The problem asks to calculate the total number of miles Margo hiked over the past two months and to represent the solution using arrays or area models. Let's break it down step by step.

Information from the problem:

• Last month: Margo hiked 12 miles 13 times.
• This month: Margo hiked 14 miles 12 times.

Total number of miles hiked:

1. Last month: $12 \times 13 = 156 \text{ miles}$

2. This month: $14 \times 12 = 168 \text{ miles}$

3. Total miles hiked: $156 + 168 = 324 \text{ miles}$

Array or Area Model:

You can represent these calculations using arrays or area models as follows:

• For 12 miles hiked 13 times, you could create a rectangular area with a length of 12 and a width of 13, representing the total number of miles as the area of this rectangle.
• For 14 miles hiked 12 times, similarly, a rectangle with length 14 and width 12 represents the total number of miles for this month.

These visual models help to understand multiplication as repeated addition or an area calculation.

Would you like further explanation on how to draw these models, or do you have any questions?

Here are 5 related questions for further practice:

1. If Margo hikes 10 miles 15 times next month, how many miles will she hike in total?
2. What is the difference in the number of miles hiked between last month and this month?
3. If Margo increased her daily hike by 2 miles each month, how many miles would she hike after 2 more months?
4. How could you represent this problem using a bar model instead of an area model?
5. If Margo continues hiking at this pace, how many miles will she hike in 5 months?

Tip:

When using arrays or area models, remember that the total area or array of units corresponds directly to the product in multiplication problems. This visual tool can help break down larger problems into simpler parts.