MathSphere Year 3 Maths Worksheets - Free Printable

Let's solve the problem step by step.

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🔍 Understanding the Task

We are given three dice:
- Blue die
- Red die
- Black die

Each die shows a number of dots (like a standard die), and we need to find even totals when rolling all three dice.

The goal is to:
> Find combinations of numbers from the three dice such that their sum is even, and record them in the table.

But here’s an important point: The image doesn't show actual rolled values — it only shows the dice with some dots. Let's interpret what’s shown:

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🎲 Interpreting the Dice Faces

Looking at the dice in the image:

1. Blue Die: Shows 5 dots (top face) → So, this die shows 5
2. Red Die: Shows 4 dots → So, this die shows 4
3. Black Die: Shows 6 dots → So, this die shows 6

So, we’re not rolling randomly — we're using these specific values:
- Blue = 5
- Red = 4
- Black = 6

Wait! But the question says:
> "What even totals can you score when you roll three dice?"

This implies we should consider all possible outcomes when rolling three dice, but the image only shows one configuration.

However, since the worksheet asks us to “record your answers below” in a table with seven rows, and gives fixed labels for each die (Blue, Red, Black), it seems like we’re supposed to use the values shown on the dice as starting points or examples.

But let’s think carefully.

Actually, the dice are labeled Blue, Red, Black, and each has a fixed number of dots shown. That suggests that these are specific dice showing specific values, so perhaps we are meant to use these exact values?

Wait — but if Blue=5, Red=4, Black=6, then the total is:

> 5 + 4 + 6 = 15 → which is odd

But the task is asking: *What even totals can you score?* — implying we should find combinations that give even totals.

So perhaps the dice are just placeholders, and we are supposed to imagine rolling any numbers on the dice (standard 1–6), and list combinations where the sum is even.

But the table has columns: Blue, Red, Black, Total is even — suggesting we fill in numbers for each die.

So likely, the intention is:

> Use standard six-sided dice (values 1–6). Roll three dice (blue, red, black), and find different combinations where the sum is even.

And record several such combinations.

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✔ Mathematical Insight: When is the sum of three numbers even?

The sum of three numbers is even if:
- All three are even, or
- One is even and two are odd.

Because:
- Even + Even + Even = Even
- Odd + Odd + Even = Even
- Other combinations give odd sums.

So, we need combinations where:
- Either all three dice show even numbers (2, 4, 6)
- Or exactly one die shows even, and two show odd (1, 3, 5)

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🧮 Step-by-step Plan

We’ll generate some valid combinations where the sum is even.

Let’s pick a few examples.

#### Example 1:
- Blue: 2 (even)
- Red: 3 (odd)
- Black: 5 (odd)
→ Sum = 2 + 3 + 5 = 10 → even ✔

#### Example 2:
- Blue: 4 (even)
- Red: 6 (even)
- Black: 2 (even)
→ Sum = 4 + 6 + 2 = 12 → even ✔

#### Example 3:
- Blue: 1 (odd)
- Red: 1 (odd)
- Black: 2 (even)
→ Sum = 1 + 1 + 2 = 4 → even ✔

#### Example 4:
- Blue: 3 (odd)
- Red: 5 (odd)
- Black: 4 (even)
→ Sum = 3 + 5 + 4 = 12 → even ✔

#### Example 5:
- Blue: 6 (even)
- Red: 1 (odd)
- Black: 3 (odd)
→ Sum = 6 + 1 + 3 = 10 → even ✔

#### Example 6:
- Blue: 2 (even)
- Red: 2 (even)
- Black: 4 (even)
→ Sum = 2 + 2 + 4 = 8 → even ✔

#### Example 7:
- Blue: 5 (odd)
- Red: 3 (odd)
- Black: 6 (even)
→ Sum = 5 + 3 + 6 = 14 → even ✔

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✔ Final Answer: Fill in the Table

| Blue | Red | Black | Total is even |
|------|-----|-------|----------------|
| 2 | 3 | 5 | 10 |
| 4 | 6 | 2 | 12 |
| 1 | 1 | 2 | 4 |
| 3 | 5 | 4 | 12 |
| 6 | 1 | 3 | 10 |
| 2 | 2 | 4 | 8 |
| 5 | 3 | 6 | 14 |

> ✔ All sums are even.

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💡 Additional Notes

- The minimum possible even sum: 1+1+2 = 4
- The maximum possible even sum: 6+6+6 = 18
- Possible even totals: 4, 6, 8, 10, 12, 14, 16, 18

So, you could also explore: Which even totals between 4 and 18 are possible?
Answer: All of them are possible.

But the worksheet just asks for examples of even totals.

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✔ Conclusion

You can score many even totals when rolling three dice. Some examples include:

- 4, 6, 8, 10, 12, 14, 16, 18

And here are seven combinations that give even totals:

| Blue | Red | Black | Total |
|------|-----|-------|--------|
| 2 | 3 | 5 | 10 |
| 4 | 6 | 2 | 12 |
| 1 | 1 | 2 | 4 |
| 3 | 5 | 4 | 12 |
| 6 | 1 | 3 | 10 |
| 2 | 2 | 4 | 8 |
| 5 | 3 | 6 | 14 |

✔ These are all valid answers to the problem.