A Middle School Mental Math 'Practical' Problem

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You're on a superhighway in the middle of nowhere at 10 PM, your fuel tank shows about a quarter of a tank remaining, your trip odometer shows you've gone about 180 miles since the last fill-up and you just passed a fuel rest stop. The sign reads "Next Rest Area and Gas - 58 miles." Are you in trouble or will you make it?

Comments
(1) Unrealistic scenario? Rest areas rarely that far apart on the Interstate? Why didn't the driver realize that he was low on gas and just stop! Why not just get off the Interstate and look for a local station or call AAA or Onstar if needed or use a navigation system to locate another gas station? (Do all of us have access to these technologies?). Does the student have to know that one still has some fuel remaining even when the gauge points to empty? Should a discussion of these kinds of practical issues be an integral part of 'real-world' problem-solving?

(2) Is this type of question fairly common in the texts you're using?

(3) What prerequisite skills and conceptual understandings are needed for this problem? Should most 7th or 8th graders be able to do this?

(4) Why do you think I suggested a mental math approach? Should we eliminate the mental math/estimation aspect altogether or use it as a starting point for further discussion?

(5) How do you think your students would fare on this problem? How many students would recognize the 1:3 ratio between gas remaining to gas consumed? Is this part:part construct something stressed in texts and in our classrooms? Should it be? Is it worthwhile discussing several approaches to this problem?

(6) Do you have a favorite visual model for this kind of ratio problem? Your thoughts?

Was the First Super Bowl More or Less Than a BILLION Seconds Ago?

Hey, another kind of "over-under"!!
Just some food for thought to put the number one billion and history in perspective...

A billion seconds ago it was about 1976.
A billion minutes ago Jesus was alive.
A billion hours ago our ancestors were living in the Stone Age.
A billion days ago no creature walked the earth on two feet.
And a billion dollars lasts 8 hours and 20 minutes at the rate our
Government spends it.

There are many references for this on the web and I'm sure you've seen it before. You can check the accuracy (perhaps the last one is a little off!). I still like sharing this with students as it not only puts the concept of a billion in perspective but it does offer a wonderful application of 1-significant digit estimates, scientific notation and orders of magnitude. Can you imagine asking students to estimate that a billion seconds is roughly 32 years without a calculator!!

Where are these kinds of estimates currently in our math curriculum? More likely occurring in a science class? Do they belong somewhere in our classes or are they just amusing curiosities? You can guess where my thoughts lie!