Free 3rd grade math worksheet templates to customize - Free Printable

Let's solve each equation and identify the property of operations used for each one. Then, we'll determine the correct color based on the key.

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🔹 Color Key:

- Blue: Associative Property
- Pink: Commutative Property
- Green: Identity Property
- Purple: Zero Property
- Orange: Distributive Property

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We’ll go through each scoop (equation) one by one.

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## 🍦 Ice Cream Cone 1 (Left)

1. 6 × 7 =

- Answer: 42
- Property Used? This is just multiplication — no property being applied directly here.
- But notice: This is a basic fact, not involving any special property like commutative or associative in the solving process.
- However, since it's a single multiplication, no specific property is needed to solve it.
- Wait — let’s look at the next ones more carefully. Actually, we are supposed to recognize which property was used to simplify or solve.

But let’s reevaluate: The problem says "solve each equation" and then use the property you used to solve it.

So if an equation involves a property (like zero property, identity, etc.), that’s what we use.

Let’s analyze each one.

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1. 6 × 7 =

- Solve: 6 × 7 = 42
- No special property involved — just basic multiplication.
- But this might be intended to test recognition of commutative property because 6×7 = 7×6, but it’s not used here.
- Since it's just solved directly, maybe no property applies?

Wait — perhaps the commutative property is implied? But it's not used in solving.

Actually, this is likely meant to be solved without relying on a property, so maybe it's not colored? But every scoop has an equation.

Alternatively, maybe the property is inferred from the structure.

Let’s look at the others.

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2. 3 × 2 × 5 =

- Solve: 3 × 2 = 6; 6 × 5 = 30 → 30
- Or group as (3×2)×5 = 6×5 = 30
- Could also do 3×(2×5) = 3×10 = 30 → same answer
- So grouping changes — this uses the Associative Property of multiplication.

✔ Property: Associative Property → Blue

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3. 18 × 4 =

- Solve: 18 × 4 = 72
- No obvious property used. Just multiplication.
- But wait — could it be distributive? Like 18×4 = (10+8)×4 = 10×4 + 8×4 = 40 + 32 = 72
- That would be Distributive Property!

Yes! Even though not shown, the distributive property can be used to break down 18×4.

So:

✔ Property: Distributive Property → Orange

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Now back to 6 × 7 = — is there a property used?

Not really — unless they expect us to think of commutative (6×7 = 7×6), but that’s not helping in solving.

So maybe none? But all scoops must be colored.

Wait — perhaps 6 × 7 is just a basic fact and doesn’t involve a property.

But let’s look at the middle cone.

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## 🍦 Middle Cone

1. 3 × 0 =

- Solve: 3 × 0 = 0
- Any number times zero is zero → Zero Property of Multiplication

✔ Property: Zero Property → Purple

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2. 1 × 8 =

- Solve: 1 × 8 = 8
- Multiplying by 1 keeps the number the same → Identity Property

✔ Property: Identity Property → Green

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3. 0 ÷ 5 =

- Solve: 0 ÷ 5 = 0
- Zero divided by any number is zero → Zero Property of Division

✔ Property: Zero Property → Purple

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## 🍦 Right Cone

1. 7 ÷ 1 =

- Solve: 7 ÷ 1 = 7
- Dividing by 1 gives the same number → Identity Property

✔ Property: Identity Property → Green

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2. 6 × 2 × 4 =

- Solve: 6×2=12, 12×4=48
- Or (6×2)×4 = 12×4 = 48
- Or 6×(2×4)=6×8=48
- Grouping changed → Associative Property

✔ Property: Associative Property → Blue

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3. 5 × 3 =

- Solve: 5 × 3 = 15
- Could also write 3 × 5 = 15 → order changed → Commutative Property

✔ Property: Commutative Property → Pink

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Now, let’s go back to the first cone:

1. 6 × 7 =

- 6 × 7 = 42
- Is there a property used? Not really. But maybe commutative? Because 6×7 = 7×6, but again, not used in solving.

But notice: There’s no indication of grouping, zero, or identity.

However, perhaps it's meant to be solved using commutative property? Unlikely.

Alternatively, maybe the first one (6×7) is just a basic fact and doesn't use a property.

But every scoop must be colored.

Wait — let’s check if any of the equations require a property.

But actually, the purpose is to recognize which property is demonstrated in the equation.

Let’s reconsider:

Re-evaluating: What property does each equation demonstrate?

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#### ✔ 6 × 7 =
- No property is required. But perhaps the commutative property is implied?
- But commutative is about order: a×b = b×a
- Here, it's just written as 6×7, not showing rearrangement.

So no clear property.

But wait — maybe all equations are designed to show a property, even if not explicitly stated.

Alternatively, perhaps 6×7 is just a simple multiplication, and the property isn't needed, but we're supposed to recognize that no property is used? But that contradicts the instructions.

Wait — perhaps I missed something.

Let’s look at the third cone:

- 7 ÷ 1 = → Identity Property (green)
- 6 × 2 × 4 = → Associative (blue)
- 5 × 3 = → Commutative (pink)

So 5×3 shows commutative? But 5×3 is just multiplication.

But if we think about commutative property, it says 5×3 = 3×5.

So if someone uses that idea, it's commutative.

Similarly, 6×7 could be thought of as 7×6 → commutative.

But unless the problem shows both sides, it's ambiguous.

But perhaps the intent is that:

- 6 × 7 is just a basic fact → no property?
- But that can't be.

Wait — perhaps each equation is testing a different property, and 6×7 is meant to be solved using commutative? But how?

Maybe the coloring is based on the operation type, not the solution method.

But let’s list all equations and assign properties clearly.

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Final Analysis:

| Equation | Solution | Property | Color |
|--------|---------|----------|-------|
| 6 × 7 = | 42 | ??? | ? |
| 3 × 2 × 5 = | 30 | Associative (grouping) | Blue |
| 18 × 4 = | 72 | Distributive (18×4 = (10+8)×4) | Orange |
| 3 × 0 = | 0 | Zero Property | Purple |
| 1 × 8 = | 8 | Identity Property | Green |
| 0 ÷ 5 = | 0 | Zero Property | Purple |
| 7 ÷ 1 = | 7 | Identity Property | Green |
| 6 × 2 × 4 = | 48 | Associative | Blue |
| 5 × 3 = | 15 | Commutative (5×3 = 3×5) | Pink |

Now only 6 × 7 = is missing.

But 6 × 7 = 42 — is there a property?

Wait — maybe it's commutative? But not shown.

Alternatively, perhaps it's just a basic multiplication, and no property is used, but that can't be.

Wait — maybe 6 × 7 is meant to be solved using commutative property (i.e., thinking of 7×6), so it's pink.

Similarly, 5×3 is pink because 5×3 = 3×5.

So 6×7 could be pink too — commutative property.

But that seems weak.

Alternatively, is there a better fit?

Wait — what about distributive?

Can we use distributive for 6×7?

6×7 = 6×(5+2) = 6×5 + 6×2 = 30 + 12 = 42 → Yes!

So distributive property can be used.

So 6×7 can be solved using distributive property → Orange

Similarly, 18×4 is also solved with distributive.

So both 6×7 and 18×4 can use distributive.

But 18×4 is already assigned to orange.

So maybe both use distributive?

But that’s okay — multiple equations can use the same property.

So:

- 6 × 7 = → Use distributive: 6×(5+2) = 6×5 + 6×2 = 30+12=42 → Distributive Property → Orange
- 18 × 4 = → (10+8)×4 = 10×4 + 8×4 = 40+32=72 → Distributive Property → Orange

Yes!

And 5×3 → commutative → pink

6×2×4 → associative → blue

3×2×5 → associative → blue

3×0 → zero → purple

1×8 → identity → green

0÷5 → zero → purple

7÷1 → identity → green

So now we have:

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✔ Final Assignments:

#### Left Cone:
1. 6 × 7 = → Distributive Property → Orange
2. 3 × 2 × 5 = → Associative Property → Blue
3. 18 × 4 = → Distributive Property → Orange

#### Middle Cone:
1. 3 × 0 = → Zero Property → Purple
2. 1 × 8 = → Identity Property → Green
3. 0 ÷ 5 = → Zero Property → Purple

#### Right Cone:
1. 7 ÷ 1 = → Identity Property → Green
2. 6 × 2 × 4 = → Associative Property → Blue
3. 5 × 3 = → Commutative Property → Pink

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✔ Summary of Colors:

| Scoop | Equation | Property | Color |
|-------|---------|----------|-------|
| 1 | 6 × 7 = | Distributive | Orange |
| 2 | 3 × 2 × 5 = | Associative | Blue |
| 3 | 18 × 4 = | Distributive | Orange |
| 4 | 3 × 0 = | Zero | Purple |
| 5 | 1 × 8 = | Identity | Green |
| 6 | 0 ÷ 5 = | Zero | Purple |
| 7 | 7 ÷ 1 = | Identity | Green |
| 8 | 6 × 2 × 4 = | Associative | Blue |
| 9 | 5 × 3 = | Commutative | Pink |

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🎨 Coloring Instructions:

- Orange: 6×7, 18×4
- Blue: 3×2×5, 6×2×4
- Purple: 3×0, 0÷5
- Green: 1×8, 7÷1
- Pink: 5×3

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✔ Answers:

#### Left Cone:
- Top: 6 × 7 = 42 → Orange
- Middle: 3 × 2 × 5 = 30 → Blue
- Bottom: 18 × 4 = 72 → Orange

#### Middle Cone:
- Top: 3 × 0 = 0 → Purple
- Middle: 1 × 8 = 8 → Green
- Bottom: 0 ÷ 5 = 0 → Purple

#### Right Cone:
- Top: 7 ÷ 1 = 7 → Green
- Middle: 6 × 2 × 4 = 48 → Blue
- Bottom: 5 × 3 = 15 → Pink

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📝 Final Answer:

> Color each scoop according to the property used:
>
> - Orange: 6×7, 18×4 (Distributive)
> - Blue: 3×2×5, 6×2×4 (Associative)
> - Purple: 3×0, 0÷5 (Zero Property)
> - Green: 1×8, 7÷1 (Identity)
> - Pink: 5×3 (Commutative)

You can now color the ice cream scoops accordingly! 🍦🎉