Patterns & Function Machine Worksheets | Free - Distance Learning ... - Free Printable

Let’s solve each problem one by one. We’ll look at the pattern in each table and figure out the rule that connects the two columns. Then we’ll use that rule to find the answer for the question asked.

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Problem 1: Customers on day 13

Table:
- Day 5 → 8 customers
- Day 6 → 9 customers
- Day 7 → 10 customers
- Day 8 → 11 customers

Look at how customers change as days go up:
From day 5 to 6: +1 customer
Day 6 to 7: +1
Day 7 to 8: +1

So, every day, customers increase by 1.

That means:
Customers = Day + 3? Let’s check:
Day 5 → 5 + 3 = 8 ✔
Day 6 → 6 + 3 = 9 ✔
Yes! So rule is: Add 3 to the day number

For day 13: 13 + 3 = 16

But wait — the options are about what operation to do, not the actual number.

Options:
A. Multiply 3 by 13 → 39 ✘
B. Add 8 to 13 → 21 ✘
C. Add 3 to 13 → 16 ✔
D. Add 5 to 13 → 18 ✘

✔ Correct choice: C. Add 3 to 13

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Problem 2: Cook time for 10 pieces of chicken

Table:
- Pieces 1 → Cook Time 8
- Pieces 2 → Cook Time 16
- Pieces 3 → Cook Time 24
- Pieces 4 → Cook Time 32

Check the pattern:
1 × 8 = 8
2 × 8 = 16
3 × 8 = 24
4 × 8 = 32

So, cook time = pieces × 8

For 10 pieces: 10 × 8 = 80 minutes

Options:
A. Add 1 to 10 → 11 ✘
B. Multiply 8 by 10 → 80 ✔
C. Add 8 to 10 → 18 ✘
D. Multiply 8 by 10 → same as B? Wait, let me read again.

Actually, option B says “Multiply 8 by 10” → that’s 8×10=80
Option D says “Multiply 8 by 10” — wait, no, looking back:

Original options:
A. Add 1 to 10
B. Multiply 8 by 10
C. Add 8 to 10
D. Multiply 8 by 10 ← Wait, that can’t be right. Maybe typo?

Wait — rechecking original image text:

In your transcription, it says:
> A. Add 1 to 10
> B. Multiply 8 by 10
> C. Add 8 to 10
> D. Multiply 8 by 10

Hmm, B and D are same? That must be a mistake in transcription.

Looking at standard version of this worksheet (common core sheets), Problem 2 options are usually:

A. Add 1 to 10
B. Multiply 8 by 10
C. Add 8 to 10
D. Multiply 10 by 8 ← which is same as B mathematically, but wording differs.

But since both B and D say “Multiply 8 by 10”, perhaps it's a copy error.

Actually, in the real worksheet, option D is often “Multiply 10 by 8” — which is same thing.

But logically, the correct operation is multiply 8 by the number of pieces.

So for 10 pieces: 8 × 10

Either B or D would work if they’re identical — but likely intended answer is B. Multiply 8 by 10

Wait — let me double-check with the pattern.

Pieces → Cook Time: always multiply pieces by 8.

So to get cook time for 10 pieces, you multiply 8 by 10.

✔ Answer: B. Multiply 8 by 10

*(Note: If D was meant to be different, like “Multiply 10 by 8”, it’s still correct — multiplication is commutative. But based on given options, B is listed first and matches.)*

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Problem 3: Cans for 12 bags

Table:
- Bags 5 → Cans 20
- Bags 6 → Cans 24
- Bags 7 → Cans 28
- Bags 8 → Cans 32

Pattern:
5 × 4 = 20
6 × 4 = 24
7 × 4 = 28
8 × 4 = 32

So, cans = bags × 4

For 12 bags: 12 × 4 = 48 cans

Options:
A. Add 5 to 12 → 17 ✘
B. Multiply 4 by 12 → 48 ✔
C. Multiply 5 by 12 → 60 ✘
D. Multiply 20 by 12 → way too big ✘

✔ Correct: B. Multiply 4 by 12

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Problem 4: Money at end of week 9

Table:
- Week 3 → $27
- Week 4 → $36
- Week 5 → $45
- Week 6 → $54

Check differences:
36 - 27 = 9
45 - 36 = 9
54 - 45 = 9

So each week, money increases by $9.

Also, check multiplication:
Week 3 → 3 × 9 = 27 ✔
Week 4 → 4 × 9 = 36 ✔
Week 5 → 5 × 9 = 45 ✔
Week 6 → 6 × 9 = 54 ✔

So money = week × 9

For week 9: 9 × 9 = $81

Options:
A. Multiply 9 by 9 → 81 ✔
B. Add 3 to 9 → 12 ✘
C. Multiply 27 by 9 → 243 ✘
D. Multiply 3 by 9 → 27 ✘

✔ Correct: A. Multiply 9 by 9

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Problem 5: Points at level 11

Table:
- Level 3 → Points 24
- Level 4 → Points 32
- Level 5 → Points 40
- Level 6 → Points 48

Check pattern:
Level 3: 3 × 8 = 24 ✔
Level 4: 4 × 8 = 32 ✔
Level 5: 5 × 8 = 40 ✔
Level 6: 6 × 8 = 48 ✔

So points = level × 8

For level 11: 11 × 8 = 88

Options:
A. Multiply 24 by 11 → 264 ✘
B. Add 3 to 11 → 14 ✘
C. Multiply 8 by 11 → 88 ✔
D. Add 8 to 11 → 19 ✘

✔ Correct: C. Multiply 8 by 11

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Problem 6: Pictures for 13 pages

Table:
- Pages 4 → Pictures 8
- Pages 5 → Pictures 10
- Pages 6 → Pictures 12
- Pages 7 → Pictures 14

Pattern:
4 × 2 = 8
5 × 2 = 10
6 × 2 = 12
7 × 2 = 14

So pictures = pages × 2

For 13 pages: 13 × 2 = 26

Options:
A. Multiply 2 by 13 → 26 ✔
B. Multiply 8 by 13 → 104 ✘
C. Add 2 to 13 → 15 ✘
D. Multiply 4 by 13 → 52 ✘

✔ Correct: A. Multiply 2 by 13

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Now, compiling all answers:

1. C
2. B
3. B
4. A
5. C
6. A

Final Answer:
1. C
2. B
3. B
4. A
5. C
6. A