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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.

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To find the product of -2 and 5 using addition with integer tiles and a number line, we can follow these steps:

Integer Tiles Method:

  1. Understanding Tiles: In this method, we represent integers using tiles. Use red tiles for positive numbers (to represent +1) and yellow tiles for negative numbers (to represent -1). For -2, we would have 2 yellow tiles (representing -1 each).

  2. Grouping: To find the product -2 x 5, we are essentially looking to add -2 a total of 5 times. So, we can represent this as: \[ -2 + (-2) + (-2) + (-2) + (-2) \]

    You would set up 5 groups of 2 yellow tiles. Each group represents the score of -2.

  3. Adding the Tiles:

    • In the first step, you take the first group of -2 (which is 2 yellow tiles).
    • You then keep adding another group of -2 (another 2 yellow tiles) to your total.
    • Repeat this process until you've added all five groups together:
      • 1st addition: 2 yellow tiles = -2
      • 2nd addition: 2 yellow tiles + 2 yellow tiles = 4 yellow tiles = -4
      • 3rd addition: 4 yellow tiles + 2 yellow tiles = 6 yellow tiles = -6
      • 4th addition: 6 yellow tiles + 2 yellow tiles = 8 yellow tiles = -8
      • 5th addition: 8 yellow tiles + 2 yellow tiles = 10 yellow tiles = -10

  4. Final Result: After combining all five groups of -2, you end up with 10 yellow tiles, which represents -10. Thus, -2 x 5 = -10.

Number Line Method:

  1. Starting Point: Draw a number line and mark the integers on the line. Starting from 0, you would mark the positions for -1, -2, -3, and so forth.

  2. Counting Backwards: Since you're multiplying by a negative number, you will start at 0 and move to the left (backwards) because all steps represent negative values.

    • From 0, you would move left 2 units (for the first -2) to reach -2.
    • Repeat this step a total of 5 times:
      • Move left from 0 to -2 (1st time)
      • Move left again from -2 to -4 (2nd time)
      • Move left again from -4 to -6 (3rd time)
      • Move left again from -6 to -8 (4th time)
      • Move left one more time from -8 to -10 (5th time)

  3. Final Result: After moving left 2 units five times, you land at -10 on the number line. Therefore, the product of -2 and 5 is -10.

In summary, both the integer tiles method and the number line method demonstrate that multiplying -2 by 5 results in -10.