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.(2 points)
To model the expression −17−(−3) using a two-color counter model, we can use two sets of counters: one set representing -17 and the other set representing -3.
First, we start with 17 counters of one color to represent -17. Then, we take 3 counters of the opposite color to represent -3.
To subtract -3 from -17, we remove 3 counters of the opposite color from the 17 counters. This leaves us with 14 counters of the original color, which represents -14.
Therefore, if we count the final number of counters and it matches Elaine's answer of -14, then her answer is correct. If the number of counters is different, then her answer is incorrect.
To connect the expression −17−(−3) to a two-color counter model, we can represent the numbers using two-color counters.
Step 1: Representing -17
To represent -17 using two-color counters, we need 17 counters of one color (let's say red) and no counters of the other color (let's say blue). So, we place 17 red counters on the table.
Step 2: Representing -(−3)
To represent -(−3), we need to flip the signs of the counters set aside for −3. Since there are no counters set aside for −3, we have no counters to flip.
Step 3: Subtracting
Now, we need to subtract the value of -(−3) from -17. Since we have no counters to subtract, we can conclude that the result is still -17.
Based on the two-color counter model, it confirms that Elaine's answer of -14 is not correct. The model shows that subtracting -(−3) does not change the value of -17, so the correct answer is still -17.