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7-87.

Draw the table below on your paper and look carefully at the algebra tiles to fill in each of the steps. Use your own numbers in the trials, again considering fractions, decimals, and zero.

Steps

Trial 1

Trial 2

Trial 3

Algebra Tile Picture

1. Pick a number.

1 x tile.

2. Add ____.

x-tile plus 3 unit tiles

3. Multiply by ____.

3 x-tiles + 9 unit tiles

4. Subtract ____.

3 x-tiles + 9 unit tiles

5. Divide by ____.

x-tile plus 2 unit tiles

6. Subtract the original number.

two unit tiles

Notice how the tiles increase or decrease after each step.

By how much did the algebra tiles increase in Step 2? The third row of the table, first column, now says: 2. Add 3

By how much was that number multiplied in Step 3?
Now complete the rest of the steps using this method. The fourth row of the table, first column, now says: 3. Multiply by, 3.

Substitute in your own numbers for each trial. The fifth row of the table, first column, now says: 4. Subtract, 3. The sixth row of the table, first column, now says: 5. Divide by, 3.

The second column of the table, now says: Trial 1, 3, 6, 18, 15, 5, 2.

 The third row of the table, first column, now says: 2. Add 3

 The fourth row of the table, first column, now says: 3. Multiply by, 3.

 The fifth row of the table, first column, now says: 4. Subtract, 3. The sixth row of the table, first column, now says: 5. Divide by, 3.

 The second column of the table, now says: Trial 1, 3, 6, 18, 15, 5, 2.