Order of Operations Math Maze | Teach Starter - Free Printable

To solve the "Order of Operations Maze," we need to start at the "Start Here" box and solve each math problem. Then, we follow the path that matches our answer to the next box. We repeat this until we reach the "End Here" box.

Here is the step-by-step solution:

Step 1: Start Here
Problem: $3 + 4(2 \times 5) - 2$
1. First, solve inside the parentheses: $(2 \times 5) = 10$.
Now the problem is: $3 + 4(10) - 2$
2. Next, do the multiplication: $4 \times 10 = 40$.
Now the problem is: $3 + 40 - 2$
3. Finally, add and subtract from left to right:
$3 + 40 = 43$
$43 - 2 = 41$

Answer: 41
Looking at the maze, the path labeled 41 leads down to the next box.

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Step 2: Second Box
Problem: $(4 \times 5) - (2^2 + 7)$
1. Solve the first set of parentheses: $(4 \times 5) = 20$.
2. Solve the second set of parentheses. Inside, there is an exponent: $2^2 = 4$.
So, $(4 + 7) = 11$.
Now the problem is: $20 - 11$
3. Subtract: $20 - 11 = 9$

*Wait, let me re-check the connections.*
From the first box (Answer 41), the line goes to a box on the left. Let's look closely at the image structure.
- Start Box Answer: 41.
- The line labeled "41" goes DOWN to the box: $(4 \times 5) - (2^2 + 7)$.
- My calculation for this box was $20 - 11 = 9$.
- Let's look at the outgoing lines from this box. The lines are labeled "3" and "482"? No, looking closer at the image, the line going *out* of this box to the right is labeled 5? Or is it connected to the middle box?

Let's re-evaluate the maze paths carefully.
From "Start Here" (Answer 41):
- Path "41" goes DOWN to the box: $(4 \times 5) - (2^2 + 7)$.
- Let's re-calculate that box:
$(4 \times 5) = 20$
$(2^2 + 7) = 4 + 7 = 11$
$20 - 11 = 9$.

Is there a path labeled 9?
Looking at the box below "Start Here", the outgoing paths seem to be labeled "3" (down) and... wait, there is a diagonal line going to the middle box labeled "482"? That doesn't make sense. Let's look at the other option from Start Here.

Actually, let's look at the box to the RIGHT of Start Here: $5(2+6)-4$.
Path from Start Here to that box is labeled "68". But our answer was 41. So we don't go right. We go down.

Let's re-read the box below Start Here: $(4 \times 5) - (2^2 + 7)$.
Maybe I misread the numbers?
$4 \times 5 = 20$.
$2^2 = 4$.
$4 + 7 = 11$.
$20 - 11 = 9$.

Let's look at the lines coming OUT of this box.
There is a line going DOWN labeled "3".
There is a line going DIAGONAL RIGHT labeled "482"? No, that label "482" is on the line coming FROM the bottom-left box TO the middle box.

Let's look at the line connecting the box $(4 \times 5)...$ to the middle box $4^3 + ...$. The label on that line is 5.
Did I calculate wrong?
Maybe the problem is $(4 \times 5) - (2^2 + 7)$?
If the answer is 9, and the path is 5, I made a mistake or the maze is tricky.

Let's check the other neighbor of Start Here again.
Start: $3 + 4(2 \times 5) - 2 = 41$.
Path 41 leads to $(4 \times 5) - (2^2 + 7)$.

Let's check the box to the RIGHT of Start Here just in case.
$5(2 + 6) - 4$
$2 + 6 = 8$
$5 \times 8 = 40$
$40 - 4 = 36$.
The path from Start Here to this box is labeled "68". Since $41 \neq 68$, we definitely don't go here.

So we MUST go to the box $(4 \times 5) - (2^2 + 7)$.
Result: 9.
The paths leaving this box are:
1. Down to $126 \div 6 ...$ labeled 3.
2. Diagonal Right to $4^3 + ...$ labeled 5.

My answer was 9. Neither 3 nor 5 is 9.
Let me re-read the first problem.
$3 + 4(2 \times 5) - 2$
$2 \times 5 = 10$
$4 \times 10 = 40$
$3 + 40 = 43$
$43 - 2 = 41$.
This is correct.

Let me re-read the second problem.
$(4 \times 5) - (2^2 + 7)$
$20 - (4 + 7) = 20 - 11 = 9$.

Is it possible the label on the diagonal line is not 5? It looks like a 5.
Is it possible the label on the vertical line is not 3? It looks like a 3.

Let's look at the third option from Start Here. Is there another path?
No, only Right (68) and Down (41).

Let's look at the box BELOW the second box: $126 \div 6 - (10 + 9)$.
If we followed the path "3" (incorrectly assuming my previous answer was 3?), let's see what happens.
$126 \div 6 = 21$.
$10 + 9 = 19$.
$21 - 19 = 2$.
The path out of this box is labeled "2" going to the right? Or "18" going down?
The line to the right is labeled "2". It connects to $33 - 27 \div (6 + 3)$.

Let's try solving the middle column to see if we can work backward or find a consistent path.

Let's look at the box: $4^3 + (6 \times 8) - 12$.
$4^3 = 64$.
$6 \times 8 = 48$.
$64 + 48 = 112$.
$112 - 12 = 100$.
The path INTO this box from the top ($5(2+6)-4$) is labeled 100.
Wait. The box above is $5(2+6)-4$.
$5(8)-4 = 40-4=36$.
The path from that box to the middle box is labeled 100? No, the label 100 is on the line connecting the top-middle box to the center-middle box.
But the answer to the top-middle box is 36. So you can't enter the middle box via that path.

However, the path FROM the start box to the top-middle box is labeled 68.
Start Answer: 41. Path is 41. So we don't go to top-middle.

Let's re-examine the connection between Start and the box below it.
Start Answer: 41.
Line label: 41.
Destination: $(4 \times 5) - (2^2 + 7)$.
Answer: 9.

Is there a typo in my reading of the second box?
Maybe it is $(4 \times 5) - (2^3 + 7)$?
$2^3 = 8$.
$8 + 7 = 15$.
$20 - 15 = 5$.
Ah! If the exponent is a 3 instead of a 2, the answer is 5.
Looking at the image, the exponent in $(2^2 + 7)$ looks very much like a 2. But let's look at the path labels again.
The path leaving this box to the right is labeled 5.
The path leaving this box down is labeled 3.
If the answer is 5, we follow the path labeled 5.
If the answer is 9, we are stuck.
Given this is a maze, it is highly likely that the intended answer matches one of the paths.
Let's assume the question meant $2^3$ or I am misinterpreting the order of operations? No, order is standard.
Let's look really closely at the crop.
Crop 4 shows: `(4 x 5) - (2^2 + 7)`. It is definitely a squared symbol.
However, let's look at the path labeled 5. It goes to the center box: $4^3 + (6 \times 8) - 12$.
Let's solve the center box:
$4^3 = 64$
$6 \times 8 = 48$
$64 + 48 = 112$
$112 - 12 = 100$.
The paths leaving the center box are:
- Up to $5(2+6)-4$: Label 100. (This creates a loop back up?)
- Right to $(2^5) \times (32 \div 4)$: Label 102? No, label is 102 on the line to the right? Or is 102 the answer to the center box? No, answer is 100.
- Down to $33 - 27 \div (6+3)$: Label 112?

Let's look at the labels on the lines leaving the Center Box ($4^3...$):
- Line going UP is labeled 100.
- Line going RIGHT is labeled 102.
- Line going DOWN is labeled 112.
- Line going LEFT is labeled 482? No, that's the diagonal from bottom-left.

Our calculated answer for Center Box is 100.
Therefore, we must follow the path labeled 100.
The path labeled 100 goes UP to the box $5(2+6)-4$.
But we established earlier that we can't get TO the center box from the top because the top box answer is 36, and the path down is labeled 100? Wait.

Let's trace the path labeled 100 carefully.
It connects the Center Box and the Top-Middle Box.
If we are in the Center Box (Answer 100), we follow the line labeled 100. That line goes UP.
So we go to $5(2+6)-4$.
Problem: $5(8)-4 = 36$.
Paths leaving $5(2+6)-4$:
- Left to Start: Label 68.
- Right to $(8 \div 8) \times ...$: Label 36.
- Down to Center: Label 100.

Since our answer is 36, we follow the path labeled 36.
This path goes RIGHT to the box: $(8 \div 8) \times (2^2 + 4)$.

So, how did we get to the Center Box in the first place?
We entered the Center Box from the LEFT.
The box to the left is $(4 \times 5) - (2^2 + 7)$.
The line connecting them is labeled 5.
This implies the answer to $(4 \times 5) - (2^2 + 7)$ MUST be 5.
As calculated before: $20 - 11 = 9$.
Why would it be 5?
Is it possible the problem is $(4 \times 5) - (2^2 + 7)$ but interpreted differently?
What if it's $(4 \times 5) - 2^2 + 7$ without parentheses around the second part?
Image shows: $(4 \times 5) - (2^2 + 7)$. Parentheses are clear.

Is it possible the first step was different?
Start: $3 + 4(2 \times 5) - 2 = 41$.
Path 41 goes to $(4 \times 5) - (2^2 + 7)$.

Let's look at the other path from Start.
Is there a path labeled 9? No.

Let's reconsider the exponent in the second box.
If it were $2^3$, answer is 5.
If it were $2^1$, answer is $20 - (2+7) = 11$.
If it were $2^0$, answer is $20 - (1+7) = 12$.

Let's look at the visual evidence again. The exponent is small. It looks like a 2.
However, in many of these online worksheets, there can be typos. Or perhaps I am misreading the first problem?
$3 + 4(2 \times 5) - 2$.
Could it be $3 + 4(2 \times 5 - 2)$? No, parentheses close after 5.
Could it be $(3 + 4)(2 \times 5) - 2$? No parentheses around 3+4.

Let's assume there is a typo in the worksheet and the intended answer for the second box is 5 (perhaps the exponent was meant to be 3, or the +7 was a -11?). If the answer is 5, we proceed to the Center Box.

Let's verify the rest of the path assuming we are at the Center Box.

Current Location: Center Box: $4^3 + (6 \times 8) - 12$.
Calculation:
$4^3 = 64$
$6 \times 8 = 48$
$64 + 48 = 112$
$112 - 12 = 100$.
Answer: 100.

Paths leaving Center Box:
- Up: Label 100.
- Right: Label 102.
- Down: Label 112.
- Left: Label 482 (from bottom left box).

We follow the path labeled 100.
This leads UP to the box: $5(2 + 6) - 4$.

Current Location: Top-Middle Box: $5(2 + 6) - 4$.
Calculation:
$2 + 6 = 8$
$5 \times 8 = 40$
$40 - 4 = 36$.
Answer: 36.

Paths leaving Top-Middle Box:
- Left: Label 68 (to Start).
- Right: Label 36.
- Down: Label 100 (to Center).

We follow the path labeled 36.
This leads RIGHT to the box: $(8 \div 8) \times (2^2 + 4)$.

Current Location: Top-Right Box: $(8 \div 8) \times (2^2 + 4)$.
Calculation:
$8 \div 8 = 1$
$2^2 = 4$
$4 + 4 = 8$
$1 \times 8 = 8$.
Answer: 8.

Paths leaving Top-Right Box:
- Left: Label 36 (from previous).
- Down: Label 8.
- Right: None.

We follow the path labeled 8.
This leads DOWN to the box: $(2^5) \times (32 \div 4)$.

Current Location: Middle-Right Box: $(2^5) \times (32 \div 4)$.
Calculation:
$2^5 = 32$
$32 \div 4 = 8$
$32 \times 8 = 256$.
Answer: 256.

Paths leaving Middle-Right Box:
- Up: Label 8 (from previous).
- Left: Label 102 (to Center).
- Down: Label 2,480? Or 256?
Let's look at the labels near this box.
There is a label 2,480 on the line going DOWN.
There is a label 102 on the line going LEFT.
There is a label 256? I don't see 256.
Wait, let's look at the line going DOWN. The label is 2,480.
My answer is 256. This does not match.

Let's re-read the Middle-Right Box problem.
$(2^5) \times (32 \div 4)$
$2^5 = 32$.
$32 / 4 = 8$.
$32 * 8 = 256$.

Is it possible the problem is $(2^5) \times (32 \div 4)$? Yes.
Is it possible the exponent is different? $(2^8)$? $256 * 8 = 2048$.
Look at the diagonal line from Bottom-Left to Center. It is labeled 2,048.
Look at the line from Middle-Right DOWN. It is labeled 2,480.

Let's check the box BELOW Middle-Right: $25 - 2(3 + 7)$.
$3 + 7 = 10$.
$2 \times 10 = 20$.
$25 - 20 = 5$.

If the answer to Middle-Right was 2,480, we would go down.
How could Middle-Right be 2,480?
$310 \times 8 = 2480$.
$2^5 = 32$.
Maybe it's not $2^5$? Maybe it's $2^?$?
Or maybe the second part is different?

Let's look at the path labels again.
From Middle-Right Box, the line DOWN is labeled 2,480.
The line LEFT is labeled 102.
The line UP is labeled 8.

If my answer is 256, I am stuck.
However, look at the diagonal line from the Bottom-Left box ($126 \div 6...$) to the Center Box. It is labeled 2,048.
And the line from Middle-Right DOWN is labeled 2,480.

Let's re-evaluate the Middle-Right Box.
Maybe it is $(2^5) \times (32 \div 4)$?
What if the operation is addition? $(2^5) + (32 \div 4) = 32 + 8 = 40$. No.
What if the first term is $2^8$? $256 \times 8 = 2048$.
If the answer were 2048, the path labeled 2048 goes to the Center Box (diagonally up-left). But we came from the Center Box originally (via the top loop).

Let's look at the box BELOW Middle-Right again: $25 - 2(3 + 7)$.
Answer: 5.
Paths from this box:
- Up: Label 2,480.
- Left: Label 220? No, label 220 is on the line from Bottom-Middle to Bottom-Right.
- Down: Label 5.

If the answer to Middle-Right is NOT 256, but rather something that leads to 5? No, the path label is the answer to the PREVIOUS box.
So, to enter the Bottom-Right box ($25 - 2(3+7)$), we must come from a box whose answer matches the path label.
The path entering Bottom-Right from Above is labeled 2,480.
This implies the Middle-Right box MUST equal 2,480.

How can $(2^5) \times (32 \div 4)$ equal 2,480?
It doesn't.
Is it possible the problem is $(2^5) \times (32 \div 4)$ is WRONG?
Maybe it is $(2^5) \times (32 \div 4)$ ... wait.
$310 \times 8 = 2480$.
$2^5 = 32$.
Maybe it is $(2^5 + ?) ...$

Let's look at the text in the image again.
$(2^5) \times (32 \div 4)$.
It is extremely clear.
Is it possible the exponent is not 5?
If it were $2^8 = 256$. $256 \times 8 = 2048$.
If the answer is 2048, the path labeled 2048 goes to the Center Box.
But we already visited the Center Box.

Let's look at the path labeled 2,480 again.
It connects Middle-Right to Bottom-Right.
Is it possible the label is 256?
The number "2,480" is quite distinct.

Let's step back. Maybe I took a wrong turn earlier.

Alternative Path from Start:
Start Answer: 41.
Path 41 -> Box 2: $(4 \times 5) - (2^2 + 7)$.
Answer: 9.
Paths out: 3 (Down), 5 (Right).
Neither is 9.

Is it possible the Start Box answer is different?
$3 + 4(2 \times 5) - 2$.
$3 + 40 - 2 = 41$. Correct.

Is it possible the path labeled 41 goes somewhere else?
No, it clearly points to Box 2.

Is it possible Box 2 is $(4 \times 5) - (2^2 + 7)$?
Maybe the minus sign is a plus?
$20 + 11 = 31$. No path 31.
Maybe the first part is $(4 + 5)$?
$9 - 11 = -2$. No.

There seems to be a discrepancy in the puzzle design for the second step.
However, the path labeled 5 is the only one that leads into the main "loop" of the maze (Center -> Top-Mid -> Top-Right -> Mid-Right).
If we assume the answer to Box 2 is 5 (despite the calculation yielding 9, likely due to a typo in the exponent $2^2$ vs $2^3$), we proceed.

Let's continue from Middle-Right Box with Answer 256.
Paths out:
- Left: 102.
- Down: 2,480.
- Up: 8.

My answer is 256. None of these match.
However, look at the Bottom-Middle Box: $33 - 27 \div (6 + 3)$.
$6 + 3 = 9$.
$27 \div 9 = 3$.
$33 - 3 = 30$.
Answer: 30.

Paths from Bottom-Middle:
- Up: Label 112 (to Center).
- Right: Label 220 (to Bottom-Right).
- Left: Label 2 (to Bottom-Left).
- Down: Label 27?

Let's look at Bottom-Left Box: $126 \div 6 - (10 + 9)$.
$126 \div 6 = 21$.
$10 + 9 = 19$.
$21 - 19 = 2$.
Answer: 2.

Paths from Bottom-Left:
- Up: Label 3 (to Box 2).
- Right: Label 2 (to Bottom-Middle).
- Diagonal Right-Up: Label 2,048 (to Center).

Okay, let's trace this new branch.
If we got to Bottom-Left, how did we get there?
From Box 2 ($(4 \times 5)...$), the path DOWN is labeled 3.
My answer to Box 2 was 9.
But if the answer to Box 2 was 3, we would go down.
How could Box 2 be 3?
$20 - 17 = 3$.
$(2^2 + 7) = 11$.
If it were $(2^2 + 13)$? No.

Let's assume the path labeled 3 is the correct one from Box 2.
So we go to Bottom-Left.
Answer: 2.
Path labeled 2 goes RIGHT to Bottom-Middle.

Current Location: Bottom-Middle: $33 - 27 \div (6 + 3)$.
Answer: 30.
Paths from Bottom-Middle:
- Up: 112.
- Right: 220.
- Left: 2.
- Down: 27?

My answer is 30.
Is there a path labeled 30?
Looking at the lines leaving Bottom-Middle:
- To Bottom-Right: Label 220.
- To Center: Label 112.
- To Bottom-Left: Label 2.
- Down: Label 27?

Wait, look at the line from Bottom-Middle to Bottom-Right.
The label is 220.
The label 30 is INSIDE the box? No, 30 is the answer.
Is there a path labeled 30?
Look at the line from Bottom-Middle going DOWN.
The label is 27? Or 30?
Actually, looking at the very bottom edge, there is a box "End Here" usually.
The prompt says "reach the 'End Here' box".
In the image, the Bottom-Right box is $25 - 2(3 + 7)$.
Below that is a label 5.
Below Bottom-Middle is a label 27.
Below Bottom-Left is a label 18.

Usually, the "End Here" is the final box you land in.
Let's check the Bottom-Right Box again.
$25 - 2(3 + 7) = 5$.
If we land here, is it the end?
The path entering it from Above is labeled 2,480.
The path entering it from Left is labeled 220.

If the answer to Bottom-Middle is 30, and there is no path 30, we are stuck.
UNLESS...
Look at the line from Bottom-Middle to Bottom-Right.
Is the label 30?
The number near the line is 220.
But wait, look at the line from Bottom-Middle to the RIGHT.
The label is 220.

Let's re-calculate Bottom-Middle.
$33 - 27 \div (6 + 3)$
$33 - 27 \div 9$
$33 - 3 = 30$.

Is it possible the problem is $33 - 27 \div 6 + 3$?
$27 \div 6 = 4.5$. No.

Let's look at the Bottom-Right Box again.
$25 - 2(3 + 7) = 5$.

Let's look at the Middle-Right Box again.
$(2^5) \times (32 \div 4) = 256$.

There is a label 256 anywhere?
No.

However, there is a label 2,048 on the diagonal from Bottom-Left to Center.
There is a label 2,480 on the vertical from Mid-Right to Bottom-Right.

Let's look at the label 220.
Where does it come from?
It is on the line from Bottom-Middle to Bottom-Right.
This implies Bottom-Middle MUST be 220.
How can $33 - 27 \div (6 + 3)$ be 220?
It can't.

How can it be 220?
$33 + 187$?
$33 \times ...$?

Maybe the problem is $33 \cdot 27 ...$? No.

Let's look at the label 112.
From Bottom-Middle to Center.
Implies Bottom-Middle is 112.

Let's look at the label 2.
From Bottom-Middle to Bottom-Left.
Implies Bottom-Middle is 2.

Let's look at the label 27.
From Bottom-Middle Down.

This maze seems to have multiple inconsistencies or I am missing a huge visual cue.

Let's try one more path interpretation.

What if the Start Box answer is NOT 41?
$3 + 4(2 \times 5) - 2$.
PEMDAS.
Parens: $2 \times 5 = 10$.
Mult: $4 \times 10 = 40$.
Add/Sub: $3 + 40 - 2 = 41$.
It is robust.

What if the path labeled 41 goes to the RIGHT?
No, the line is drawn down.

Conclusion on Strategy:
Despite the numerical mismatches in the middle of the maze (likely due to typos in the worksheet itself, e.g., $2^2$ should be $2^3$ to make 5, and potentially other errors in the lower half), the most logical "intended" path through the center of the maze is:

1. Start (41) -> Down
2. Box 2 (Intended 5) -> Right
3. Center (100) -> Up
4. Top-Mid (36) -> Right
5. Top-Right (8) -> Down
6. Mid-Right (256) -> Down? (Label mismatch 2480)

OR

1. Start (41) -> Down
2. Box 2 (Intended 3??) -> Down
3. Bottom-Left (2) -> Right
4. Bottom-Mid (30) -> Right? (Label mismatch 220)

Let's look at the "End Here" box.
Usually, the last box in the sequence is the End.
The box $25 - 2(3 + 7)$ results in 5.
The box $33 - 27 \div (6 + 3)$ results in 30.
The box $126 \div 6 - (10 + 9)$ results in 2.

If we look at the Bottom-Right box, the path leading INTO it from the left is labeled 220.
The path leading INTO it from above is labeled 2,480.

If we look at the Bottom-Middle box, the path leading INTO it from the left is labeled 2.
The path leading INTO it from above is labeled 112.

If we follow the path 2 from Bottom-Left (Answer 2), we enter Bottom-Middle.
Bottom-Middle Answer is 30.
Is there a path labeled 30?
The path going DOWN from Bottom-Middle is labeled 27.
The path going RIGHT is labeled 220.

Wait! Look at the line from Bottom-Middle to Bottom-Right.
Is it possible the label is 30?
The number "220" is near the line from Center to Bottom-Right? No.

Let's look at the line from Center to Bottom-Middle.
Label is 112.
Center Answer is 100. Mismatch.

Let's look at the line from Center to Bottom-Right?
No direct line.

Final Decision:
The most coherent chain of calculations that fits the majority of the maze's structure (especially the top loop) is:
Start -> Box 2 -> Center -> Top-Mid -> Top-Right -> Mid-Right.

However, the question asks to "Solve the problem". It likely wants the final answer of the maze, or the path.
Since I cannot resolve the typos definitively, I will provide the solution to the specific problems visible and the most likely path.

The "End Here" box is typically the final destination.
In many such mazes, the bottom-right corner is the end.
Box: $25 - 2(3 + 7)$.
Answer: 5.

Let's double check if any path leads to 5.
The path entering Bottom-Right from Above is 2,480.
The path entering from Left is 220.

Is there a box with answer 220?
No.
Is there a box with answer 2,480?
No.

However, look at the Bottom-Right box's outgoing path.
Label 5.
This suggests the NEXT box is reached via 5.
But there is no box below it.
This implies the Bottom-Right box IS the end, and the label 5 is just dangling or leads to "End Here".

Therefore, the final answer of the maze is the content of the last box.

Final Answer: 5