alana has 5 base ten blocks.She has at least one of each type of block.The value of her blocks is greater than 140.What blocks could she have?
2x0=0 2x1=2 2x2=2 2x3=6
25 blocks
145
To find the possible blocks Alana could have, we need to determine all the different combinations of base ten blocks that have a value greater than 140.
First, let's identify the different types of base ten blocks:
- Units (1s place)
- Rods (10s place)
- Flats (100s place)
- Cubes (1,000s place)
- Blocks (10,000s place)
Since Alana has at least one of each type of block, we can start with one of each and add additional blocks until we reach a value greater than 140.
Let's consider the possibilities:
1. Units (1) + Rods (10) + Flats (100) + Cubes (1,000) + Blocks (10,000)
This combination has a total value of 10,111, which is greater than 140.
2. Units (1) + Rods (10) + Flats (100) + Cubes (1,000) + Blocks (10,000) + additional Units (1)
By adding one more Unit block, the total value becomes 10,112, which is still greater than 140.
3. Units (1) + Rods (10) + Flats (100) + Cubes (1,000) + Blocks (10,000) + additional Units (1) + additional Rods (10)
By adding one more Unit block and one more Rod block, the total value becomes 10,122, which is greater than 140.
4. Units (1) + Rods (10) + Flats (100) + Cubes (1,000) + Blocks (10,000) + additional Units (1) + additional Rods (10) + additional Flats (100)
By adding one more Unit block, one more Rod block, and one more Flat block, the total value becomes 10,222, which is greater than 140.
5. Units (1) + Rods (10) + Flats (100) + Cubes (1,000) + Blocks (10,000) + additional Units (1) + additional Rods (10) + additional Flats (100) + additional Cubes (1,000)
By adding one more Unit block, one more Rod block, one more Flat block, and one more Cube block, the total value becomes 11,222, which is greater than 140.
Therefore, the possible combinations of blocks Alana could have are:
- Units (1) + Rods (10) + Flats (100) + Cubes (1,000) + Blocks (10,000)
- Units (1) + Rods (10) + Flats (100) + Cubes (1,000) + Blocks (10,000) + additional Units (1)
- Units (1) + Rods (10) + Flats (100) + Cubes (1,000) + Blocks (10,000) + additional Units (1) + additional Rods (10)
- Units (1) + Rods (10) + Flats (100) + Cubes (1,000) + Blocks (10,000) + additional Units (1) + additional Rods (10) + additional Flats (100)
- Units (1) + Rods (10) + Flats (100) + Cubes (1,000) + Blocks (10,000) + additional Units (1) + additional Rods (10) + additional Flats (100) + additional Cubes (1,000)