I need help raking my leaves

Brian has spent too much time thinking about his leaves. He's worried about raking them alone and thinking about how long the job would take if people helped. In this activity students see the inverse relationship between number of workers and time to complete the whole job. They graph hyperbolas and consider how long the extreme condition of zero people raking might take to complete the job.   Useful extension ideas:

In the middle of a ratio unit?  Use this to see if kids apply proportional reasoning to this situation: Example: If it takes 1 person 12 hours then will it would take 2 people 24 hours?

Studying linear relationships?  Use this to show that not all relationships are linear.  Check out the table, rule and graph compared to linear relations.

They discover that you can't divide by zero.  With 4 people it takes 3 hours to rake my leaves, because 4x3=12 or 12/3=4.  What about 6 people? 6x2=12 or 12/6=2?  What about zero people? Can't happen because nothing multiplied by zero makes 12 and you can't divide 12 up by zero people.

CCSS: 5.G.1 , 5.G.2, 6.EE.6, 6.EE.7, 6.EE.9, 8.F.4, 8.F.5, HSA.CED.2,  HSA.REI.10, HSF.IF.4, HSF.IF.5, HSF.IF.7 MP7, MP8