In a life time, might a human drink every one of the water in a lake, such together Crater Lake pictured below?

## IM Commentary

The purpose of this job is for students to settle a volume problem in a modeling paper definition (MP.4). It needs multiple switch using systems of time and also volume. It also requires thinking about some reasonable hypotheses for exactly how much one individual drink each work and likewise how many days there space in the individual"s lifetime. Countless different, reasonable answers room possible. The teacher might wish to have a course discussion in bespeak to choose uniform values for this numbers, however it is likewise appropriate to have actually students work-related in groups and also then each group can pick values and then discuss and justify them as a totality group.

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Students very first study volume in fifth grade (5.MD.C.3) and also start symbolic manipulations for the purpose of unit counter in sixth grade (6.RP.A.3.c). In fifth and 6th grade they also solve volume difficulties involving right rectangle-shaped prisms (5.G.C.3, 6.G.A.2), yet it isn"t till 7th grade that they room asked to fix more complex volume-related problems. This job asks student to occupational with quantities that perform not have a well-defined shape, and so is an ext abstract than it appears. The truth that the volume that a liquid remains the exact same regardless that the shape of the container it is in is not obvious and also depends on understanding of the physical world (namely, the liquids are incompressible). When the standards execute not specifically address when students should have the ability to solve together problems, 7th grade appears appropriate. That is when students space using the fact that the volume that a number can be discovered by decomposing it into non-overlapping pieces, finding the volume the the pieces, and also then adding their quantities (as comprise by 7.G.B.6), indicating that they are occurring a more abstract expertise of volume 보다 is referred to as for in 5th and 6th grade.

One advantage to the metric device of measure up is the the physical properties the water attach different units: one liter that water has actually a massive of 1 kilogram and it takes up 1000 cubic centimeters that space. If we work-related in the U.S. Customary System, then the liquid measures of cups, pints, quarts, and also gallons call for an extra counter in order to be associated to various other volume systems such together cubic inches or cubic feet. In order to transform liquid measures right into volume units, we can convert gallons come liters, liters come cubic centimeters, and cubic centimeters come cubic inches. The third solution makes these conversions if the second solution continues to be within the U.S. Customary System, make an estimate of how much spae a gallon of water occupies. The an initial solution functions in metric devices throughout.

Some information about the old adage come drink 8 glasses of water a job (the quantity supplied in one solution) is obtainable here: http://www.mayoclinic.com/health/water/NU00283. Much much more information around Crater Lake have the right to be uncovered here: http://en.wikipedia.org/wiki/Crater_Lake. Contained is an calculation for the quantity of water in Crater Lake, 18.7 cubic * kilometers. * While question (c) definitely has a an unfavorable answer, an engaging follow as much as this question would be whether or not every one of the world in a city (or country) could drink the water in Crater Lake in their life times. Follow to the estimates of the very first solution, an average human being drinks just 60 cubic meter of water in a lifetime: since there are 1000 $ imes$ 1000 $ imes$ 1000 cubic meter in a cubic kilometer, this way that it would take around 300,000,000 world to consume every one of the water in Crater Lake, throughout their lifetimes. So there is virtually enough water in Crater Lake because that the entire population of the united States!!

This job is based upon difficulty 1 in Class activity 11K of Sybilla Beckmann"s * math for Elementary school Teachers, * Pearson, 2011. Principles from the commentary and solution have actually been gathered native a autumn 2013 class of prospective teacher at the university of brand-new Mexico.

## Solutions

Solution:1 utilizing Liters

A typical recommendation is the we have to make certain to drink at least 8 glasses of water every day. There room 4 glasses in a quart for this reason this is the same as two quarts the water. A quart is really close to a liter for this reason we will certainly assume that the average human being drinks 2 liters of water every day.

Next we require to identify how countless days there room in the person"s lifetime. If we take 80 years for an median lifetime, climate there space 365 days in annually so this gives$$80 imes 365 = 29,200 ext days.$$The number is just approximate for this reason 30,000 days would certainly be a an excellent round estimate.If the average person drinks 2 liters of water every day and also lives for about 30,000 job this will certainly be$$30,000 imes 2 = 60,000$$liters of water spend in a lifetime.

A liter that water occupies 1000 cubic centimeters of space so 60,000 liters the water will take up$$60,000 imes 1,000 ext cm^3 = 60,000,000 ext cm^3.$$To see just how much room this would certainly take up, we deserve to think that the 1,000 cubic centimeters as a cube which is 10 cm by 10 cm by 10 cm. One thousand of these cubes might be placed in 10 layers v each great containing 10 rows and 10 columns. For this reason one 1000 that the one liter cubes would certainly take increase a space 10 times as wide, 10 times together long, and 10 times together high. Due to the fact that 10 $ imes$ 10 cm = 100 cm, this means that a cube one meter wide, one meter long, and one meter high would host 1,000 liters of water. To acquire 60,000 liters of water we deserve to increase the broad by a element of 5, the size by a aspect of 6 and the height by a factor of 2. Therefore this method that a 5 meter through 6 meter by 2 meter container can hold 60 that the 1 meter cubes and 60,000 liters the water. This container would certainly be around the dimension of a large room.

Crater Lake is a big lake in Oregon recognized for the exceptional color of that is glacier water and its great depth. The trees on the island offer an idea of how huge the lake is. This would be countless times much more water than we calculated over so even enabling for various estimates, it is not possible that a person could drink every one of the water in Crater Lake in a life time. In fact, a person might not drink every one of the water in a huge pond follow to the calculations in part (b): 5 meters by 6 meter by 2 meters is the size of a tiny swimming pool.

Solution:2 using U.S. Customary Units

Rather than the proverbial 8 glasses the water a day, below we will occupational with a larger estimate the 1 gallon a day. There space 4 quarts in a gallon, 2 pints in a quart, and also 2 cups in a pint for this reason there space 4 $ imes$ 2 $ imes$ 2 = 16 cups of water in a gallon: this is double as much water as we considered in the first solution.

Next we require to determine how numerous days there room in the person"s lifetime. If us take 80 years for an typical lifetime, climate there are 365 days in annually so this gives$$80 imes 365 = 29,200 ext days.$$The number is only approxomate for this reason 30,000 days would certainly be a great round estimate.If the average person drinks a gallon of water every day and also lives for about 30,000 days this will certainly be30,000gallons of water spend in a lifetime.

To discover out exactly how much space a gallon occupies, we can take approximate dimensions of a gallon (or fifty percent gallon) container that water or milk for example. For a gallon container that milk, the dimensions are around 6 customs by 6 inches at the base and also 8 inches to the to fill line because that the milk. This will give an overestimate due to the fact that the container has rounded edges and it is tapered where the manage is yet it must be an excellent enough to provide an idea of how much space the 30,000 gallons that water will occupy. If we transform to feet (inches are too small of a unit to gain a good idea that the room 30,000 gallons of water will certainly take up) then this is$$frac12 ext foot imes frac12 ext foot imes frac23 ext foot.$$Multiplying this out gives $frac16$ that a cubic foot. If one gallon of water takes increase $frac16$ that a cubic foot, climate 30,000 gallons the water will certainly take up 5,000 cubic feet. This would fit in a an are that is 20 feet by 25 feet by 10 feet which would be about the dimension of a swimming pool.

The lake in the photo is much larger (and also much deeper) than a swimming pool. It is not feasible that a person can drink all of the water in this lake.

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Solution:3 convert U.S. Customary units to metric devices for part (b)

Here we job-related with the estimate from the second solution, 60,000 gallons that water, and find out just how much space this will occupy by converting to metric units and also using the truth that one liter that water occupies 1000 cubic centimeters of space.

We use the truth that one gallon is around 3.8 liters. So 30,000 gallons is$$30,000 imes 3.8 ext liters approx 110,000 ext liters.$$One liter rectal 1000 cubic centimeters for this reason 110,000 liters the water will certainly occupy 110,000 $ imes$ 1000 cubic centimeters or 110,000,000 cubic centimeters. There are 2.54 centimeters in one inch and so there space 2.54$^3$ cubic centimeters in a cubic inch. For this reason our water would occupy$$110,000,000 div 2.54^3 ext cubic inches approx 7,000,000 ext cubic inches.$$There room 12 customs in a foot and also so