Math Forum - Problem of the Week


Containers

Introduction

To measure from 1 to 12 oz. of liquid, which two measuring cups would allow you to measure the most? a 3 oz. cup and an 8 oz. cup, or a 4 oz. cup and a 10 oz. cup?

Simulation 1

Test a 3 oz. cup and an 8 oz. cup. Use the simulation (applet) to determine which amounts listed in Table 1 can be measured.
Click To Show Applet Window

A few answers are filled in to get you started. You might want to copy or print out Table 1.

Table 1
oz. Yes No
1    
2    
3    
4    
5    
6    
7 X  
8    
9    
10 X  
11    
12    

Simulation 2

Next, try a 4 oz. and a 10 oz. cup. Use the simulation (applet) to determine which amounts listed in Table 2 can be measured.
Click To Show Applet Window

A few answers are filled in to get you started. You might want to copy or print out Table 2.

Table 2
oz. Yes No
1    
2    
3    
4    
5    
6    
7   X
8    
9    
10 X  
11    
12    

Questions:

  1. Do you notice any patterns in Table 1? Explain.

  2. Do you notice any patterns in Table 2? Explain.

  3. Compare the patterns in your two tables. Think about the combinations you used. What do you notice about even and odd numbers?

  4. What are your conclusions about the amounts that can (or cannot) be measured using the two different pairs of measuring cups?

  5. Which pair of cups would measure the most amounts?

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