shoshana is going to use 12 base-ten blocks 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 numbers?

921 and 129

To determine the largest and smallest possible numbers less than 999 using 12 base-ten blocks, we need to consider the place value of each digit.

In a base-ten system, the place values of each digit from right to left are: ones, tens, hundreds.

1. Largest Possible Number:
To find the largest possible number, we need to distribute the 12 base-ten blocks in a way that maximizes each place value.

Start with the largest place value, which is the hundreds place. Since we want a number less than 999, we can use a maximum of 9 hundreds blocks.

Next, move on to the tens place. Each tens block represents 10, so we can use any number of blocks from 0 to 9 to represent the tens place. In this case, we will use the maximum of 9 tens blocks.

Finally, for the ones place, we use any number of blocks from 0 to 9 to represent the ones place. Here, we use the remaining 12 - 9 - 9 = 6 ones blocks.

So, the largest possible number less than 999 using 12 base-ten blocks is 999 - 900 - 90 - 6 = 999 - 996 = 3.

2. Smallest Possible Number:
To find the smallest possible number, we need to distribute the 12 base-ten blocks in a way that minimizes each place value.

Again, start with the hundreds place. Since we want a number less than 999, we will use a minimum of 0 hundreds blocks.

Next, move to the tens place. We need to distribute the remaining blocks after the hundreds place, which is 12 - 0 = 12 blocks. Each tens block represents 10, so we can use a maximum of 1 tens block. We will use 1 tens block.

For the ones place, we use any number of blocks from 0 to 9 to represent the ones place. Here, we use the remaining 12 - 0 - 1 = 11 ones blocks.

So, the smallest possible number less than 999 using 12 base-ten blocks is 100 + 10 + 11 = 121.

Therefore, the largest possible number is 3, and the smallest possible number is 121.