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

Let's solve each pattern step by step and determine which letter best completes the pattern.

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1) Pattern: Cherries, Apple, Cherries, Apple, Cherries, Apple, Cherries, ?

Sequence:
- Cherry, Apple, Cherry, Apple, Cherry, Apple, Cherry, ?

We can see a repeating pattern of:
- Cherry → Apple (alternating)

So the sequence alternates between Cherry and Apple.

Positions:
1. Cherry
2. Apple
3. Cherry
4. Apple
5. Cherry
6. Apple
7. Cherry
8. ???

Since position 8 follows a Cherry (position 7), it should be Apple.

Now look at the choices:
- A. Cherries ✔
- B. Apple 🍎 → Correct
- C. Pear
- D. Strawberry

✔ Answer: B. Apple

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2) Pattern: Pencil, Pencil, Eraser, Marker, Pencil, Pencil, Eraser, Marker, ?

Sequence:
- Pencil, Pencil, Eraser, Marker, Pencil, Pencil, Eraser, Marker, ?

Look for repetition:
Grouped as:
- (Pencil, Pencil, Eraser, Marker) → repeats twice so far

So the next item should be the first in the group, which is Pencil.

But wait — let’s list them:

1. Pencil
2. Pencil
3. Eraser
4. Marker
5. Pencil
6. Pencil
7. Eraser
8. Marker
9. ??

Yes, the cycle is every 4 items: Pencil, Pencil, Eraser, Marker

So after Marker (position 8), the next is Pencil.

Choices:
- A. Pencil ✔
- B. Marker
- C. Eraser
- D. Paperclip

✔ Answer: A. Pencil

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3) Pattern: Square, Square, Star, Square, Square, Star, Square, ?, Star

Sequence:
- Square, Square, Star, Square, Square, Star, Square, ?, Star

Look at positions:
1. Square
2. Square
3. Star
4. Square
5. Square
6. Star
7. Square
8. ?
9. Star

Notice that the pattern seems to be:
- Two Squares, then a Star → repeated

So:
- Group 1: Sq, Sq, Star
- Group 2: Sq, Sq, Star
- Group 3: Sq, ?, Star

So the missing one (position 8) should be Square, to complete the second square in the third group.

Then position 9 is Star.

So position 8 = Square

Choices:
- A. Circle
- B. Square ✔
- C. Star
- D. Triangle

✔ Answer: B. Square

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4) Pattern: Basketball, Football, Baseball, Soccer, Basketball, Football, Baseball, ?, Soccer

Sequence:
- Basketball, Football, Baseball, Soccer, Basketball, Football, Baseball, ?, Soccer

Looks like a repeating cycle of 4 sports:
- Basketball → Football → Baseball → Soccer → repeat

Check:
1. Basketball
2. Football
3. Baseball
4. Soccer
5. Basketball
6. Football
7. Baseball
8. ?
9. Soccer

So after Baseball (position 7), comes Soccer (position 8), then again Soccer? Wait — no!

Wait! Position 9 is Soccer, but if the cycle is:
- Basket → Foot → Base → Soccer → repeat

Then after Baseball (7), should be Soccer (8), then next would be Basketball, but position 9 is Soccer — that doesn’t match.

Wait — maybe we miscount.

Let’s write it clearly:

Position:
1. Basketball
2. Football
3. Baseball
4. Soccer
5. Basketball
6. Football
7. Baseball
8. ?
9. Soccer

So from 1–4: full cycle
5–7: start of cycle again
Then 8: should be Soccer (to complete the cycle)
Then 9: should be Basketball — but it’s Soccer.

Wait — contradiction.

Wait, position 9 is Soccer, but if the pattern is repeating every 4, then:

After position 7 (Baseball), position 8 should be Soccer, and position 9 should be Basketball — but it’s Soccer.

Hmm — but position 9 is Soccer, so maybe the pattern isn't repeating every 4?

Wait — perhaps there’s a different logic.

Wait — look at positions:

1. Basketball
2. Football
3. Baseball
4. Soccer
5. Basketball
6. Football
7. Baseball
8. ?
9. Soccer

So positions 1–4: all four types
5–7: same as 1–3
Then 8: ???
9: Soccer

Wait — maybe the pattern is:

- Cycle: Basketball, Football, Baseball, Soccer → repeat

So:
- 1: Basket
- 2: Foot
- 3: Base
- 4: Soccer
- 5: Basket
- 6: Foot
- 7: Base
- 8: Soccer ← should be here
- 9: Basket ← but it’s Soccer — not matching

But in the image, position 9 is Soccer, so that breaks the cycle.

Wait — unless the pattern is not repeating every 4.

Wait — perhaps the pattern is:

- Basketball, Football, Baseball, Soccer → repeat

But let’s check:

After 4: Soccer
5: Basketball → yes
6: Football → yes
7: Baseball → yes
8: ??? → should be Soccer
9: ??? → should be Basketball

But in the image, position 9 is Soccer, not Basketball.

Wait — but the image shows:

> ... Basketball, Football, Baseball, ?, Soccer

Wait — let me recheck the original:

"4) [Basketball] [Football] [Baseball] [Soccer] [Basketball] [Football] [Baseball] [?] [Soccer]"

So:

1. Basket
2. Foot
3. Base
4. Soccer
5. Basket
6. Foot
7. Base
8. ?
9. Soccer

So the last item is Soccer, and before that is Baseball, so what comes after Baseball?

In the first cycle: After Baseball (3) → Soccer (4)
After Baseball (7) → ? → then Soccer (9)

So between 7 and 9, we have:
- 7: Baseball
- 8: ?
- 9: Soccer

So if the pattern is: Baseball → Soccer, then ? should be Soccer?

But that would mean two Soccer balls in a row? That doesn’t fit the earlier pattern.

Wait — maybe the pattern is not repeating the full 4-item cycle, but something else.

Wait — look at the positions:

From 1–4: Basket, Foot, Base, Soccer
From 5–7: Basket, Foot, Base
Then 8: ?
Then 9: Soccer

So the second cycle only has 3 items so far (5–7), then 8 and 9.

Maybe the pattern is: repeat the first three items, then last item?

No — not clear.

Alternative idea: Maybe the pattern is grouped as: (Basket, Foot, Base, Soccer) repeated.

So:
- 1–4: full cycle
- 5–8: next cycle → 5: Basket, 6: Foot, 7: Base, 8: Soccer
- Then 9: should be Basket, but it's Soccer → conflict

But in the image, position 9 is Soccer, so that can't be.

Wait — perhaps I'm misreading.

Let me count carefully:

The sequence is:

1. Basketball
2. Football
3. Baseball
4. Soccer
5. Basketball
6. Football
7. Baseball
8. ?
9. Soccer

So after 7 (Baseball), we have 8 (?), then 9 (Soccer)

So the pattern from 1–4 is: Basket → Foot → Base → Soccer

Then 5–7: Basket → Foot → Base → so next should be Soccer → so 8 should be Soccer

Then 9 should be Basket → but it's Soccer → contradiction.

Unless the pattern is not repeating every 4.

Wait — maybe the pattern is every 4 items, but the 9th item is Soccer, which is the same as 4th and 8th?

So maybe:

- Positions: 1,5: Basketball
- 2,6: Football
- 3,7: Baseball
- 4,8: Soccer
- 9: Soccer

So 4 and 8 are both Soccer — so maybe the pattern is:

- Every 4th item is Soccer?

But 4, 8, and 9 are Soccer? That would make 8 and 9 both Soccer — possible.

But 1–4: Basket, Foot, Base, Soccer
5–8: Basket, Foot, Base, Soccer
Then 9: Soccer

So 9 is extra? But why?

Wait — perhaps the pattern is just repeating every 4 items, and the 9th item is not part of the cycle? But that doesn’t make sense.

Alternatively, maybe the pattern is:

- The last item is always Soccer, and the previous items follow a cycle?

No.

Wait — another possibility: maybe the pattern is two cycles of (Basket, Foot, Base, Soccer), but the second one is cut short?

But 5: Basket, 6: Foot, 7: Base, 8: ?, 9: Soccer

So if 8 is Soccer, then 9 should be Basket — but it's not.

Unless the pattern is only 4 items, and the rest are just continuation.

Wait — perhaps the pattern is:

- Basket, Foot, Base, Soccer → repeat

So:
- 1: Basket
- 2: Foot
- 3: Base
- 4: Soccer
- 5: Basket
- 6: Foot
- 7: Base
- 8: Soccer
- 9: Basket

But in the image, position 9 is Soccer, not Basket — so contradiction.

Wait — unless I misread the image.

Looking back at the problem:

> "4) [Basketball] [Football] [Baseball] [Soccer] [Basketball] [Football] [Baseball] [?] [Soccer]"

So the 9th item is Soccer, and the 4th is also Soccer, and the 8th is missing.

So the sequence is:

1. Basket
2. Foot
3. Base
4. Soccer
5. Basket
6. Foot
7. Base
8. ?
9. Soccer

So from 5–7: Basket, Foot, Base → same as 1–3

Then 8: ?
Then 9: Soccer

So if the pattern is to repeat the entire 4-item cycle, then after Base (7), we need Soccer (8), then Basket (9)

But 9 is Soccer, not Basket → contradiction.

But if the pattern is that after every Base, comes Soccer, then:

- After 3 (Base) → 4 (Soccer)
- After 7 (Base) → 8 (?) → should be Soccer
- Then 9: Soccer — so two Soccer in a row?

That could be possible.

So maybe the pattern is:
- Basket, Foot, Base, Soccer → repeat

But then 8 should be Soccer, and 9 should be Basket — but it's Soccer.

Wait — unless the 9th item is not following the cycle — but it's shown as Soccer, so maybe the cycle is broken.

Wait — perhaps the pattern is not repeating every 4, but rather alternating groups?

Another idea: maybe the pattern is:

- Group 1: Basket, Foot, Base, Soccer
- Group 2: Basket, Foot, Base, Soccer
- But Group 2 is incomplete?

But 5–7: Basket, Foot, Base — so missing Soccer

Then 8: ?
9: Soccer

So if 8 is Soccer, then 9 is Soccer — two in a row — not ideal.

But if 8 is something else, then 9 is Soccer.

Wait — perhaps the pattern is every 4th item is Soccer, and the others follow a cycle.

But 4 and 9 are both Soccer — not every 4th.

4, 8, 9? Not regular.

Wait — perhaps the pattern is:

- The sequence is: (Basket, Foot, Base, Soccer), (Basket, Foot, Base, ?), (Soccer)

No.

Wait — maybe the pattern is repeating the first three items, and then the fourth is Soccer?

But 4 is Soccer, 8 is ?, 9 is Soccer.

Not helpful.

Wait — perhaps the pattern is based on types, not order.

Another idea: maybe the pattern is cycle of 4, and the 9th item is a mistake? But unlikely.

Wait — let's think differently.

Maybe the pattern is Basketball, Football, Baseball, Soccer, and then it repeats.

So:
- 1: Basket
- 2: Foot
- 3: Base
- 4: Soccer
- 5: Basket
- 6: Foot
- 7: Base
- 8: Soccer
- 9: Basket

But in the image, 9 is Soccer, not Basket.

But wait — in the image, the last item is Soccer, and it's labeled as ?, but no — wait.

Look at the question:

> "4) [Basketball] [Football] [Baseball] [Soccer] [Basketball] [Football] [Baseball] [?] [Soccer]"

So the question mark is at position 8, and position 9 is Soccer.

So the sequence is:

1. Basket
2. Foot
3. Base
4. Soccer
5. Basket
6. Foot
7. Base
8. ?
9. Soccer

So the pattern from 1–4: full cycle
5–7: Basket, Foot, Base — so missing Soccer
Then 8: ?
9: Soccer

So if the cycle is every 4 items, then 8 should be Soccer, and 9 should be Basket — but 9 is Soccer, so maybe the cycle is off.

Wait — perhaps the pattern is:

- Repeat: (Basket, Foot, Base, Soccer)

So:
- 1–4: cycle 1
- 5–8: cycle 2 → 5: Basket, 6: Foot, 7: Base, 8: Soccer
- 9: should be Basket — but it's Soccer

So unless the pattern is not continuing, or there's a typo.

But maybe the pattern is not cycling every 4, but instead:

- The items alternate between two sets?

No.

Wait — another possibility: maybe the pattern is Basket, Foot, Base, Soccer, and then it repeats, but the last item is Soccer, so it's just showing the end of the cycle.

But then 8 should be Soccer, and 9 should be Basket — but 9 is Soccer, so maybe the pattern is Soccer at the end.

But that doesn't help.

Wait — perhaps the pattern is:

- The fourth, eighth, ninth are Soccer — so maybe it's a coincidence.

But more likely: the pattern is repeating every 4 items, and the 9th item is not part of the pattern — but it is.

Wait — perhaps I made a mistake in counting.

Let me count the items:

1. Basketball
2. Football
3. Baseball
4. Soccer
5. Basketball
6. Football
7. Baseball
8. ?
9. Soccer

So after 7 (Baseball), we have 8 (?), then 9 (Soccer)

If the pattern is: Basket, Foot, Base, Soccer → repeat

Then:
- 5: Basket
- 6: Foot
- 7: Base
- 8: Soccer
- 9: Basket

But 9 is Soccer, not Basket.

So unless the pattern is not repeating, or the 9th item is not following the cycle.

But that doesn't make sense.

Wait — perhaps the pattern is only 4 items, and the rest are just examples, but the question is to find the 8th item.

But the 8th item is after 7 (Baseball), so it should be Soccer.

And the 9th is Soccer, so maybe it's okay — perhaps the cycle is broken, or it's just a long sequence.

But in the context of patterns, it's likely that the cycle is Basket, Foot, Base, Soccer, and it repeats.

So:
- 1: Basket
- 2: Foot
- 3: Base
- 4: Soccer
- 5: Basket
- 6: Foot
- 7: Base
- 8: Soccer
- 9: Basket

But in the image, 9 is Soccer, so either:
- The image has a mistake, or
- My understanding is wrong.

Wait — let's look at the choices:

A. Soccer ball ✔
B. Baseball
C. Basketball
D. Football

So choice A is Soccer ball.

If the pattern is that after Baseball comes Soccer, then 8 should be Soccer.

And 9 is also Soccer — maybe it's acceptable.

So even though 9 is Soccer, perhaps the pattern is simply: after Baseball comes Soccer.

So:
- 3: Base → 4: Soccer
- 7: Base → 8: Soccer
- 9: Soccer — extra, or part of new cycle?

But then 9 should be Basket.

Perhaps the pattern is not strictly cyclic, but the rule is: after every Baseball, the next is Soccer.

So 8 should be Soccer.

Even if 9 is Soccer, it might be a typo or continuation.

Given that, the most logical answer is Soccer.

So Answer: A. Soccer ball

✔ Answer: A. Soccer ball

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5) Pattern: Candy cane, Lollipop, Gum, Candy cane, Lollipop, Gum, Candy cane, Lollipop, ?

Sequence:
1. Candy cane
2. Lollipop
3. Gum
4. Candy cane
5. Lollipop
6. Gum
7. Candy cane
8. Lollipop
9. ?

Pattern: Repeating every 3 items:
- Candy cane, Lollipop, Gum → repeat

So:
- 1–3: C, L, G
- 4–6: C, L, G
- 7–9: C, L, ?

So after Lollipop (8), should be Gum

Choices:
- A. Gum box ✔
- B. Lollipop
- C. Candy cane
- D. Chocolate bar

A is a gum pack — matches the "Gum" in the pattern.

So Answer: A. Gum box

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Final Answers:

1. B. Apple
2. A. Pencil
3. B. Square
4. A. Soccer ball
5. A. Gum box

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✔ Answers:

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

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