Proportional Relationships and Equations

Warmup

Activity #1

Plot a Table of Proportional Relationship

A plane flew at a constant speed between Denver and Chicago. It took the plane 1.5 hours to fly 915 miles.

• Complete the table, and answer the questions that follow.

(1.) How far does the plane fly in one hour?

(2.) How far would the plane fly in  t hours at this speed?

(3.) If d represents the distance that the plane flies at this speed for t hours, write an equation that relates t and d.

(4.) How far would the plane fly in 3 hours at this speed? in 3.5 hours? Explain or show your reasoning.

Activity #2

Plot a Table of Proportional Relationship

A recipe says that 6 spring rolls will serve 3 people.

• Complete the table as you answer the questions below. Explain your reasoning.

(1.) How many people will 1 spring roll serve?

(2.) How many people will 10 spring rolls serve? 16 spring rolls? 25 spring rolls?

(3.) How many people will n spring rolls serve?

Activity #3

Can Different Shapes be Jointly Used to Tile the Plane ?

A bakery uses 8 tablespoons of honey for every 10 cups of flour to make bread dough. Some days they bake bigger batches and some days they bake smaller batches, but they always use the same ratio of honey to flour.

• Complete the table below and also answer the questions that follow.

(1.) If f  is the cups of flour needed for h  tablespoons of honey, write an equation that relates f  and h.

(2.) How much flour is needed for 15 tablespoons of honey? 17 tablespoons? Explain or show your reasoning.

A certain ceiling is made up of tiles. Every square meter of ceiling requires 10.75 tiles.

• Fill in the table with the missing values.

Challenge #1

(1.) The table below represents a proportional relationship. Find the constant of proportionality, and write an equation that represents the relationship.

(i.) Constant of proportionality =

(ii.) Equation: P =

(2.) The table below represents a proportional relationship. Find the constant of proportionality, and write an equation that represents the relationship.

(i.) Constant of proportionality =

(ii.) Equation: C =

Challenge #2

A rocky planet orbits Proxima Centauri, a star that is about 1.3 parsecs from Earth. This planet is the closest planet outside of our solar system.

(1.) How long does it take light from Proxima Centauri to reach Earth? (A parsec is about 3.26 light years. A light year is the distance light travels in one year.)

(2.) There are two twins. One twin leaves on a spaceship to explore the planet near Proxima Centauri traveling at 90% of the speed of light, while the other twin stays home on Earth. How much does the twin on Earth age while the other twin travels to Proxima Centauri? (Do you think the answer would be the same for the other twin? Consider researching “The Twin Paradox” to learn more.)

Challenge #3

On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled in miles, d,  to the number of hours flying, t, is t = d. How long will it take the airplane to travel 800 miles?