Multiplying integers with algebra tiles involves representing the integers with the tiles and then arranging them to form a rectangle or square to visually determine the product.
Here's a breakdown of the process:
Representing Integers with Tiles:
- Positive Integers: Represented by shaded tiles. A positive one (+1) is represented by a small shaded square.
- Negative Integers: Represented by unshaded tiles. A negative one (-1) is represented by a small unshaded square.
The Multiplication Process:
Think of multiplication as creating groups. So, "2 x -5" means "two groups of -5". Also consider the first number of a multiplication problem represents the number of groups being made. The second number represents the number of tiles within each group.
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Set up the problem: Determine what integer is creating groups, and what integers are inside each group.
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Create the groups: Arrange the tiles to represent the groups. For example, to calculate 2 x (-5), you would create two groups that each contains 5 negative tiles.
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Determine the result: Count the total number of tiles, and note the color to determine the sign of the answer. In our example of 2 x (-5), there are a total of ten tiles that are negative. Therefore, 2 x (-5) = -10.
Example:
- 2 x (-5):
- This means "two groups of negative five".
- Represent each group with five unshaded tiles (representing -5).
- You now have two groups of five unshaded tiles.
- Count all the unshaded tiles. There are ten.
- Therefore, 2 x (-5) = -10.
A Note about the "First Factor"
The first factor is not only the number of groups but can also represent "how much to remove of the second number."
Tips:
- Always remember the color convention for positive and negative integers.
- Visualizing the multiplication with the tiles makes it easier to understand the concept, especially for students who are visual learners.
