Sketch base-ten pieces for the number 2056 and explain how they can be used to illustrate the test for divisibility by 8.
To sketch base-ten pieces for the number 2056, we can start by representing each digit separately. In this case, we have four digits: 2, 0, 5, and 6. Each digit can be represented by a different base-ten piece.
1. The digit 2 can be represented by two cubes or blocks stacked on top of each other.
2. The digit 0 can be represented by an empty space or by a flat base-ten piece with no height.
3. The digit 5 can be represented by five small rods or sticks positioned together horizontally.
4. The digit 6 can be represented by six small cubes or blocks arranged in a pattern, such as a rectangle or tower.
Now, let's illustrate the test for divisibility by 8 using these base-ten pieces:
To determine if a number is divisible by 8, we observe the last three digits of that number. If the three-digit value formed by the last three digits is divisible by 8, then the original number is also divisible by 8.
In our example, the last three digits of 2056 are 0, 5, and 6. Let's combine the base-ten pieces representing these digits to form a visual representation:
2056 (number)
| 2 | 0 | 5 | 6 | (base-ten pieces)
The base-ten pieces visually depict the number 2056. Now, let's focus on the last three digits, which are 056.
| 0 | 5 | 6 | (base-ten pieces)
To test for divisibility by 8, we check if the three-digit value formed by the last three digits (056) is divisible by 8. In this case, 056 is indeed divisible by 8, and since the last three digits satisfy the divisibility rule, the whole number 2056 is also divisible by 8.
By visually representing the number and breaking it down into base-ten pieces, we can easily identify the last three digits and determine if they are divisible by 8 to validate the divisibility of the original number.