to show how many grams of food the shrimp is fed over different numbers of days.

1 day = ?? g

Open Ended

Complete the table to show how many grams of food the shrimp is fed over different numbers of days.

7 days = ?? g

Open Ended

Complete the table to show how many grams of food the shrimp is fed over different numbers of days.

30 days = ?? g

Open Ended

What is the constant of proportionality? What does it tell us about the situation?

Open Ended

If we switched the columns in the table, what would be the constant of proportionality? Explain your reasoning.

Open Ended

Use d for number of days and f for amount of food in grams that a shrimp eats to write two equations that represent the relationship between d and f.

Open Ended

If a tank has 10 shrimp in it, how much food is added to the tank each day?

Open Ended

If the aquarium manager has 300 grams of shrimp food for this tank of 10 shrimp, how many days will it last? Explain or show your reasoning.

Poll

How I feel after this lesson

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