Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create a rectangular prism with a volume that is less than 100 cubic units. What’s the least volume? What’s the greatest volume?
Hint
What do you notice about using 5 as a dimension?
Answer
There are several possible answers that work. Some include:
• 1 x 3 x 8 = 24
• 2 x 4 x 7 = 56
• 3 x 4 x 6 = 72
• 2 x 6 x 7 = 84
• 3 x 4 x 8 = 96
• 1 x 3 x 8 = 24
• 2 x 4 x 7 = 56
• 3 x 4 x 6 = 72
• 2 x 6 x 7 = 84
• 3 x 4 x 8 = 96
Source: Kari Frazier
Least=1x5x4 is 20
Greatest=3x4x8 is 96
Least = 1x5x2 is 10
Greatest is 4x3x8 is 96
Greatest is 6x8x2=96
All solutions:
1 * 3 * 8 = 24
1 * 3 * 9 = 27
1 * 4 * 7 = 28
1 * 4 * 8 = 32
1 * 4 * 9 = 36
1 * 6 * 7 = 42
1 * 6 * 9 = 54
1 * 7 * 8 = 56
1 * 7 * 9 = 63
1 * 8 * 9 = 72
2 * 3 * 9 = 54
2 * 4 * 7 = 56
2 * 6 * 7 = 84
3 * 4 * 6 = 72
3 * 4 * 8 = 96
Least: 1 * 3 * 8 = 24
Greatest: 3 * 4 * 8 = 96
My answer:
Least=5x1x4 is 20
Greatest=3x8x4 is 96
This is one of my most uneasy questions when there is no length including width and most likely height! But a volume that is less is 1 x 3 x 8 = 24 one other is greater which is 3 x 4 x 8 = 96!