Using Addition and Subtraction: Critical Thinking Printable (2nd ... - Free Printable

It looks like you've uploaded an image with a math puzzle titled "Critical Thinking". The task is:

> Where do these boxes go? Find the clue in the code above. Then circle the number at the bottom of the page.

Below the title, there are several sets of numbers arranged in a grid-like format, and then a list of numbers at the bottom:
15 10 8 7 2

We are to determine which number from that list should be circled based on some pattern or code in the numbers above.

Let’s analyze the image content step by step.

---

Step 1: Examine the Grids

There are five grids shown, each with three rows and four columns (though some appear to have fewer entries). Let's look at them one by one.

#### Grid 1:
```
16 10
–8 –8
```

Wait — this seems like subtraction. Let's interpret it as:
- Top row: 16, 10
- Bottom row: –8, –8

But maybe it's meant to be a subtraction problem?

Wait — perhaps the top two numbers are being subtracted by the bottom ones?

Let’s suppose each column represents a subtraction:

- Column 1: 16 - (-8) = 16 + 8 = 24
- Column 2: 10 - (-8) = 10 + 8 = 18

But that doesn't seem helpful yet.

Alternatively, could the numbers be part of a pattern?

Wait — let's look more carefully at the structure.

Actually, looking again, the layout appears to be:

Each "box" has a top row and a bottom row. But the formatting is odd.

Let me re-express what's visible:

---

First Box:

```
16 10
–8 –8
```

This might represent:
- 16 - (-8) = 24
- 10 - (-8) = 18

But again, not clear.

Wait — perhaps it's showing that:

In the first box:
- Top: 16 and 10
- Bottom: –8 and –8

Maybe we’re supposed to subtract the bottom from the top?

But why would that matter?

Wait — let's look at the second box.

---

Second Box:

```
3 8 10 10
–4 –4 –4 –4
```

So:
- 3 - (-4) = 7
- 8 - (-4) = 12
- 10 - (-4) = 14
- 10 - (-4) = 14

Still not obvious.

Wait — maybe the bottom numbers are clues?

But notice: In the first box, both bottom numbers are –8.

In the second, all are –4.

Third:
```
15 7 8 15
–8 –8 –8 –8
```

All bottom numbers are –8.

Fourth:
```
12 5 7 12 9
–8 –8 –8 –8 –8
```

All –8.

Fifth:
```
12 9 15 6
–8 –8 –8 –8
```

Again, all –8.

Wait — only the second box has –4.

So perhaps the value of the bottom numbers is important.

Let’s list them:

- Box 1: –8, –8 → value: –8
- Box 2: –4, –4, –4, –4 → value: –4
- Box 3: –8, –8, –8, –8 → value: –8
- Box 4: –8, –8, –8, –8, –8 → value: –8
- Box 5: –8, –8, –8, –8 → value: –8

Only Box 2 has –4.

Now look at the top numbers.

Let’s see if there's a pattern in the top numbers.

Box 1: 16, 10 → sum = 26? difference = 6?

Box 2: 3, 8, 10, 10 → sum = 31

Not helpful.

Wait — maybe the number of digits or positions?

Another idea: Perhaps the bottom numbers indicate how much to subtract, and the result is something meaningful?

But let’s look at the final question: “Where do these boxes go?” and “Find the clue in the code above.”

Then we are to circle one number from:
15 10 8 7 2

So likely, one of these numbers is the answer.

Let’s consider the possibility that the bottom numbers are codes.

Notice:

- Most boxes have –8 on the bottom.
- Only one box has –4.

That’s unusual.

Also, observe the number of entries in each box:

- Box 1: 2 entries on top, 2 on bottom
- Box 2: 4 on top, 4 on bottom
- Box 3: 4 on top, 4 on bottom
- Box 4: 5 on top, 5 on bottom
- Box 5: 4 on top, 4 on bottom

So box 4 has 5 entries, others have 2, 4, 4, 4.

Box 1 has only 2.

But still.

Wait — perhaps the difference between top and bottom gives us something.

Try this:

For each box, compute top minus bottom, but since bottom is negative, it becomes addition.

But maybe we're supposed to find a pattern in the results.

Let’s try computing top minus bottom for each column.

But wait — another idea: maybe the bottom numbers are clues to how many times something happens?

Or perhaps the absolute values of the bottom numbers are important.

All bottom numbers are either –8 or –4.

So absolute values: 8 or 4.

Now look at the top numbers.

Let’s list the top numbers:

- Box 1: 16, 10 → both even
- Box 2: 3, 8, 10, 10 → mixed
- Box 3: 15, 7, 8, 15 → mixed
- Box 4: 12, 5, 7, 12, 9 → mixed
- Box 5: 12, 9, 15, 6 → mixed

Hmm.

Wait — let’s look at the first box again:

```
16 10
–8 –8
```

If we do 16 - (-8) = 24, 10 - (-8) = 18 → 24 and 18

But no.

What if we do top divided by bottom?

16 / (-8) = -2, 10 / (-8) = -1.25 → not integers.

Not helpful.

Wait — here’s a new idea.

Look at the bottom numbers — they are all multiples of 4: –8, –4.

And –8 is twice –4.

Now, look at the number of entries in each box.

- Box 1: 2 entries
- Box 2: 4 entries
- Box 3: 4 entries
- Box 4: 5 entries
- Box 5: 4 entries

Only Box 4 has 5 entries.

Box 2 has –4 instead of –8.

So perhaps the value of the bottom number relates to the number of entries?

Box 2 has 4 entries and uses –4.

Box 1 has 2 entries and uses –8.

Box 3 has 4 entries and uses –8.

Box 4 has 5 entries and uses –8.

Box 5 has 4 entries and uses –8.

So only Box 2 uses –4, and it has 4 entries.

But Box 3, 4, 5 also have 4 or more entries and use –8.

So not consistent.

Wait — unless the value of the bottom number is related to the sum of the top numbers?

Try:

Box 1: top sum = 16 + 10 = 26; bottom = –8 each → total bottom = –16

26 + 16 = 42? Not helpful.

Box 2: top sum = 3+8+10+10 = 31; bottom sum = –16 → 31 + 16 = 47

No.

Another idea: Maybe the difference between top and bottom gives a constant?

Wait — perhaps the bottom number is a code for a letter?

–8 → H? No, letters are positive.

But absolute value: 8 → H, 4 → D.

But we have –8 and –4.

But that might be overcomplicating.

Wait — look at the last line of the image:

> Where do the go?
> head tail mouth nose ear

And below that: 15 10 8 7 2

So likely, these numbers correspond to body parts.

And we are to choose which number corresponds to the correct answer.

But the instruction says: “Find the clue in the code above” — so the grids are the code.

Let’s think differently.

Perhaps the bottom numbers are subtracting from the top, and the result is a word or something.

Wait — look at the second box:

```
3 8 10 10
–4 –4 –4 –4
```

Do 3 - (-4) = 7
8 - (-4) = 12
10 - (-4) = 14
10 - (-4) = 14

So: 7, 12, 14, 14

Not helpful.

But 7, 12, 14, 14 — no pattern.

Wait — what if we look at the top numbers and see if they form words when mapped to letters?

A=1, B=2, ..., Z=26

Try Box 1: 16, 10 → P, J → "PJ"? Not meaningful.

Box 2: 3,8,10,10 → C,H,J,J → "CHJJ"? No.

Box 3: 15,7,8,15 → O,G,H,O → "OGHO"?

Box 4: 12,5,7,12,9 → L,E,G,L,I → "LEGLI"?

Box 5: 12,9,15,6 → L,I,O,F → "LIOF"?

None seem meaningful.

But wait — Box 3: 15,7,8,15 → O,G,H,O — close to "OCHO"? No.

Wait — 15,7,8,15 — O G H O — not a word.

But look at Box 4: 12,5,7,12,9 → L,E,G,L,I — "LEGLI"? No.

Wait — what if we look at the bottom numbers?

They are all –8 or –4.

Only Box 2 has –4.

And Box 2 has 4 entries.

Is there a pattern where the number of entries equals the absolute value of the bottom number?

Box 2: 4 entries, bottom = –4 → yes.

Box 1: 2 entries, bottom = –8 → no.

Box 3: 4 entries, bottom = –8 → no.

Box 4: 5 entries, bottom = –8 → no.

Box 5: 4 entries, bottom = –8 → no.

Only Box 2 matches.

So perhaps Box 2 is special.

But why?

Maybe the clue is that only one box has bottom value –4, and it has 4 entries.

So the number 4 is significant.

But 4 is not in the final list: 15, 10, 8, 7, 2.

So not directly.

But 4 is not listed.

Wait — the final list is: 15 10 8 7 2

And the options are: head, tail, mouth, nose, ear.

So likely, we need to map one of those numbers to a body part.

But the question is: “Where do these boxes go?” — meaning, perhaps, which body part?

But we need a clue.

Let’s go back to the title: “Critical Thinking”

And the instruction: “Find the clue in the code above.”

Let’s look at the structure of the boxes.

Another idea: Perhaps the bottom numbers are not part of the calculation, but rather, the top numbers are to be used, and the bottom numbers indicate which one to use.

But all bottom numbers are negative.

Wait — perhaps the absolute value of the bottom number tells us how many times to apply something.

But still.

Wait — look at the first box:

Top: 16, 10
Bottom: –8, –8

If we do 16 - 8 = 8, 10 - 8 = 2

Result: 8, 2

But 8 and 2 are in the list!

The list is: 15, 10, 8, 7, 2

So 8 and 2 are both there.

But we have two numbers.

Similarly, Box 2: top: 3,8,10,10; bottom: –4,–4,–4,–4

3 - 4 = –1, 8 - 4 = 4, 10 - 4 = 6, 10 - 4 = 6 → –1,4,6,6 — not in list.

Box 3: 15,7,8,15; bottom: –8 → 15-8=7, 7-8=–1, 8-8=0, 15-8=7 → 7,–1,0,7 — 7 is in list.

Box 4: 12,5,7,12,9; –8 → 4,–3,–1,4,1 — 4 not in list.

Box 5: 12,9,15,6; –8 → 4,1,7,–2 — 7 is in list.

So 7 appears in multiple.

But earlier, from Box 1, we got 8 and 2.

Now, notice: in Box 1, if we do 16 - 8 = 8, 10 - 8 = 2

And 8 and 2 are both in the final list.

But the final list has only one to circle.

But wait — perhaps the answer is 8 or 2, but which one?

Alternatively, maybe the sum of the results.

But 8 + 2 = 10, and 10 is in the list.

Ah! 10 is in the list.

So from Box 1: 16 - 8 = 8, 10 - 8 = 2, sum = 10.

And 10 is in the list.

Now check other boxes.

Box 2: 3-4=–1, 8-4=4, 10-4=6, 10-4=6 → sum = –1+4+6+6 = 15

15 is in the list!

Box 3: 15-8=7, 7-8=–1, 8-8=0, 15-8=7 → sum = 7–1+0+7 = 13 → not in list.

Box 4: 12-8=4, 5-8=–3, 7-8=–1, 12-8=4, 9-8=1 → sum = 4–3–1+4+1 = 5 → not in list.

Box 5: 12-8=4, 9-8=1, 15-8=7, 6-8=–2 → sum = 4+1+7–2 = 10 → 10 again.

So:

- Box 1: sum = 10
- Box 2: sum = 15
- Box 3: sum = 13
- Box 4: sum = 5
- Box 5: sum = 10

So sums are 10, 15, 13, 5, 10

Which are in the list: 15, 10, 8, 7, 2

So 15 and 10 appear.

But only one number to circle.

But wait — perhaps the only box with unique bottom value is Box 2, with –4.

And its sum is 15.

Others have –8.

So Box 2 is different.

And its sum is 15.

And 15 is in the list.

But Box 1 and 5 also give 10.

But Box 2 is the only one with –4.

So maybe 15 is the answer.

But let’s see the final part:

> Where do the go?
> head tail mouth nose ear

And numbers: 15 10 8 7 2

So perhaps the number corresponds to a body part.

But what does the code tell us?

Wait — another idea.

Look at the bottom numbers — they are all –8 except Box 2 which is –4.

And Box 2 has 4 entries.

So perhaps the value of the bottom number is related to the number of entries.

But only Box 2 satisfies: 4 entries, –4.

So it’s special.

And its top numbers: 3,8,10,10

Sum = 31

But 31 not in list.

But earlier, after subtracting, sum was 15.

And 15 is in the list.

Now, look at the word "head" — could it be related?

But we need a better clue.

Wait — perhaps the number of times a certain number appears.

But let’s think about the title: “Critical Thinking”

And the instruction: “Find the clue in the code above.”

Let’s look at the layout of the boxes.

Another idea: Perhaps the bottom numbers are indicating a position.

But they are negative.

Wait — perhaps the absolute value of the bottom number is the code.

So –8 means 8, –4 means 4.

So most boxes have 8, one has 4.

So the "different" one is Box 2 with 4.

So the clue is 4.

But 4 is not in the list.

But 4 is not in {15,10,8,7,2}

So not directly.

Unless it's a code for a letter.

4 = D.

But not helpful.

Wait — what if we look at the top numbers and see if any match the list.

List: 15,10,8,7,2

Look at Box 3: 15,7,8,15 — has 15,7,8

Box 1: 16,10 — has 10

Box 2: 3,8,10,10 — has 8,10

Box 4: 12,5,7,12,9 — has 7

Box 5: 12,9,15,6 — has 15

So many boxes have numbers from the list.

But the key might be the bottom numbers.

Wait — here’s a breakthrough.

Look at the bottom numbers — they are all –8 or –4.

But notice: in all boxes except Box 2, the bottom number is –8.

Only Box 2 has –4.

And Box 2 has 4 entries.

So perhaps the value of the bottom number is equal to the negative of the number of entries.

Box 2: 4 entries, bottom = –4 → yes.

Box 1: 2 entries, bottom = –8 → no.

Box 3: 4 entries, bottom = –8 → no.

So only Box 2 satisfies.

Therefore, Box 2 is the "correct" one.

Its top numbers: 3,8,10,10

Sum = 31

But 31 not in list.

But earlier, when we did top - bottom, we got: 7,12,14,14

Sum = 47

No.

But wait — perhaps the result of the operation is the clue.

Another idea: Perhaps the number of times the bottom number appears.

But it's always repeated.

Wait — look at the first box:

16 and 10

–8 and –8

16 - 8 = 8

10 - 8 = 2

8 and 2 are both in the list.

And 8 and 2 are the results.

But the list has 8 and 2.

But we need to choose one.

But notice: in the final list, 8 is third, 2 is last.

But perhaps the sum is 10, and 10 is in the list.

And 10 is the second number.

But also, Box 5 gives sum 10.

Box 2 gives sum 15.

But Box 2 is unique.

Let’s calculate the average of the results.

But not helpful.

Wait — perhaps the answer is 8, because it appears in the first box, and the first box has 16 and 10, and 16 - 8 = 8, 10 - 8 = 2.

And 8 is in the list.

But why 8?

Another idea: Perhaps the bottom number is the code for the answer.

Most boxes have –8, so the code is 8.

And 8 is in the list.

So circle 8.

But Box 2 has –4, so it's different.

But the majority have –8.

So perhaps the common code is 8.

So answer is 8.

But let’s see the final part: “Where do the go?” with body parts.

And numbers: 15 10 8 7 2

Perhaps the number corresponds to a body part.

But what does the code tell us?

Wait — look at the top numbers in Box 1: 16 and 10

16 - 8 = 8

10 - 8 = 2

8 and 2

Now, 8 is in the list, 2 is in the list.

But 8 is the number that is the result of the operation.

And 8 is also the bottom number's absolute value.

So perhaps the answer is 8.

Moreover, in the list, 8 is the third number.

But let’s see if there's a better clue.

Wait — look at the last box:

12,9,15,6

–8,-8,-8,-8

12 - 8 = 4

9 - 8 = 1

15 - 8 = 7

6 - 8 = -2

Results: 4,1,7,-2

Only 7 is in the list.

7 is in the list.

And 7 is the fourth number.

But in Box 3: 15,7,8,15

After -8: 7, -1, 0, 7

So 7 appears.

So 7 appears in multiple.

But only Box 1 gives both 8 and 2.

But perhaps the intended answer is 8.

Let’s look at the very first box.

16 and 10

–8 and –8

16 - 8 = 8

10 - 8 = 2

8 and 2

Now, 8 is in the list, and it's the same as the bottom number's absolute value.

So perhaps the code is 8.

And since most boxes have –8, the clue is 8.

So the answer is 8.

Moreover, in the list, 8 is present.

So circle 8.

But let’s see if there's a connection to the body parts.

Perhaps "mouth" is 8, or "nose".

But without more context, hard to say.

But the instruction is to circle the number at the bottom.

And the clue is in the code.

The code is the bottom numbers: mostly –8, so the number is 8.

Therefore, the answer is 8.

But let’s double-check.

Another possibility: the number of boxes with –8 is 4, so 4 is the answer.

But 4 not in list.

Number of entries: varies.

But only Box 2 has –4, so it's special.

But its sum after subtraction is 15.

15 is in the list.

And 15 appears in the top numbers of several boxes.

But 15 is also in the list.

So possible answers: 8, 15, 10, 7, 2.

But which one?

Let’s count how many times each number in the list appears in the top numbers:

- 15: appears in Box 3 (twice), Box 5 → 3 times
- 10: appears in Box 1, Box 2 (twice) → 3 times
- 8: appears in Box 1, Box 2, Box 3 → 3 times
- 7: appears in Box 3, Box 4 → 2 times
- 2: appears in Box 1 (result) → 1 time

So 15,10,8 appear 3 times.

But 8 is also the bottom number.

So perhaps 8 is the answer.

Moreover, in the first box, 16 - 8 = 8, so it's self-referential.

So the clue is that the bottom number is –8, and the result is 8.

So the answer is 8.

Therefore, circle 8.

Final answer: 8