Suppose that Andrea told you that "Blake and I started out with the same number of marbles, but I gave him one of mine. Now Blake has one more marble than me." Why is Andrea's reasoning incorrect? How can you address her misunderstanding? Choose the answer below that best explains the misunderstanding. A. Andrea meant to say that after giving Blake one of her marbles, she would have one less than Blake. B. Andrea has one less than she started with. Blake has one more than he started with. Therefore, Blake has two more than Andrea. D. Andrea meant to say that she took one of her marbles away and not give it to Blake. Therefore, Blake would only have one more than her. Choose the best way to address the misunderstanding. A. Teach Andrea algebra. B. Use actual marbles with Andrea. C. Draw a picture for Andrea. D. Review the properties of adding and subtracting whole numbers with Andrea. Dill have one more than Andrea. Dirst. Then, Andrea can give him one of hers. Thus, Blake will D.

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UpStudy AI · Accepted Answer

To analyze Andrea's reasoning, let's break down the situation step by step.

1. **Initial Condition**: Andrea and Blake start with the same number of marbles. Let's denote the number of marbles each has as $$ x $$.

2. **Action Taken**: Andrea gives one marble to Blake. After this action:
   - Andrea now has $$ x - 1 $$ marbles.
   - Blake now has $$ x + 1 $$ marbles.

3. **Final Condition**: Andrea claims that now Blake has one more marble than she does. This can be expressed mathematically as:
   $$
   x + 1 = (x - 1) + 1
   $$
   Simplifying the right side gives:
   $$
   x + 1 = x
   $$
   This is incorrect because it implies that $$ 1 = 0 $$, which is not true.

### Addressing the Misunderstanding

Now, let's evaluate the options provided to explain Andrea's misunderstanding:

- **Option A**: "Andrea meant to say that after giving Blake one of her marbles, she would have one less than Blake."  
  This option correctly identifies that after giving away one marble, Andrea should have one less than Blake, which is true.

- **Option B**: "Andrea has one less than she started with. Blake has one more than he started with. Therefore, Blake has two more than Andrea."  
  This option is also correct in its reasoning but does not directly address Andrea's misunderstanding about the relationship between their marbles after the transaction.

- **Option C**: "Andrea meant to say that she took one of her marbles away and not give it to Blake. Therefore, Blake would only have one more than her."  
  This option is incorrect because it misrepresents the action taken (giving a marble, not taking one away).

### Best Way to Address the Misunderstanding

Now, let's evaluate the best way to address Andrea's misunderstanding:

- **Option A**: "Teach Andrea algebra."  
  While this could help in the long run, it may not be the most immediate or effective way to clarify her misunderstanding.

- **Option B**: "Use actual marbles with Andrea."  
  This is a practical approach that allows Andrea to visualize the situation and understand the relationship between the quantities.

- **Option C**: "Draw a picture for Andrea."  
  This could also be effective, as visual aids can help clarify concepts.

- **Option D**: "Review the properties of adding and subtracting whole numbers with Andrea."  
  This is a good option but may not directly address the specific misunderstanding in this context.

### Conclusion

The best explanation for Andrea's misunderstanding is **Option A**: "Andrea meant to say that after giving Blake one of her marbles, she would have one less than Blake."

The best way to address her misunderstanding is **Option B**: "Use actual marbles with Andrea." This hands-on approach will help her see the situation clearly and understand the relationship between her and Blake's marbles after the transaction.
Andrea's reasoning is incorrect because after giving Blake one marble, she should have one less than Blake, not the same number. To address her misunderstanding, using actual marbles with Andrea is the best approach.

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