Shosahanna is going to us 12 base-ten blocks to model the largest possible number less than 999. Then she will use another 12 blocks to model the smallest posible number less than 999. What are the two numbers? explain me in detail

921 and 129. 9+2+1=12 and 1+2+9=12

To determine the largest possible number less than 999 using 12 base-ten blocks, let's start by understanding how base-ten blocks are represented. In the base-ten system, each block represents a power of ten, from the unit's place on the right to the thousands on the left.

There are four main types of base-ten blocks:

1. Units: Representing ones.
2. Rods (tens): Representing tens.
3. Flats (hundreds): Representing hundreds.
4. Cubes (thousands): Representing thousands.

Since we have 12 blocks, we can distribute them among these categories to create the largest possible and smallest possible numbers less than 999.

Let's begin with the largest possible number.

To get the largest number, we need to distribute the blocks in such a way that they cover the three categories, thousands, hundreds, and tens, while also maximizing each place value.

Since there are only 12 blocks, we cannot use any cubes (thousands) as three cubes would already exceed the limit. However, we can still use flats (hundreds) and rods (tens).

Let's use all 12 blocks in the following way:

- 9 flats (hundreds): Each flat represents 100, so 9 flats would give us 900.
- 1 rod (tens): Each rod represents 10, so 1 rod would give us 10.
- 2 units (ones): Each unit represents 1, so 2 units would give us 2.

Combining these values, we get:
900 + 10 + 2 = 912

So, the largest possible number less than 999 using 12 base-ten blocks is 912.

Now, let's move on to the smallest possible number.

To get the smallest number, we distribute the blocks in such a way that they cover the three categories, thousands, hundreds, and tens, while minimizing each place value.

Again, since we have 12 blocks, we cannot use any cubes (thousands) or flats (hundreds), but we can still use rods (tens) and units (ones).

Let's use all 12 blocks in the following way:

- 9 rods (tens): Each rod represents 10, so 9 rods would give us 90.
- 3 units (ones): Each unit represents 1, so 3 units would give us 3.

Combining these values, we get:
90 + 3 = 93

So, the smallest possible number less than 999 using 12 base-ten blocks is 93.

Therefore, the two numbers are:
Largest: 912
Smallest: 93