Multiplicative Comparisons worksheet with comparison statements, models, and equations.

Let's solve this "Multiplicative Comparisons" worksheet step by step. We are given a table with three columns: Comparison Statement, Model, and Equation. Our goal is to fill in the missing parts based on the information provided.

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🔹 Row 1:

- Comparison Statement: *15 is 3 times bigger than 5*
- Model: (empty)
- Equation: (empty)

#### ✔ Step-by-step:
- "15 is 3 times bigger than 5" means:
$ 5 \times 3 = 15 $
- So, the equation is:
$ 5 \times 3 = 15 $
- For the model, we can draw 3 groups of 5, or one group of 5 and then show it repeated 3 times.

> 🟦 Model: Draw three boxes each labeled 5, or one box with 5 and an arrow pointing to three such boxes.

✔ Answer:
- Model: Three boxes each with “5”
- Equation: $ 5 \times 3 = 15 $

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🔹 Row 2:

- Comparison Statement: (empty)
- Model: One box with “8” above five boxes with “8” → total of 6 boxes of 8
- Equation: (empty)

#### ✔ Step-by-step:
- The model shows 6 groups of 8.
- So, total = $ 6 \times 8 = 48 $
- This means: 48 is 6 times as much as 8, or 8 is 1/6 of 48
- But since the top box has one “8” and the bottom row has five more, it's comparing one group of 8 to six groups of 8.

So the comparison statement could be:
👉 *"48 is 6 times as much as 8"*
or
👉 *"6 times as much as 8 is 48"*

✔ Answer:
- Comparison Statement: *6 times as much as 8 is 48*
- Equation: $ 6 \times 8 = 48 $

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🔹 Row 3:

- Comparison Statement: (empty)
- Model: (empty)
- Equation: $ 6 \times 7 = 42 $

#### ✔ Step-by-step:
- Equation: $ 6 \times 7 = 42 $
- So, 42 is 6 times as much as 7
- Or: 6 times as much as 7 is 42

For the model, we can draw 6 boxes, each labeled 7, or one box of 7 repeated 6 times.

✔ Answer:
- Comparison Statement: *6 times as much as 7 is 42*
- Model: Six boxes each labeled “7”

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🔹 Row 4:

- Comparison Statement: *2 times as much as 12 is 24*
- Model: (empty)
- Equation: (empty)

#### ✔ Step-by-step:
- “2 times as much as 12 is 24” → $ 2 \times 12 = 24 $
- So equation: $ 2 \times 12 = 24 $
- For the model: two groups of 12, or two boxes labeled “12”

✔ Answer:
- Model: Two boxes each labeled “12”
- Equation: $ 2 \times 12 = 24 $

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🔹 Row 5:

- Comparison Statement: (empty)
- Model: One box with “6”, and three more boxes below it — so four boxes of 6
- Equation: (empty)

Wait — actually, the model shows:
- One box with “6” on top
- Below it: three boxes with “6” → total of 4 boxes of 6

But that’s 4 × 6 = 24

But wait — let's check:
The model shows:
```
[6]
[6][6][6]
```
That’s four 6s, so total = $ 4 \times 6 = 24 $

So the equation should be: $ 4 \times 6 = 24 $

But in the next row, the equation is $ 4 \times 7 = 28 $, so this must be a separate row.

Wait — actually, this row has:
- Model: Four boxes of 6 → total 24
- Equation: (missing)

So:
- Total = $ 4 \times 6 = 24 $
- So: 4 times as much as 6 is 24

✔ Answer:
- Comparison Statement: *4 times as much as 6 is 24*
- Equation: $ 4 \times 6 = 24 $

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🔹 Row 6:

- Comparison Statement: (empty)
- Model: (empty)
- Equation: $ 4 \times 7 = 28 $

#### ✔ Step-by-step:
- $ 4 \times 7 = 28 $
- So: 4 times as much as 7 is 28
- Model: four boxes each labeled “7”

✔ Answer:
- Comparison Statement: *4 times as much as 7 is 28*
- Model: Four boxes each labeled “7”

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✔ Final Completed Table:

| Comparison Statement | Model | Equation |
|---------------------------------------------|--------------------------------------------|------------------|
| 15 is 3 times bigger than 5 | Three boxes labeled “5” | $ 5 \times 3 = 15 $ |
| 6 times as much as 8 is 48 | Six boxes labeled “8” | $ 6 \times 8 = 48 $ |
| 6 times as much as 7 is 42 | Six boxes labeled “7” | $ 6 \times 7 = 42 $ |
| 2 times as much as 12 is 24 | Two boxes labeled “12” | $ 2 \times 12 = 24 $ |
| 4 times as much as 6 is 24 | Four boxes labeled “6” | $ 4 \times 6 = 24 $ |
| 4 times as much as 7 is 28 | Four boxes labeled “7” | $ 4 \times 7 = 28 $ |

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📌 Summary of Key Ideas:

- Multiplicative comparisons use multiplication to compare quantities.
- The phrase “X times as much as Y” means $ X \times Y $
- Models help visualize groups (e.g., 4 groups of 6).
- Always match the comparison statement, visual model, and equation.

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