Let's work through each of the questions from the image you provided:

8. 487 + 104 + 13

To group these addends, you can pair the numbers to make the addition easier. One possible way: $(487 + 13) + 104 = 500 + 104 = 604$

9. 178 + 234 + 522

You can group these addends as follows: $(178 + 522) + 234 = 700 + 234 = 934$

10. 239 + 124 + 346

To make it easier, you can group: $(239 + 346) + 124 = 585 + 124 = 709$

11. Rod's grocery bills: $38 + $44 + $52

Rod adds these to get: $(38 + 44) + 52 = 82 + 52 = 134$ Another way Rod can add these bills to get the same total is: $38 + (44 + 52) = 38 + 96 = 134$ This shows that the grouping does not affect the final result due to the associative property of addition.

12. Rope lengths: 34 feet and 52 feet

Jimmy uses $34 + 52$ and Camille uses $52 + 34$. Both methods will give the same total, which is: $34 + 52 = 52 + 34 = 86 \, \text{feet}$ This works because of the commutative property of addition, which means the order in which you add numbers doesn't change the result.

13. Tina's flight costs: 205 + 413 + 147

To rearrange the addends for easier addition, group: $(205 + 147) + 413 = 352 + 413 = 765$ This simplifies the addition by pairing numbers that sum up to an easier value.

Would you like more details on any of the explanations above? Here are five related questions to expand on these topics:

1. What is the associative property of addition, and how does it help in rearranging addends?
2. Why does the commutative property allow numbers to be added in any order?
3. Can you think of another way to group the numbers in problem 8?
4. What is the importance of grouping numbers in larger addition problems?
5. Can grouping addends be useful for subtraction as well?

Tip: When adding multiple numbers, try to group numbers that round easily (like multiples of 10 or 100) for faster mental calculations!