Shoshanna is going to use 12 base-ten bloacks to model the largest possible number less than 999. Then she will use another 12 blocks to model the smallest possible number less than 999. What are the two numbers?
To find the largest and smallest possible numbers less than 999 using 12 base-ten blocks, we need to understand how to represent numbers using base-ten blocks.
Base-ten blocks are a physical or visual representation tool used to represent numbers using units, rods, flats, and cubes. Each block represents a certain place value:
- Units (ones): represented by a single cube.
- Rods (tens): represented by a horizontal line of 10 cubes.
- Flats (hundreds): represented by a flat piece made up of 10 rods (100 cubes).
Now, let's start with finding the largest possible number.
1. Start by using the largest value first, which is a flat (hundreds block). Place one flat on the table to represent 900.
2. We have used 1 block so far, and we have 11 remaining.
3. We want to maximize the remaining blocks' value, so we would use rods (tens blocks) next. Place nine rods on the table to represent 90.
4. We have used 10 blocks so far, and we have 2 remaining.
5. For the 2 remaining blocks, we use units (ones block), which means placing 2 individual cubes on the table. This will represent 2.
6. Now, combine the values represented by each block: 900 + 90 + 2 = 992.
Therefore, the largest possible number less than 999, using 12 base-ten blocks, is 992.
Now, let's find the smallest possible number.
1. Start by using the smallest value first, which is a unit (ones block). Place one cube on the table to represent 1.
2. We have used 1 block so far, and we have 11 remaining.
3. Next, we use rods. Place nine rods on the table to represent 90.
4. We have used 10 blocks so far, and we have 2 remaining.
5. Finally, for the 2 remaining blocks, we use flats (hundreds blocks). Place two flats on the table to represent 200.
6. Now, combine the values represented by each block: 1 + 90 + 200 = 291.
Therefore, the smallest possible number less than 999, using 12 base-ten blocks, is 291.
So, the two numbers are:
- The largest possible number: 992.
- The smallest possible number: 291.