Question

In golf, shooting par is scored as a 0. A score of 2 below par on a hole in golf is called an eagle. Jacob’s friend Michelle scored an eagle on each of her first five holes.

Explain how you would use addition to find the product of –2 and 5 using the integer tiles and the number line.x

Answer 1

To find the product of -2 and 5 using addition, we can use integer tiles and a number line to visually represent the multiplication. Here's how we can approach this:

### Step 1: Understanding the Product
Multiplying -2 by 5 means we are essentially adding -2 to itself a total of 5 times. In mathematical terms:
\[
-2 \times 5 = -2 + -2 + -2 + -2 + -2
\]

### Step 2: Using Integer Tiles
Imagine we have tiles that represent positive and negative integers:
- A red tile represents -1 (negative).
- A yellow tile represents +1 (positive).

To represent -2, we would use two red tiles (since -2 is equal to -1 + -1).

For the product of -2 and 5, we need to perform the addition of -2 five times:
- Add two red tiles (for the first -2).
- Add two more red tiles (for the second -2).
- Keep adding until you have a total of five sets of two red tiles.

Counting all the red tiles:
- First set: 2 red tiles (representing the first -2)
- Second set: 2 red tiles (representing the second -2)
- Third set: 2 red tiles (representing the third -2)
- Fourth set: 2 red tiles (representing the fourth -2)
- Fifth set: 2 red tiles (representing the fifth -2)

### Total:
We would have a total of 10 red tiles, which represents -10.

### Step 3: Using the Number Line
Using a number line helps to visualize the process as well:
- Start at 0.
- The first step: move 2 units to the left (to -2).
- The second step: move another 2 units to the left (to -4).
- The third step: move another 2 units to the left (to -6).
- The fourth step: move another 2 units to the left (to -8).
- The fifth step: move another 2 units to the left (to -10).

### Result:
After five steps of moving 2 units left, you end up at -10.

Therefore, the product of -2 and 5 is:
\[
-2 \times 5 = -10
\]

### Summary:
Both methods—using integer tiles and the number line—demonstrate that multiplying -2 by 5 results in -10.