How Big Is The Vehicle That Uses Those Tires?

 

You are driving on the freeway when you see a large truck carrying these enormous tires.
 

• How big is the vehicle that uses those tires?

 

These questions may be useful in helping students down the problem solving path:

• What are we measuring when we are talking about how “big” something is?
• What is a guess that is too low for how tall those tires are when they are standing up?
• What is a guess that is too high for how tall those tires are when they are standing up?
• What portion of a vehicle’s height is a tire usually?
• What is a guess that is too low for how tall the vehicle is that uses these tires?
• What is a guess that is too high for how tall the vehicle is that uses these tires?
• What information would be useful in figuring this out?

 

I debated whether to call this lesson “How tall is the vehicle that uses those tires?”  The word “big” is not a mathematically precise term as it could imply height, length, width, weight, or more.  Ultimately I decided to leave it as “big” as I thought it would be a good way to authentically bring up the importance of “attend[ing] to precision” as part of Math Practice 6.  Measuring height is probably easiest, but different groups could measure different aspects of the vehicle to assess multiple meanings of “big”.  Between the Wikipedia information and the brochure, there is enough information to determine height, length, width, and weight.

I am not a dump truck expert but the resources I have included mention a Cat 797, Cat 797B, and Cat 797F.  For the scope of this lesson, I am considering all dump truck models to be the same dimensions.

The images listed below are not meant to be given out all at once.  I would begin by letting students have nothing more than the picture of the tires being transported on the truck.  Let students come up with guesses for the tire’s and vehicle’s dimensions.

Once they have that, you can give them the picture below.  This will help students revise their guesses without giving them any actual measurements and little perspective as to how massive the truck is.

• A picture of what the vehicle that uses these tires looks like (without something to compare it to)

 

Next give them the tire’s measurements.  Using this information, they should be able to have a rough idea of what the vehicle’s height actually is.

• Tire information

 

Once they have their answers for the dump truck’s height, give student their first look at how big the truck is compared to something they are familiar with.  Have them check to see if their answers seem reasonable still.

• A picture of what the vehicle that uses these tires looks like (with something to compare it to)

 

The dimensions listed below come from a Caterpillar brochure and have all the dimension needed including the actual vehicle height of 25 feet, 4 inches.  This PDF (included in the “Download files” button) can also be used for answers to how wide the truck is and more.

• A Cat 797’s dimensions

 

Finally, a video showing the dump truck in action.

• Video showing a Cat 797

 

• CCSS 7.RP.2 – Recognize and represent proportional relationships between quantities.

 

• Caterpillar
• Wikipedia