Question

Which area model represents 4×56?
Responses

A rectangle divided into 5 horizontal rows and 5 vertical columns. The top 4 rows of every column are shaded.
Image with alt text: A rectangle divided into 5 horizontal rows and 5 vertical columns. The top 4 rows of every column are shaded.

A rectangle divided into 6 horizontal rows and 5 vertical columns. The top 4 rows of every column are shaded.
Image with alt text: A rectangle divided into 6 horizontal rows and 5 vertical columns. The top 4 rows of every column are shaded.

A rectangle divided into 5 horizontal rows and 4 vertical columns. The top 4 rows of every column are shaded.
Image with alt text: A rectangle divided into 5 horizontal rows and 4 vertical columns. The top 4 rows of every column are shaded.

A rectangle divided into 6 horizontal rows and 4 vertical columns. The top 5 rows of every column are shaded.
Image with alt text: A rectangle divided into 6 horizontal rows and 4 vertical columns. The top 5 rows of every column are shaded.

Answer 1

To represent the multiplication \(4 \times 56\) using an area model, we need a rectangle that correctly breaks down the dimensions into parts that correspond to the factors.

In this case, we can interpret \(56\) as \(50 + 6\) and \(4\) as the other dimension.

We can visualize this using an area model as follows:

- A rectangle that has a height of \(4\) (for the \(4\) in \(4 \times 56\)) and a width that represents \(56\).
- To accurately create an area model for \(56\), you could also break it down further into two rectangles: one rectangle with width \(50\) and the other with width \(6\).

So, the appropriate representation would be:

1. A rectangle divided into \(4\) horizontal rows (to represent the \(4\)) and \(56\) as the total width, appropriately conceptualized.

Out of the options provided:
- The one that corresponds with the multiplication \(4 \times 56\) is likely the second option: **A rectangle divided into 6 horizontal rows and 5 vertical columns. The top 4 rows of every column are shaded.**

This option depicts the concept of \(4\) rows being shaded, which corresponds with the \(4\) from the equation. While \(56\) is not directly depicted, in terms of row divisions, it's the closest match given the configurations available.

However, make sure to consider the specific shading and interpretations, as the dimensions themselves should align logically for \(4\) and \(56\).