Math worksheet for determining function machine rules using input-output tables.

To find the rule for each function machine, we need to look at how the "In" number changes to become the "Out" number. We can check if we are adding, subtracting, multiplying, or dividing by a specific number.

Here is the step-by-step solution for each problem:

1)
* Look at the first pair: $31 \rightarrow 35$. The difference is $35 - 31 = 4$.
* Check the next pair: $34 + 4 = 38$. This works.
* Check another: $44 + 4 = 48$. This works.
* Rule: Add 4

2)
* Look at the first pair: $21 \rightarrow 15$. The difference is $21 - 15 = 6$. Since the output is smaller, we are subtracting.
* Check the next pair: $24 - 6 = 18$. This works.
* Check another: $35 - 6 = 29$. This works.
* Rule: Subtract 6

3)
* Look at the first pair: $17 \rightarrow 13$. The difference is $17 - 13 = 4$.
* Check the next pair: $27 - 4 = 23$. This works.
* Check another: $29 - 4 = 25$. This works.
* Rule: Subtract 4

4)
* Look at the first pair: $20 \rightarrow 10$. The difference is $20 - 10 = 10$.
* Check the next pair: $26 - 10 = 16$. This works.
* Check another: $38 - 10 = 28$. This works.
* Rule: Subtract 10

5)
* Look at the first pair: $39 \rightarrow 24$. The difference is $39 - 24 = 15$.
* Check the next pair: $45 - 15 = 30$. This works.
* Check another: $46 - 15 = 31$. This works.
* Rule: Subtract 15

6)
* Look at the first pair: $17 \rightarrow 30$. The difference is $30 - 17 = 13$.
* Check the next pair: $19 + 13 = 32$. This works.
* Check another: $20 + 13 = 33$? Wait, the table says 43. Let me re-check.
* $17 \rightarrow 30$ ($+13$)
* $19 \rightarrow 32$ ($+13$)
* $20 \rightarrow 43$? $20 + 13 = 33$. The table says 43. Let me look closer at the image. Ah, row 3 is Input 20, Output 43? No, looking at crop 2, it is Input 20, Output 43? Let me re-read crop 2 carefully.
* Crop 2 shows:
* 17 -> 30
* 19 -> 32
* 20 -> 43 ?? That seems inconsistent with +13. Let's check the next one.
* 41 -> 54 ($54-41=13$)
* 47 -> 60 ($60-47=13$)
* Let's re-examine the third row in box 6. Input 20, Output 43. Is it possible the input is 30? If input is 30, $30+13=43$. Looking at the full image, the number looks like a 20. However, every other pair follows the "Add 13" rule perfectly ($17+13=30$, $19+13=32$, $41+13=54$, $47+13=60$). It is highly likely there is a typo in the worksheet for that specific cell (should be 33) or the input is actually 30. Given the strong pattern of +13 in 4 out of 5 pairs, the rule is definitely Add 13.
* Rule: Add 13

7)
* Look at the first pair: $12 \rightarrow 17$. The difference is $17 - 12 = 5$.
* Check the next pair: $35 + 5 = 40$. This works.
* Check another: $37 + 5 = 42$. This works.
* Rule: Add 5

8)
* Look at the first pair: $17 \rightarrow 30$. The difference is $30 - 17 = 13$.
* Check the next pair: $24 + 13 = 37$. This works.
* Check another: $35 + 13 = 48$. This works.
* Rule: Add 13

9)
* Look at the first pair: $34 \rightarrow 24$. The difference is $34 - 24 = 10$.
* Check the next pair: $44 - 10 = 34$. This works.
* Check another: $46 - 10 = 36$. This works.
* Rule: Subtract 10

10)
* Look at the first pair: $29 \rightarrow 14$. The difference is $29 - 14 = 15$.
* Check the next pair: $33 - 15 = 18$. This works.
* Check another: $34 - 15 = 19$. This works.
* Rule: Subtract 15

11)
* Look at the first pair: $28 \rightarrow 43$. The difference is $43 - 28 = 15$.
* Check the next pair: $31 + 15 = 46$. This works.
* Check another: $33 + 15 = 48$. This works.
* Rule: Add 15

12)
* Look at the first pair: $15 \rightarrow 23$. The difference is $23 - 15 = 8$.
* Check the next pair: $21 + 8 = 29$. This works.
* Check another: $26 + 8 = 34$. This works.
* Rule: Add 8

Final Answer:
1. Add 4
2. Subtract 6
3. Subtract 4
4. Subtract 10
5. Subtract 15
6. Add 13
7. Add 5
8. Add 13
9. Subtract 10
10. Subtract 15
11. Add 15
12. Add 8