Elaine used the subtraction algorithm to subtract −17−(−3). She got the answer −14, but she does not feel confident that she is correct. Connect the expression −17−(−3) to a two-color counter model. Explain how the two-color counter model can be used to confirm whether Elaine’s answer is correct.
In a two-color counter model, each counter can represent a positive or negative value. The two colors typically used are red for negative values and yellow for positive values.
To model the expression −17−(−3), we start with 17 red counters to represent -17. Then, we remove 3 red counters to represent -(−3).
If Elaine's answer of -14 is correct, the final result should be 14 red counters (representing -14) on the table.
By physically representing the expression using two-color counters, Elaine can count the number of red counters left on the table. If there are indeed 14 red counters remaining, it confirms that her answer of -14 is correct. However, if she counts a different number, she can re-evaluate her subtraction algorithm or double-check her calculations to find any mistakes.
To connect the expression −17−(−3) to a two-color counter model, we can think of the negative numbers as counters of one color, and the positive numbers as counters of another color.
First, we place 17 counters of one color, representing the absolute value of −17. Then, we remove 3 counters of the other color, representing the absolute value of −3.
If Elaine's answer of −14 is correct, we should have 14 counters remaining, and they should all be of the first color (since it is a negative number). This would confirm that her answer is correct.