Function Table Worksheets | Function Table & In and Out Boxes ... - Free Printable

Let’s solve each problem step by step, following the given rules or deducing them from the patterns.

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Section 1: Fill in the Empty Boxes (Rules Given)

1) Rule: Subtract 4

In → Out
9 → 9 - 4 = 5
12 → 12 - 4 = 8
15 → 15 - 4 = 11
18 → 18 - 4 = 14

✔ Out: 5, 8, 11, 14

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2) Rule: Subtract 5

In → Out
7 → 7 - 5 = 2
12 → 12 - 5 = 7
15 → 15 - 5 = 10
16 → 16 - 5 = 11

✔ Out: 2, 7, 10, 11

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3) Rule: Subtract 1

In → Out
4 → 4 - 1 = 3
6 → 6 - 1 = 5
12 → 12 - 1 = 11
13 → 13 - 1 = 12

✔ Out: 3, 5, 11, 12

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4) Rule: Subtract 3

In → Out
4 → 4 - 3 = 1
5 → 5 - 3 = 2
10 → 10 - 3 = 7
14 → 14 - 3 = 11

✔ Out: 1, 2, 7, 11

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5) Rule: Subtract 1

In → Out
6 → 6 - 1 = 5
10 → 10 - 1 = 9
13 → 13 - 1 = 12
14 → 14 - 1 = 13

✔ Out: 5, 9, 12, 13

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6) Rule: Add 2

In → Out
3 → 3 + 2 = 5
8 → 8 + 2 = 10
9 → 9 + 2 = 11
11 → 11 + 2 = 13

✔ Out: 5, 10, 11, 13

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7) Rule: Add 3

In → Out
0 → 0 + 3 = 3
6 → 6 + 3 = 9
9 → 9 + 3 = 12
12 → 12 + 3 = 15

✔ Out: 3, 9, 12, 15

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8) Rule: Add 2

In → Out
8 → 8 + 2 = 10
9 → 9 + 2 = 11
10 → 10 + 2 = 12
14 → 14 + 2 = 16

✔ Out: 10, 11, 12, 16

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Section 2: Write the Rule and Fill in the Empty Boxes

We need to find the pattern (rule) from the In → Out pairs, then apply it to fill blanks.

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9)

In | Out
0 → 4
2 → 6
6 → 10
7 → ?

Look at differences:
0 → 4 → +4
2 → 6 → +4
6 → 10 → +4
So rule is Add 4

7 → 7 + 4 = 11

✔ Rule: Add 4
✔ Out: 11

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10)

In | Out
? → 2
6 → 10
14 → 18
15 → 19

Check differences:
6 → 10 → +4
14 → 18 → +4
15 → 19 → +4
So rule is Add 4

Then: ? → 2 → so In = 2 - 4 = -2

✔ Rule: Add 4
✔ In: -2

*(Note: Negative numbers may be acceptable depending on grade level — if not, check for error. But mathematically correct.)*

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11)

In | Out
1 → 2
12 → 15
14 → 15? Wait — 14 → 15 → +1? But 1 → 2 → +1, 12 → 15 → +3? Not consistent.

Wait — let’s recheck:

1 → 2 → +1
12 → 15 → +3
14 → 15 → +1? That doesn’t make sense.

Wait — perhaps typo? Or maybe:

Actually, 1→2, 12→15, 14→15, 15→16

Try:
1 → 2 → +1
12 → 15 → +3
14 → 15 → +1
15 → 16 → +1 — inconsistent.

Alternative idea: Maybe Add 1 but only sometimes? Unlikely.

Wait — look again:
Perhaps the “Out” for 14 is a typo? Because 12→15 (+3), 15→16 (+1) — no.

Another approach: Maybe Add the digit sum? No.

Wait — what if it's Add 1 for all except 12? That seems arbitrary.

Wait — perhaps it’s “Add 1” and the 12→15 is a mistake? Or maybe we misread.

Looking at original image description: It says "12 → 15", "14 → 15", "15 → 16"

That’s odd. Let’s assume it’s meant to be:

Maybe 12 → 13? But it says 15.

Alternatively — perhaps the rule is “Add 1 if number < 13, else add 0”? Doesn’t fit.

Wait — another possibility: Maybe it’s “Add the number of letters in English name”?

1 → “one” → 3 letters → 1+3=4 ≠2 → no.

This one is problematic. Let’s look for a different pattern.

What if it’s “Add 1” and the 12→15 is an error? Or perhaps it’s “Add 1” and 12→15 is a typo for 12→13?

But since 15→16 is +1, and 1→2 is +1, maybe 12→15 is supposed to be 12→13? But we must go with what’s written.

Wait — perhaps the rule is “Add 1” and the 12→15 is a mistake. But that’s risky.

Alternatively — maybe it’s “Add 1” for most, but for 12 it’s +3? No clear rule.

Wait — let’s try this: What if the rule is “Add 1” and the “15” for 14 is a typo? If 14→15 is meant to be 14→15? Still +1.

But 12→15 is +3. That breaks the pattern.

Unless... maybe the rule is “Add 1, except for multiples of 3?” 12 is multiple of 3 → +3? Then 15 is multiple of 3 → should be +3 → 15+3=18, but it’s 16. Doesn’t work.

This might be an error in the worksheet. But let’s try to force a rule.

Notice:

1 → 2
12 → 15 → difference +3
14 → 15 → +1
15 → 16 → +1

Not consistent.

Perhaps it’s “Add 1” and the 12→15 is a misprint for 12→13? That would make sense.

Since this is likely for elementary students, probably a typo. I’ll assume Rule: Add 1, and 12→13 (but written as 15 by mistake). But since we can’t change the given, perhaps we should say:

Actually, looking at 15→16 and 1→2, both +1, and 14→15 is +1, so maybe 12→15 is wrong. But we have to answer based on given.

Wait — another idea: Maybe it’s “Add the number of factors?” Too advanced.

I think the most reasonable assumption is that there’s a typo, and it should be 12→13. So rule is Add 1.

But to be safe, let’s note the inconsistency.

However, in many such worksheets, if 3 out of 4 follow a pattern, we go with that.

So: 1→2, 14→15, 15→16 → all +1. 12→15 is outlier. Probably typo.

✔ Rule: Add 1
(And assume 12→13 was intended, but since not asked to correct, just state rule.)

But the question asks to write the rule and fill empty boxes — here, no empty box, just find rule.

In row 11, all Out are filled, so just write rule.

Given the majority, I’ll say:

✔ Rule: Add 1

*(With note that 12→15 may be an error.)*

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12)

In | Out
4 → 1
9 → 6
11 → 8
17 → ?

Differences:
4 → 1 → -3
9 → 6 → -3
11 → 8 → -3
So rule is Subtract 3

17 → 17 - 3 = 14

✔ Rule: Subtract 3
✔ Out: 14

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13)

In | Out
4 → ?
5 → 10
9 → 14
10 → 15

Look at 5→10 → +5
9→14 → +5
10→15 → +5
So rule is Add 5

Then 4 → 4 + 5 = 9

✔ Rule: Add 5
✔ Out: 9

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14)

In | Out
5 → 0
6 → 1
8 → ?
13 → 8

Differences:
5 → 0 → -5
6 → 1 → -5
13 → 8 → -5
So rule is Subtract 5

8 → 8 - 5 = 3

✔ Rule: Subtract 5
✔ Out: 3

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## ✔ Final Answers:

Section 1:

1) Out: 5, 8, 11, 14
2) Out: 2, 7, 10, 11
3) Out: 3, 5, 11, 12
4) Out: 1, 2, 7, 11
5) Out: 5, 9, 12, 13
6) Out: 5, 10, 11, 13
7) Out: 3, 9, 12, 15
8) Out: 10, 11, 12, 16

Section 2:

9) Rule: Add 4; Out: 11
10) Rule: Add 4; In: -2 *(or possibly typo, but mathematically correct)*
11) Rule: Add 1 *(assuming 12→15 is a typo for 12→13)*
12) Rule: Subtract 3; Out: 14
13) Rule: Add 5; Out: 9
14) Rule: Subtract 5; Out: 3

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📌 Note for #11: The given data has an inconsistency (12→15 while others suggest +1). If this is for young students, it might be intended as “Add 1”, and 12→15 is a printing error. In real classroom, you’d clarify with teacher.

All other problems follow clear arithmetic rules.

Let me know if you want this formatted as a worksheet answer key!