Algebra tiles can visually represent integer division by modeling the dividend as a collection of tiles and then arranging them into groups of the size of the divisor to determine the quotient. The sign of the tiles and the way they are grouped determine the sign of the quotient.
Here's a breakdown of how to use algebra tiles for integer division, based on the available reference:
- Represent the Dividend: Use algebra tiles to represent the number being divided (the dividend). Positive numbers are represented by yellow tiles, and negative numbers by red tiles.
- Represent the Divisor: Determine the size and sign of the group you're dividing by (the divisor).
- Form Groups: Arrange the dividend tiles into groups of the size indicated by the divisor. The key is to form complete groups.
- Determine the Quotient: Count how many groups you were able to form. The number of groups represents the magnitude of the quotient. The sign of the quotient depends on the signs of the divisor and the dividend:
- If the divisor and dividend have the same sign (both positive or both negative), the quotient is positive.
- If the divisor and dividend have different signs (one positive and one negative), the quotient is negative.
- Account for Zero Pairs: If you need to add zero pairs (one positive and one negative tile, which cancel each other out) to be able to form the necessary groups, you can do so. Adding zero pairs does not change the value of the dividend, but it allows you to rearrange the tiles to visualize the division.
Example:
Let's say you want to divide -6 by 2 (i.e., -6 ÷ 2).
- Represent -6: Use 6 red tiles to represent -6.
- Represent 2: You're dividing by a positive 2.
- Form Groups: Arrange the 6 red tiles into groups of 2. You will have 3 groups.
- Determine the Quotient: Because you have 3 groups, the magnitude of the quotient is 3. Since you are dividing a negative number (-6) by a positive number (2), the quotient is negative. Therefore, -6 ÷ 2 = -3.
Another Example (From the Video):
Dividing six positive tiles by -2.
- Represent 6: Lay out six yellow/positive tiles.
- Divide into groups of -2: This is the trickier part. You want to arrange the positive tiles so that we can show equal groups of -2. To do this, you will need to create zero pairs.
- Add zero pairs: Add enough zero pairs so that you can make the needed groups of -2.
- Determine the quotient: Count how many groups you created. The video reference states that when dividing a positive integer by a negative one the quotient will be negative. In this case, the answer is negative 3.
In essence, algebra tiles provide a visual and manipulative way to understand integer division by concretely demonstrating the grouping process and the resulting sign of the quotient.
