Visual models illustrating the multiplication of 4 × 4,777 using place value decomposition.

We are asked to determine which model represents the multiplication problem:

$$
4 \times 4,777
$$

We are given two models (visual representations using place value blocks), and we need to identify which one correctly represents this multiplication.

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Step 1: Understand what $4 \times 4,777$ means

We're multiplying 4 by the number 4,777. Let's break down 4,777 into its place values:

$$
4,777 = 4,000 + 700 + 70 + 7
$$

Now multiply each part by 4:

- $4 \times 4,000 = 16,000$
- $4 \times 700 = 2,800$
- $4 \times 70 = 280$
- $4 \times 7 = 28$

So:
$$
4 \times 4,777 = 16,000 + 2,800 + 280 + 28 = 19,108
$$

But we’re not being asked for the answer — we’re being asked which model correctly represents the multiplication process using place value blocks.

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Step 2: Analyze the two models

#### Model 1:

- Shows:
- $4 \times 4,000$ → 4 yellow blocks labeled "4,000"
- $4 \times 700$ → 4 teal blocks labeled "700"
- $4 \times 70$ → 4 orange blocks labeled "70"
- $4 \times 7$ → 4 pink blocks labeled "7"

Wait — actually, looking at the image description:

> Model 1 has:
> - 4 × 4,000 → one block of 4,000
> - 4 × 700 → one block of 700
> - 4 × 70 → one block of 70
> - 4 × 7 → one block of 7

But that’s not correct. The model shows one block of each value, but it's being multiplied by 4. So the model should show 4 groups of each component.

Let’s interpret carefully.

Actually, from the layout:

It appears that both models show a single row of blocks representing one copy of the number, with a "4" on the side, suggesting that the entire number is being multiplied by 4.

So:

- In Model 1, the number being multiplied is:
- 4,000 + 700 + 70 + 7 = 4,777
- Then multiplied by 4 → so this model represents $4 \times 4,777$

- In Model 2, the number is:
- 2,000 + 700 + 70 + 7 = 2,777
- Then multiplied by 4 → so this represents $4 \times 2,777$

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Step 3: Compare to the original problem

The question asks: Which model represents $4 \times 4,777$?

Only Model 1 shows the number 4,777 broken into:
- 4,000
- 700
- 70
- 7

Then multiplied by 4.

Model 2 shows 2,000, not 4,000, so it represents $4 \times 2,777$, which is incorrect.

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✔ Final Answer:

Model 1 represents $4 \times 4,777$.

Because it correctly breaks down 4,777 into 4,000 + 700 + 70 + 7 and multiplies each part by 4.

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🟩 Correct Answer: The first model (top one)