Integer chips are a visual model used to represent integers, often in a math context to help understand operations. Dividing integers using integer chips involves representing the dividend with chips and then dividing them into groups based on the divisor.
Here's a breakdown of how to divide integers using integer chips:
1. Represent the Dividend:
- Use positive chips (usually yellow or white) to represent positive integers.
- Use negative chips (usually red or black) to represent negative integers.
- The dividend is the number you are dividing. Represent this number using the appropriate number of positive or negative chips.
2. Determine the Divisor:
- The divisor is the number you are dividing by. The divisor indicates either:
- The size of the groups you want to create (measurement/repeated subtraction model).
- The number of groups you want to create (partitive/fair share model).
3. Create Groups:
- If the divisor is positive: Create groups of the size indicated by the divisor, ensuring each group contains the same type of chips (all positive or all negative). The number of chips in each group represents the quotient.
- If the divisor is negative: This is trickier. Think of it as trying to remove groups of negative chips from the dividend. You might need to add zero pairs (one positive chip and one negative chip, which cancel each other out) to the dividend in order to create the groups of negative chips you need to remove. The number of groups you remove will determine if the result is positive or negative. Since you're removing negative groups, the answer will be positive if you were removing the correct type of chip.
4. Determine the Quotient:
- Count how many groups you were able to make (if using the measurement/repeated subtraction model). Each group must contain the amount shown in the dividend.
- Count the number of chips in one group if you have determined the number of groups needed (if using the partitive/fair share model).
- The sign of the quotient depends on the signs of the dividend and divisor:
- Positive ÷ Positive = Positive
- Negative ÷ Negative = Positive
- Positive ÷ Negative = Negative
- Negative ÷ Positive = Negative
Example 1: 6 ÷ 2
- Represent 6 with 6 positive chips.
- The divisor is 2 (positive). You want to split the 6 chips into groups of 2.
- You can make 3 groups of 2 positive chips.
- Therefore, 6 ÷ 2 = 3.
Example 2: -6 ÷ 2
- Represent -6 with 6 negative chips.
- The divisor is 2 (positive). You want to split the 6 negative chips into groups of 2.
- You can make 3 groups of 2 negative chips.
- Therefore, -6 ÷ 2 = -3.
Example 3: 6 ÷ -2
- Represent 6 with 6 positive chips.
- The divisor is -2. This means you need to figure out how many groups of -2 you can create from a zero balance. Since you are looking for the opposite of your chips, the answer will be negative. Create zero pairs and remove a group of two negative chips. You can do this three times.
- You removed three groups, so the answer will be -3.
- Therefore, 6 ÷ -2 = -3
Example 4: -6 ÷ -2
- Represent -6 with 6 negative chips.
- The divisor is -2. You want to find out how many groups of -2 are in -6.
- You can make 3 groups of -2 using the -6 chips.
- Therefore, -6 ÷ -2 = 3.
