How Do You Use a Chip Model?

Using a chip model is a hands-on visual strategy to understand and perform mathematical operations, especially addition and subtraction. It uses colored chips to represent numbers and their values, making abstract concepts more concrete.

Representing Numbers with Chips

• Typically, positive numbers are represented by chips of one color (e.g., yellow or green).
• Negative numbers are represented by chips of a different color (e.g., red).
• Each chip represents a unit value (usually 1).

Addition with a Chip Model

1. Represent each addend: Create sets of chips representing each number being added. Use the appropriate color for positive or negative values.
2. Combine the chips: Put all the chips together into one group.
3. Create zero pairs (if applicable): A zero pair consists of one positive chip and one negative chip. Each zero pair cancels each other out (1 + -1 = 0). Remove all zero pairs from the group.
4. Count the remaining chips: The color and number of the remaining chips represent the sum.

Subtraction with a Chip Model

1. Represent the minuend: Create a set of chips representing the first number (the number being subtracted from).
2. Represent the subtrahend: Determine what chips need to be taken away (the number being subtracted).
3. Take away the chips: Remove the chips representing the subtrahend from the group representing the minuend. If you don't have enough chips of the correct color to take away, you'll need to "add zero."
4. Add zero (if necessary): If you need to subtract a positive chip but don't have any, add a zero pair (one positive and one negative) to the minuend. This doesn't change the value, but now you can take away the positive chip. Repeat as needed. The same logic applies to subtracting negative chips.
5. Count the remaining chips: The color and number of the remaining chips represent the difference.

Example: Addition

Let's add 5 + (-3) using a chip model.

1. Represent 5: Use 5 yellow chips (representing +5).
2. Represent -3: Use 3 red chips (representing -3).
3. Combine: Put all the chips together.
4. Zero pairs: You have 3 yellow chips and 3 red chips, so you can remove 3 zero pairs.
5. Remaining: You are left with 2 yellow chips.

Therefore, 5 + (-3) = 2.

Example: Subtraction

Let's subtract 2 - 5 using a chip model.

1. Represent 2: Use 2 yellow chips (representing +2).
2. Subtract 5: We need to take away 5 yellow chips, but we only have 2.
3. Add zero: Add 3 zero pairs (3 yellow and 3 red chips) to the group. We now have 5 yellow and 3 red chips.
4. Subtract: Now we can take away 5 yellow chips.
5. Remaining: We are left with 3 red chips.

Therefore, 2 - 5 = -3.

The chip model provides a visual and tactile way to grasp the concepts of positive and negative numbers and perform arithmetic operations. This approach is particularly useful for students who benefit from hands-on learning.