Modeling Prompt

This prompt is very open-ended and a large part of the goal is to “define appropriate quantities for the purpose of descriptive modeling.” Encourage students to come up with a variety of ways to represent their answers. Which ones are precise? Which ones communicate clearly? Which ones sound impressive?

Students will need to decide what information to look up and how they compare to the average data. They will also need to convert among units (ounces to gallons or gallons to cubic feet). Students who find information in metric units instead will have a much easier time with these conversions.

When describing containers, encourage students to go beyond a container they can look up the volume of and instead create a container. For example, it would be interesting for students to consider the volume of the classroom and how many times they might fill that space in a lifetime.

A good connection to the geometry content of the course is to consider how scaling up (from week to month to year) affects the dimensions of a container. Students can apply the scale factor (4 or 52) directly when considering how many water bottles or bathtubs it would fill, but students should only apply the scale factor to a single dimension of a box to accurately scale the volume.

1. How much water do you drink each day?

2. How much water do you use each week?

3. Describe containers that would hold the amount of water you use in a week, a month, a year, and a lifetime.

This prompt is less open ended than Task Statement 1. If students brainstorm additional rows they will need to decide what information to look up and how they compare to the average data. They will also need to convert among units (ounces to gallons or gallons to cubic feet).

A good connection to the geometry content of the course is to consider how scaling up (from week to month to year) effects the dimensions of a container. Students can apply the scale factor (4 or 52) directly when considering how many water bottles or bathtubs it would fill, but students should only apply the scale factor to a single dimension of a box to accurately scale the volume.

1. Some health experts suggest people drink 8 glasses filled with 8 ounces of water each day.

   1. How many 16.9 ounce disposable water bottles is that?

   2. How many 32 ounce reusable water bottles is that?

   3. How many 2.75 inch diameter cylindrical glasses filled to a 5 inch height with water is that?

2. How much water do you use each week? Complete the table to find out.

   	gallons of water per each	times per day	times per week	volume of water
   brush teeth	0.5
   wash hands	1
   flush toilet	1.6
   shower for 1 minute	2
   hand wash dishes from 1 meal	3
   run dishwasher	10
   load of laundry	25
   total

3. Describe containers that would hold the amount of water you use in a week, a month, a year, and a lifetime.

   1. How many 16.9 ounce disposable water bottles?

   2. How many 40 gallon bathtubs?

   3. How many 20,000 gallon swimming pools?

   4. Design your own container. Give the dimensions needed to calculate its volume. Consider if it could safely hold that much water.