Question

mateo made the model below to represent the number of miles he swims in the pool each week for exercise. use the drop-down menus to explain his model. click the arrows to choose an answer from each menu. the number of times mateo swims each week is represented by the choose... in the model. the distance, in miles, that mateo swims each time he goes to the pool is represented by the choose...

Explanation:

Step1: Analyze the model structure

Looking at the model, there are 4 groups (the number of rectangles or bars) and each group has 2 shaded parts (with the key saying 1 shaded part = 1 mile? Wait, no, the key is a single shaded block = 1 mile? Wait, the model has 4 columns (or groups) of blocks. Each column has some shaded and unshaded. Wait, the first part: "The number of times Mateo swims each week" – that should be the number of groups (columns), so 4. Then "the distance each time" – each group has 2 shaded blocks, and since each shaded block is 1 mile (from the key: \(\boldsymbol{\text{shaded block}} = 1\) mile), so each time he swims 2 miles. Wait, but the question is about the model's representation. Let's re-express:

1. Number of times swimming: the number of columns (or the number of "units" representing times) – here, there are 4 columns, so the number of times is represented by the number of columns (or the number of groups).

1. Distance per time: each column has 2 shaded blocks, and each shaded block is 1 mile, so each time he swims 2 miles, represented by the number of shaded blocks per column.

But since the problem is about the model's elements:

• Number of times: number of columns (4 columns), so the "number of rectangles (columns)" or "number of groups" – in the model, the number of times is represented by the number of columns (4), so the first "Choose..." should be "number of columns (or number of groups)" but in the model, the columns are the times.

• Distance per time: each column has 2 shaded blocks, each shaded block is 1 mile, so the number of shaded blocks per column (2) represents the distance per time.

But since the problem is using the model with columns (each column is a swim session) and shaded blocks (each shaded block is 1 mile). So:

• Number of times: number of columns (4 columns) → so the "number of rectangles (columns)" or "number of groups" in the model.

• Distance per time: number of shaded blocks per column (2 shaded blocks per column) → so the "number of shaded blocks per column" or "number of shaded parts per rectangle".

But to answer the first part: "The number of times Mateo swims each week is represented by the [number of columns (or number of rectangles/groups)] in the model."

Second part: "The distance, in miles, that Mateo swims each time he goes to the pool is represented by the [number of shaded blocks per column] (since each shaded block is 1 mile, so 2 shaded blocks mean 2 miles per time)."

But since the problem is a drop-down, let's assume the options are like "number of columns" (for times) and "number of shaded blocks per column" (for distance per time).

Answer:

For the first drop - down: number of columns (or number of groups/rectangles)
For the second drop - down: number of shaded blocks per column

(Note: Since the exact drop - down options are not fully visible, but based on the model, the number of times is the number of columns (4 columns, so 4 times a week), and distance per time is the number of shaded blocks per column (2 shaded blocks, so 2 miles per swim session, as each shaded block is 1 mile).)