The problem asks to find the total number of miles Margo hiked during the past two months, and suggests drawing arrays or area models to help. Let's break it down mathematically:

• Last month, Margo hiked 12 miles each time for 13 times.
• This month, Margo hiked 14 miles each time for 12 times.

Total miles for last month:

$12 \times 13 = 156 \, \text{miles}$

Total miles for this month:

$14 \times 12 = 168 \, \text{miles}$

Total for both months:

$156 + 168 = 324 \, \text{miles}$

So, Margo hiked a total of 324 miles during the past two months.

Arrays or Area Models Explanation:

• For 12 miles, 13 times: You can visualize a 12 by 13 array (12 rows and 13 columns) representing the total number of miles for last month.
• For 14 miles, 12 times: You can visualize a 14 by 12 array (14 rows and 12 columns) for this month’s hikes.

Would you like a further breakdown or details on how to draw the arrays?

Here are 5 questions that build upon this:

1. How would the result change if Margo hiked 15 miles 10 times next month?
2. Can you create a similar problem but for a different physical activity like swimming?
3. What would be the difference in total miles if Margo had hiked 11 miles each time for 13 times last month?
4. How do area models help visualize multiplication problems like this?
5. Can you explain why multiplying two numbers can be represented as an area of a rectangle?

Tip: Breaking problems into smaller parts often makes complex calculations much easier to manage!